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badger-writes · 3 years

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Star Wars OC Ship Week 2021 - “for light and love”

3 - Angst/Drama

When Jedi found themselves troubled, they visited the Room of a Thousand Fountains.

Throughout its history, this chamber of the Jedi Temple ziggurat had always been set aside as a meditative refuge, a sanctuary of verdant greenery and trickling waters. Assembled herein one could find a collection of flora both native and foreign, from blartree blossoms and chrysanthis shrubs to a bahnsgresk bush grove to trebala and assari trees, shading the walkways with their trunks and branches - a garden of a thousand worlds.

Though the caretakers of this special corner of the Temple had always strived to enforce a kind of olamic traditionalism to its furnishings, the spirit of the times sometimes encroached upon this timeless space; and so the High Republic crept into the Room of a Thousand Fountains by way of its masonry, which now favored heavy geometric influences, stylized decorative reliefs, and smooth, streamlined lines which swept their way around the room in a sheen of gold and marble. These elements existed alongside their landscaped counterpoints in a carefully cultivated balance; a chamber with one foot in the ageless past, and the next in the bold, brilliant future that the Republic promised to all.

Here, one could pause for a moment, immersed in the energy of the Living Force, and reflect upon themselves and their place in the universe.

It was not a place Sskeer visited often.

Though the paths were lined with benches to encourage thoughtful rest, he preferred to keep moving, pacing through the gardens at a stride just above his typical walking speed; his feet seemed to slap the stone walkways no matter how he tried to control himself, trying to beat out his frustrations through their soles. Not for the first time, he considered that the best place for him to ruminate on his disquiet was not the Room of a Thousand Fountains. In the sparring chambers, at least, he would be less… disruptive.

He rounded a corner, emerging from a grove of hedges, and stopped. At the end of the short path rolling out before him lay a plaza surrounding one of the chamber’s great sculpted fountain fixtures; a great bowl-shaped basin spread out from its center, and rising into the air within its circumference were several other, smaller basins, overflowing with hanging moss and vines and pakiphanto ear plants, each of them carrying a tiny stream of clear water which trickled from their highest point to their lowest and back again. A tiny column-shaped islet rose out of the center of the basin, only large enough to hold the holoprojector installed in its capital; out of the projector’s eye shimmered an image of one of the era’s eventual Great Works, the Starlight Beacon. The huge space station, when it was finished, would be an outpost of progress and charity to all the worlds of the Outer Rim, a promise of the prosperity of the Republic and the justice of the Jedi. It hovered above the surface of the waters, framed by the hanging gardens, spinning slowly on its axis. Even on this much, much smaller scale, Sskeer couldn’t help but be impressed.

Someone else was standing at the edge of the basin - a Rodian with pale skin and a rather distinctive topknot. Sskeer crossed the way over to his side.

“Healer Lem,” he rumbled, crossing his arms. “It’s good to see you.”

“Oh,” Kelto mumbled, glancing. “Hello, Sskeer.”

“You appear troubled.”

“Am I so obvious?”

“It is no sin. I find myself frustrated tonight as well.”

Kelto hummed. The sound of it was hollow - less inquisitive, more melancholy. “I don’t know if I can help with that, but, you know… let me know.”

Sskeer cocked his head. “Why would you think that?”

“I just - I’m not a Consular, that’s all. Cuts and bruises, I can handle. The talking thing, it’s… I don’t do that so well.”

“Perhaps. But even so, as long as you’re here... I would appreciate your company. And I sense you would benefit from mine.”

“I… maybe. I guess.”

The Trandosham crossed his arms and raised an brow. “Perhaps you would like to discuss what’s been troubling you?”, he suggested.

Kelto opened his mouth… and closed it. “No, no. That’s okay. Thank you, but... I’ll manage.”

“Are you sure?”

“I mean, it’s pretty late already. The last thing you must want is to stand here and listen to my problems.”

“Try me.”

A shrug.

Sskeer exhaled slowly through his nose. His gaze flicked back to the pool before them, where waterlilies floated tranquilly upon the rippling face of the waters.

“I think I should insist,” he said quietly. “As a friend.”

“... I don’t want to burden you.”

“It wouldn’t be a burden.” A pause. “Not from you.”

Sighing, Kelto fell silent. He, too, kept his eyes fixed on the pond’s mirrorlike surface. Then, slowly, his gaze turned upwards, towards the hologram suspended above them.

“That’s really something,” he said wonderingly. “Isn’t it? The Beacon, I mean. It’s just... incredible. That the Republic and the Jedi can build something like that? Imagine what it can do for people living on the frontier.”

Nodding, Sskeer studied the diagram as well. “A space station on the galactic fringe can do little by itself,” he commented. “It needs people, too. Diplomats, explorers…”

“Guardians,” Kelto said wryly.

“Yes. And healers.” Sskeer gave him a sympathetic glance. “It would be an honor to be stationed there, would it not?”

The Rodian pursed his lips. They flattened into a noncommittal line as he shrugged. “Not really my thing,” he mumbled.

“I find it hard to believe you’d refuse an assignment where you could do so much good so easily.”

“Yeah, well.” And then Kelto went silent, leaning against the rim of the fountain.

Sskeer let his arms fall to his sides, brow furrowing. “You’re serious.”

A sad little shrug.

“You’d really waste your talents hiding in the Temple, rather than using them for the good of others? Without even an explanation? Are you so callous?”

In truth, he almost regretted saying it. But it did, at least, provoke a reaction from Kelto, who turned away from the fountain at last. “I’m not callous.”

“Selfish, then. Hoarding your knowledge and abilities for one one’s benefit but your own. Or perhaps just cowardly?”

“W-what is this, Sskeer? An inquisition? I thought you were trying to help me!”

“I am,” he said firmly. “But I don’t know what’s wrong. Blast it, Lem, it’s as if you’ve just… given up!”

Irritation launched his voice an octave higher than he meant, transforming a sentence into a bark. The lilies bobbed on the water. For a moment, Starlight Beacon flickered.

For a moment, Kelto stared at him agape, and Sskeer noticed his eyes (the first thing he’d noticed about him had been his eyes, long months ago, and the shiny white spots lying just under their aqueous outer membrane, that peculiar Rodian quality of seeming to hold a sky’s worth of stars in their surface) seemed brittle, now, and dull. Where there had once been light there was now not dark, but … an absence. An open pit in the soul.

Sskeer’s heart panged with sorrow. What frustration still lingered on his face passed like a fleeting shadow. Silently, he waited.

At last, Kelto sighed, clasping his hands back behind his waist; his fingers continued to fidget and twiddle as he turned back to the pond. For a moment, Sskeer feared he had broken their friendship, perhaps irrepairably.

Then Kelto said, “So the thing is… I’m kind of a bad Jedi.”

“No,” the Trandoshan insisted in a whisper.

“I am, Sskeer. What you said is true. And what’s more, you’re right to call me out. I’m cowardly, and selfish, and I hide myself in the healing wards instead of really doing anything with the talent and opportunities that I’ve been given. I…” He snorted, shaking his head. “I’m at the point where I fear being in public more than I fear the dark side. How stupid is that?”

Sskeer swallowed, mouth dry. He wondered what he could possibly say.

“I just… I don’t know how it happened. I was fine in the creche, I think. I- I had friends, I got along with people. I could… Star’s End, I could hold one conversation with somebody else without falling all to pieces, like I do with you.”

“That’s not your fault,” Sskeer said quickly. “I - that is, we - there’s... extenuating circumstances. Passion is just - ”

“Yeah, HoloNet news flash: feelings are hard,” Kelto murmured darkly. “Believe me, big guy, I know.”

“I only wanted to--” Sskeer grunted, biting his tongue. If only Jora Malli were here to help him talk some sense into Kelto.

“But then I grew up,” Kelto continued. “And I was still, you know, okay! I could… work with my Master, and with others, and I helped people… and then I was knighted, and I just… there was all this shyness and anxiety inside of me, and it just kept growing and growing and growing until… until I just couldn’t take other people anymore, except when I had the energy for it.

“I think that’s the real reason I transferred back to the Temple. I just… couldn’t take it anymore, putting myself out there. At least in the medical bay, it’s just a job. You can find a niche and serve and go back to your quarters. You don’t have to… to be seen all the time.

“But who did I serve, huh? Younglings with scraped knees and bloody noses. Nobody who really needed it. Nobody who would’ve died if I hadn’t been there. Meanwhile, how many people on the frontier do you think need a healer right now? How many won’t last the night? Because right now, Sskeer, I’m letting down all of them. And believe me, I know it.”

Kelto paused, taking a gulp of air, and looked up at the brilliant blue hologram again. “And then I heard about Starlight Beacon. And I felt… I felt something, deep down. Like the Force was trying to give me a second chance. Like I could - like I could make up for all of it, if I could only just get over myself.

“And I tried to,” he said thickly, snout quivering. “Please, Sskeer - believe whatever you want about me, but please, please believe I tried to fix whatever’s wrong with me. But-- b-but I just--”

Sskeer took him by the elbow and turned him back towards himself, grasping his much smaller arms in his clawed fingers. “Don’t talk this way,” he murmured. “Whatever you’re thinking, it’s not true.”

“W-well, maybe it is,” Kelto hiccupped, eyes wet. His face crumpled more and more the longer he spoke. “After everything with me, and then you, and the Code -- maybe I just can’t hack it as a Jedi. Maybe I was never supposed to, a-and I just got lucky, and now - and now I - ”

“What, Kelto?”

“And now I’m dragging you down with me.”

For a long moment, they stood there, staring at each other. Kelto sniffled horribly, scrubbing at his eyes with the heel of one hand. Sskeer’s mouth hung slightly agape, but his mind seemed to be lost somewhere, thrown far away.

“Just let me go,” he whispered, blinking hard. “Please. I- I’ll go, okay? I can just… leave. The Jedi - they’ll all be better off, and - a-and so will you.”

“No,” Sskeer said suddenly. His grip tightened around Kelto’s arms like a vise.

“I-I’m serious, big guy. I think… I think I’m done. I tried, and-- and I failed.”

“You listen to me, little healer. You will not leave, and you will not give up on yourself, do you understand? I won’t allow it. I refuse to.”

“Sskeer - Sskeer, please, come on. I’m not worth it--”

“Yes you are,” the Trandoshan hissed. “Even if you won’t see it.”

“Look here,” he continued, seizing one of the Rodian’s wrists. He pushed the palm of Kelto’s hand into his chest, letting his fingers splay out against his robes, over his heart. “Remember what you did here, for someone you barely knew. Remember how you used your gift for nothing else than to help a creature in need. Does that seem like failure to you?”

Kelto shrugged weakly, trembling.

“And then you confronted that fear and anxiety inside, that same day, and every day after that. All for the sake of me. Would a coward do that, Kelto?”

“I… I don’t know. Maybe?” He swallowed. “I-it was hard, sometimes.”

“I know this now, Kelto. I wish I had before. Perhaps I could have… helped, somehow. Or found some way to help you reach out.”

“It wouldn’t have mattered,” the Rodian muttered, hanging his head. “This - this isn’t something you could have fixed, Sskeer. It was always my problem alone.”

Sskeer growled, deep in his throat. When he turned back to face the pond, he kept his arm around Kelto’s back, still clasping his arm - holding him gently against his side.

“You remind me of myself,” he said finally.

“Now that’s a joke,” Kelto said, sniffing. “I’m - I’m a hot mess, Sskeer. You, you’re just… you’re everything a Jedi Knight should be. You’re magnificent. How could you possibly compare yourself to somebody like me?”

“Did you think you were the only one who doubted his place in the Order?”

Kelto looked up at Sskeer, stunned. The Trandoshan, in turn, stared into the fountain. Starlight Beacon’s reflection glimmered in his eyes; slowly, as he let a sigh out through his nostrils, they fell shut.

“I have… often found myself uncertain about my place in the Jedi,” he said at length. “There are times when our teachings and precepts seem to be... fundamentally incompatible with - who I am. Or, what I am.”

He raised one three-fingered hand out before him, looking down at it, turning it this way and that. He examined the thick scales which lined his skin, the blunt claws that tipped each finger. Shame crept into the lines of his face.

“I am Trandoshan. I know this is no surprise to you - and I, myself, have had many years to acquaint myself with this truth. But for many in the galaxy, when they meet a Jedi Knight for the first time, it is a… surprising thing. For some, it’s even… repulsive. And for that, I cannot judge them.

“The T’doshok may be my race, but I could never call them my people. Not for their instincts for slaughter and cruelty, not for their hunters who trap animals and slaves for their sport, not their ‘Scorekeeper’ who tallies points to the scale of their butchery - the very thought of It is anathema to life itself. A… disgusting perversion of the natural order of the universe. I can be party to none of it.

“And yet-- if not for the Seekers, I might have been. Had the course of my life taken one turn and not another, it would be I hunting the innocent and the weak, soaking my claws in the blood and the filth of that detestable culture. And I’m reminded of that whenever I meet those I’m oathsworn to protect - and the world I’ve left behind is all of myself that they can see.”

“W-well - well, that’s just - that’s just other people, Sskeer, they don’t know any better. And besides, you’ve - you’ve overcome that through your training, right? And your discipline. So.. so it’s not even a problem.”

“Were it so easy to believe,” Sskeer exhaled, clenching his fist.

“What do you mean?”

“There are… moments. When I speak, when I act. When I swing my lightsaber. There’s a - it’s like a beast, Kelto. Like a dragon, inside of me, coiled around my heart. My intensity, ferocity… my frustration… I think this is where they come from. For a long time I believed I was battling the Dark Side, the little bit of it within us all, as a Jedi should. But… perhaps it is deeper than that. Perhaps it is an instinct, a genetic memory. Something in the blood.

Perhaps, as you said, it’s something about myself that can’t be fixed.”

He didn’t know what he’d expected would happen - perhaps a weight would lift from his shoulders. Perhaps the shadow which clung to his heart and his mind would finally pass when he was able to find the words, and speak them. But something would happen, surely, when he finally let this secret shame pass his lips.

Instead, he felt exactly the same. Life was proceeding exactly as it had before. Nothing had changed.

He was still a Jedi. He was still a Trandoshan.

Kelto was still looking at him. He still seemed stricken, but no longer as badly rattled. Sskeer let his hand fall back to his side and turned his face back towards the hologram of Starlight Beacon.

“But perhaps that’s not the point,” he continued. “If we could all banish the flaws within ourselves for all time with only a little effort, we would all be totally perfect creations. Perhaps the point is not whether our feet will always keep to the path of the righteous, but that we walk it as best we can, because the promise of something better lies at its end. Perhaps how far we can walk it does not matter, so long as we remain willing to take another step.

“That is what I think, anyway. And that is why I stay. And as long as I believe that, I can beat back the darkness inside of me a little longer.”

Kelto stared up at him wonderingly. He turned to watch the hologram as well, and for a moment’s pause they watched it slowly turning on the surface of the water, surrounded by verdant, flowering life.

“Every life saved, every battle won, every choice made - every time we turn towards the light, is its own victory. All of it, so that we might bring a light as brilliant as this into the universe,” Sskeer observed. “But we must confront our fears and doubts, and conquer them, before they extinguish our own. How else can we make such things be?”

Kelto tried to swallow, and choked. He brought his fingers up to clasp the Trandoshan’s where they curled around his arm. They didn’t feel monstrous at all. They felt like a friend’s.

“You… you really think I can do it?”

“I know it.”

“I-- gods,” he whispered. “I just-- I’ve tried to go it alone for so long.”

“You shall do so no longer.” Gently, Sskeer turned the Rodian to face him, clasping his hands in his own. “On my oath as a Guardian, Kelto Lem, I vow to do all I can to help you conquer these inner demons. If I must, I will protect you from yourself, as I have tonight. From this moment forward, your pain shall be mine, too - until we banish it forever, no matter how long that takes.

“In turn, I must ask that you swear to join me in this effort with equal vigor and equal determination, until - by virtue of our own will and discipline - you are once more the Jedi that I believe you can be.

“For light and for life.”

“...For light and for life,” Kelto echoed.

Sskeer hummed, nodding. He touched his knuckle against the bottom of Kelto’s chin. “You’re on your oath, now,” he rumbled. “No more talk of leaving.”

“R-right.” The healer took a shaky breath, swallowing, then forced it out slowly through his lips. “I-- thank you, Sskeer. This - this was a dark night for me. The darkest in a while.”

“I shall ward them away,” he replied, a hand to his chest. “That they may torment you no longer. And,” he added, smiling, “you in turn, I think, shall do the same for me.”

Kelto smiled too, brittlely, lips trembling at their corners. Finally, when he could bear it no longer, he threw himself into Sskeer’s arms, burying his face in his chest.

“Thank you,” he mumbled through happy sobs. “Thank you, thank you, thank you…!”

Slowly, Sskeer returned the hug, wrapping his arms as securely around Kelto as he could without crushing him. The Rodian was stood on his toes, swaying, trying to make himself as tall as himself; he shushed into his ear softly, stroking the back of his head with the pads of his fingers.

“I love you so much, Sskeer,” Kelto confessed.

Sskeer shushed him again. The healer was already emotionally compromised enough for one night. There would be time enough to untangle those feelings later - time enough for them both.

Instead, Sskeer held Kelto against his chest and gazed up at the dream of Starlight Beacon, and hoped that one day, both of them would be worthy enough to reach it.

#StarWarsOCShipWeek2021 #star wars #high republic #sskeer #original character #oc x canon #fanfic

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wisdomrays · 3 years

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TAFAKKUR: Part 394

THE SECRET OF DIMENSIONS

The beginning of the verse proclaims that God is the only Deity of the heavens, the earth, and all in between:

He is the Lord of the heavens and of the earth, and all that lies between them; He is the Lord of the Lasts. (Saffat, 37.5)

The concept of the Lord of everything is defined in this setting and within the limits of our knowledge. Since the earth, the sky and all else in between have been mentioned, a different reality or a different spatial continuum is not in question. The verse does not end there, however. A new concept is added: 'He is the Lord of the Lasts.'

So, in addition to the earth, the sky and all in between, we have the concept of 'Easts'. In Arabic, the plural form is used for three or more things. Therefore, God is the Lord of at least three Fasts, or of many Easts. What kind of scientific concept does this verse introduce? Before seeking an answer to this question, let us call to mind certain facts.

It is a commonplace that we conceive of space in terms of three dimensions. The existence of an object is determined by the space it occupies with respect to the dimensions of length, width and height, in addition to its position.

But is the universe composed of, and space constituted by, these three dimensions alone? Until Einstein's Special and General Theories of Relativity, scientists believed that the universe consisted of three dimensions. The world-famous physicist, however, determined on the basis of mathematical calculations that there are more than three dimensions and that a fourth, fifth or higher number of dimensions would introduce different concepts of space.

According to Einstein, the fourth dimension is time. Time is not simply a matter of reading a clock, but a dimension of the same order as height, width and length. It is coextensive with the other dimensions. Our visual perception, however, can see in only three dimensions and no more. In fact, some organisms cannot even see the dimension of depth: lizards and snakes see the world in two dimensions, like a photograph or a movie cartoon.

Starting from this milestone of physics, we would have to conceive of spaces other than ours, and in addition to the physical space we observe in the universe at large. In these spaces, velocity is different, time is different, action is different; and so are translation, convergence and regression. This is why the concept of 'worlds' introduced by the Qur'an is an expression of such diverse spaces. The world of angelic beings, Heaven, Hell, and the world of spirits all lie in the domain of such spatial continua. Our difficulty in conceiving of them stems from the perceptual deficiencies of our three-dimensional habits.

Having noted this, let us now recall the final part of the verse: 'He is the Lord of the Easts.

'East' is the expression of a direction, a dimension. This expression occurred for the first time in connection with the sun. The word 'orientation' or finding one's bearings implies the Orient or East as the first or primary dimension. Although the expression Lord of the Easts and of the Wests occurs in many verses in the Qur'an, only the Easts are mentioned in this verse. This is why we are dwelling on this point at such length.

The point is that 'the Easts' are proclaimed as a set of directions, quite apart from the existents we refer to as the earth and sky. With this verse, God draws our attention to other directions and dimensions, indicating the existence of worlds and spaces composed of dimensions other than the physical world we are familiar with. In a sense, He says I am the Lord of the Easts in order to introduce the notion of infinite dimensions, which contemporary physics is just beginning to discover. But why only the Easts? Because in the definition of dimensions, the first dimension is the East, whereas the West is simply an extension of the Eastern dimension in the opposite direction. We can say that this verse clearly heralds the existence of thousands of spaces and worlds embedded in an infinite-dimensional matrix.

Many other meanings derive from the verse besides the meaning discussed above. I would like to mention two of these.

The meaning 'births' can also be derived indirectly from the plural mashariq. In this case the meaning points to a different scientific truth. The East, which is where the sun rises, also symbolizes the direction in which the earth moves around the sun. But, do we have only one East, or only one motion in the universe?

No. While the earth revolves around the sun within the solar system, the sun is also revolving around the Milky Way galaxy together with its family of planets. The Milky Way, in turn, is revolving around the central axis of the supergalaxy or local cluster of galaxies to which we belong. Thus, we may well speak of three different Easts.

This meaning, therefore, is also hidden within the statement 'Lord of the Easts' (rabbul-mashariq). The very fact that magharib (Wests) does not succeed mashariq (Easts) in this verse is a confirmation of this. We shall see while interpreting future verses that there are many statements in the Qur'an pointing to the rotation of the earth. For this reason 'East' in reference to the earth's revolution is in the plural, indicating that these rotations occur at many levels.

If we take the verse from the standpoint of a direction on earth, the concept of the East differs for each location on the globe. The east of Turkey is in the east with respect to its western regions, while our east is actually west from the standpoint of Iran, which lies even further east. Therefore, the East concept is different at every point on earth, and these concepts form an ensemble of Easts. This concept geometrically defines the surface of a sphere.

Let us now reread the verse in order to discover another significant scientific observation: He is the Lord of the heavens and of the earth, and all that lies between them; He is the Lord of the Easts (Saffat, 37.5).

The heavens, as we also see from other Qur'anic verses, are very diverse spheres. So what does the expression 'between the heavens and the earth' mean? It is known that meteors, stars, even angels and various unknown beings, can be encountered at various levels of the sky. What are 'those between earth and the sky'? As far as we can tell, they are invisible rays which form the basic building blocks of matter and energy. These rays, earlier lumped together under the generic term 'cosmic rays', are differentiated in modern physics within the broad categories of nucleons, haryons, leptons and fermions. These are the subatomic constituents of matter and energy.

With the expression 'He is the Lord of the heavens and of the earth, and all that lies between them' God explains that all these energetic particles and rays constitute a vast physical order subject to God's attribute of Lordship. Modern physics has viewed these incomprehensible energy dissipations and rays with unease, almost seeing them as dangers threatening the destruction of the universe. The Qur'anic verse reveals that, on the contrary, they form a gigantic physical balance under the superintendence of God.

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correspondencearchive · 3 years

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1. Hong Hong & Alex Paik

Hong Hong and Alex Paik discuss paper, the exiled body, and resistance vs interdependence

Hong Hong, Composition for an Emergent Brightness and Its Lesser Return, mulberry bark, dust, hair, pollen, fiber-reactive dyes, repurposed paper, water from Lake Erie, and foliage: Milkweed and Winged Sumac, 87 (H) x 90 (W) x 36 (D) inches, 2020

Alex Paik (AP): One thing I am especially drawn to in your work is your commitment to paper, a material that we are both deeply interested in. Paper is its own living and breathing material that bears the scars and memories of anything it comes in contact with -- the leftover grooves and scratches from graphite, the slight buckling and warping from being exposed to water, or even fading as it is exposed to light. You talk about this quality as it relates to the body and the experience of diasporic and exiled bodies. Can you speak a little more about this relationship?

Hong Hong (HH):

The process of making paper relates to three different kinds of bodies.

The Biological Body: In papermaking, the body is a soft machine. Papermakers use their bodies to transform different materials into paper by intentionally exposing them to heat, weight, water, time, and gravity. Hand paper formation involves a specific sequence of steps, which are repeated each time paper is made. Like choreography, it is an act that vanishes. The surface of paper is the sedimentation of these movements and gestures. It gives form to the biological act of living. You speak of leftover grooves of graphite, and the slight buckling and warping from being exposed to water. There are also often lines where each sheet has been folded and unfolded. These qualities, over time, reveal how we touch the world and how the world touches us: existence is additive and reductive.

I also think about the horizontal and vertical axis a lot. We defy gravity to walk upright. We give into gravity during rest: our bodies are prone when we sleep. We can say the same of our bodies during the process of dying. The floor and wall components in recent work reference these two distinct states of being: 1) The horizontal (intuitive): where we acquiesce to physical circumstance and where we dream 2) The vertical (rational): where we attempt to assert our agency and make decisions

My Own Body: I was the first grandchild born to my grandparents. I was a girl, but they were not disappointed with me. My mama, apoor, gonggong, and I all lived together in the same apartment. This is not unusual in China. My grandmother used to make me stand against the wall, so she could mark my height once a week. It was always a joyous occasion.

My grandparents are no longer with me. I wonder nowadays: How can I perceive and understand my own changing boundaries without them? How does a single body locate itself in a room or in a landscape? So, I work outside daily, on a surface that measures a little less than 12 ft x 8 ft. These dimensions are the exact distances I can reach without losing control of my balance. The lengths have changed over time: I’ve lost about two to three inches in the last four years. They remind me of time and of life, as the effort it takes in order to cross both.

There is an intimacy to making paper: I think about my apoor measuring my height against the wall. This is not legible to others. But that’s okay.

The Exiled Body: There is an old Chinese myth about the beginning of the world. In a time before time, all that existed was an egg and a giant who slept inside of it. His name was Pangu. His repose was the universe. His stillness was the one and the all. His body was an origin and an end. One day, he wakes up. In darkness, he swings his axe to separate the sky from the earth. He slowly pushes the sky away from land. After thousands of years, he dies. His hair becomes forests and trees, his eyes are the sun and the moon, and his voice is thunder. I’m fascinated by notions of world-building and stories of how we came to be. I don’t think that this is surprising, given that I immigrated to the US when I was young.

Exile, for me, has always been about the irrevocable distance between myself and something else. Distance is blue. That’s why this color surfaces a lot in my work. Blue is also the sky,, which is everywhere, no matter where I am. The sky is a taciturn blue passing over everyone. There is something sad and comforting about its ubiquitous silence. Exile is also about the legibility of my body and experiences. Abstraction is anything that is mediated by symbols. The body begins as a collection of material, the same way that landscapes do. I think identity is both an experience and an image, read or seen by others.

I travel to faraway places to make paper. These journeys to make paper in different locations are attempts to reimagine my own experiences in border-crossing. In some ways, it is also tied to ideas of navigation and a continuous sense of movement from place to place. A lot of my recent work consists of four different sheets of paper tacked together to form a floor and ceiling work. They reference the cardinal directions. I work outside. All the work puts my body in spaces where I am estranged from myself and separated from my identity. This is somehow necessary. All work is the work of this body. All work is a search for this body. Therefore, all work is always the same work.

AP: This is so beautiful. When you talk about the horizontal/vertical shift it makes me think of Yi Fu Tuan’s Space and Place, where he talks about babies going from prone to walking and how that relates to a baby’s sense of agency and place in the world. I certainly feel this conversation between agency and acquiescence happening in your work and your process, especially with how you are manipulating paper/letting paper be manipulated. You are working with paper not so much as a metaphor for the body but as a body, and the intimacy of seeing the record of your body in relation to the paper’s body comes through quite clearly: a marker of time, and a measure of your body as it shrinks over time.

Hong Hong, documentation of complete environmental pour, Vermont 2019

AP: Was there ever a shift in your work when you went from using manufactured paper to making your own, or have you always made your own paper? What is important to you about the papermaking process?

HH: I’ve never worked with manufactured paper the way that I do with handmade paper. Manufactured paper functioned, for me, as a substrate. I’ve always been interested in drawing and painting as processes of accumulation, where each action has the potential to become an abstract temporal measurement (like a breath or the swing of a pendulum). I also love materials that can hover between object and image. I like the flattening that happens in representation. I also love dealing with gravity. I don’t think these processes are separable or different: they are ultimately about the transformation of energy into form. I think I was able to make the jump between painting and papermaking because of these interests.

I learned how to make paper when I was in graduate school. I went for Painting (long story short: had to go to grad school because of visa issues). In graduate school, I felt alienated from the history of painting, as it was presented by a primarily white institution. Papermaking seemed to offer something different. It seemed to say that what I was learning about and exposed to, is not the only narrative. I also kind of loved that my painting professors hated it! I love that paper, before anything else, is an object. I loved that I had my own memories of burning holy paper at temples when I was young. I believe objects have the capacity to materialize complex beliefs into concrete things (value) that are tangible and exchangeable. They carry tacit values about specific moments in time. The conditions for the production, usage, and erosion of objects are both personal and collective.

Hong Hong, The Mountain Which Does Not Describe a Circle II, mulberry bark, sun, dust, hair, pollen, fiber-reactive dyes, repurposed paper, water, and foliage: Loblolly Pine and leaves from an unknown tree, 91 (H) x 128 (W) inches, 2021

AP: This idea of something hovering between object and image is something I think about, too. My geometric units function both as images and as the material with which I build each installation. In terms of composition the temporary nature of each iteration of my pieces resists the idea of a static composition and links the image to the potential of the materials (the folded painted geometric units).. When I was making paintings I never felt comfortable making an image out of thin air -- I always needed some sort of resistance (like projecting old video game screenshots) as a way of having something to work against. The white of a canvas is very different from the white of paper (even if it is manufactured). To me the white of a canvas feels like starting from zero, while the white of the paper already has a sort of history and aliveness to it to respond to.

When I decided to move to only working with paper over ten years ago it felt like I had come home. I was especially drawn to the way paper softened the geometric forms I was working with. Looking back now I think it has to do with never feeling like I quite belonged in the (white) history of art and painting specifically and wanting to find a way to approach and relate to this history from another perspective. I still love and appreciate a lot of Western painting, but I don’t think I can ever go back to it. It’s so funny how people talk about paper as a “humble” material, only because it makes me think about how Euro-American painting is perhaps, by extension, the opposite lol. Our work is fragile and easily damaged. I am ok with my work having a finite lifespan, and I think about how presumptuous and egotistical it is to be a painter who wants their work to live on forever. To me the idea of paper being “humble” is more the product of wanting to privilege other materials and traditions than any sort of inherent humility in paper itself.

HH: My partner, Jamey, is a painter. He’s reading a book called Almost Nothing. It’s a collection of writing about precarious practices. He told me a phrase yesterday that is really beautiful: “the syntax of weakness.” Openness to touch is the first condition of any object’s creation. Mark-making is only possible when a material chooses to absorb a gesture or a movement. In some way, it is about acceptance. A sheet of paper is the same as a boulder or the moon: they are changed by heat, pressure, impact, and time. Their malleability and porousness leads to material instability. In this way, all things engage with the act of writing their own histories. To live is to disappear: form records this disappearance.

Making paper is an arduous, physically demanding process. It depletes my resources each time it occurs. Something is born, as I die. For me, manual labor is a way for time to enter into my body. It returns me back to matter. This quality of impermanence is also in the body of the work. I, like you, was largely uninterested in the plasticity of paint. I also wasn’t necessarily interested in its immortality (I say this, and I love the work of so many painters). I didn’t know it at the time, but I wanted to work with something that is alive. This is also why I choose to work outdoors. You speak of resistance, and I feel that too, when I make paper. Limitations are wonderful. They tell me where I am.

I feel it when it rains on my work. I feel it when I go to new places and the object cannot come into being the same way it did in a previous location (do you sense this, when you create installations?).

AP: I do! Each space has different lighting conditions and a different scale, which I unconsciously and consciously adapt to as I am onsite building the installation. Sometimes I literally have to work around/against awkwardly placed outlets and “architectural features.” At other times there are even time constraints -- if I am traveling or only have a certain amount of time to finish due to childcare/scheduling/etc.

Alex Paik, Partial Diamond (Slice), gouache, colored pencil, paper, nails, dimensions variable, 2019, installed at Praxis New York, 2019 (approx. 5.5 x 6.5 x 11 feet)

HH: Everything changes due to season, humidity, weather, and millions of other factors that sort of seamlessly flow together to become landscape, and our tactile and sensorial understanding of it. For me, making paper separates experience into its distinct, constituent parts: sun, heat, collision, water, foliage, weather, gravity, etc. And the paper, once dry, stitches these segments together to form a whole. When I make paper, I feel something pushing back at or rising up against me. In a way, I’m fighting it. But I want to be accepted by it too. There is a simultaneous sense of absorption and alienation. In a recent interview with Artmaze, Bridget Mullen was talking about painting and they said that alienation teaches us empathy. Now I think of that when I work.

I love painting. I also love what you said about painting being the process of creating something out of thin air. I think of what I do as painting, if painting is a depository process and not a creative one. I think that life can be irrevocably difficult, but there are moments when the world is still and beautiful, like a drawing. That’s what I love most of all. A lot of my work is about erosion, alienation, exile, etc. But it is also about pleasure and happiness. I always wake up early in the day and start working at dawn, in the blue-dark. I feel the sun on my back and the coolness of the water between my hands. I feel the temperature rise. The wind shifts. Parts of me can disappear in those moments. Like painting, papermaking unfolds within quotidian time. Sometimes time can be unwavering in its perpetuity. But sometimes time becomes significant and bigger. It touches on the eternal and transforms into something unfathomable and long, like the sky. I am free here. I belong here. No one can take that away from me.

Can you speak more about resistance, as it relates to your work? There is a sense of vibrational geometry in your improvisations and installations: how is this related to the imagery you were working with in your paintings? Can you also tell me more about the temporary nature of the work? How do the compositions come into being (you speak of feeling)? Do they only come into being once and never again? Are parts disassembled and reassembled (reincarnation) to become other pieces? What perspectives did your decision to work with paper bring you?

I wrote a lot! It’s a nice day here.

AP: I love it! So I’ll answer your questions in reverse order. My modular installations are made up of hundreds of the same geometric form, which are then hung up with nails temporarily on a wall when I have a show. Now that I think about it, in a way I am also making my own material like you are making paper. Each resulting composition is a unique iteration or performance of the same piece that will never be repeated in exactly the same way. In other words, the piece itself (a collection of individual units) has no static form or image but rather only has the potential to combine and recombine into almost endless combinations. I saw this great quote by Sanford Biggers recently that talks about how the basic logic of patchwork/quilt making is “to constantly be rebirthed in a new form, using the same materials.” And that is a very succinct way of describing what my work is about. And although these new relationships and forms are on the surface primarily concerned with shape and color, they become metaphors for speaking about other types of rebuilding - whether it is the way that a nation can reassemble itself with the same flawed individuals or how we as individuals can rebirth ourselves constantly using the same elements of our identities, either through code-switching depending on the social context or through sustained unlearning/relearning.

I think less about resistance in my work but more about interdependence. That resistance of paper as a living material can also be described as an interdependent relationship -- I can coax it into certain shapes by folding/gluing/painting but then the paper also responds by warping, sagging, etc. The installations themselves have an interdependent relationship with the walls and the lighting -- the forms need walls and lights to reflect their painted colors onto. What is most visible when looking at my work is actually not the material itself (the paper and folded forms) but rather the results of this interdependent relationship: the reflected, hazy color.

HH: I love thinking about the work as “a collection of individual units that has no static form or image”, but rather as “potential”. It breaks down barriers between the inanimate and animal, object and art, as well as the past, present, and future. I also love thinking about resistance in the context of interdependence. This is a helpful framework with which we can not only consider and approach ourselves, but also larger systems: political, social, geographical, mythical, etc.

Alex Paik, Partial Equilateral Triangle (Two Right), gouache, colored pencil, paper, nails, dimensions variable, 2020, installed in studio, 2020 (approx. 4 x 8.5 feet)

Hong Hong is a visual artist whose practice spans craft, painting, and earthwork. Born in Hefei, China, she immigrated with her family to North Dakota in 1999 and earned her MFA from University of Georgia in 2014. Hong has exhibited at Crystal Bridges Museum of American Art, Georgia Museum of Art, Real Art Ways, Art League Houston, Penland School of Craft, and Jewett Arts Center. Her projects have been reviewed by Art21, Hyperallergic, Virtual Asian American Art Museum, Art New England, Southwest Contemporary, and Glasstire. Hong is the recipient of fellowships and grants from National Endowment for the Arts, MacDowell, Yaddo, Houston Center for Contemporary Craft, Connecticut Office of the Arts, and Foundation for Contemporary Arts.

www.honghong.studio @honghongstudio

Alex Paik is an artist living and working in Los Angeles. His modular, paper-based wall installations explore perception, interdependence, and improvisation within structure while engaging with the complexities of social dynamics. He has exhibited in the U.S. and internationally, with notable solo projects at Praxis New York, Art on Paper 2016, and Gallery Joe. His work has also been featured in group exhibitions at BravinLee Projects, Lesley Heller Workspace, and MONO Practice, among others.

Paik is Founder and Director of Tiger Strikes Asteroid, a non-profit network of artist-run spaces and serves on the Advisory Board at Trestle Gallery, where he formerly worked as Gallery Director.

www.alexpaik.com @alexpaik

#honghong #hong hong #alexpaik #alex paik #honghongalexpaik

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noctuaalba · 6 years

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Hi! I'm struggling with drawing heads at a 3/4 angle :( I love your art as well! Do you have any advice or tutorials on 3/4 heads?

hey there! I apologize if it’s a bit shitty but I had little time to put this quick explanation together. I also want to say that I am by all means not a master, I am still learning too! but I’ll try ok, first of all, why are ¾ heads so hard to draw? The reason is that while profiles and front views are more ‘flat’ and symmetrical, and easier to boil down to lines, in a ¾ view there is a lot of tridimensionality involved. Angles and planes shift,and without a basic grasp of the structures it’s easy for the face to look weird. Which brings us to the first step: basic head construction.It’s something that should always be done, especially while learning, because it’s what will really make you progress. Understanding how 3d objects behave in space, and ‘seeing’ the geometrical structures that make basic shapes is the key to learning how to draw. I’ll make it very quick because it takes a book to explain it thoroughly, but

The basic shapes to draw a head are just…circles. (1) In case of a frontal portrait, we’re gonna use two circles interlocking (drawn in red) for the upper and bottom part. I drew a feminine, softy face, but by making them larger or narrower you can alter the proportions of the face. Then we have a vertical center line, also drawn in red. This is very important, it’s your symmetry axis to draw the other features when frontal and your guide to keep the features where they should be! It crosses points like the nose bridge, the center of the mouth, the spot where the nose meets the lip. Then you can start adding elements - please be messy. Draw as many structure lines you need, especially horizontal ones that help keeping everything lined: draw at least one horizontal axis. The step that will lead you to ¾ effectively is in fact this very central axis. In (2) you can see that I’ve drawn a ¾ using the same construction (plus a circle for the back of the head - very important!) and you can see how the central line has moved to the left from the center. The more it shifts to the side, the more your face will be turned, but that remains the ‘center’ of the face you’re drawing. it acts as a sort of anchorage point: the middle of your lips, the base of the nose, they will all have to fall (roughly) over that line. in picture (3) you can see how mastering this structure allows you to draw all the angles you want! the horizontal structure lines are very important here, they become rounder the more the head is tilted, but they still do their job of defining the tridimensional structure of the face and help you draw everything in the right place

once you’ve drawn your guide lines, you can start adding the features. again, basic shapes are the way to go, and be messy - you’re not trying to get everything right at the first attempt. The nose is nothing but a glorified pyramid: the base will be the base of your nose, etc. Again, by altering the lengths and proportions you can draw any nose! You can see how I’ve drawn the other structures following that basic shape + a ball for the tip of the nose. The middle point of the base side, and the top of the pyramid will have to fall on the vertical axis. The horizontal structure lines here will help you understand the correct tilt of the nose.

and now the eyes, especially the ‘other’ eye, the bane of the every artist’s existence. I would love to give you the scientific formula to place it correctly but there is none (sigh). We can pray, be mindful when we’re drawing, and rely on good old structure! I’ve shown you the basic construction of an eye, which is no big deal when we’re drawing frontal, but see how it changes when we’re going ¾? those diagonal lines help us define the perspective,with the axis progressively shifting to the side as the head turns - but eyes are also spheres, so we’re going to give it a bit of volume with curved lines, to make it ‘bulge’ a bit.

you can see how the axis shifts and how the base rectangle becomes narrower as the head turns!You can also see another thing: how the nose bridge will progressively cover the inner angle of the eye the more the head turns. Of course, a button nose will cover less eye than a strong nose will, you will ‘feel’ what is right.Which leads us to cheekbones, another common mistake that often ruins the drawing when they’re drawn at the wrong angle. In fact the ‘angled’ cheekbone line starting right next to the eye is something that happens only when the head is half turned or more. With gentler angles, cheekbones and the eye’s bone structures are still pretty visible and the ‘other eye’ is quite in the middle rather than on the side

sorry I did this in literally 5 minutes cause it’s 5 am, but I tried to make the change through movement of cheeks/eyes/nosebridge more understandable. The back of the head will also show more - we have a psychologic bias that makes us draw it smaller than it should be, so if you’re not quite sure maybe take a look at yourself in a mirror for instant reference!Ok I guess this is the end of the shittiest tutorial ever, I hope I made some sense and/or this was helpful in any way. Tl;dr Geometry is your friend! Also, references! Look at pictures and try to see the structure if the face! Study them! Where is the axis? How do the features work together? What are the angles like? Read more about structure, draw lots of lines, don’t be afraid to make mistakes because sometimes you will even if you’ve been drawing for years, don’t forget to have fun!

#tutorials #asks #sorry if it's shitty #btw feel free to ask anytime #Anonymous

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worldscienceassociation · 4 years

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The Experimental Confirmation of the General Theory of Relativity

From a systematic theoretical point of view, we may imagine the process of evolution of an empirical science to be a continuous process of induction. Theories are evolved and are expressed in short compass as statements of a large number of individual observations in the form of empirical laws, from which the general laws can be ascertained by comparison. Regarded in this way, the development of a science bears some resemblance to the compilation of a classified catalogue. It is, as it were, a purely empirical enterprise.

But this point of view by no means embraces the whole of the actual process; for it slurs over the important part played by intuition and deductive thought in the development of an exact science. As soon as a science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms. We call such a system of thought a theory. The theory finds the justification for its existence in the fact that it correlates a large number of single observations, and it is just here that the " truth " of the theory lies.

Corresponding to the same complex of empirical data, there may be several theories, which differ from one another to a considerable extent. But as regards the deductions from the theories which are capable of being tested, the agreement between the theories may be so complete that it becomes difficult to find any deductions in which the two theories differ from each other. As an example, a case of general interest is available in the province of biology, in the Darwinian theory of the development of species by selection in the struggle for existence, and in the theory of development which is based on the hypothesis of the hereditary transmission of acquired characters.

We have another instance of far-reaching agreement between the deductions from two theories in Newtonian mechanics on the one hand, and the general theory of relativity on the other. This agreement goes so far, that up to the preseat we have been able to find only a few deductions from the general theory of relativity which are capable of investigation, and to which the physics of pre-relativity days does not also lead, and this despite the profound difference in the fundamental assumptions of the two theories. In what follows, we shall again consider these important deductions, and we shall also discuss the empirical evidence appertaining to them which has hitherto been obtained.

(a) Motion of the Perihelion of Mercury

According to Newtonian mechanics and Newton's law of gravitation, a planet which is revolving round the sun would describe an ellipse round the latter, or, more correctly, round the common centre of gravity of the sun and the planet. In such a system, the sun, or the common centre of gravity, lies in one of the foci of the orbital ellipse in such a manner that, in the course of a planet-year, the distance sun-planet grows from a minimum to a maximum, and then decreases again to a minimum. If instead of Newton's law we insert a somewhat different law of attraction into the calculation, we find that, according to this new law, the motion would still take place in such a manner that the distance sun-planet exhibits periodic variations; but in this case the angle described by the line joining sun and planet during such a period (from perihelion—closest proximity to the sun—to perihelion) would differ from 3600. The line of the orbit would not then be a closed one but in the course of time it would fill up an annular part of the orbital plane, viz. between the circle of least and the circle of greatest distance of the planet from the sun.

According also to the general theory of relativity, which differs of course from the theory of Newton, a small variation from the Newton-Kepler motion of a planet in its orbit should take place, and in such away, that the angle described by the radius sun-planet between one perhelion and the next should exceed that corresponding to one complete revolution by an amount given by

+24π³a²/[T²c²(1 -e²)]

(N.B. — One complete revolution corresponds to the angle 2π in the absolute angular measure customary in physics, and the above expression giver the amount by which the radius sun-planet exceeds this angle during the interval between one perihelion and the next.) In this expression a represents the major semi-axis of the ellipse, e its eccentricity, c the velocity of light, and T the period of revolution of the planet. Our result may also be stated as follows: According to the general theory of relativity, the major axis of the ellipse rotates round the sun in the same sense as the orbital motion of the planet. Theory requires that this rotation should amount to 43 seconds of arc per century for the planet Mercury, but for the other Planets of our solar system its magnitude should be so small that it would necessarily escape detection. ¹

In point of fact, astronomers have found that the theory of Newton does not suffice to calculate the observed motion of Mercury with an exactness corresponding to that of the delicacy of observation attainable at the present time. After taking account of all the disturbing influences exerted on Mercury by the remaining planets, it was found (Leverrier: 1859; and Newcomb: 1895) that an unexplained perihelial movement of the orbit of Mercury remained over, the amount of which does not differ sensibly from the above mentioned +43 seconds of arc per century. The uncertainty of the empirical result amounts to a few seconds only.

(b) Deflection of Light by a Gravitational Field

It has been already mentioned that according to the general theory of relativity, a ray of light will experience a curvature of its path when passing through a gravitational field, this curvature being similar to that experienced by the path of a body which is projected through a gravitational field. As a result of this theory, we should expect that a ray of light which is passing close to a heavenly body would be deviated towards the latter. For a ray of light which passes the sun at a distance of Δ sun-radii from its centre, the angle of deflection (a) should amount to

a = 1.7 seconds of arc/ Δ

It may be added that, according to the theory, half of Figure 05 this deflection is produced by the Newtonian field of attraction of the sun, and the other half by the geometrical modification (" curvature ") of space caused by the sun.

This result admits of an experimental test by means of the photographic registration of stars during a total eclipse of the sun. The only reason why we must wait for a total eclipse is because at every other time the atmosphere is so strongly illuminated by the light from the sun that the stars situated near the sun's disc are invisible. The predicted effect can be seen clearly from the accompanying diagram. If the sun (S) were not present, a star which is practically infinitely distant would be seen in the direction D₁, as observed front the earth. But as a consequence of the deflection of light from the star by the sun, the star will be seen in the direction D₂, i.e. at a somewhat greater distance from the centre of the sun than corresponds to its real position.

In practice, the question is tested in the following way. The stars in the neighbourhood of the sun are photographed during a solar eclipse. In addition, a second photograph of the same stars is taken when the sun is situated at another position in the sky, i.e. a few months earlier or later. As compared with the standard photograph, the positions of the stars on the eclipse-photograph ought to appear displaced radially outwards (away from the centre of the sun) by an amount corresponding to the angle a.

We are indebted to the [British] Royal Society and to the Royal Astronomical Society for the investigation of this important deduction. Undaunted by the [first world] war and by difficulties of both a material and a psychological nature aroused by the war, these societies equipped two expeditions — to Sobral (Brazil), and to the island of Principe (West Africa) — and sent several of Britain's most celebrated astronomers (Eddington, Cottingham, Crommelin, Davidson), in order to obtain photographs of the solar eclipse of 29th May, 1919. The relative discrepancies to be expected between the stellar photographs obtained during the eclipse and the comparison photographs amounted to a few hundredths of a millimetre only. Thus, great accuracy was necessary in making the adjustments required for the taking of the photographs, and in their subsequent measurement.

The results of the measurements confirmed the theory in a thoroughly satisfactory manner. The rectangular components of the observed and of the calculated deviations of the stars (in seconds of arc) are set forth in the following table of results.

It has been shown that in a system K’ which is in rotation with regard to a Galileian system K, clocks of identical construction, and which are considered at rest with respect to the rotating reference-body, go at rates which are dependent on the positions of the clocks. We shall now examine this dependence quantitatively. A clock, which is situated at a distance r from the centre of the disc, has a velocity relative to K which is given by

v = ωr

where ω represents the angular velocity of rotation of the disc K’ with respect to K. If v₀, represents the number of ticks of the clock per unit time (" rate " of the clock) relative to K when the clock is at rest, then the " rate " of the clock (v) when it is moving relative to K with a velocity v, but at rest with respect to the disc, will be given by

v = v₂√(1 -v²/c²)

or with sufficient accuracy by

v = v₀(1 - ½ v²/c²)

This expression may also be stated in the following form:

v = v₀[1 – (1/c²)(ω²r²/2)]

If we represent the difference of potential of the centrifugal force between the position of the clock and the centre of the disc by φ, i.e. the work, considered negatively, which must be performed on the unit of mass against the centrifugal force in order to transport it from the position of the clock on the rotating disc to the centre of the disc, then we have

φ = ω²r²/2

From this it follows that

v = v₀(1 – φ/c²)

In the first place, we see from this expression that two clocks of identical construction will go at different rates when situated at different distances from the centre of the disc. This result is also valid from the standpoint of an observer who is rotating with the disc.

Now, as judged from the disc, the latter is in a gravitational field of potential φ, hence the result we have obtained will hold quite generally for gravitational fields. Furthermore, we can regard an atom which is emitting spectral lines as a clock, so that the following statement will hold:

An atom absorbs or emits light of a frequency which is dependent on the potential of the gravitational field in which it is situated.

The frequency of an atom situated on the surface of a heavenly body will be somewhat less than the frequency of an atom of the same element which is situated in free space (or on the surface of a smaller celestial body).

Now φ = - K (M/r), where K is Newton's constant of gravitation, and M is the mass of the heavenly body. Thus a displacement towards the red ought to take place for spectral lines produced at the surface of stars as compared with the spectral lines of the same element produced at the surface of the earth, the amount of this displacement being

(v₀ - v)/v₀ = (K/c²)(M/r)

For the sun, the displacement towards the red predicted by theory amounts to about two millionths of the wavelength. A trustworthy calculation is not possible in the case of the stars, because in general neither the mass M nor the radius r are known.

It is an open question whether or not this effect exists, and at the present time (1920) astronomers are working with great zeal towards the solution. Owing to the smallness of the effect in the case of the sun, it is difficult to form an opinion as to its existence. Whereas Grebe and Bachem (Bonn), as a result of their own measurements and those of Evershed and Schwarzschild on the cyanogen bands, have placed the existence of the effect almost beyond doubt, while other investigators, particularly St. John, have been led to the opposite opinion in consequence of their measurements.

Mean displacements of lines towards the less refrangible end of the spectrum are certainly revealed by statistical investigations of the fixed stars ; but up to the present the examination of the available data does not allow of any definite decision being arrived at, as to whether or not these displacements are to be referred in reality to the effect of gravitation. The results of observation have been collected together, and discussed in detail from the standpoint of the question which has been engaging our attention here, in a paper by E. Freundlich entitled “Zur Prüfung der allgemeinen Relativitäts-Theorie” (Die Naturwissenschaften, 1919, No. 35, p. 520: Julius Springer, Berlin).

At all events, a definite decision will be reached during the next few years. If the displacement of spectral lines towards the red by the gravitational potential does not exist, then the general theory of relativity will be untenable. On the other hand, if the cause of the displacement of spectral lines be definitely traced to the gravitational potential, then the study of this displacement will furnish us with important information as to the mass of the heavenly bodies. [A]

Footnotes

1) Especially since the next planet Venus has an orbit that is almost an exact circle, which makes it more difficult to locate the perihelion with precision.

[A] The displacement of spectral lines towards the red end of the spectrum was definitely established by Adams in 1924, by observations on the dense companion of Sirius, for which the effect is about thirty times greater than for the Sun. R.W.L. — translator

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tparadox · 7 years

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I watched some math videos about math problems that concern the complex plane and YouTube suggested a video titled “Imaginary Numbers Are Real!” Sure, I’ll watch that.

It introduces the idea that all polynomial functions must cross the X axis an equal number of times to their highest degree, but some don’t seem to until you include imaginary numbers and complains that they get dismissed in perceived importance because of the name, but they’re vital. Okay, makes sense. Continue to part two for why they were invented. Uh, okay.

Part two is about how we had to expand out from the natural numbers because we found cases where math breaks if we don’t. Fractions, negatives, irrationals. Yes, good. And then it states on a story that covers at least four generations of mathematicians working out what to do with rooting squares across three more parts. This history of deriving math concepts is interesting, but uh, how long is this? Thirteen parts! Well I guess this is what I’m doing for the rest of the night.

Once it’s derived the complex plane, it goes into using it to geometrically solve problems, and how that demonstrates that “Imaginary” numbers aren’t a hack to get around a wall, but make our understanding of numbers more complete.

You may think this has proven the thesis of the title, but it keeps going. Now that numbers themselves are two-dimensional, it goes on to describe how Cartesian plotting is broken and we need a new way to visualize the inputs and outputs of functions. After all, now we have four dimensions involved, and that makes our brains hurt.

Actually, it turns out what really makes my brain hurt is Riemann Surfaces. But once it’s taken three videos to develop those, it’s finally ready to come back to the problem it introduced an hour and a half ago, with only two episodes to break down what’s happening with the complex graph of x²=1.

I gained a deeper understanding of math I’ve used competently, I learned what people are on about when they talk about converting to Polar, and then I lost the plot a bit, but it looked cool.

Anyway, here’s the entire video course I accidentally found that goes from high school basics to graduate studies.

Okay, I guess it only seemed like so many parts at the end because the last video is three times the length of any other.

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nox-lathiaen · 5 years

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BSME - Design of Multi-Axis Motion Mechanisms - Waukesha, WI

Seeking degreed Mechanical Engineer with 3+ years experience using 2D & 3D software to support the design of robots for super high precision, high speed, high performance applications, such as: micro-electro-mechanical assembly, aligning, coating, stacking, precision pick & place, bonding, semiconductor & circuit board packaging, etc. Must have experience designing Robotic End Effector type devices which are used to transfer substrates and components. Requires proficiency with stress and failure analysis calculations including GD&T (Geometrical Dimensioning & Tolerancing), FEA (Finite Element Analysis) AND CFD (Computational Fluid Dynamics) and experience designing multi-axis motion mechanisms. COMPANY: Collaborative environment where engaged employees share their knowledge and suggestions. Team is entrusted to use their own discretion and common sense. Staff to management communication is promoted and encouraged. Family atmosphere. Promotes opportunities and incentives for employees to learn, develop and grow. Culture of continuous improvement. Employee efforts, achievements and performance are formally recognized and honored on a regular basis. A fun and playful attitude is maintained throughout the organization. Adrian Gostick and Scott Christopher, in their book The Levity Effect: Why It Pays To Lighten Up, suggest if people are having fun, they're going to work harder, stay longer, maintain their composure in a crisis, and take better care of the organization. We believe this is their kind of company. Enjoy the career path opportunities that only a growing company can provide while earning a top salary plus bonuses, and full company paid benefits Medical, dental and a vision plan, prescription drug plan, flexible spending account, short and long-term disability coverage, 401(k) plan with dollar-for-dollar company match, discount stock purchase plan, tuition assistance, employee assistance program, life and accidental death & disability insurance, and company sponsored and paid certification training programs. For complete details contact James Franco at: (609) 584-9000 ext 283 Or submit resume online at: dmc9.com/jef/app.asp Or email to: 1000037591_10007335 AT jobbank301.com Please reference #38588156 when responding. Education Requirements: Some College Minimum Experience Requirements: 5-10 years Job City Location: Waukesha Job State Location: WI Job Country Location: USA Salary Range: $65,000 to $120,000 Diedre Moire Corporation, Inc. Diedremoire_dot_com WE ARE AN EQUAL OPPORTUNITY EMPLOYER and our employment decisions are made without regard to race, color, religion, age, sex, national origin, handicap, disability or marital status. We reasonably accommodate individuals with handicaps, disabilities and bona fide religious beliefs. Jobs Career Position Hiring. CONSIDERED EXPERIENCE INCLUDES: Senior Mechanical Engineer Design Engineer Project Engineer BSME MSME Mechanical Engineering Mechanical Design Custom Equipment Automation Associates CAD Computer Aided Design ProE Pro Engineer PTC Creo DISCLAIMER: We will make every effort to consider applications for all available positions and shall use one or more of the contact methods and addresses indicated in resume or online application. Indicated location may be proximate or may be desirable point of embarkation for paid or unpaid relocation to another venue. Job descriptions may fit single or multiple presently available or anticipated positions and are NOT an offer of employment or contract implied or otherwise. Described compensation is not definite nor precise and may be estimated and approximate and is negotiable depending on market conditions and candidate availability and other factors and is solely at the discretion of employers. Linguistics used herein may use First Person Singular and First Person Plural grammatical person construction for and with the meaning of Third Person Singular and Third Person Plural references. We reserves the right to amend and change responsibilities to meet business and organizational needs as necessary. Response to a specific posting or advertisement may result in consideration for other opportunities and not necessarily the incentive or basis of the response. Nothing herein is or may be considered a promise, guarantee, offer, pledge, agreement, contract, or oath. If you submit an application or resume which contains your email address, we will use that email address to communicate with you about this and other positions. We use an email quality control service to maintain security and a remove and dead address filter. To cancel receiving email communications, simply send an email from your address with the word "remove" in the subject line to pleaseremove_AT_candseek4.com Or, visit the website at jobbankremove_dot_com. If you have further concern regarding email received from us, call (609) 584-5499. Reference : BSME - Design of Multi-Axis Motion Mechanisms - Waukesha, WI jobs Source: http://jobrealtime.com/jobs/technology/bsme-design-of-multi-axis-motion-mechanisms-waukesha-wi_i4172

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archangelmichaelus-blog · 5 years

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Astrological summary 2019-2021. Ready for a Pole-Shift?

Earth level

For all those who want an easy summary…. Jupiter is in his home, the Sagittarius, and is ready to dispense his blessings. He is pretty much having a good time with Neptune. Together they build big dreams, with enthusiasm and even love. You are launching wonderful projects. Mars is ready to give all his energy for action to happen, often in synchronicity with Uranus.

Uranus would prefer to challenge or innovate the system big time, give a kick in the projects that Neptune and Mars want to manifest. Uranus likes to create upheavals… gilets jaunes for instance… But… Saturn, time, might still be eating his children…. Saturn says: “slow down, not yet, not enough wisdom, still karma to handle… not until you have definitively dealt with my friend Pluto, Lord of Underworld”. In his corner, Mercury tries to find a solution, to organize things better with the help of the Capricorn or just make sense of the situation.

Heaven level (Hypothesis)

The forever big guys have a conversation. Jupiter, on Skype, calling Saturn, in his home, the Capricorn, who happens to entertain a guest and friend, Pluto, Lord of Hades and Death. Jupiter, an Earthly king, is ready to be kingly and distribute bounties; In close collaboration with the Old Dragon and the Cosmic Lords, Jupiter prepares to pull out his sword and free the Earth-Axis, with Mars. But the situation might be too explosive. Saturn, his father, is advising patience. Cranking the system, time, darkness, finances is on schedule, but the Underworld is still full of people on probation. Pluto cannot release them unless they finish their time or get kicked by the gangs. More harmony is needed between Mars and Venus, which could happen at the next eclipse (January 20-21).

-That won’t be enough, says the Old Dragon, unless enough humans can access the dimensional and time portal, we MIGHT HAVE TO IMPOSE A DRASTIC MOVE, eventually a POLE SHIFT.

– Saturn: Yeah, a little more time; why don’t we wait a few months, when we can all gather in my home, Capricornus? (January 2020).

-The Old Dragon: maybe, but, still too early…. we need more couple therapy for Sun and Moon. Moon wants to dominate the dance. The specific tango staged in 2003, takes 6586 steps. This specific act, this dance, will end in May-June 2021. We have chances to end this part of the play smoothly. Remember, this was the wish expressed by My Heavenly Counterpart, the Archangel Michael, in 2003.

“A geometrical form emerged from Heaven, magnificent and radiant… the Celestial Jerusalem is now anchored on Earth, as announced in the prophecies….the main vortex of Mont Saint Michel is being activated, overshadowed by the New Jerusalem. The Archangel Michael says: “it is time to reconstruct the poles. A movement of the vortices is starting… if I direct the movement slowly, with kindness and compassion, we will be able to avoid a brutal reaction of the physical bodies of the planet, and thus, as much as possible, spare the human race.” etc

(More in the books Kiss for Lucifer, annex, Cosmic Love: timelines and Wesak reports 2001 and 2003).1/6/19 The Archangel Michael Speaks… less and less because everyone knows everything…

The world in general, everyone wants to be seen and be in power; in 3D, the situation manifests into impossible governability mixed with disillusion about democracy and globalism. In truth, men have rightfully discovered segments of truth about self, religions, Aliens, about spirituality and science. Yet, they cannot see the big picture and are still polishing their low ego. In consequence, they have decided that God is dead instead of rephrasing the meaning of God and gods, and how to joyfully merge with the Universal Consciousness. The result is a possible fracture between the Spiritual Hierarchies and the human world. We can cut the umbilical cord between a mother and a baby. But, no one can decide to live separated from What sustains Life Itself, from Consciousness manifested in many layers, one of them being your Spiritual Government. This fracture might come with consequences, more struggle than needed to ascend.

In truth, the Archangel Michael, My Spiritual Self, does not speak to human beings; as His/My Consciousness are so far out that such an exercise is impossible. Yet, My Consciousness has generated an Embodiment of Myself, an expression and anchor for My Frequency. This Embodiment has been overshadowed, performing specific tasks, teaching and guiding mankind, leading its evolution. An Embodiment is a precious tool, for the spiritual Hierarchies and for humans. It is a bridge between realities that mostly do not connect.

In other words, I, the Embodiment can transmit information about the Earth and human reality to Higher levels of Consciousness, easing the Earth transformational process. And… I can give you some clues. Do you like driving with your eyes closed? That is exactly what most humans do. How can you efficiently assist the Earth, your neighbors, and your family while stopping to use the compass that the universe compassionately provided for you?

What have you understood, integrated with the last 5 articles (Since John Dee)? How have you used this knowledge in your personal life? Ok, you are not Dee and this is none of your business. The astrological trends are way over your head and you still do not know how to use them? Remember, we can work on that together.

Do you know what astral cyclic mechanisms can help you navigate life? The easiest one to consider in the present is the arrival of Jupiter in his house, the Sagittarius. Again, easy, just remember what you were focusing on 12 years ago. Have you grasped how to use the eclipses, 4 to 5 windows per year?

It seems that readers did not comprehend the full meaning of the last article: Human journey between Sirius and Vega. I am trying not to make predictions for the future, but I thought that the audience who has followed my teachings for years would get it. So, do we need a webinar? Or is it time to reset your vibration and consciousness with a retreat? That’s what retreats and workshops are about. Re-center, focus on spiritual matters, reset. Remove all worldly affairs and interferences for a few days; meet again your soul as well as the Archangel Frequency, My Frequency.

An answer to one of our readers: ABOUT DISEASE AND SELF-HEALING:

(I am repeating the same things, but it seems necessary. Dear One, we spoke about your problem on our very first meeting, and again later, a few times).

Disease and pain are the body’s manifestation of:

Inner world: you and you

– Inner struggle: you in the third dimension, fighting with your soul, your karma, your purpose. Self-demolition.

– Inner pain: you, dealing with or denying a trauma, a situation and all the consequences of this trauma on your personality, life, perceptions, and body.

Fight with the outer world:

Dealing with the environment: weather, wind, sun, work, viruses, cars and trees (creating accidents) …. entities, implants …. and people!

Others imposing their will, their desires, their needs on you and your unhealthy response to the situations.

Others imposing their energies on you: this is the ultimate consequence of all the above and has many manifestations that translate into diseases.

First-aid-kit: read again several chapters of the Book I Am That I Am: Subconscious, karma, energy relationships and APPLY the techniques. Oh, the book is not on Kindle… bad… when is the last time that you have cut the links with others? Or, have you ever cut the energy connections with almost everyone as recommended in the book? The only beings that you are not suggested to nicely clean out of your energy field are the babies and young children. All the rest is complaisance and complicity.

Or, is your denial so deep that you did it with such compassion for your abusers that they became your vampire-lovers? That’s exactly what humans do. Better marry a vampire than navigating life alone. As you see, I am in the mood for humor.

PRAYER:

Prayer, praying for self and receiving other’s prayers is a good tool at the moment. It helps to keep the head of out the water or to decrease the pain, but it is a band-aid if the problem has not been identified and dealt with.

Denial and the habit of pushing the dirt under the carpet are the most convenient way to avoid facing the mirror and continue being a victim.

INVASIONS of YOUR ENERGY FIELD and BODY:

How it translates: invasion of one or more of your chakras. This is the easiest and most common cause of disease. If you cannot see or feel your chakras, just clean them every month or every spring, like your house! (again, I Am Book). Some examples:

Sexual organs and area: invasion of the second chakra, physically, by force, abuse or emotional struggle (i.e. the lack of respect of a husband, a drunk; last of self-respect: sleeping with someone that you do not want to be with because it is convenient!).

Loss of love: most breast cancers are the consequences of emotional traumas and losses.

Sexual parasites and all forms of itching: invasion by a human or by an entity

Digestive and abdomen pain, dysfunction, inflammation:

Always the reflection of the problem with other’s power or personal power. In work and family situations, in the couple, there is always the same question: who is in power and can we deal with not being the one in power? A consensus exists. Is it what we wish or not?

Then, if there is a struggle, people just jump in other’s 3rd chakra and stay there forever, incognito. As most do not ever deal with that, they will have to marry again or be abused again by the same person in the next incarnation!

The disease can also occur if you are powerful, yet not in the right position to exert your power accordingly => self – disbalance. Example: a bright young man with a high IQ, who did not go to school and has to flip burgers for a living.

Back, lower back pain, degenerating in pinched nerves, back surgery: something, generally someone finds you and your energy very attractive and tasteful and decided to eat your substance (spiritual vampire). Find the culprit and get your back straight again and pain-free.

Inflammation of the nerves: neck, back: a foreign energy, often an entity is attached to you.

Headaches: many roots, difficult to summarize in a few words. What is the area affected? Liver and Gall bladder are most often the culprits. It can also be a friendly visit in your crown chakra, and that could affect your thinking process, your nervous system.

HOW to use HOMEOPATHIC SESSIONS:

One session, isolated within a few years, is rarely enough, because the homeopath needs to clean up the system (motor oil and filters), work on the last layers of disbalance (the accident of last summer, the antibiotics are taken in hast, the grief of losing a friend), then, then, reset your life-force.

We recommend a follow-up session every 4- 6 months, or when your body is honestly screaming that there is a crisis to deal with. If you are never sick or know how to rebalance yourself after each of the above, bravo. As long as your body did not become a burden, all is perfect.

Love and Blessings

#Astrological #summary #2019 #new year 2019 #Ready for a Pole-Shift?#2019-2021 #Books #Book #Review #History #ArchangelMichael

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watchilove · 4 years

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In this crowning expression of the ties binding H. Moser & Cie. and MB&F for more than ten years, Edouard Meylan and Maximilian Büsser have composed a duet recital in the form of an exceptional concerto for devotees of fine watchmaking. For the first time in its history, MB&F is contributing to a Performance Art endeavour flowing in both directions in an entirely reciprocal manner. Within this framework, the two Maisons are co-signing a pair of creations whose DNA blends the main characteristics of each. A story of friendship between two men against a backdrop of shared values, for the pleasure of building and sharing, and then of jointly presenting the results of this extraordinary project.

Project Origins

H. Moser & Cie. and MB&F are both independent, human-scale Swiss companies. They are run by two passionate personalities, longstanding acquaintances who both appreciate and respect each other on both a personal and professional level. The brands have in fact been working together for more than ten years, with Precision Engineering AG – a sister company of H. Moser & Cie. – notably supplying MB&F’s balance springs.

Maximilian Büsser and Edouard Meylan

It is therefore not surprising that MB&F asked Edouard Meylan to take part as a „friend“ to help create a Performance Arts piece. The latest aspect of this collaboration lies in its being a two-way street. Maximilian Büsser says: „When I called Edouard to tell him that I wanted to collaborate on a creation, I mentioned that I really liked the double balance-spring, the Moser fumé dials and the Concept watch series. Edouard immediately told me that he would let me borrow these features, but on condition that he could also reinterpret one of my machines. After an initial moment of surprise, I gave it some thought. Being 50% Indian and 50% Swiss, I am firmly convinced that mixing DNA creates interesting results, so why not try the experiment in watchmaking? I therefore agreed and suggested the FlyingT model, which is particularly dear to my heart.“

In a spirit of sharing and openness, while cultivating the notion of strength in unity, H. Moser & Cie. and MB&F have thus jointly created two models, available in several versions and issued in 15-piece limited series. This number is a nod to the 15th anniversary of MB&F as well as honouring the 15th anniversary of the relaunch of H. Moser & Cie. By pooling their strengths, these two competing yet friendly brands are working to harness the combined strengths of talented artisans, entirely in keeping with the philosophy adopted by MB&F.

Endeavour Cylindrical Tourbillon H. Moser × MB&F

H. Moser & Cie. has borrowed from MB&F the concept of three-dimensional movements, a strong element of the Geneva Maison’s identity, protected by a sapphire dome and featuring a one-minute flying tourbillon that rises above the main dial through a ventricular opening appearing at 12 o’clock. Benefiting from the expertise of its sister company Precision Engineering AG, H. Moser & Cie. has equipped its tourbillon with a cylindrical balance spring, the same as that developed by Precision Engineering AG for MB&F’s LM Thunderdome.

Invented in the 18th century, the cylindrical balance spring is reminiscent of a worm- or corkscrew, rising perpendicularly around the upper rod of the balance staff. Commonly used in historical marine chronometers at the time, it offers the advantage of developing concentrically, and therefore geometrically, since it works perfectly along the axis of its pivots. This gives it a significant advantage over the flat balance spring, whose opposite ends tend to exert forces on the pivots, despite the Philips or Breguet terminal curves which were specifically developed to partially correct the non-concentric opening of the balance spring.

Fitted with a Breguet overcoil at both attachment points, the cylindrical balance spring reduces pivot friction and greatly improves isochronism. Due to its specific shape, the cylindrical balance spring is far more difficult to produce and takes ten times longer to make than a traditional balance spring.

Another reference to MB&F’s identity lies in the tilted dials, which H. Moser & Cie. has adopted for its hour and minute subdial. This is inclined at 40° so that the owner of the watch is the only one to whom it reveals the secret of time, and mounted on a conical gear train ensuring optimal torque transmission from one plane to the other.

As Edouard Meylan explains: „We have Moserized the MB&F universe by developing a sapphire subdial, which melts into the background so as to highlight the beauty of our fumé dials. And to preserve the purity and elegance of this true work of horological art, we have inscribed our logo like a watermark on the sapphire subdial, thereby underlining the personal character and intimate relationship binding it to its owner“.

Available in five different versions, the Endeavour Cylindrical Tourbillon H. Moser × MB&F model comes in a steel case topped by Funky Blue, Cosmic Green, Burgundy, Off-White or Ice Blue dials, all of the fumé variety.

LM101 MB&F × H. Moser

The Legacy Machine 101 distils the very quintessence of mechanical watchmaking: the balance wheel, the power reserve and the passing of time. It is therefore no coincidence that MB&F has chosen to revisit this model – one of the purest and „simplest“ in its collection – since it is indeed minimalism that guided the creation of the LM101 MB&F × H. Moser model.

Like H. Moser & Cie. and the “back to basics” approach embodied in its Concept watch series, MB&F has chosen to remove its logo and return to its roots and indeed to the very origins of horology, when only the movements were signed. In the same understated spirit, it has abandoned the floating domed subdials to display the hours and minutes as well as the 45-hour power reserve by means of hands placed directly on the main dial.

The fumé dials borrowed from H. Moser & Cie. can thus be expressed in complete freedom, also enhanced by a refined bezel. Four fumé dials have been chosen for the LM101 MB&F × H. Moser: Red fumé, Cosmic Green fumé, Aqua Blue fumé and, of course, the famous Funky Blue fumé. Topped with a domed sapphire crystal, the case is made of steel, for only the third time in the history of MB&F.

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The mesmerising large suspended balance wheel continues to take centre stage, albeit completely redesigned on the LM101 MB&F × H. Moser in order to highlight the beauty of the fumé dials. This beating heart, which represents the quintessence of watchmaking in the eyes of Maximilian Büsser, has been fitted with a double balance spring produced by Precision Engineering AG.

Thanks to this pair of matching balance springs, the displacement of the point of gravity undergone by each spring as it expands is corrected, significantly improving precision and isochronism in a continuous quest for perfection. In addition, the paired balance springs also reduce the friction effect normally encountered with a single balance spring, resulting in optimised isochronism.

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Through the case back, the curved sapphire crystal reveals the ‘engine’ driving this timepiece. Unlike the base movement of the Legacy Machine 101, of which the finishes were determined by co-creator Kari Voutilainen, the aesthetics of the calibre that powers the LM101 MB&F × H. Moser is more contemporary, with a subtle NAC treatment to enhance its beauty.

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Fruitful Cooperation

Edouard Meylan and Maximilian Büsser are delighted with this rewarding collaborative project, which has achieved results far exceeding their expectations. In addition to the beauty of the models created in tandem, two bodies of expertise and two sets of DNA have been blended and mutually enriched. The two different communities of the two Maisons have also pooled their skills in a wonderful spirit of openness and transparency. This experience leaves Edouard and Maximilian with a keen sense of coming back to a sense of pleasure: the pleasure of working together and of creating.

Maximilian Büsser and Edouard Meylan

H. Moser X MB&F Endeavour Cylindrical Tourbillon Technical Specifications

Reference 1810-1200

Steel model, Funky Blue fumé dial, black alligator leather strap, limited edition of 15 pieces

Reference 1810-1201

Steel model, Burgundy fumé dial, black alligator leather strap, limited edition of 15 pieces

Reference 1810-1202

Steel model, Cosmic Green fumé dial, black alligator leather strap, limited edition of 15 pieces

Reference 1810-1203

Steel model, Off-White fumé dial, blued hours and minutes hands, black alligator leather strap, limited edition of 15 pieces

Reference 1810-1205

Steel model, Ice Blue fumé dial, black alligator leather strap, limited edition of 15 pieces

Case

Steel topped by a high domed sapphire crystal

Diameter: 42.0 mm

Height: 19.5 mm

Height without crystal sapphire: 9.4 mm

Crown at 9 o’clock, engraved with a “M“

See-through sapphire crystal case back

Dial

Main dial: Funky Blue fumé, Burgundy fumé, Cosmic Green fumé, Off-White fumé or Ice Blue fumé with sunburst pattern

Hours and the minutes displayed on a 40° vertically tilted sapphire dial at 6 o’clock

The leaf-shaped hour and minute hands, blued on the reference 1810-1203

Movement

HMC 810 three- dimensional automatic Manufacture calibre

Diameter: 32.0 mm or 14 1/4 lignes

Height: 5.5 mm

Frequency: 21,600 vibrations/hour

29 jewels

184 components

Automatic bi-directional pawl winding system

Oscillating weight in 18-carat gold with engraved H. Moser & Cie. logo

Power reserve: minimum 72 hours

Cylindrical hairspring

One-minute flying tourbillon at 12 o’clock with skeletonised bridges

Functions

Hours and minutes

Strap

Hand-stitched black alligator leather

Steel folding clasp engraved with the Moser logo

MB&F × H. Moser LM101 Technical Specifications

Reference LM101 MB&F × H. Moser

Steel model,

Funky Blue fumé,

Cosmic Green fumé,

Red fumé or

Aqua Blue fumé dial,

Calfskin leather strap,

limited edition of 15 pieces for each reference

Engine

Three-dimensional horological movement developed in-house by MB&F

Movement aesthetics and finishing specifications: Kari Voutilainen

Manual winding with single mainspring barrel

Power reserve: 45 hours

Balance wheel: Bespoke 14mm balance wheel with four traditional regulating screws floating above the movement

Balance spring: Straumann® double hairspring

Balance frequency: 18,000bph/2.5Hz

221 components

23 jewels

Chatons: gold chatons with polished countersinks

Fine finishing: superlative 19th century-style hand finishing throughout; internal bevel angles highlighting hand craft; polished bevels; Geneva waves; hand-made engravings, NAC black bridges

Functions

Hours, minutes and power reserve indicator

Large balance wheel suspended above the dial

Case

Available in 4 limited editions of 15 pieces in stainless steel 316, including a special edition with Aqua Blue fumé dial made for the retailer Ahmed Seddiqi & Sons.

Diameter: 40.0 mm

Height: 16.0 mm

35 components

High domed crystal sapphire on top and box sapphire crystal on back, both with anti-reflective coating on both sides

Dial

Funky Blue fumé,

Cosmic Green fumé,

Red fumé

Aqua Blue fumé with sunburst pattern

Strap

Hand-stitched calfskin strap

Steel 316L and titanium folding clasp

H. Moser & Cie.

H. Moser & Cie. was created by Heinrich Moser in 1828. Based in Neuhausen am Rheinfall, it currently employs around 60 people, has developed 14 in-house calibres to date and produces more than 1,500 watches per annum. Through its sister company Precision Engineering AG (PEAG), H. Moser & Cie. manufactures parts such as regulating organs and balance-springs, which are used for its own production as well as to supply its partner companies. Independent company incorporated into Moser Watch Holding in 2012, Precision Engineering AG specialises in watch components for escapements, from their initial design to the production of a quality product ready to be integrated into the watch movement it must regulate. H. Moser & Cie. is honoured to have a Moser family member with the company as Honorary Chairman and President of the Heinrich and Henri Moser Foundation. The aim of the Moser Foundation, created by one of Heinrich Moser’s descendants, is to keep the family history alive and seek out antique pieces for the Moser Museum, located in Charlottenfels Manor, Heinrich Moser’s family home. With its substantial watchmaking expertise and highly acclaimed experience in the sector, MELB Holding holds shares in H. Moser & Cie. and Hautlence. MELB Holding is an independent family group, based in the heart of the legendary Vallée de Joux.

MB&F

After a 15-year career in management at prestigious brands, Maximilian Büsser left his role as CEO of Harry Winston in 2005 to create MB&F – Maximilian Büsser & Friends. MB&F is a laboratory dedicated to art and micromechanical engineering, set up to design and create small editions of radical watches, the fruit of collaboration with exceptional professional watchmakers, chosen by Maximilian Büsser for their talent and working methods.

In 2007, MB&F unveiled the HM1, its first Horological Machine. With its sculptural three-dimensional case and finely decorated movement, the HM1 set the tone for the Horological Machines that were to follow – Machines which symbolise time rather than merely Machines used to read it.

In 2011, MB&F released the Legacy Machines collection. These round pieces are more classic than MB&F’s other creations, and pay tribute to the watchmaking excellence of the 19th century, reinterpreting the complications from innovative key watchmaking figures as objects of contemporary art.

H. Moser X MB&F Endeavour Cylindrical Tourbillon and MB&F X Moser LM101 Image Gallery

Maximilian Büsser and Edouard Meylan

H. Moser X MB&F Endeavour Cylindrical Tourbillon and MB&F X Moser LM101 In this crowning expression of the ties binding H. Moser & Cie. and MB&F for more than ten years, Edouard Meylan and Maximilian Büsser have composed a duet recital in the form of an exceptional concerto for devotees of fine watchmaking.

#Endeavour Cylindrical Tourbillon #H Moser #H. Moser Endeavour Cylindrical Tourbillon #LM101 #MB&F X Moser #MB&F X Moser LM101 #news #Press release

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felord · 5 years

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CS 189 Introduction to Machine Learning HW3 Solved

Deliverables: Submit your predictions for the test sets to Kaggle as early as possible. Include your Kaggle scores in your write-up (see below). The Kaggle competition for this assignment can be found at: https://www.kaggle.com/c/cs189-hw3-mnist https://www.kaggle.com/c/cs189-hw3-spam Submit a PDF of your homework, with an appendix listing all your code, to the Gradescope assignment entitled “HW3 Write-Up”. You may typeset your homework in LaTeX or Word (submit PDF format, not .doc/.docx format) or submit neatly handwritten and scanned solutions. Please start each question on a new page. If there are graphs, include those graphs in the correct sections. Do not put them in an appendix. We need each solution to be self-contained on pages of its own. In your write-up, please state with whom you worked on the homework. • In your write-up, please copy the following statement and sign your signature next to it. (Mac Preview and FoxIt PDF Reader, among others, have tools to let you sign a PDF file.) We want to make it extra clear so that no one inadverdently cheats. “I certify that all solutions are entirely in my own words and that I have not looked at another student’s solutions. I have given credit to all external sources I consulted.” Submit all the code needed to reproduce your results to the Gradescope assignment entitled “HW3 Code”. Yes, you must submit your code twice: once in your PDF write-up (above) so the readers can easily read it, and once in compilable/interpretable form so the readers can easily run it. Do NOT include any data files we provided. Please include a short file named README listing your name, student ID, and instructions on how to reproduce your results. Please take care that your code doesn’t take up inordinate amounts of time or memory. If your code cannot be executed, your solution cannot be verified. The assignment covers concepts on Gaussian distributions and classifiers. Some of the material may not have been covered in lecture; you are responsible for finding resources to understand it.

1 Gaussian Classification

Let P(x | Ci) ∼ N(µi,σ2) for a two-category, one-dimensional classification problem with classes C1 and C2, P(C1) = P(C2) = 1/2, and µ2 > µ1. Find the Bayes optimal decision boundary and the corresponding Bayes decision rule. The Bayes error is the probability of misclassification, Pe = P((misclassified as C1) | C2) P(C2) + P((misclassified as C2) | C1) P(C1). Show that the Bayes error associated with this decision rule is 1 Z ∞ −z2/2 Pe = √ e dz 2π a µ2 − µ1 where a = . 2σ

2 Isocontours of Normal Distributions

Let f(µ,Σ) be the probability density function of a normally distributed random variable in R2. Write code to plot the isocontours of the following functions, each on its own separate figure. You’re free to use any plotting libraries available in your programming language; for instance, in Python you can use Matplotlib.     11 and Σ = 10 20. f(µ,Σ), where µ =     −1 2 1 f(µ,Σ), where µ =  2  and Σ = 1 3.       2 2 1 f(µ1,Σ1) − f(µ2,Σ2), where µ1 = 2, µ2 = 0 and Σ1 = Σ2 = 1 1.         2 2 1 2 1 f(µ1,Σ1) − f(µ2,Σ2), where µ1 = 2, µ2 = 0, Σ1 = 1 1 and Σ2 = 1 3.  f(µ1,Σ1) − f(µ2,Σ2), where µ1 = 11, µ2 = −−11, Σ1 = 20 10 and Σ2 = 12 12.

3 Eigenvectors of the Gaussian Covariance Matrix

Consider two one-dimensional random variables X1 ∼ N(3,9) and X 4), where N(µ,σ2) is a Gaussian distribution with mean µ and variance σ2. Write a program that draws n = 100 random two-dimensional sample points from (X1, X2) such that the ith value sampled from X2 is calculated based on the ith value sampled from X1. In your code, make sure to specify the Random Number Generator seed that was used so your simulation is reproducible. For each of the following parts, include the corresponding output of your program. Compute the mean (in R2) of the sample. Compute the 2 × 2 covariance matrix of the sample. Compute the eigenvectors and eigenvalues of this covariance matrix. On a two-dimensional grid with a horizonal axis for X1 with range and a vertical axis for X2 with range , plot all n = 100 data points, and arrows representing both covariance eigenvectors. The eigenvector arrows should originate at the mean and have magnitudes equal to their corresponding eigenvalues. Let U = be a 2 × 2 matrix whose columns are the eigenvectors of the covariance matrix, where v1 is the eigenvector with the larger eigenvalue. We use U> as a rotation matrix to rotate each sample point from the (X1, X2) coordinate system to a coordinate system aligned with the eigenvectors. (As U> = U−1, the matrix U reverses this rotation, moving back from the eigenvector coordinate system to the original coordinate system). Center your sample points by subtracting the mean µ from each point; then rotate each point by U>, giving xrotated = U>(x − µ). Plot these rotated points on a new two dimensional-grid, again with both axes having range .

4 Classification

Suppose we have a classification problem with classes labeled 1,...,c and an additional “doubt” category labeled c + 1. Let r : Rd → {1,...,c + 1} be a decision rule. Define the loss function  λ0r L(r(x) = i,y = j) = λs if i = j i, j ∈ {1,...,c}, if i = c + 1, otherwise, where λr ≥ 0 is the loss incurred for choosing doubt and λs ≥ 0 is the loss incurred for making a misclassification. Hence the risk of classifying a new data point x as class i ∈ {1,2,...,c + 1} is c X R(r(x) = i|x) = L(r(x) = i,y = j) P(Y = j|x). j=1 Show that the following policy obtains the minimum risk when λr ≤ λs. Choose class i if P(Y = i|x) ≥ P(Y = j|x) for all j and P(Y = i|x) ≥ 1 − λr/λs; Choose doubt otherwise. What happens if λr = 0? What happens if λr > λs? Explain why this is consistent with what one would expect intuitively.

5 Maximum Likelihood Estimation

Let X1,..., Xn ∈ Rd be n sample points drawn independently from a multivariate normal distribution N(µ,Σ). Suppose the normal distribution has an unknown diagonal covariance matrix Σ = σ21 σ22 σ23   ...    σd2  and an unknown mean µ. Derive the maximum likelihood estimates, denoted ˆµ and ˆσi, for µ and σi. Show all your work. Suppose the normal distribution has a known covariance matrix Σ and an unknown mean Aµ, where Σ and A are known d × d matrices, Σ is positive definite, and A is invertible. Derive the maximum likelihood estimate, denoted ˆµ, for µ.

6 Covariance Matrices and Decompositions

As described in lecture, the covariance matrix Var(R) ∈ Rd×d for a random variable R ∈ Rd with mean µ is    Var(R1) Cov(R1,R2) ... Cov(R1,Rd)  Var(R) = Cov(R,R) = E =  Cov(R..2,R1) Var(R2) ... Cov(Var(R...R2,dR)d) ,



 Cov(R.d,R1) Cov(Rd,R2) ... where Cov(Ri,Rj) = E and Var(Ri) = Cov(Ri,Ri). If the random variable R is sampled from the multivariate normal distribution N(µ,Σ) with the PDF f(x) = 1 e−((x−µ)>Σ−1(x−µ))/2, p(2π)d|Σ| then Var(R) = Σ. Given n points X1, X2,..., Xn sampled from N(µ,Σ), we can estimate Σ with the maximum likelihood estimator n ˆ 1 X(Xi − µ)(Xi − µ)>, Σ = n i=1 which is also known as the covariance matrix of the sample. The estimate Σˆ makes sense as an approximation of Σ only if Σˆ is invertible. Under what circumstances is Σˆ not invertible? Make sure your answer is complete; i.e., it includes all cases in which the covariance matrix of the sample is singular. Express your answer in terms of the geometric arrangement of the sample points Xi. Suggest a way to fix a singular covariance matrix estimator Σˆ by replacing it with a similar but invertible matrix. Your suggestion may be a kludge, but it should not change the covariance matrix too much. Note that infinitesimal numbers do not exist; if your solution uses a very small number, explain how to calculate a number that is sufficiently small for your purposes. Consider the normal distribution N(0,Σ) with mean µ = 0. Consider all vectors of length 1; i.e., any vector x for which |x| = 1. Which vector(s) x of length 1 maximizes the PDF f(x)? Which vector(s) x of length 1 minimizes f(x)? (Your answers should depend on the properties of Σ.) Explain your answer.

7 Gaussian Classifiers for Digits and Spam

In this problem, you will build classifiers based on Gaussian discriminant analysis. Unlike Homework 1, you are NOT allowed to use any libraries for out-of-the-box classification (e.g. sklearn). You may use anything in numpy and scipy. The training and test data can be found on in the post corresponding to this homework. Don’t use the training/test data from Homework 1, as they have changed for this homework. Submit your predicted class labels for the test data on the Kaggle competition website and be sure to include your Kaggle display name and scores in your writeup. Also be sure to include an appendix of your code at the end of your writeup. Taking pixel values as features (no new features yet, please), fit a Gaussian distribution to each digit class using maximum likelihood estimation. This involves computing a mean and a covariance matrix for each digit class, as discussed in lecture. Hint: You may, and probably should, contrast-normalize the images before using their pixel values. One way to normalize is to divide the pixel values of an image by the l2-norm of its pixel values. (Written answer) Visualize the covariance matrix for a particular class (digit). How do the diagonal terms compare with the off-diagonal terms? What do you conclude from this? Classify the digits in the test set on the basis of posterior probabilities with two different approaches. Linear discriminant analysis (LDA). Model the class conditional probabilities as Gaussians N(µC,Σ) with different means µC (for class C) and the same covariance matrix Σ, which you compute by averaging the 10 covariance matrices from the 10 classes. To implement LDA, you will sometimes need to compute a matrix-vector product of the form Σ−1x for some vector x. You should not try to compute the inverse of Σ (nor the determinant of Σ). Instead, you should find a way to solve the implied linear system without computing the inverse. Hold out 10,000 randomly chosen training points for a validation set. Classify each image in the validation set into one of the 10 classes (with a 0-1 loss function). Compute the error rate and plot it over the following numbers of randomly chosen training points: . (Expect some variance in your error rate when few training points are used.) Quadratic discriminant analysis (QDA). Model the class conditionals as Gaussians N(µC,ΣC), where ΣC is the estimated covariance matrix for class C. (If any of these covariance matrices turn out singular, implement the trick you described in Q6.(b). You are welcome to use k-fold cross validation to choose the right constant(s) for that trick.) Repeat the same tests and error rate calculations you did for LDA. (Written answer.) Which of LDA and QDA performed better? Why? Using the mnistdata.mat, train your best classifier for the trainingdata and classify the images in the testdata. Submit your labels to the online Kaggle competition. Record your optimum prediction rate in your submission. You are welcome to compute extra features for the Kaggle competition. If you do so, please describe your implementation in your assignment. Please use extra features only for the Kaggle portion of the assignment. In your submission, include plots of error rate versus number of training examples for both LDA and QDA. Similarly, include a plot of training and test error for each digit. Which digit is easiest to classify? Include written answers where indicated. Next, apply LDA or QDA (your choice) to spam. Submit your test results to the online Kaggle competition. Record your optimum prediction rate in your submission. If you use additional features (or omit features), please describe them. Optional: If you use the defaults, expect relatively low classification rates. The TAs suggest using a bag-of-words model. You may use third-party packages to implement that if you wish. Also, normalizing your vectors might help. Read the full article

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onblogg · 5 years

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On Coordinate Systems

Buckle up. This is going to be a long one.

The idea of a coordinate system comes from a simple fact: you can write vectors as some combination of other vectors. There are many different coordinate systems, each with their own strengths and weaknesses. I will begin with two coordinate systems in two dimensions, then I will describe three common coordinate systems in three dimensions.

For the following two dimensional system, consider the vector, $\boldsymbol{v}$:

The most basic coordinate system is the Cartesian coordinate system. It’s also the most easily defined coordinate system. First, define one direction, called the $x$ direction, by placing a vector, called $\hat{x}$ (said aloud as “x hat”), in that direction:

Second, define a second direction that is perpendicular to the first, called the $y$ direction, by placing a vector, called $\hat{y}$, in that second direction. Both vectors should have the same length:

These two vectors, the coordinate vectors or basis vectors, are very special. As we have constructed, they define the two directions in space. They also define the fundamental length. In our system, we define the length of the coordinate vectors to be a length of $1$ unit. Now that we have these two basis vectors, we can write the vector $\boldsymbol{v}$ as a sum of the two basis vectors:

In this case, \[ \boldsymbol{v} = 3 \hat{x} + 1 \hat{y} \]

The numbers that we used in that sum, in this case, $3$ and $1$, are called the components of $\boldsymbol{v}$. If everyone agrees on using this basis for describing the plane, we can do away with writing $\boldsymbol{v}$ as this sum of basis vectors and instead refer to $\boldsymbol{v}$ using just the components. In other words, we can write \[ \boldsymbol{v} = \left(3 ,1 \right) \]

This is usually how people learn how to write down vectors in high school. Now, here’s one subtlety that pervades our entire discussion of coordinate systems. I, again, emphasize that spatial vectors are geometric objects that are independent of the mathematical framework we build around them. Coordinate systems are one such mathematical framework. While the components of a vector refer to the vector, the vector is not the coordinates. Just writing down the list of numbers can be confusing! To make this clear, I could have defined our coordinate system differently. Suppose I defined it this way instead:

Now, the directions are completely different, and so are the lengths! The new components are (not surprisingly) completely different than the old components (for the curious, the new components are $ \left(-2, -2\right)$). Nevertheless, these new components describe the same vector! The vector never changed, the coordinates did. To make things exactly clear what coordinate system you’re using, always draw your coordinate vectors in your diagrams. For clarity, I will usually write down vectors using the basis vectors rather than just the components.

One final point on the Cartesian system for completeness. Using the coordinate vectors, we can create a grid that can easily tell us what the coordinates of a point are:

When a high school student thinks of “coordinates” or “coordinate system”, this grid is what they usually have in mind.

We can describe the same vector using a different coordinate system. This next system is the polar coordinate system. This system uses concentric circles to describe the position of any point. For two dimensions, we need to (again) define two pieces of information. First, we have to specify an origin point, $\vec{0}$. This point is the center of the concentric circles and defines where the radius is zero. If we’re just describing a single vector, it is convenient to place the origin at the tail of the vector. By placing a unit vector that points radially outward, called $\hat{r}$, we define the units of constant radius:

Second, we have to define some axis where we begin measuring angle:

By convention, angle is measured increasing counterclockwise and is denoted by the Greek letter “phi”, $\phi$. Once we have defined these two things, a radius and an angle, we can write any point on the plane using these two quantities. In this case, the point at the tip of $\boldsymbol{v}$ can be written as the ordered pair \[ \left(r, \phi \right) = \left( 3.16, \frac{18.43}{180} \pi \right) \]

(If you’re unfamiliar with using radians, using $\pi$ to measure angles, don’t worry! I can cover that quickly later if there is demand.) This is great, but we would like to associate basis vectors with these quantities. We have already defined the radial basis vector, $\hat{r}$. It points in the direction of increasing radius. We can define an angular basis vector, $\hat{\phi}$, similarly. It points in the direction of increasing angle. Unlike the Cartesian coordinate system, though, these basis vectors aren’t so simple. The polar coordinate system (as well as many coordinate systems in general) is a system where the basis vectors are a function of position. Let’s see what this means. Consider the basis vectors at this point:

Now consider the basis vectors at this point:

Just by changing what point we’re considering, the basis vectors have changed direction! The basis vectors depend on where you are. That’s because the concepts of “radially outward” and “direction of increasing angle” are different for different points on the plane. Radially outward is simply directly away from $\vec{0}$, and the direction of increasing angle is perpendicular to the radially outward direction pointing in the counterclockwise direction. In other words, the directions of the polar basis vectors are locally defined.

Let’s look at one consequence of this. Suppose we are given the position vector of a moving particle \[ \boldsymbol{x}\left(t\right) = r \left(t\right) \hat{r} + \phi \left(t\right) \hat{\phi} \]

Suppose I ask you to calculate the velocity of this particle. The naive approach would be to say \[ \frac{d\boldsymbol{x}}{dt} = \frac{dr}{dt} \hat{r} + \frac{d\phi}{dt} \hat{\phi} \]

This would be wrong though. Since the basis vectors are themselves functions of position, we must differentiate them as well using the chain rule \[ \frac{d\boldsymbol{x}}{dt} = \frac{dr}{dt} \hat{r} + r \frac{d\hat{r}}{dt} + \frac{d\phi}{dt} \hat{\phi} + \frac{d\hat{\phi}}{dt} \]

Many physics problems are best described using circles, so when we discuss Newton’s Laws (which involve time derivatives) this complication will show up.

Finally, just like in the Cartesian system, we can define a similar “grid” for the polar system, but this time, we have circles of constant radius and lines of constant angle:

It is critical to note that for these two dimensional coordinate systems, we only needed two basis vectors to describe any point in the plane. That is to say, in two dimensions, we need two vectors to span the space. It shouldn’t surprise you that in three dimensions, we need three vectors to span the space. Let’s look at a few coordinate systems in three dimensions.

For the Cartesian coordinate system, the generalization is straightforward. Simply find a direction that is perpendicular to the two existing directions, then place another basis vector (usually called $\hat{z}$) in that direction.

With that minor adjustment, you’re done. Except, not quite. You see, there is another direction that is perpendicular to the $xy$ plane. We could have instead defined $\hat{z}$ like this:

So which direction do we use? Technically, both answers are valid, but historically we have developed a convention to deal with this ambiguity. We demand that in three dimensions we use a right-handed coordinate system. What does this mean? This diagram (I shamelessly took from here) should explain:

Take your right hand. Point your index finger in the $\hat{x}$ direction. Point your middle finger perpendicular to your index finger so that it is in the $\hat{y}$ direction. When you point your thumb up, this will be in the $\hat{z}$ direction. I will explain why we choose right-handed systems in a little bit.

Generalizing polar coordinates is not as straightforward. There are two natural directions to go with this. We can keep the same two planar polar coordinates (radius and polar angle) and then specify which plane you’re on by using a $\hat{z}$ coordinate. This gives us the cylindrical coordinate system:

We could also use a single radius and specify two angles (the polar and azimuthal angles typically). This gives us the spherical coordinate system:

For both systems, the basis vectors (not pictured here) point in the direction of increasing coordinate. As with planar polar coordinates, these two polar coordinate systems have the disadvantage that their basis vectors aren’t constant.

Now that we know about coordinate systems, it becomes easy to talk about the two vector products. These two vector products are more mathematical framework that we introduce on top of vector arithmetic. One product will take two vectors and give us a number, while the other will take two vectors and give us a vector. Each product has a geometrical definition.

Consider two vectors, $\boldsymbol{v}$ and $\boldsymbol{w}$. Let the angle between them be denoted by $\theta$. Also, let the length of $\boldsymbol{v}$ and the length of $\boldsymbol{w}$ be denoted by $v$ and $w$ respectively.

The dot product between two vectors, denoted $ \boldsymbol{v} \cdot \boldsymbol{w} $, is defined by multiplying the lengths of the two vectors with the cosine of the angle between them. That is to say, \[ \boldsymbol{v} \cdot \boldsymbol{w} = v w \cos\left(\theta\right) \]

Notice that the dot product of two vectors produces a scalar. That means it doesn’t make much sense to write down $ \boldsymbol{a} \cdot \boldsymbol{b} \cdot \boldsymbol{c} $ since you can’t take the dot product between a scalar and a vector.

Here’s a few properties of the dot product. Again, I’m stating these without proof (if you want the proofs please let me know!). If you take the dot product of a vector with itself, you get back the length of the vector squared \[ \boldsymbol{v} \cdot \boldsymbol{v} = v^2 \]

It doesn’t matter in what order you take the dot product \[ \boldsymbol{v} \cdot \boldsymbol{w} = \boldsymbol{w} \cdot \boldsymbol{v} \]

The dot product is distributive \[ \left( \boldsymbol{a} + \boldsymbol{b} \right) \cdot \boldsymbol{c} = \boldsymbol{a} \cdot \boldsymbol{c} + \boldsymbol{b} \cdot \boldsymbol{c} \]

The next few properties deal with that cosine in the definition. One consequence is that when two vectors are perpendicular, their dot product is zero since $\cos\left(\frac{\pi}{2}\right)=0$.

Since the cosine of an angle is always between $-1$ and $1$, we get the Cauchy-Schwarz Inequality \[ \left| \boldsymbol{v} \cdot \boldsymbol{w} \right| \leq \left|v\right| \left|w\right| \]

As a consequence of the Cauchy-Schwarz Inequality, we get the triangle inequality \[ \left| \boldsymbol{v} + \boldsymbol{w} \right| \leq \left|v\right| + \left| w \right| \]

Let’s think about what happens when we take dot products using our coordinate vectors. In Cartesian coordinates, our coordinate vectors are of unit length, and they are perpendicular to each other. This means their dot products are \[ \hat{x} \cdot \hat{y} = \hat{y} \cdot \hat{z} = \hat{z} \cdot \hat{x} = \cos\left(\frac{\pi}{2}\right) = 0 \]

Now, let’s see what happens when we take the dot product of two basis vectors with themselves. Again in Cartesian coordinates, \[ \hat{x} \cdot \hat{x} = \hat{y} \cdot \hat{y} = \hat{z} \cdot \hat{z} = \cos\left(0\right) = 1 \]

These two properties are given special names. When the dot product between two nonzero vectors is zero, we say those vectors are orthogonal. When a vector has unit length, it is said to be normalized. If the vectors in a basis are mutually orthogonal and are all normalized, the basis is said to be orthonormal. Orthonormality can be summed up in the statement \[ \hat{e}_i \cdot \hat{e}_j = \delta_{ij} \]

Where $\delta_{ij} $ is the Kronecker delta symbol. The Kronecker delta is defined as \[\delta_{ij}=\begin{cases}1 & i=j\\\0 & \text{otherwise}\end{cases}\]

Orthonormality is not unique to the Cartesian basis. Since all of the bases I have described above have mutually orthogonal, normalized basis vectors, they are all orthonormal systems. Well, they are to some extent. Remember the business with the polar coordinate systems? Their basis vectors change with location. This has a subtle consequence. Consider the coordinate vector $\hat{r}\left(\boldsymbol{r}\right) $ at two locations, $\boldsymbol{r}=\boldsymbol{a}$ and $\boldsymbol{r}=\boldsymbol{b}$. One would naively expect that \[ \hat{r}\left(\boldsymbol{a}\right) \cdot \hat{r}\left(\boldsymbol{b}\right) = 1 \]

But this is not the case! $\hat{r}\left(\boldsymbol{a}\right)$ and $\hat{r}\left(\boldsymbol{b}\right)$ could point in completely different directions, so it is not guaranteed that this inner product is $1$. While the Cartesian system is globally orthonormal, the polar coordinate systems are only locally orthonormal. That means that statements like this are OK: \[ \hat{r}\left(\boldsymbol{a}\right) \cdot \hat{\theta}\left(\boldsymbol{a}\right) = \hat{\theta}\left(\boldsymbol{a}\right) \cdot \hat{\phi}\left(\boldsymbol{a}\right) = \hat{\phi}\left(\boldsymbol{a}\right) \cdot \hat{r}\left(\boldsymbol{a}\right) = 1 \]

But statements like this are BAD: \[ \hat{r}\left(\boldsymbol{a}\right) \cdot \hat{\theta}\left(\boldsymbol{b}\right) = \hat{\theta}\left(\boldsymbol{b}\right) \cdot \hat{\phi}\left(\boldsymbol{a}\right) = \hat{\phi}\left(\boldsymbol{a}\right) \cdot \hat{r}\left(\boldsymbol{a}\right) = 1 \]

As such, as is in many situations, it is often less confusing to convert from other coordinate systems back into Cartesian coordinates before performing many operations. So why is it easier to talk about the dot product now that we have coordinate systems? Well, in the Cartesian coordinate system, suppose we have two vectors written in terms of its components \[ \boldsymbol{v} = v_x \hat{x} + v_y \hat{y} + v_z \hat{z} \]

\[ \boldsymbol{w} = w_x \hat{x} + w_y \hat{y} + w_z \hat{z} \]

Let’s compute their dot product. We can write the vectors in terms of their components \[ \boldsymbol{v} \cdot \boldsymbol{w} = \left(v_x \hat{x} + v_y \hat{y} + v_z \hat{z}\right) \cdot \left(w_x \hat{x} + w_y \hat{y} + w_z \hat{z}\right) \]

Since the dot product is distributive, we can distribute this out into nine terms. However, since the basis is orthonormal, the cross terms (terms where things like $ \hat{x}\cdot\hat{y} $ appear) will become zero. What we’re left with is \[ \boldsymbol{v} \cdot \boldsymbol{w} = v_x w_x + v_y w_y + v_z w_z \]

If we have the Cartesian components of each vector, then the dot product becomes very easy to compute. The dot product allows us to do one more thing, though. It actually gives us a recipe to get those components! Suppose we don’t know the components of $ \boldsymbol{v} $, and we want to write it as \[ \boldsymbol{v} = v_x \hat{x} + v_y \hat{y} + v_z \hat{z} \]

To find any component we can exploit orthonormality. To find the $\hat{x}$ component, take the dot product with $\hat{x}$: \[ \boldsymbol{v} \cdot \hat{x} = v_x \]

The definition of the dot product says that this product should be \[ \boldsymbol{v} \cdot \hat{x} = v \cos\left(\theta\right) \]

Where $\theta$ is the angle between $\boldsymbol{v}$ and $\hat{x}$. Since these are both the same dot product, they must be equal \[v_x = v \cos\left(\theta\right) \]

We can do this with the other basis vectors to find the other components. This operation, finding the length of one vector in the direction of another, is called projection.

One final remark about the dot product before we move on. The dot product is one of a larger class of operations called inner products. Inner products are defined for more general vectors (the mathematician’s definition of vectors), but many of the properties are similar. In fact, I tend to define orthogonality more generally than I just did above. If the inner product between two nonzero vectors is zero, they are orthogonal. When defining orthogonality this way, it liberates the inner product from any sense of geometry or angle. When discussing more general mathematical vectors, it doesn’t make as much sense to talk about the “angle” between two vectors and I think that trying to do so is misleading (looking at you Griffiths!). I will definitely come back to talk about inner products in their own dedicated essay.

Let’s define the other vector product. This will make clear why we chose right-handed coordinate systems. The vector cross product takes two vectors and returns another vector. Before I talk about how it’s defined and how to calculate it, I want to say a few general remarks about the cross product. First, the cross product only makes sense in three dimensions. There exists no two dimensional version of the cross product. If you go to higher than three dimensions, the cross product (or at least the operation that looks like the cross product) produces a tensor (a more complicated object) rather than a vector. Second, while the dot product is part of a larger collection of operations, the cross product is not. Finally, the cross product doesn’t always produce actual vectors. Instead, it sometimes produces pseudovectors, or axial vectors. I won’t go into much detail on what these things are until much later. Even though the output of the cross product isn’t a “real” vector in a sense, for brevity I will still call the cross product’s result a vector.

Let’s look at how to compute the cross product. The cross product between two vectors, denoted by $ \boldsymbol{v} \times \boldsymbol{w} $, is given by doing two things. Since the output of the cross product is a vector, we have to provide a method of getting the size and the direction of that vector. The size of the new vector is defined similarly to the dot product \[ \left| \boldsymbol{v} \times \boldsymbol{w} \right| = v w \sin\left(\theta\right) \]

Then, the direction of the new vector is perpendicular to the plane of the original two vectors. Here, the same confusion arises as before with defining the coordinate systems. Which perpendicular direction should be used? Again, the answer is given by the right hand rule. This diagram (which I shamelessly stole from here), shows what to do:

I will only highlight three properties of the cross product. First, due to the sine in the definition, the length of the cross product is maximum when the two vectors are perpendicular, and the cross product is zero if both vectors point in either the same direction or in opposite directions.

Second, due to the right hand rule, the cross product is anticommutative \[ \boldsymbol{v} \times \boldsymbol{w} = - \boldsymbol{w} \times \boldsymbol{v} \]

Finally, the cross product, like the dot product, is distributive \[ \left(\boldsymbol{a} + \boldsymbol{b} \right) \times \boldsymbol{c} = \boldsymbol{a} \times \boldsymbol{c} + \boldsymbol{b} \times \boldsymbol{c} \]

Again, let’s think of what happens when we take the cross product of coordinate vectors. This will explain why we choose right-handed systems. In the Cartesian system, $\hat{x}$ and $\hat{y}$ are perpendicular to each other and are of unit length. This means that \[ \left| \hat{x} \times \hat{y} \right| = 1 \]

When we use the right hand rule to find the direction of the cross product, we find that it points in the $\hat{z}$ direction. This means that \[ \hat{x} \times \hat{y} = \hat{z} \]

A pretty cool result, no? Doing this for the other basis vectors produces a similar pattern \[ \hat{y} \times \hat{z} = \hat{x} \]

\[ \hat{z} \times \hat{x} = \hat{y} \]

Flip the order, you get a minus sign from anticommutativity. This pattern is called cyclic permittivity. This property, again, isn’t unique to the Cartesian system. Any right-handed coordinate system will allow you to locally cross two directions into the third direction.

Now, if you have two vectors written in terms of Cartesian components, \[ \boldsymbol{v} = v_x \hat{x} + v_y \hat{y} + v_z \hat{z} \]

\[ \boldsymbol{w} = w_x \hat{x} + w_y \hat{y} + w_z \hat{z} \]

Since the cross product is distributive, we could write down the components, distribute, figure out how the basis vectors cross into each other, and then write out the new vector. I leave this as an exercise to the reader to actually do this painful task. Fortunately, doing this once with these general components will reveal a general pattern for the components of the resulting vector. In practice people usually compute the cross product by computing the following determinant \[ \boldsymbol{v}\times\boldsymbol{w}=\left|\begin{array}{ccc} \hat{x} & \hat{y} & \hat{z}\\\ v_{x} & v_{y} & v_{z}\\\ w_{x} & w_{y} & w_{z} \end{array}\right| \]

When we calculate this determinant, this is equivalent to doing the entire distribution. It gives the following formula for the cross product: \[\boldsymbol{v}\times\boldsymbol{w}=\left(v_{y}w_{z}-w_{y}v_{z}\right)\hat{x}+\left(w_{x}v_{z}-v_{x}w_{z}\right)\hat{y}+\left(v_{x}w_{y}-w_{x}v_{y}\right)\hat{z}\]

One final remark about the vector products is that calculus still works on them. Suppose the vectors, $\boldsymbol{v}$ and $\boldsymbol{w}$, are both functions of time. Taking the time derivative of either product still invokes the product rule \[ \frac{d}{dt} \left( \boldsymbol{v} \cdot \boldsymbol{w} \right) = \frac{d \boldsymbol{v} }{dt} \cdot \boldsymbol{w} + \boldsymbol{v} \cdot \frac{d \boldsymbol{w} }{dt} \]

\[ \frac{d}{dt} \left( \boldsymbol{v} \times \boldsymbol{w} \right) = \frac{d \boldsymbol{v} }{dt} \times \boldsymbol{w} + \boldsymbol{v} \times \frac{d \boldsymbol{w} }{dt} \]

Now that we have coordinate systems under our belts, we can set up a problem, describe the geometry using a coordinate system, then work exclusively in components. These components will generalize into the concept of coordinates which I will develop in the next essay.

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qoholiccom · 5 years

Text

BSME - Design of Multi-Axis Motion Mechanisms - Waukesha, WI

Seeking degreed Mechanical Engineer with 3+ years experience using 2D & 3D software to support the design of robots for super high precision, high speed, high performance applications, such as: micro-electro-mechanical assembly, aligning, coating, stacking, precision pick & place, bonding, semiconductor & circuit board packaging, etc. Must have experience designing Robotic End Effector type devices which are used to transfer substrates and components. Requires proficiency with stress and failure analysis calculations including GD&T (Geometrical Dimensioning & Tolerancing), FEA (Finite Element Analysis) AND CFD (Computational Fluid Dynamics) and experience designing multi-axis motion mechanisms. COMPANY: Collaborative environment where engaged employees share their knowledge and suggestions. Team is entrusted to use their own discretion and common sense. Staff to management communication is promoted and encouraged. Family atmosphere. Promotes opportunities and incentives for employees to learn, develop and grow. Culture of continuous improvement. Employee efforts, achievements and performance are formally recognized and honored on a regular basis. A fun and playful attitude is maintained throughout the organization. Adrian Gostick and Scott Christopher, in their book The Levity Effect: Why It Pays To Lighten Up, suggest if people are having fun, they're going to work harder, stay longer, maintain their composure in a crisis, and take better care of the organization. We believe this is their kind of company. Enjoy the career path opportunities that only a growing company can provide while earning a top salary plus bonuses, and full company paid benefits Medical, dental and a vision plan, prescription drug plan, flexible spending account, short and long-term disability coverage, 401(k) plan with dollar-for-dollar company match, discount stock purchase plan, tuition assistance, employee assistance program, life and accidental death & disability insurance, and company sponsored and paid certification training programs. For complete details contact James Franco at: (609) 584-9000 ext 283 Or submit resume online at: dmc9.com/jef/app.asp Or email to: 1000037591_10007335 AT jobbank301.com Please reference #38588156 when responding. Education Requirements: Some College Minimum Experience Requirements: 5-10 years Job City Location: Waukesha Job State Location: WI Job Country Location: USA Salary Range: $65,000 to $120,000 Diedre Moire Corporation, Inc. Diedremoire_dot_com WE ARE AN EQUAL OPPORTUNITY EMPLOYER and our employment decisions are made without regard to race, color, religion, age, sex, national origin, handicap, disability or marital status. We reasonably accommodate individuals with handicaps, disabilities and bona fide religious beliefs. Jobs Career Position Hiring. CONSIDERED EXPERIENCE INCLUDES: Senior Mechanical Engineer Design Engineer Project Engineer BSME MSME Mechanical Engineering Mechanical Design Custom Equipment Automation Associates CAD Computer Aided Design ProE Pro Engineer PTC Creo DISCLAIMER: We will make every effort to consider applications for all available positions and shall use one or more of the contact methods and addresses indicated in resume or online application. Indicated location may be proximate or may be desirable point of embarkation for paid or unpaid relocation to another venue. Job descriptions may fit single or multiple presently available or anticipated positions and are NOT an offer of employment or contract implied or otherwise. Described compensation is not definite nor precise and may be estimated and approximate and is negotiable depending on market conditions and candidate availability and other factors and is solely at the discretion of employers. Linguistics used herein may use First Person Singular and First Person Plural grammatical person construction for and with the meaning of Third Person Singular and Third Person Plural references. We reserves the right to amend and change responsibilities to meet business and organizational needs as necessary. Response to a specific posting or advertisement may result in consideration for other opportunities and not necessarily the incentive or basis of the response. Nothing herein is or may be considered a promise, guarantee, offer, pledge, agreement, contract, or oath. If you submit an application or resume which contains your email address, we will use that email address to communicate with you about this and other positions. We use an email quality control service to maintain security and a remove and dead address filter. To cancel receiving email communications, simply send an email from your address with the word "remove" in the subject line to pleaseremove_AT_candseek4.com Or, visit the website at jobbankremove_dot_com. If you have further concern regarding email received from us, call (609) 584-5499. Reference : BSME - Design of Multi-Axis Motion Mechanisms - Waukesha, WI jobs source http://www.qoholic.com/jobs/technology/bsme-design-of-multi-axis-motion-mechanisms-waukesha-wi_i5783

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jobsaggregationco · 5 years

Text

BSME - Design of Multi-Axis Motion Mechanisms - Waukesha, WI

Seeking degreed Mechanical Engineer with 3+ years experience using 2D & 3D software to support the design of robots for super high precision, high speed, high performance applications, such as: micro-electro-mechanical assembly, aligning, coating, stacking, precision pick & place, bonding, semiconductor & circuit board packaging, etc. Must have experience designing Robotic End Effector type devices which are used to transfer substrates and components. Requires proficiency with stress and failure analysis calculations including GD&T (Geometrical Dimensioning & Tolerancing), FEA (Finite Element Analysis) AND CFD (Computational Fluid Dynamics) and experience designing multi-axis motion mechanisms. COMPANY: Collaborative environment where engaged employees share their knowledge and suggestions. Team is entrusted to use their own discretion and common sense. Staff to management communication is promoted and encouraged. Family atmosphere. Promotes opportunities and incentives for employees to learn, develop and grow. Culture of continuous improvement. Employee efforts, achievements and performance are formally recognized and honored on a regular basis. A fun and playful attitude is maintained throughout the organization. Adrian Gostick and Scott Christopher, in their book The Levity Effect: Why It Pays To Lighten Up, suggest if people are having fun, they're going to work harder, stay longer, maintain their composure in a crisis, and take better care of the organization. We believe this is their kind of company. Enjoy the career path opportunities that only a growing company can provide while earning a top salary plus bonuses, and full company paid benefits Medical, dental and a vision plan, prescription drug plan, flexible spending account, short and long-term disability coverage, 401(k) plan with dollar-for-dollar company match, discount stock purchase plan, tuition assistance, employee assistance program, life and accidental death & disability insurance, and company sponsored and paid certification training programs. For complete details contact James Franco at: (609) 584-9000 ext 283 Or submit resume online at: dmc9.com/jef/app.asp Or email to: 1000037591_10007335 AT jobbank301.com Please reference #38588156 when responding. Education Requirements: Some College Minimum Experience Requirements: 5-10 years Job City Location: Waukesha Job State Location: WI Job Country Location: USA Salary Range: $65,000 to $120,000 Diedre Moire Corporation, Inc. Diedremoire_dot_com WE ARE AN EQUAL OPPORTUNITY EMPLOYER and our employment decisions are made without regard to race, color, religion, age, sex, national origin, handicap, disability or marital status. We reasonably accommodate individuals with handicaps, disabilities and bona fide religious beliefs. Jobs Career Position Hiring. CONSIDERED EXPERIENCE INCLUDES: Senior Mechanical Engineer Design Engineer Project Engineer BSME MSME Mechanical Engineering Mechanical Design Custom Equipment Automation Associates CAD Computer Aided Design ProE Pro Engineer PTC Creo DISCLAIMER: We will make every effort to consider applications for all available positions and shall use one or more of the contact methods and addresses indicated in resume or online application. Indicated location may be proximate or may be desirable point of embarkation for paid or unpaid relocation to another venue. Job descriptions may fit single or multiple presently available or anticipated positions and are NOT an offer of employment or contract implied or otherwise. Described compensation is not definite nor precise and may be estimated and approximate and is negotiable depending on market conditions and candidate availability and other factors and is solely at the discretion of employers. Linguistics used herein may use First Person Singular and First Person Plural grammatical person construction for and with the meaning of Third Person Singular and Third Person Plural references. We reserves the right to amend and change responsibilities to meet business and organizational needs as necessary. Response to a specific posting or advertisement may result in consideration for other opportunities and not necessarily the incentive or basis of the response. Nothing herein is or may be considered a promise, guarantee, offer, pledge, agreement, contract, or oath. If you submit an application or resume which contains your email address, we will use that email address to communicate with you about this and other positions. We use an email quality control service to maintain security and a remove and dead address filter. To cancel receiving email communications, simply send an email from your address with the word "remove" in the subject line to pleaseremove_AT_candseek4.com Or, visit the website at jobbankremove_dot_com. If you have further concern regarding email received from us, call (609) 584-5499. Reference : BSME - Design of Multi-Axis Motion Mechanisms - Waukesha, WI jobs source http://jobsaggregation.com/jobs/technology/bsme-design-of-multi-axis-motion-mechanisms-waukesha-wi_i4172

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cvwing · 5 years

Text

BSME - Design of Multi-Axis Motion Mechanisms - Waukesha, WI

Seeking degreed Mechanical Engineer with 3+ years experience using 2D & 3D software to support the design of robots for super high precision, high speed, high performance applications, such as: micro-electro-mechanical assembly, aligning, coating, stacking, precision pick & place, bonding, semiconductor & circuit board packaging, etc. Must have experience designing Robotic End Effector type devices which are used to transfer substrates and components. Requires proficiency with stress and failure analysis calculations including GD&T (Geometrical Dimensioning & Tolerancing), FEA (Finite Element Analysis) AND CFD (Computational Fluid Dynamics) and experience designing multi-axis motion mechanisms. COMPANY: Collaborative environment where engaged employees share their knowledge and suggestions. Team is entrusted to use their own discretion and common sense. Staff to management communication is promoted and encouraged. Family atmosphere. Promotes opportunities and incentives for employees to learn, develop and grow. Culture of continuous improvement. Employee efforts, achievements and performance are formally recognized and honored on a regular basis. A fun and playful attitude is maintained throughout the organization. Adrian Gostick and Scott Christopher, in their book The Levity Effect: Why It Pays To Lighten Up, suggest if people are having fun, they're going to work harder, stay longer, maintain their composure in a crisis, and take better care of the organization. We believe this is their kind of company. Enjoy the career path opportunities that only a growing company can provide while earning a top salary plus bonuses, and full company paid benefits Medical, dental and a vision plan, prescription drug plan, flexible spending account, short and long-term disability coverage, 401(k) plan with dollar-for-dollar company match, discount stock purchase plan, tuition assistance, employee assistance program, life and accidental death & disability insurance, and company sponsored and paid certification training programs. For complete details contact James Franco at: (609) 584-9000 ext 283 Or submit resume online at: dmc9.com/jef/app.asp Or email to: 1000037591_10007335 AT jobbank301.com Please reference #38588156 when responding. Education Requirements: Some College Minimum Experience Requirements: 5-10 years Job City Location: Waukesha Job State Location: WI Job Country Location: USA Salary Range: $65,000 to $120,000 Diedre Moire Corporation, Inc. Diedremoire_dot_com WE ARE AN EQUAL OPPORTUNITY EMPLOYER and our employment decisions are made without regard to race, color, religion, age, sex, national origin, handicap, disability or marital status. We reasonably accommodate individuals with handicaps, disabilities and bona fide religious beliefs. Jobs Career Position Hiring. CONSIDERED EXPERIENCE INCLUDES: Senior Mechanical Engineer Design Engineer Project Engineer BSME MSME Mechanical Engineering Mechanical Design Custom Equipment Automation Associates CAD Computer Aided Design ProE Pro Engineer PTC Creo DISCLAIMER: We will make every effort to consider applications for all available positions and shall use one or more of the contact methods and addresses indicated in resume or online application. Indicated location may be proximate or may be desirable point of embarkation for paid or unpaid relocation to another venue. Job descriptions may fit single or multiple presently available or anticipated positions and are NOT an offer of employment or contract implied or otherwise. Described compensation is not definite nor precise and may be estimated and approximate and is negotiable depending on market conditions and candidate availability and other factors and is solely at the discretion of employers. Linguistics used herein may use First Person Singular and First Person Plural grammatical person construction for and with the meaning of Third Person Singular and Third Person Plural references. We reserves the right to amend and change responsibilities to meet business and organizational needs as necessary. Response to a specific posting or advertisement may result in consideration for other opportunities and not necessarily the incentive or basis of the response. Nothing herein is or may be considered a promise, guarantee, offer, pledge, agreement, contract, or oath. If you submit an application or resume which contains your email address, we will use that email address to communicate with you about this and other positions. We use an email quality control service to maintain security and a remove and dead address filter. To cancel receiving email communications, simply send an email from your address with the word "remove" in the subject line to pleaseremove_AT_candseek4.com Or, visit the website at jobbankremove_dot_com. If you have further concern regarding email received from us, call (609) 584-5499. Reference : BSME - Design of Multi-Axis Motion Mechanisms - Waukesha, WI jobs source http://cvwing.com/jobs/technology/bsme-design-of-multi-axis-motion-mechanisms-waukesha-wi_i5605

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