Exploration

(by definition this page is work in progress...)

 

 

"The universe is full of magical things patiently waiting for our wits to grow sharper."

--- Eden Phillpotts

Life is fundamentally interesting: Everything in life is interesting if you study it deeply enough. Whether you do physics or basket-weaving, eventually, if you pursue your work with care and increasing attention to detail, you should come to see equivalently beautiful (though probably quite different) aspects of Nature. It seems that Nature doesn't care which way we go about understanding her, if we care to at all. After all, human ancestors were content with a life of hitting each other over the head with bones and such for many millennia. But if you don't use this marvelous thing, your mind, which is given to you for free by birthright, what a waste!

"Laziness, far from being a natural impulse, generally is caused by infirmity, fear, protest, or some other disturbance."

--- Rudolf Arnheim

 

"The Cosmos is in an explosion of improvement, and Life is just the latest phase of that."

--- Nicholas Kersting

 

Variety: Leibniz apparently believed that the cosmos we live in is the one which exhibits the greatest possible variety. I find this theory attractive and it would be interesting to test it quantitatively.

 

What's Wrong with Money?: Money is packaged human service. With unlimited money, you can get all the people on Earth to do things for you: build you a house, a car, deliver it to your doorstep, drive it for you while someone makes your dinner, an army conquers a small country for you, etc. But there are limits: "Money can't buy me love" for example, although for some people extremely dedicated service might be acceptably-close to true love (yet the difference exists!). And surely money cannot buy scientific progress: even if all 9 billion people on Earth gave you 100% of their time, a successful theory of quantum gravity may just not be obtainable, at least not yet. We all know you can get money by giving someone service, and you spend money by obtaining service, but you can also lose money by e.g. gambling, being cheated or robbed, etc. which gives rise to very wealthy individuals that didn't really earn it, so to speak. Of course you can also burn money, which is total loss to society -- that's like working hard to build something and then immediately destroying it. So here we have it, society runs on this very limited currency (limited to human service, that is) which does not obey certain conservation laws you might expect, like "you get what you pay for," and is subject to fluctuating utility: if I work an hour and make $10, put it in my pocket for 20 years and then try to spend it, I'll be lucky to afford a peanut. What about using something like packaged entropy instead, e.g. energy cells. Energy can always be converted to the usual dollars, because human service depends on energy in one form or another, but more importantly energy can be directly used to do things, yes maybe even scientific progress if it is used to fuel an autonomous AI computer system. This may not be a panacea since the definition of energy (whether potential or kinetic energy, or force exerted over a distance) may collapse in certain extreme environments (e.g. near black holes), so perhaps something even more fundamental (information?) is called for.

Related to information is communication -- something else I'm deepely intrigued by. How and why do we communicate the way we do? Ordinary human communication is actually very "quantum mechancial" in the sense that what I am about to say influences what you were going to say had I not spoken. This can be a big deal. For example, take match-making, e.g. whether a boy and girl who just met will start dating: obviously this all depends on who expresses positive interest first, and is not rejected by the other. Indeed the fear of rejection may prevent either one from speaking up, even if they both like each other, forming something of a tragedy. The academic name for this problem is "privacy-preserving match-making", and has a number of algorithmic solutions. Surprisingly I thought of one just now that is very simple and can be played in a noisy bar (a plus!): take a deck of cards and put all the red cards on top of the black cards, face down. The boy (say) closes his eyes while the girl either a) does nothing to the stack (if she likes the boy), or (b) takes one card from the bottom and places on top without looking at it (if she respectfully declines the boy). Then the girl closes her eyes and the boy performs his choice. Finally the top card is revealed to both of them: if it is Black, then there is no mutual interest, and in fact no one's feelings need be hurt because there is no way to know who put the Black card on top, i.e. if the girl knows she put a black card on top, she doesn't know whether the boy did the same, so she cannot feel so haughty and make the boy feel awkward, and conversely if she didn't put a black card on top, the boy doesn't know that, so her dignity is preserved. This can be done with N players to test for mutual N-fold interest, or to perform secure voting on an issue (the number of black cards on top indicates the number of "nay"s, for example). I'm actually more interested in general privacy-preserving matching of interests: one experiment of mine in idea-sharing is based on simply matching sets of words ("Bag of Words")in a provably secure fashion (based on private set intersection). This experiment is called "Quantum Repoire" and I invite you to try it!

"You do any problem that you can, regardless of field" --- Richard P. Feynman

The beauty of Nature has always been there, if we just care to uncover it for ourselves, and what potential there is for that! There is also the tantalizing possibility that Nature is so grand that we cannot ever fathom out its structure, but only study a little corner here and there where the rules simplify tremendously ... if you want to feel a little of this humility, try playing wei-qi against a professional-level player --- even this human-contrived game probably cannot ever be completely understood by humans!

 

"Most basic ideas of science are essentially simple and can usually be expressed in a language that everyone understands."

--- Albert Einstein

 

What is Art? I have a working definition of Art: "anything which is arbitrary." This is suggested by the common phrase ¡°There¡¯s an art to it.¡± In other words, how you do it is somewhat arbitrary: everyone does it slightly differently, some better than others, because there¡¯s no provably best way. Once there is a provably best way, it is no longer art but mathematical truth. What is not Art, then? Anything which has known rules that completely determine its existence, like a mathematical equation (in fact all of known mathematics is the antithesis of Art). Physical lines drawn by humans are always art because there is some arbitrariness to the inevitable deviations from a perfect line, which we accept and attribute to the skill of the human. Physical lines drawn by machines, however, are usually not considered Art because it is socially accepted that the machine¡¯s output is completely fixed as the mathematically perfect line. Although there are also inevitable deviations from a perfect line, we either unconsciously ignore them or attribute them to a faulty machine. It is interesting to apply this to ¡°digital art.¡± A single digital line segment is completely specified by two numbers ¡°m¡± and ¡°b¡± in ¡°y = mx + b¡±, its endpoints, a thickness in pixels, and the properties of the display hardware. If these are all fixed, then it is not Art. An image of two digital line segments is again not Art, as it is determined by the individual segments. This argument extends to any number of digital line segments. Why then is a digital scan of Mona Lisa, which is fundamentally just a collection of digital line segments, nonetheless Art? It must be because there is still some arbitrariness in the image: I can move the segments a little this way and that, probably making an aesthetically worse image, but possibly a better one. It¡¯s that uncertainty, that degree of arbitrariness, that makes it Art. If you could prove that exactly one configuration of the pixels makes the best Mona Lisa possible, then it would no longer be Art, but a tremendous mathematical statement taking into account color, geometry, and all of human psyche. Take on the other hand a digital image of the Mandelbrot Set, which is completely determined by the iterative formula ¡°zn+1 = z2n + c¡± for a fixed constant ¡°c¡± with ¡°z1 = 0¡± : there¡¯s nothing arbitrary about it, you don¡¯t have the freedom to change a single pixel. The Mandelbrot Set is not Art. Note that the same item may be Art to some observers, but not to others. You can buy posters of the Mandelbrot Set to hang in your office, for example, but I know the Mandelbrot Set is completely determined by a particular mathematical formula. To me it is not Art, though the coloring and framing of the poster may be. To someone who doesn¡¯t know that it is generated from a formula, however, it probably passes as Art. Incidentally, all this might also fix a definition for Science. Classically, Science has always been the guessing game of what subset of Mathematics describes Nature. It is also an Art because we are constantly tweaking our theories in arbitrary ways to match new data. Ironically, Science strives to be expressed as a theory of everything, which however would necessarily place it in the realm of pure Mathematics because it would be insensitive to data. You might then say that Science is an Art which strives to demote itself as such. Or more symmetrically speaking, Science is the process of Art turning into Mathematics.

"The generation which commences a revolution rarely completes it" --- Thomas Jefferson

 

China: my interest in Chinese (and other Asian) culture stems from the systematic way in which the world is therein characterized. This is especially evident in the language: for example "television" and "flint" in Chinese are both two-character words that share the common character for "electric": flint is "electric stone" and TV is "electric vision." I will be fleshing out this treatment here these months so be sure to check back now and then.

"Music is the silence coming true" --- Philip Roth

 

"No point is more central than this, that empty space is not empty. It is the seat of the most violent physics."

--- John Archibald Wheeler

 

 

"The very point which appears to complicate a case is, when duly considered and scientifically handled, the one which is most likely to elucidate it"

--- Sherlock Holmes

 

I strongly suspect the world must be discrete and not continuous as conventionally (but thus far usefully) assumed in physics. Specifically, space-time (and any extra dimensions that might be present) and fields representing elementary particles are all entities defined over finite number fields.

There is strong phenomenological evidence for the discreteness of Nature. Firstly, there is no absolute need for a continuous description of anything on a practical level, and it probably even gets in the way (e.g. of formulating a quantum theory of gravity) ---- everything we know from the continuous formalism can be translated into a discrete one, though reversing centuries of theoretical prejudice might be laborious. Secondly, everything you can experience or think about is by definition discrete! Even if you start out with continuous space time and energy, as is commonly assumed in the Big Bang theory, discrete structures (e.g. stars, galaxies, and you) inevitably evolve and become the correct "emergent degrees of freedom."

 

"In music the number of tones used is considerably smaller than the number of pitch levels distinguishable by the human ear. Hence the familiar assertion that the musical medium is limited to a number of standardized elements, whereas the painter ranges freely through the entire continuum of colors; in the language of Nelson Goodman, that music has a disjoint notation whereas painting is syntactically dense. In a purely mechanical sense it is true, of course, that a painter can work with continuous gradations of color shades. However, if instead of scanning the surface with a colorimeter we consider the picture as it is actually perceived, we find that no visual organization is readable unless it is based on a limited number of perceptual values, which constitute the skeleton of the structure into which the finer gradations are fitted. The subtler mixtures appears as secondary inflections or variations of this fundamental scale, or they form a variety of chords in which the common elements remain discernible ... The same kind of gradation is, of course, found in music if one listens to actual performance and does not confuse the music one hears with its notation."

--- Rudolf Arnheim

 

Thirdly, any continuous phenomenon can be approximated by a suitably fine discretization, but the converse is not true: various structures occur in discrete settings which we know are impossible in continuous ones. Two examples from chess: the Ladder in wei-qi, which 'causally' connects arbitrarily-distant points in space, and the phenomenon of Zugswang (German for "compulsion to move"):

Black can only move his king to b3,b4,b5,c3,or d3, in which case white will take the black pawn and win; likewise White can only move his king to f4,f5,f6,d6 or e6, and then Black takes the white pawn and wins. Whoever moves next therefore loses! Clearly the notion of "who moves next" is literally smoothed over in continuous time. Actually, in wei-qi a similar phenomenon called "seki" or "shuang-huo" (Ë«»î) arises:

If either black(white) moves at "a", then white(black) will capture the whole group. Therefore neither player will move and the entire configuration is stable.

 

I believe our minds really do operate by virtue of a network of ideas and words, which would explain much about what we do and why we do it. Physics, for example, is such a powerful (and difficult) discipline because its idea-network is so well-connected: you can't take out one link without compromising the whole structure, and conversely you can't really add a link in isolation, but have to learn groups of concepts together.

 

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