Home- Flickr
- 500px
- Vimeo
- Blog
Biswaroop Mukherjee
I like mathematical physics, landscape photography, K.L. Saigal songs, himalayan villages, philosophical discussions and aaloo paratha. Email me.
Loading,
0
% complete-
Landscapes
-
Photos
-
Videos
-
Posts
- Aug 11, 12words I like:
structure
spectrum
architecture
landscape
emergence
complexity
depth
texture
voyage
synchronized
archetypal
ethereal
evanescent
labyrinthine
tranquil
ponder
exploration
closely
preen
crystalline
tesselate - Oct 01, 12
Mr. Deepak Chopra has a worldview. He purees the fruits of the physicists’ labor, and garnishes this worldview by mixing popular science with popular spirituality. Needless to say, Mr. Chopra is popular. However, physicists are quick to dismiss his ideas as pseudoscience, but the reasons either elude the average reader, or smack of elitism.
Taking a short break from atom interferometry research at the Müller Group, I read the Huffington Post “Healthy living” article. In the process, I made a number of rather animated gestures, and decided I would write something about it.
The names of the authors and their qualifications create a compelling chunk of nametags. Mr. Chopra is accompanied by a distinguished professor of neurology at Harvard and another distinguished professor of computational physicsat Chapman University. It’s quite a far cry from the nondescript affiliation lists that grace publications, and I wonder who the true elitists are.
Mr. Chopra points out how physicists detest the misleading epithet “God particle” and adore the publicity associated with it. He then suggestively hints at the funding involved. Misleading people, Mr. Chopra, is exactly the opposite of what we try to do, even if it indirectly brings us money.
Over the next couple of paragraphs, the authors deliver a succinct and consciously inadequate summary of the idea behind the Higgs boson. However, in a quick couple of lines, Mr. Chopra adds “Physics may be getting closer to the day, in fact, when the way it views the universe classically reaches a dead end.” While it is true that the discovery of the Higgs in and of itself is at best a confirmation and not an explanation, it certainly goes a long way in showing that the classical worldview of physics is nearly dead. It is dead. It has been dead for over a century. Even more puzzling is how the article confirms this later on: “quantum theory demolished the solid, reassuring physical universe almost a century ago.” Perhaps in his fervent attacks on the physicists’ worldview, Mr. Chopra forgets that classical calculations are entirely approximations of the universe at a larger scale. Surely rounding off the 18th decimal on pi doesn’t cause us to believe that pi is exactly 3.141592653589793238. In fact, a large number of physicists believe that even the general theory of relativity is itself an approximation to a quantum universe - we are squarely in a post-classical era of physics.
The authors continue to explain the workings of the Higgs boson - with the Higgs mechanism explained as a “kind of dragging”. They attack the potential “Theory of everything” as particle-centric and unable to explain “life, evolution and the phenomena of mind and awareness”. To the physicist, those very interesting emergent phenomena are largely governed by statistics and immense sample sizes. We apply our famously arrogant reductionism and conclude that: given enough “things” and appropriate rules to govern them, life, evolution, mind, awareness, and indeed the entire Universe would all emerge out like bacteria in a pond. If frighteningly complex creatures can pop out of something as simple as Conway’s game of life, certainly the Universe’s game of everything will bring organisms more complex than introspective humans.
So then perhaps the question of “why, Universe, why?” boils down to: what are “things” and their “laws”? Baryogenesis - the still open question of why there is matter in the universe - could answer where “things” came from. The Theory of Everything - a search for fundamental laws - answers what those “appropriate rules of governance” are.
Mr. Chopra continues to attack the “materialist” worldview, with statements such as “The great quantum pioneers noted definitively that all other fundamental particles have no fixed physical attributes at all.” He is entirely wrong. Spin, charge, and rest mass continue to be highly fixed physical attributes of fundamental particles. Even though we no longer believe that particles move at a fixed velocity at a fixed position, I fear Mr. Chopra will not be able to cite a single “quantum pioneer” who thinks that every physical aspect of every fundamental particle is delocalized. I feel I gestured the most when he states “none of that is in dispute.”
Even more disastrous is the claim that quantum nonlocality and reverse causation are ‘demolishing’ the physicalist worldview. Even if we accept both ideas as deep physical truths, the physicalist worldview adapts itself to our evolving understanding of nature. Physicalism is a moving target, Mr Chopra, and it is no use to shoot bullets that have already been identified, tracked, and dodged. The new interpretations embellish the physicalist worldview; they do not destroy it. If anything, physics has taught us to doubt our “common sense notions,” and create more accurate worldviews based on new physics. Mr. Chopra fails to realize that abandoning old physics is not the same as abandoning physics.
The authors offer two reasons for the love affair between physicists and physicalism: “the mathematics works,” and grad schools don’t “bring consciousness into the mix.” We are presented as caricatures of hardheaded mathematicians molded by graduate schools to ignore immense evidence of links between consciousness and physics. If the excitement surrounding the Higgs boson has taught the layman anything, it’s that physics is a largely experiment-driven field. And if the reams of work done in string theory has taught the layman anything, it’s that mathematics that ‘happens to work’, no matter how elegant, is still questionable. Experimental proof is placed higher than mathematical proof. We believe in physics because there is evidence for it. Hard, tangible, physical evidence.
At the same time, there is a dimension of elegance and beauty in physical theory that the authors miss in their caricature of closed-minded physics. Richard Feynman once pointed out that physics (and science in general) reveals a deeper beauty in the artist’s rose. We supplement our lay intuition of beauty with a feeling that the same physical laws that govern the atoms in the rose also govern the atoms in our bodies. This sense of physical principles lying at the heart of the universe, potentially unifying every object at every scale, is by itself awe-inspiring. We have never been closer to this goal. Moreover, it appears that the laws of the universe follow mathematical principles that not only ‘work,’ but seem to encode the subtlety of the physical universe with remarkable symmetry. The possible discovery of the Higgs boson confirms both the symmetries of nature and our understanding of what happens when they are spontaneously broken. The correspondence between mathematics and physics feels more than mere coincidence, and even though we rely on experimental evidence, we must remember that the theory of Higgs et al was formulated at a time when verifying it was impossible.
The authors use quantum mechanics to suggest that an understanding of consciousness is central to our understanding of the fundamental laws of nature. While it is true that explaining the measurement problem is essential to quantum mechanics, the observer need not be conscious at all. Here’s an example: Place an electron beam source in front of two slits and you will see an interference pattern (like the patterns on screen doors) behind the slits. Now place a camera that watches the electrons as they go through the slits, and the electrons will fall through like tennis balls and the interference pattern will vanish. At first glance, it seems peculiar that a conscious observer can cause the electron to behave like a particle. However, as conscious humans, we could have merely designed such an experiment, left it to robots, and vanished. The quantum behavior would still manifest itself, and surely it would stretch Mr. Chopra’s imagination to say that the human consciousness is somehow imbued by the electronic robots to convert waves into particles. Bringing consciousness “into the mix” only complicates the already difficult problem of how a very simple unintelligent observer (aka detector sitting at slit one) appears to alter the behavior of particles or waves (detected by the interference pattern far away).
In fact, the process of wavefunction collapse (or measurement) happens all across the quantum universe without conscious observers. Mr. Chopra’s suggestion of a universal “mind” field causing these measurements brings with it a bucket of questions rather than solutions. How does this field cause the measurement collapse? What is the origin of the field? How does it connect to gravitation, spacetime, thermodynamics and the standard model? If the consciousness causes waves to turn into particles, then would the double slit experiment would respond differently to a conscious observer sitting in the control room of an experiment as opposed to an empty room? If it makes no difference, and if cameras are more skilled in observing particles, does that mean cameras have more consciousness than us?
Without asking any such questions, Mr. Chopra consciously (no pun intended) avoids intelligent design, not for its glaring misconceptions of nature, but rather because “no one except religious fundamentalists wants to be associated with it.” In a tragic denial of the philosophical complexity of the mind-body problem, Mr. Chopra asserts that consciousness merely “gives us a less-tainted word” for intelligent design.
The authors quote Freeman Dyson: “As one physicist said, ‘The universe knew that we were coming.’ ” As far as I can tell, this was Dyson’s comment in regards to what seems to be the almost divine level of fine-tuning in the fundamental constants - for they are almost exactly what is necessary for complex life. The anthropic principle has been suggested as a solution to the question of fine-tuning - in it, many universes could have been created with other fundamental constants - we are in the right one because we (ie complex life) would only appear in the right one. The vast majority of the rest of the universes will not contain life.
Physicists are only slightly more content with this anthropic principle than the idea of conscious fields creating the right physical constants, for it reduces fundamental physics to an “environmental science,” as Lawrence Krauss puts it, “it’s ugly.” In fact, the main distinction between Einstein’s God and Mr. Chopra’s consciousness appears to be that Einstein’s god is a incomprehensible god of elegance: “the manifestations of the profoundest reason and the most radiant beauty, which are only accessible to our reason in their most elementary forms,” while Chopra’s consciousness is a pseudoscientific field that neither answers questions, nor inspires awe.
Mr. Chopra’s conclusion of “God discovering the God particle” mirrors Carl Sagan’s comment “we are a way for the Universe to look at itself.” The God perspective leaves us with a simple question: why? Why would an anthropomorphic consciousness orchestrate a variety of experiments to discover what it already knows? If the God is not creating us to find out what is self-evident, then are we merely artificial intelligence experiments of this consciousness field? Or are we parts of a complex unconscious Universe that have started to ask questions?
Is it more inspiring, more miraculous, more enlightening to live with the unanswerable question of the origin of God, or to stride forth as the inquisitive harbingers of cosmic introspection?
Mr. Chopra seems content with the first worldview, physicists prefer the latter. - May 24, 12A wonderful account of wit and power:
"He (Alexander) captured ten of the Gymnosophists who had done most to get Sabbas [a king of Punjab] to revolt, and had made the most trouble for the Macedonians. These philosophers were reputed to be clever and concise in answering questions, and Alexander therefore put difficult questions to them, declaring that he would put to death him who first made an incorrect answer, and then the rest, in an order determined in like manner; and he commanded one of them, the oldest, to be the judge in the contest. The first one, accordingly, being asked which, in his opinion, were more numerous, the living or the dead, said that the living were, since the dead no longer existed. The second, being asked whether the earth or the sea produced larger animals, said the earth did, since the sea was but a part of the earth. The third, being asked what animal was the most cunning, said: "That which up to this time man has not discovered." The fourth, when asked why he had induced Sabbas to revolt, replied: "Because I wished him either to live nobly or to die nobly." The fifth, being asked which, in his opinion, was older, day or night, replied: "Day, by one day"; and he added, upon the king expressing amazement, that hard questions must have hard answers. Passing on, then, to the sixth, Alexander asked how a man could be most loved; "If," said the philosopher, "he is most powerful, and yet does not inspire fear." Of the three remaining, he who was asked how one might become a god instead of man, replied: "By doing something which a man cannot do"; the one who was asked which was the stronger, life or death, answered: "Life, since it supports so many ills." And the last, asked how long it were well for a man to live, answered: "Until he does not regard death as better than life." So, then, turning to the judge, Alexander bade him give his opinion. The judge declared that they had answered one worse than another. "Well, then," said Alexander, "thou shalt die first for giving such a verdict." "That cannot be, O King," said the judge, "unless thou falsely saidst that thou wouldst put to death first him who answered worst." "
—Plutarch, Life of Alexander, "The parallel lives," 64., - Aug 11, 12
I'm never ever going to graduation. I decline to be paraded in those ridiculous gowns and photographed by 'proud' family members (of which I have 2) and friends (of which most are acquaintances - too awkward). Ugh. My parents better not make me.
Look at them - cartwheeling, oblivious of the future ahead. Men - prancing around gaily in their black dresses, celebrating their psych degree; women - screeching together with delight at completing four years of accounting. The only people I sympathize with are the children rolling around on the grass, with no idea of what's happening.
And over there - a painfully awkward family of four, the father talking at two graduating children with the mother intently filming the process as if it were some journalistic investigation into the effects of graduation on humans. Relatives walking in unison, photographing their child standing in front of the campanile with the sun to his back - a miserably taken photograph that will undoubtedly grace their mantelpieces for generations.
Large flocks of young women in drab dresses sticking their hands into the air as if to signify their ability to hold the lofty heights of education in the palms of their hands. Grinning men poking around on their phones texting their bro from dorm days to come and see how wonderful their flabby figures look in black dress.
They're so happy, I think they should wear this pathetic academic burka for the rest of their lives. It's as if they're all getting married to the freaking grim reaper, which might be appropriate, considering unemployment rates and student loan interest rates.
Sorry for the rant.
I just don't like ceremonious anything. - May 24, 12A brief hiatus again - this time broken by the departure of spring clouds, leaving my extracurricular life exposed under dusty blue skies of summer. I have taken up the bike, and punctured as it may be by the forces of neglect, I'll return to cranking the wheels in no time. I have returned to photography, and after a significantly successful partial solar eclipse, I'm looking forward to the June lunar eclipse and venus transit. I have taken up writing the blog once more, or at least this post, before I'm distracted by something else. Not to mention doing research at full speed. I might even return to climbing - but I doubt I have the time.But pish tish and vibble, as Stephen Fry would say, to the point. Yesterday I caught the BART, stepped on, and sat down. In front of me were pamphlets - of the religious kind to be precise. god and jesus, and love and wonderful things like that. So as a dutiful Berkeley atheistic, left-wing, science loving, hippie, maniacal, gay, chinese, islamic, voodoo-worshipping, satan-screwing liberal, I got to work vandalizing divine property. To be serious, I saw the pamphlets stuck up on the seat in front of me as a forum - a paperboard for dialogue between the faithful and the sane. One-sided as it may be, perhaps some other BART patron could be amused/enraged by a mundane leaflet covered in red ink scribbles. By the time I was done, it looked like the following:Let me be clear - I'm not a militant atheist. In no sense would I want to waste my time proselytizing ignorant believers in god to ignorant believers in 'science' whatever that may be. I wanted a bit of comedy and rationalism - if anyone is offended by what I have done, the offense is entirely intended. I have nothing against christianity any more than I am against other religions. They're all primitive. If anything, our models of the universe are a belief system in a sense - the only thing differentiating religion and our models is that our models are constantly changing depending on evidence, while religion is a constant bedrock of useless, outdated and often harmful ideas on how people should live their lives (with a bit of caveman cosmology thrown in).The first sheet ended up:It's hard to read so here are excerpts:1) next to Jesus Christ, Son of God : "great to see God upholding family values," Joseph [sarcastically]2) All things were created - Including "him"?3) john 1:3 - I'd love to prove the Riemann Hypothesis by quoting an antiquated book of oral history4) Christ died for our sins - I'm pretty sure he died from Roman persecution5) rose again on the third day - trendy survival skills there6) stop ridiculous capitalization and a little repetitive maybe? (the entire book suffers from these diseases)7) [citation needed] - citing the bible is like citing wikipedia (worse - no correcting bots)8) he is condemned already because he has not believed the name of the son of god- you just told us he's Jesus Christ. We got it. Free pass to theme park heaven please?The second leaflet was yellow and ingeniously folded into the seat edging. On one side was a rather cheesy letter from god as this father figure addressing his 'children' :More excerpts:1) I know when you sit down and when you rise up -> Creepo!2) I loved you before you were born - ew3) daddy issues4) his [jesus'] death was an expression of how much I love you - wait what? you killed your other child to show me how much you love me? that's extreme. How do I know you won't kill me to show someone else your love?5) I'll throw the biggest party for you - 80's god. I prefer classical.6) Love, your Dad - WHERE IS MOM?? .. what have you done with mom?I was running out of time on the reverse side:1) as he ascended to heaven, so are we - tenses!! tsk tsk2) as he arose from the heaven, so are we - dude….3) as he died to self (?), so are we (??) - dude!!! LEARN ENGLISH!!4) too much b.s. to edit on a 45 minute train ride.Meh - it was amusing and everything, but not a serious argument or consideration of the existence of a divine power. I plan on writing a more in depth analysis of Spinoza's god, Einstein's ideas about belief, harmony and atheism, and Gödel's proof, and I will post that when I have the time.The sleepy impish vandal himself:
- May 24, 12Bored and procrastinating, I thought I'd write something. So I did. In one thought-quenching sitting:It may be what we all experience when encountered with what we describe as a "situation". It's those moments of intense despair that overwhelm human beings for no apparent reason. Powerful unneccessary feelings about matters that are so idiotic, the slightest thought would render them ridiculous. Perhaps that is the plight of the human condition - that inextinguishable vestige of animalistic ignorance that prevents us from seeing through the situation at hand - and converts the most regulated minds into catatonic disasters.It's those breath-cutting moments when we realize that something is amiss and that some intangible issue is a deep result of certain misguided choices that we made at some point. Deeply dependent on initial conditions, the chaotic spins and vortexes that pass our trajectories throw us around, and threaten humans with talk of malestroms and typhoons. The most unfortunate aspect of this analogy is that those vortices are formed by small errors in judgment, and our own erratic thought processes in reaction, blow these out of proportion. We create imaginary situations during which we become religious - deeply believing in an imaginary entity to deliver us from this imaginary condition.Imaginary? Is the loss of hard-earned money imaginary? Is the death of a child imaginary? Are we even imagining our own lives? Perhaps, but more probably not. These are only the vortices that spin into our waters. Rather, the complex nature of these incidents make them cosmically insignificant. The much more basic laws that govern these situations are permanent and significant - their collective results are as well, but to a far lesser extent.To us, these moments of despair and longing for peace and perfection become diabolic entities - indeed the demons of yesteryear - possessing us into epileptic irrationality.And it is those moments of dramatic clarity that make us jump from our seat and shout in bliss. Those sharp and precise moments of lucidity when you awaken from this dream and see the true nature of these vortices from above the repetitive waves of daily life. This perspective is rare and cherished - it is what provides humans with potential and joie de vivre.
- Aug 11, 12
% Note: this document is written in MockTeX.
% If you haven't heard of that particular distribution,
% it's because I made it up. If you haven't heard of TeX,
% it's because you're not a mathematician, and you're
% obliged to skip the preamble and go to section 1.
\documentclass{blogpost}
\usepackage{anger}
\usepackage{incoherence}
\newenvironment{rant}
\title{A couple of rants}
\author{Biswaroop Mukherjee}
\begin{document}
\maketitle
\begin{rant}
\section{}
high heels should be banned in librariesalright, high heels are ridiculous in the first place,but TOK TOK TOK Tok tok tokis just \emph{argh}.I dont get it - do they want us to think they have woodpeckers under their heels?or to think that they're actually 2 inches shorter?Well they should have labels saying "warning: objects wearing heels are shorter than they seem,"otherwise WE STUPID GUYS wont be able to figure that out.Woah it was the heels?? but they're so INVISIBLE and INAUDIBLE.I'd have NEVER noticed that they're trying to appear sexier which just implies that they aren't in the first place.
\section{}
when you dont know the answer to a question, don't say "that is a philosophical question." Say "I don't know." It's like replying "it's because you're Indian," or perhaps worse - because you're devaluing deep questioning, rather than being just a racist nitwit. And to philosophers: Stop giving answers to questions to which we cannot know the answer. Yes, I'm $5 \sigma$ sure there is a superintelligent amphibious squid (c.f.\ref{post:ThreeDee}) inside every black hole.
\section{}
if you're going to listen to bhangra music in the library, it is in in the interest of your ears and the sanity of neighbors that I ask you to turn it down. We get it - you're vibrantly indian and either you want to project that to all lifeforms in the milky way, or you love bhangra just that much. It's outdated, overused, jumpy, and only sounds great in a lorry in Ludhiana. Or perhaps in some tadka naan dhaba - the ones that suddenly appear in the middle of nowhere (north dakota). Thank you for being so punjabi. Now if you'll excuse me, I'll just squeeze some rosogollas on my head. Right here in the math library.\end{rant}
\end{document} - Aug 24, 11Here's SF from Twin Peaks. Quite a sight from up there. I took this hurriedly with a 35 f/1.8 and the D80 - it's a handheld 5-image pan, stitched with Autopano Giga and adjusted in Lightroom.
I should upload more panoramas here. - Aug 24, 11And now for something different. This is presque stream-of-consciousness. It's also non-fiction."Well - you should try and get as many of those tiny naps as possible... reminds me of jetlag.... which is total torture sometimes and unnoticeable at other times. Also reminds me of the astronomy day up at the mountain - I was insanely sleepy so I went out for a walk in the moonlight. Oh and then i didn't want to sleep during the day, so I went for another walk down and up the hill and i slept like a block of lead on the drive back home."The entire world looks different when you're pathologically sleepy. Swimmy, disconnected, discrete, interrupted, flashing, halting: its as if the entire timeline is cracked up in front of you, and the brain shuts off periodically - microsleeps... those are the worst. It is a twilight - hanging between this world and dreamland...hanging over the precipice... looking into the realm of deep sleep - where miniature monsters made of purple sand and giant marshmallows coated in chocolate surround you in fantastic unreality."It's like stumbling inside the gate between a spaceship and the void - the lack of gravity prevents you from going in either direction - and while you rapidly lose oxygen, you're also neither in nor out. That is an interesting analogy - to compare reality with a spaceship - perhaps the world of the subconscious mind is far larger than the universe?"Well if we're figuratively speaking about 'largeness', then yes: for if the physical universe is a subset of mathematics, and every (or at least some) human mind is capable of understanding mathematics, then surely it is a dark void down there in the depths of our minds, interrupted by bright stars of memories - dust clouds of hazier ones - floating in the void.... stuff that you cannot catch and yet exists there - you feel it - it blocks out the light from your brighter ones, and casts shadows into the realm of your mind's eye."Perhaps there are black holes - ideas that consume other memories and leave a mere flick of light in the universe, and perhaps beyond - in the deep dark unknown, there lies untapped potential: an ever-expanding black canvas of possibility and imminence..."Oh! if we could only fill that void with the thickest network of the brightest stars - and render the universe hot and bubbly with positivity. But alas! every star must die... and our memories lapse, giving way to sparkling blue and hot memories, shining into the universe."
- Aug 29, 11Gutentag, bonjour, hello and everything! I've been away from blogging and what not - but perhaps I want this thing back alive, breathing and snoring at whatever measly number of readers I might've had eons ago. So! Without further much ado, let's get started in something interesting.
Well, I say interesting; I mean cool. While StumblingUpon random gooey things, I came across this:
I'll take no offense at the fact that StumbleUpon considers me a nerd - after all I programmed you didn't I, StumbleUpon? I'll take that silence as an evil robotic pause.
But back to the point - even though it's entirely true that I do in fact heart math, what caught my eye was the fine print. An equation that seems to approximate the popular image of the heart to such precision! I had to replicate it in mathematica, and fiddle around with it. So:
(You will probably need the free cdf player from the awesomeocracy of Wolfram) And for those of you ever-curious about references, voici.
Of course there is nothing mathematically deep about this - its just some old function that happens to look like a heart. Not even a real heart - just one of those girlish heart hearts. Change the colorslider to red, and you'll see what I mean. Still - there are a couple of interesting things.
Firstly - surely someone must have thought a heart looked like this. Considering my aversion to blood and human bodies, I'd have agreed with them and moved on. Apparently the origins are debated - theories range from a vision of a catholic saint to a North African birth control herb.
Secondly - we have a rather neat mathematical representation of this? Quite incredible.
The eponymous cardioid graph (r=2(1+Cos(t))) does look similar:
That is a reasonably good approximation for the heart, but it turns out that a better representation is a particular level surface of 3D scalar fields that look like A = (x2 + y2 + z2 - 1)3 - x2 z3 - y2 z3 , which is in fact what I have plotted far up there. The 'heartiness' parameter selects particular level surfaces of that function - with the heart appearing at h=0. At other values of h, you get either a deformed blob, or three.
Philosophical implication time. Your favorite heart symbol was covered by mathematics - in fact, whatever inspired the symbol would have been some natural approximation of this function. Don't look so surprised: from simple fractals describing ferns to logarithmic spirals appearing on galaxies, broccoli, hurricanes and nautilus shells, mathematics is in fact, at the heart of the natural world.
To my fellow physicists, mathematics is a language (invented by physicists of course) to communicate their ideas about the natural world. This is true - but it misses a remarkable fact that hurricanes and galaxies were linked through mathematics much before we 'discovered' that. This deep level of self-similarity and pattern manifestation in nature makes mathematics nearly divine. Not to mention the infinite world of nonphysical mathematics.
More to come! - Apr 23, 11Yes. Even I have been caught up in the 3D craze that's sweeping across the entertainment world. To be precise, my interest is rather independent of the entire 3D gaming and movie industry - I have not watched avatar (the trailer I hear is necessary and sufficient). My interests lie largely in the plane of photography and nature, so I thought I'd do some stereoscopy.
I've been a fan of magiceye for a while. Ever since staring at one of their calendars over 10 years ago, I've wondered how those escheresque tilings of palm trees and waves could reveal hidden dolphins embedded in the third dimension. Was it like a hologram, was it trickery, or was it my imagination?
The idea of parallax lies at the heart of mid-range depth perception in humans. At shorter (ie less than ~ 1m) scales, the human eye lens focuses, giving an idea of depth. At longer (ie more than ~1km) scales, the only source of scale is familiar objects, such as a tree, a human, or a superintelligent amphibious squid.
The extreme ranges are well-covered in photography. A thin depth of field simulates the short-range focusing of the eye - this is why wedding photographers love 50 f/1.8 lenses. At longer ranges, we need familiar subjects in the distant landscape. This is more of a function of luck than skill. Not very many photographers can claim to have willingly inserted a superintelligent amphibious squid in their grand landscapes.
The middle range is even harder to control - usually photographers just stop down on their apertures, and throw depth perception into the depths. Here is where stereography comes into play. Tt simulates the parallax perception of the eye by taking two pictures from two angles, and then somehow tricking the brain into believing depth.
The first part is simple - just stand to one side. Take a shot. Move over by a couple of inches. Shoot again. Of course you have to keep aperture, focus, and central subject fixed, but that's trivial. The second part is remarkably difficult. The most familiar method is obviously the colored-glasses-method, or anaglyphs, that color the images separately, and use an incredibly ugly pair of glasses to channel the images into the desired eyes. At the other end of the spectrum, techniques today use different polarizations, interlacing, and/or really fast shuttering to do essentially the same thing.
I've tried two quick methods in my dear workspace. The first is lame. It's so lame, it's called 'wiggle.' The term is self-explanatory, and if you haven't caught the hint, here's an example from my workspace:
Admit it. That was lame. For a larger version and a more prolonged seizure, click on the image.
The second method has less jugglewuggle, but requires you to do something incredible. You need to cross your eyes, touch your nose to your elbow, and sing the Marseillase in a sea of chocolate mousse. No - it's just crossing your eyes until you see a third image in the middle. That one is the 3D version. It takes practice - and the method is well explained out here. Here's my workspace again:
Again, for gorgeous mind-blowing 3D, click on the image.
Trust me - it works - and I can see a sharp 3D image. If you can do it too, you're sending the left image (taken inches to the right) to the right eye, and vice versa.
In each case, you're encoding in the third dimension in one way or another, just like a hologram. The first one codes it into the time dimension, with the irritating loop providing the brain the third dimension information. The second one is more tricky - it codes it into the extra image - essentially, the larger 2D image contains the extra information. Similarly, the other methods use spatial (interlacing), temporal (shuttering), or even optical (polarization) dimensions to provide depth in a 2D image. Perhaps a challenge in current 3D technology is not only displaying 3D images, but also encoding the depth information without taking up much memory.
The truly interesting stuff is how the brain processes this stuff. A 3D image in Matlab looks like a three-dimensional array, with numbers sitting at specified row, column, and page numbers. How is it represented in the brain? Do we have arrays of information in our neurons? Or is it an ingeniously crafted sparse matrix, with only the locations of my eraser, chair, and giant invisible pot of gold stored with 3D data? It's not even 3D - probably 5D - if you include time and color. Yes, color is a dimension. For the answers, I need to read biology, and therein lies my brain aneurysm. - Mar 15, 11
"The doors are closing. Please Stand Clear of the doors," says the usual mechanized voice - some distant cousin of Stephen Hawking's speech synthesizer and Microsoft Sam. I've probably heard it over 15401 times so far - shuttling back and forth between Berkeley and Fremont twice a day.
I sit down on a green seat at the corner of the compartment and I look at the sharp fluorescent lights cutting across the ceiling of the car, brightly contrasting with the dark blue outside the window. I look out of the window - and just as I remember the failed final, my eyes meet those of my reflection. Who is that? Who's face is that, gleaming in the silhouette superimposed on the dark blue landscape outside? His eyebrows furrowed, the person looks back with contempt for my reality. Below, hands type away at a keyboard and glowing screen - writing another story, a darker mirror story. A story infiltrated by the deep blue color of the outside. I can even see the cold, expressionless clouds swoop down in misty clumps and accumulate over the imagery being typed away, covering it with damp air and unwelcome darkness.
The train starts. Sitting backwards in a train has become too familiar to me - I instinctively push back into the seat behind, while the person sitting beside me lurches forward. Slowly the train pushes ahead - accelerating along the tracks, the pillars of the station whooshing by until at last going free of the platform, the train powers ahead. Outside, colorless shadows of trees swing past - the ones closer to the train moving faster, blocking the ones behind and then uncovering them, like dark mischievous gamblers moving cards around.
I see tiny golden lights sprinkled over a street, red and green switching in the distance, cars speeding away into the dark fog, the gnarled tree branches reaching down - snatching at the humans walking by. Houses on the ground roll past in mute and quiet boredom, accepting the morning as any other, exchanging memories of yesterday's rain with experiences of today's fogscape.
Soon, a station platform materializes behind me - the train slows to a halt, and the doors open. New people, new faces enter, eyes scanning for seats, filling the compartment with their hands, their backpacks and their worries. "The doors are closing. Please Stand Clear of the doors."Inside BART - Mar 14, 11
"Six car Richmond train - now approaching, platform one," I hear a stilted voice bark out into the dark blue platform. I rush up the elevator, my wet shoes sliding on the steps, I run up the shadowed corridor of air slanting up from the station to the platform above. Narrow and thin, the diagonal concrete passageway gathers around me, attempting to break the parallel formation of its grey faces. A lady with her office baggage is blocking the way - the left lane! the one reserved for frantic commuters like me, who decide that elevators aren't fast enough vertical transport. I side step her - one! two! - and I'm ahead, the edge approaching slowly - the deep blue morning sky peeking out ahead, expanding in an strange polygon formed by the blocks of steel and concrete that make up the BART station.
"The doors are now closing - please stand clear of the doors," I hear coming from within the lit train standing on the platform. Listless faces peering out of the golden light of the interior, looking out onto the grey and blue scene of cement and sky outside. People hustling towards the train doors on the platform, eager to catch the doors and leap into the train compartment. I press my shoes into the floor, and run ahead - the doors start closing - determined to catch them halfway, I skip - I sprint, and swissssh - the doors close flat in front of my nose, leaving me panting on the black rectangle of the platform marking the doors. I've missed my train. Now I'll be late.
The feeling of missing a train is odd - it lies somewhere in the fine crack between regret and resignation. I look at the departing train - faces mushing away in the speed - the red backlights and the grinding noise of the wheels on the tracks disappearing into the dark night. From far away on the platform, I watch it curve away, and I think - what if I had walked a centimeter extra on one of my many steps to the station? - what if the lady hadn't been blocking the left portion of the elevator? - what if I hadn't been momentarily distracted by the expressionless faces staring out from the train? Would it have been any different - or is there some fatalistic 'requirement' that I miss this train here, now?
A quiet breeze blows through my hair, as if dousing me with a bit of blue sky. I sit down on a damp bench, take out my laptop, and write for a while, waiting for the next Richmond train to approach. - Mar 07, 11This post is a set of incredibly mediocre photographs I took while running from class to class on the First of March. Click on pictures to enlarge.
Claaaaassic Berkeley - Campanile Wheeler Hall - invaded by protesters nearly every year One of many resident pudgy squirrels Good old strawberry creek and the bridge The very urban campus Sather Lane, Neds, and Bancroft Green and Blue - music library Music Library Wurster Hall - the only building uglier than Evans Hall ironically houses the Architecture Dept
.Did I say? Claaaaaaaassssic Berkeley - sather gate, campanile - Mar 07, 11
I'm in Doe Library - working in Friday late afternoon. There are only a few people typing away on distant desks, illuminated by sunbeams reaching down through the windows and the shafts of dust. All of a sudden, there's this commotion entering the room. It's ghostly - pitter patter of feet. Murmuring of soft voices. Children's voices. And yet, the room is as it was: the same desks, the same shafts of light uninterrupted by the shadows of humans entering the room. I haven't heard of any stories about the Doe Library being haunted, and this was late afternoon, not 2am spooky time.
The ghosts appear one by one. In single file, they follow a rather minuscule ghost out in front, tapping their feet to emerge from behind the shelves that obscured them for a good half-minute. I have always considered children to be dangerous. They appear like this out of nowhere, suddenly demanding a right for existence and attention. They are unpredictable, complete menaces, and worst of all - rather hard not to step on in a crowd. But at the same time, they're rather interesting creatures.
Our 4ft tall ghosts now having emerged, start claiming desks and chairs, filling up my desk with their self-concerned chatter and tiny colorful bags. Their teachers rush in after them, hushing the kids' excited jabbering and emphatic marveling. The children point sharply towards the painting behind me, knit their brows and turn to each other, discussing what seems to be every fault in the painting with their fellow experienced critics. Disagreements occur, and they look out blankly into empty space, as if in a mute wish that everyone would see the world from their incredibly height-challenged angle.
Without changing their concerned expression, they pull out colored pencils and commence on their own masterpieces of infantile art - stick figures and clouds. I must say they did a better job than I could have at any time. I recall being in an odd state at their age. I had a craze for colored anything - pencils, crayons, essentially anything colorful that I could hold in my hand, snap, and then giggle about it. But at the same time, I was incredibly frustrated with art. Why would the thing not paint the picture in my mind? (Little did I know I was painting masterpieces of modern art). I thought, why is that girl in the corner so incredible at art? Is the picture in her mind any better than mine? Or is she just more patient?
Which makes me think - is communication a good indicator of understanding? Does not being able to explain physics or mathematics neccessarily imply a lack of understanding? Feynman would have said yes. The children would say no.
But then - perhaps everyone has their own language - their own set of basis vectors in which to represent their thoughts. For me at the age of five, it was exclaiming, jumping and crying, not mute two-dimensional expressions of color on paper. For these children, it seemed to be reserved comments in spanish. It was truly wonderful to hear them talking in spanish - I love multilingualism, and considering the high level of spanish attrition among Hispanic immigrants, it's good they're speaking it as a first language.
Their motions, their speech, every little expression makes me think about life in general. I have a conjecture: if anyone truly understands children, they also understand humanity. They're the base case - we can only expect adults to behave as mature versions of these menaces. We may be tamer and quieter, but every person was a child at some point. Perhaps social norms imposed on a child's mind still retain the basic structure of childishness within. Maybe this is why humanity is incomprehensible - we are merely the same hard-to- fathom children, but with a new ability to appear intelligent.Doe Library East Reading Room - Mar 03, 11
On the file cabinet of the ISI student office at SSL, Berkeley, there are magnets with common words from the dictionary. Some pessimistic grad student has arranged the magnets to create an incredibly grim picture of human life:
Roses
Chocolate
Foreplay
Heaven
Marriage
Psychiatrist
DieTo add some of my own, in the Middle Ages, it used to be:RosesRosesRosesDammit why doth she not notice me?More rosesDeath by swordfightIn the stone ages, it was probablyGarrrrBuuh?PunchSnortHeheeFlomp - Mar 03, 11"Are we from Stanford?" asks Alex Fillipenko, referring to the apparent repulsion of other galaxies from the Milky Way. "Are we lactose intolerant? - Get it - milky...way," he quips. Impressively self confident, the frequent tennis player and skier is also well known for being the best professor on campus and probably the best astronomy prof in the world. Working in competition with Saul Perlmutter (also a Berkeley prof.), Fillipenko found out in the late 90s that the universe was not only expanding, but that this expansion was accelerating in time.
On the Wednesday compass talk, he talked about Dark Energy and the runaway universe. He started with an apple: throw it up, and it comes back down. As Fillipenko mentioned, "may the net force be with you). Now if we look at the universe at large, the gravitational attraction between the massive galaxies should eventually slow down the expansion. Or should it? Theory should say that it depends on the matter density of the universe - there's some critical density below which the universe expands forever. It's a lot like the escape velocity of a rocket from the Earth. If we define , where is that critical density, then represents a continually expanding universe that asymptotically reaches an 'infinite' maximum. Now bring in experimental data - collected from meticulous observations on supernovae visible currently to telescopes. By calibrating these titanic explosions, it turns out that is negative (!) and there is something pushing the universe apart.
The idea of the cosmological constant comes into play here - opposing the gravitational force at incredibly large distance scales. Initially designed by Einstein as a fudge factor to ensure a steady state universe, it's currently what theorists believe is the cause of this crazy universe.
I was about to ask about the connection between this dark energy and inflation, but he covered that in his talk. It's possibly the only problem about the best teachers - they anticipate and answer your questions before you can ask them.
At one point, while describing the idea of using 'standard candles' to estimate these (literally) astronomic distances, he goes "Let's say we have a very large red giant in this galaxy called Charlie - we know it's it's really powerful, so we can compare it to Betelgeuse." Umm... Charlie Townes was in the row in front of me, so that was probably a token of respect for the incredibly important nobel laureate. But still - did he just call Charlie a big fat red giant?? OBJECTION!! Let's see you that fit when you're 95.
Apart from that, it was an excellent talk - and got me thinking about a number of topics that I might think about and post here.
At the end of the Q&A: "And so if we look on this side of the line, we know precisely how much dark energy we've go...Oh shit! I have to pick my kids up from school." - Mar 03, 11This blog will contain some of the photographs that I leave in Lightroom's cavernous image catalog - the ones that are too unartistic to see the light of flickr. Along with the photos, I'll offer some idea into what goes into the thought processes of a monkey with a camera. I will also post some technical tips and (maybe brief tutorials) for post- processing.
Today's post is relatively short and uncomplicated (note: that is what I thought it would be when I started writing). I do photography for a number of reasons - perhaps the most prominent is the ability to see stuff from different angles. There are two things I want in life: one is clarity of thought, the other is new perspectives. LIfe would be kafkaesque if we could only percieve from one direction - which also seems to be why religion is so convoluted and blind.
I'm tempted to add a bit of math here. When we talk about an angle - a perspective - we need some space. Some coordinate system in which we take different angles around a point. Mathematics and science have their own 'spaces'. (I'll talk about them some other time). Photography, on the other hand, has two.
The first is the actual 3D space. This is the space in which we define a visual perspective - taken from a point or around a point. This is why you see photographers leaning in and out, occasionally contorting into angles that gymnasts would envy. I am tempted to add in time - but I dont think temporal length qualifies as perspective.
The other is color - essentially adjusting color. I'm not a fan of significant post- processing, but I do believe that adding a function mapping a color space into itself is a neat way to relook at a photograph. Mostly though, my maps are onto the linear gradient - ie black and white, although occasionally I fiddle with hue and saturation. The reason I oppose adding a moon into a scene more than adjusting the color is that color perception is nearly arbitrary. Our eyes percieve colors in a particular way - and indeed the color in my head when I see a block of blue maybe different from yours. However, the color depends on the energy of the photon, and you cant really 'remap' that without adding filters. Essentially these operations on the color space correspond to functions on the fourier transform of the image - we're changing the color spectrum of the photograph.
To illustrate the first, I was walking in Central Park, Fremont, when I noticed the following dismal scene below me: (it's just mud and goose excrement, chill out)
My first reaction is "yes! finally!" and I lean down, hold my camera less than an inch off the muddy waters, and click:
That really is the same scene, from a different angle. Of course looking through the viewfinder would've helped, but it would also have resulted in a mud caked beard (which, contrary to popular perception of bearded men, is still undesirable).
Now for an illustration of the second. I think a black and white conversion is best as an example. On a rare snowfall on Mission Peak, I went for a little walk. Here's what the peak looked like from the west:Quite unremarkable, so I worked with it a bit in Lightroom, and this is what I get:
Of course I've lost the color information, but doing so only emphasizes the graphic nature of the composition, the bleakness of the landscape, and the falling snow suspended in air.
Maybe I'll upload these two to flickr, now that I think of it.
If anyone wants the LR presets, email me. - Mar 01, 11
" 'Careful enough' is a personal hygiene for mathematicians," says Ilya Zakharayevich, while scribbling with colored chalk, pausing only to peer at us over his niagaric beard. The topic arose while talking about constructing sets - the topic that usually brings out such fervent caution among mathematicians. The next day, he makes that the topic of the first ten minutes. He is probably a constructivist: most of his proofs start from some structural foundation - and build up from there. Logic is minimized; for a change, mathematics feels like playing with colored lego, rather than reading the legal defense statement of a serial killer.
He starts with a troubling statement: "Construct a set of integers that can be described with rules that have less than 1000 words." It seems as easy as picking out all the blue blocks in a bucket of lego. What if I ask you, my dearest reader, "is this a good rule?" You would have to evaluate whether it really defines a set, and for that, you need to know all rules of length less than 1000. BUT! This is a rule of length less than 1000 - so to know it, we need to know it. Logical loop. It's like "I like pikachu iff I like pikachu." (Insert your favorite character).
I remember a really good way of describing functions we were discussing in 11th grade. Lets say a classroom full of students is invaded by a generous teacher with a box of cupcakes. (Oh - and make the crazy assumption that the students are all well-behaved - ie Eric Cartman is not in the class). Let us say the teacher begins throwing cupcakes to the students. Call this crazy behaviour a 'function.'
Then there are a couple of simple situations possible here: 1) No student is left hungry. 2) No student gets two cupcakes. In the first where cupcakes are over everyone, we say the function is surjective ('sur' = 'on top' in french - stop laughing please). In the second case, where no more than one cupcake goes into a student, we say the function is injective. If both, then it's bijective.
Now let's be risquee, and assume that both cupcakes and students have a method of multiplication within themselves. Alright, for the sake of being decent, lets replace cupcakes and students with celery and rabbits. Lets have the celery function throw two rabbits celeries, and then they multiply...like rabbits. (Assume they make only one bunny). That was case one. Instead, lets say that we let them multiply before, and we somehow graft the two celeries together. When we throw it to the rabbits, a rabbit will catch it - and if that rabbit is the bunny born form the multiplication, then the function is a homomorphism (don't laugh).
Was that complicated? Of course it was. Analogies are fun, but here is a neater way to look at that: f(ab) = f(a)*f(b). The a and b are celeries, and the equality shows that it's the same bunny, regardless of the order of function and multiplication.
Why do we care at all? Look at how it 'preserves' the operation of multiplication across the transformation from celeries to bunnies. Now we can call the idea of a bijective homomorphism by a brand new name - isomorphism. How incredibly deep!
Not yet! However, we can show that this isomorphism thing splits up a set into classes - it partitions stuff. It's like the function "same color?" on lego blocks. Here, we take two lego blocks - and declare them isomorphic if they have the same color. Now we can have buckets of colored lego.
Essentially, this proves that mathematics is what children are naturally inclined to do. But then Humanities gets out of a white van and offers them candy.
Math is boring - sure - I know. But it's fun.
Dammit I missed my Berkeley station. Now I'm coasting to some Cerrito place for no reason at all. Must get off this train. NOW. At least Berkeley time is always 10 minutes late.Cerritosomething today - switching trains to go back to Berkeley:
Thats enough math for now. I'll post more creative stuff next time.
Todays set of random numbers (the first set that came to my head [is that necessarily random? {I don't know}]).
37477911974773
: )
: P - Mar 02, 11It is said frequently that a blog is a difficult thing to maintain. Apparently it requires large quantities of some perfect blend of patience and persistence- and I must say I lack that. Therefore, this blog, if you are indeed reading this post, will be a finite, yet ever expanding set of my most random thoughts. Mathematics, physics, philosophy, travels, whatever I feel is worth conveying in some form of written word, shall end up here. Perhaps I will add thoughts about my work as well.
Regarding the temporal scale of the blog - it might die out like all other blogs (and perhaps like everything else human).
