Kandinsky – Chess Theory (1937)

Kuhn’s theorem stat[es that] any finite, deterministic, sequential, noncooperative game of perfect information has an optimal strategy.
Consider Chess. The game is finite. It doesn’t involve chance, so it’s deterministic. It’s obviously sequential and noncooperative. Since you know the entire history of the game when you go to make your move, it’s also a game of perfect information. Kuhn’s theorem says there’s a best way to play chess. If the best strategies are used, every game will end up the same way. There are three possibilities:
Chess is a guaranteed win for white; there is nothing that black can do to stop this unless white makes a mistake, since white goes first.
Chess is a guaranteed win for the second player, black; there’s nothing that white can do to stop this unless black makes a mistake.
Chess is a guaranteed draw, like tic-tac-toe; neither player ever wins unless someone makes a mistake.
Now even though there are more possible strategies for chess than there are subatomic particles in the universe, [by] Kuhn’s theorem, chess strategically “equates” to tic-tac-toe. [via]
My classes for the upcoming school year: Semester 1: Research paper, Mathematical Economics, Econometrics, Current Issues in the Chinese Economy, China’s International Relations Semester 2: Research paper, Financial Economics, Industrial Organization, Game Theory and Social Structure, Economics and Law My school isn’t offering 4th-year Chinese, so I have to study it on my own time. After graduating I’ll be eligible for a fully-paid scholarship by the Chinese government to study the language for a year in China, after which I’ll be fluent. After that, I want to do a year-long masters in financial economics, which seems challenging enough that I can learn a lot, but sufficiently softcore that a mediocre mathematician like me can survive. Expect lots of posts on robots, machine learning, & China in the near future.

My classes for the upcoming school year:

  • Semester 1: Research paper, Mathematical Economics, Econometrics, Current Issues in the Chinese Economy, China’s International Relations
  • Semester 2: Research paper, Financial Economics, Industrial Organization, Game Theory and Social Structure, Economics and Law

My school isn’t offering 4th-year Chinese, so I have to study it on my own time. After graduating I’ll be eligible for a fully-paid scholarship by the Chinese government to study the language for a year in China, after which I’ll be fluent.

After that, I want to do a year-long masters in financial economics, which seems challenging enough that I can learn a lot, but sufficiently softcore that a mediocre mathematician like me can survive.

Expect lots of posts on robots, machine learning, & China in the near future.

from Nowakowski - “The History of Combinatorial Game Theory,” pp. 7-8
A bit of background: CGT is one of the more complex branches of the field, using computer science to solve pure strategy games with no random elements (+some other conditions). A commonly analyzed game is Nim, & mathematicians have taken the heaps of tokens used in Nim to construct a whole new type of numbers called ‘nimbers’. CGT can map games onto all the integers and real numbers, but more interestingly “we can extend our field of numbers to include surreal numbers like ∛∞, by defining numbers as games” (Milvang-Jensen, 2000: 3). The excerpt really helps to give an intuition of how this is possible.
The stuff of nightmares… alandistro: So when analyzing music, one of the tools you can use is a spectral analyzer. A spectral analyzer maps out the frequencies and intensities of those frequencies into an image that you can view to compare one song or recording to another. Here’s a violin concerto spectral analysis: And here’s your average rock song mp3 spectral analysis: ….and HERE is Aphex Twin’s song, “[EQUATION]”, spectral analysis: Hahah, holy shit, right? Aphex Twin encoded a picture of their creepy smiling lead singer/songwriter into the industrial noise of this song. Imagine being the first person to run a spectral analysis on this song and then PROMPTLY SHITTING YOUR PANTS!

The stuff of nightmares…

alandistro:

So when analyzing music, one of the tools you can use is a spectral analyzer. A spectral analyzer maps out the frequencies and intensities of those frequencies into an image that you can view to compare one song or recording to another.

Here’s a violin concerto spectral analysis:
image

And here’s your average rock song mp3 spectral analysis:

image

….and HERE is Aphex Twin’s song, “[EQUATION]”, spectral analysis:

image

Hahah, holy shit, right? Aphex Twin encoded a picture of their creepy smiling lead singer/songwriter into the industrial noise of this song.

Imagine being the first person to run a spectral analysis on this song and then PROMPTLY SHITTING YOUR PANTS!

“While the rat runs the maze we record where it is, and simultaneously how the cells in the hippocampus are firing. The cell firing patterns are thrown into a mathematical algorithm which finds the pattern that best matches each bit of the maze. The language of the cells is no less complex, but now we have a Rosetta Stone against which we can decode it. We then test the algorithm by feeding it freshly recorded patterns, to see if it correctly predicts where the rat was at the point that pattern was recorded. [U]sing this technique, the team was able to show that the specific sequence of cell firing repeated in the brain of the rat when it slept after running the maze (and, as a crucial comparison, not in the sleep it had enjoyed before it had run the maze). Fascinatingly, the sequence repeated faster during sleep – around 20 times faster. This meant that the rat could run the maze in their sleeping minds in a fraction of the time it took them in real life. This could be related to the mnemonic function of sleep; by replaying the memory, it might have helped the rat to consolidate its learning. And the fact that the replay was accelerated might give us a glimpse of the activity that lies behind sudden insights, or experiences where our life “flashes before our eyes”; when not restrained, our thoughts really can retrace familiar paths in “fast forward”. Subsequent work has shown that these maze patterns can run backwards as well as forwards – suggesting that the rats can imagine a goal, like the end of the maze, and work their way back from that to the point where they are. One application of techniques like these, which are equal parts highly specialised measurement systems and fiercely complicated algorithms, has been to decode the brain activity in patients who are locked in or in a vegetative state. These patients can’t move any of their muscles, and yet they may still be mentally aware and able to hear people talking to them in the same room. First, the doctors ask the patients to imagine activities which are known to active specific brain regions – such as the hippocampus. The data is then decoded so that you know which brain activity corresponds to certain ideas. During future brain scans, the patients can then re-imagine the same activities to answer basic questions. For instance, they might be told to imagine playing tennis to answer yes and walking around their house to answer no – the first form of communication since their injury.”
medresearch:

Game Theory Reveals Vulnerability of Metastatic Cancer Cells
Cancer’s no game, but researchers at Johns Hopkins University are borrowing ideas from evolutionary game theory to learn how cells cooperate within a tumor to gather energy. Their experiments could identify the ideal time to disrupt the cells’ cooperation and make a tumor more vulnerable to anti-cancer drugs.
Funding: Robert Veltri, Ph.D., of the Brady Urological Institute was also involved in the study, which was supported by the National Institutes of Health’s National Cancer Institute (U54CA143803).
Read more
“The mathematician John von Neumann and the economist Oskar Morgenstern were the first to tackle the subject, in a book they were planning to call A General Theory of Rational Behavior. By the time it was published in 1944, they had changed the title to Game Theory and Economic Behavior, an inspired move. The book postulated, as did all follow-up texts on game theory for generations, that players are rational—that they can figure out the payoff of all possible moves and always choose the most favorable one.”
“As opposed to conventional war techniques, game theory in cyberspace allows for the use of grand strategies aiming at fast and easy disintegration of the respective opponent. Not only can a player make multiple, simultaneous moves at the same time (as if he or she were composed of multiple selves), but both players also can make multiple, simultaneous moves coincidentally. In most games, players alternate moves. In cyberspace, this is not true anymore. An opponent can launch multiple, simultaneous attacks easily and quickly (Littman, 1994). What this also means is that time is not ‘constraining’ in the context of cyberterrorism. In other words, opponents in cyberspace are under no time control constraints (Carmel & Markovtich, 1996). Timing for move and state updates is neither fixed nor defined. In actual space, time is ‘perspectival’ (Gebser, 1985), while in cyberspace, time is ‘aperspectival’. For this reason, time becomes a “fluxing intensity, rather than a fixed extensity, and as such it is not prone to being fragmented into identical and repetitive units of measurement such as past, present, or future” (Kramer, 1997, p. 122). This is postmodernism.”
“Turing’s functional realizability of human is a thesis about constructability. It suggests there is no essentialist limit to the reconstructability of the human or what really human significance consists in. However, it goes even further by proposing that the consequences of constructing the mind outside of its natural habitat, reconstruction becomes tantamount to reconstitution. It is in this sense that Turing’s project highlights a rupture in the truth of humanity, between the meaning of being human and its ramifications. It practically elaborates that to be human does not entail the understanding of the consequences of what it means to be human or coming to terms with such consequences. Indeed these two couldn’t be further apart. To be human is neither sufficient condition for understanding what is happening to human[s] nor is it a sufficient condition for recognizing what the human is becoming. It can neither fathom the consequences of revising the meaning of the human nor the scope of constructing the human according to this revisionary wave. By functionally realizing the human, Turing draws a new link between emancipation (here the emancipation of human significance at the level of activities or functions) and the liberation of intelligence as a vector of self-realization. Both Turing’s computationalism and functionalism are significant because the ramifications of these programs—no matter what their current state is and what setbacks they have suffered—cannot be thought by their present implications. In this sense, by definition humanity as we identify it in the present cannot grapple with and realize the scope of Turing’s project.”