## Saturday, July 07, 2007

### Are Japanese Washing Machines (and Japanese Trains, Cameras, etc.) Fuzzy or Non-Fuzzy?

Joost van Steenis, Mathematical Chip:
In Japan they use a kind of fuzzy logic based on discrete numbers. Washing machines determine with sensors a value that tells something about the amount of dirt. The weight is also measured and a third sensor looks at the colours. Then an algorithm determines how much water and washing powder is needed and what the temperature of the water has to be. These variables are independent from each other and they can be quantified. So you get a washing machine with thousands of programs. This pseudo fuzzy logic is also used in lifts, which on their own accord travel to those floors where most people are waiting. And in cameras to compensate for tremors in the human hand. But this is not real fuzzy logic. The fuzzy situation is split up into very small steps after which discrete values are allotted to the parts. These values can be used in calculations according to the Boolean logic. Boolean logic is by the way a special part of fuzzy logic. It looks fuzzy but it is still discrete. This soft Japanese computing is still computing. Vague concepts are being converted into numbers that can be used in a computer. But our brain works with real fuzzy computing.
Earlier I wondered if it would be possible to bring order and system to fuzzy interactions between fuzzy parts of a proof process. The following comment by Mr. Steenis (id.) sounds both reassuring and discouraging:
So you start with a fuzzy input that leads via fuzzy dependency, fuzzy thinking, fuzzy judgement and fuzzy logic to a fuzzy output. On the basis of a fuzzy complex the brain decides which piece or pawn has to move. And the brain includes in its judgement also fuzzy ideas about such fuzzy facts as the aggressiveness of the opponent. The discrete position on the board gives rise to a fuzzy process that results in a discrete decision: only one move can be executed on the board. For this kind of fuzzy process techniques we do not have any theory. We do not know how we can obtain a fuzzy output from a fuzzy input.
Is Mr. Steenis correct?

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Mr. Steenis shortly grows (pleasingly) philosophical (and whimsical):

When problems get complicated thinking becomes even more difficult and it is even more important to change the way of thinking. It is striking that in conversations most people understand fuzzy concepts fairly well. Words as about, maybe, long, short, nice and agreeable are all fuzzy. In a conversation these words are never described exactly. Even the question what is life is fuzzy. Viruses grow but they can not reproduce. Are they alive? People are alive but when does human life begins? With the first two cells from which later a human will grow? Or is it needed that there are 4, 8, 16, 32, 64, 1024, 8192 or even still more cells before we can call a living entity human? The whole abortion discussion turns around such fuzzy concepts. Fuzzy exists, the consequences are everywhere and it is strange that scientists mostly avoid this reality. In some simple cases they use fuzziness but when problems get more complex fuzzy disappears and all is expressed in absolute values. But in complicated problems precise descriptions become meaningless and meaningful descriptions are not precise. Let humans become a little more chaotic.

### Victory

I am happy to report that I won my first fuzzy chess game.

I regret to report that the computer I played was not programmed to look very far ahead.

But I'll take a victory whenever I can get it. (I won't be reporting my losses, if you please.)
It strikes me that in real fuzzy chess, the moves themselves would be fuzzified, and not just the descriptions the players give of the moves they make.
One notable feature: This particular fuzzy chess program allows Mulligans. If a player indicates he, she, or it will move a particular piece, the player remains free to move any other piece in any way that the (normal) rules of chess allow. There is something akilter here: the human player is given an advance opportunity to peer into the mind of the computer. I guess the developer wanted to give human players warm fuzzy feelings about fuzzy chess.

### Musings about How One Is To Address the Question, "What Is [Judicial or Juridical] Proof?"

Proof in legal settings such as litigation is a social process or phenomenon.

A social phenomenon has numerous ingredients.

Proof in litigation has numerous ingredients.

Some or many of those numerous ingredients probably have causative force; i.e., some or many of the ingredients or parts of proof influence how proof works.

Some of those causative ingredients have or may have a logic or a conceptual structure.

But, if so, such logics or conceptual forms are sometimes, often, or always fuzzy or rough.

Moreover, the interactions among those frequently-fuzzy logics or forms are themselves sometimes, often, or always fuzzy or rough.

An observer can try to describe the fuzzy or rough logics or conceptual forms that seem to drive or may drive (to some extent) the process of proof in litigation.

An observer can perhaps also try to describe how those fuzzy or rough logics or conceptual forms interact -- or, if you prefer, collide.

There are possible corollaries of the propositions or hypotheses that have been stated or hinted at above. There are also many questions. Perhaps I will deal with such corollaries and questions later. What you see above is very, very abstract. It is also very imprecise in an invidious sense -- i.e., it is a very imprecise, rough, and vague account of an imprecise process. But I am neither a logician nor a mathematician, and I have to start somewhere. I will try to start with simple description (of the ingredients of proof in the United States), if that is possible. Perhaps then my description can be made more systematic -- by other people if not by me. (But whether systematic description of the parts of proof and their interaction is possible remains to be seen.)

I fear that my project is too ambitious.

Stay tuned for further developments.

### Fuzzy Chess?

Image Reproduced under GNU Free Documentation License

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Being slated to take part in a discussion of fuzzy logic, soft computing, etc., and law later this summer (in Las Vegas, b'gosh!), I have been having more than my share of fuzzy thoughts recently. Well, no, that's not it. I misspoke. (Forgive me.) I meant to say that I have been thinking, quite precisely (in my usual fashion), more than I usually do about fuzzy features of law.

In any event, having just thought about chess and then having thought (roughly, next) about fuzzy phenomena (for reasons that I may explain momentarily), I thought, "What about fuzzy chess? Would that be possible?"

In today's GOOGLE world no question like this goes unanswered for very long.

GOOGLE reveals that, yes, there is such a thing as fuzzy chess and people already play the game. See, e.g., Fuzzy Chess (Be patient: allow time for the applet with a fuzzy chess board to load.)

Well, waddaya know? Isn't that neat?

The author of "Fuzzy Chess" (id.) states in part:

The [Fuzzy] Chess game play follows the exact same rules as a normal chess game however before each move the player is required to enter a description of this move and the computer will respond by displaying to the player a description of its move. Both these descriptions should be imprecise.

This allows the player to base [her] decision of the actual move [she] will make, at least partly, on the computer's response. The player is using vague information to make [her] decision which is just like how [she] will make decision in real life situations.The rules are pretty simple, before you make any move you will need to enter a description of that move. This description can be as vague as you like - in fact the less specific the better. Once you have entered your description the computer will display a description of the move it may make in response to your move. Now you can actually make your move, this move does not necessary need to match the description you entered. The computer will then make its move based on your actual move. You are white and the computer is black.

The author also has a link that apparently describes the sorts of imprecise move descriptions the computer will accept.

### Botvinnik to Go?

I recently bought a book that I greatly enjoyed when I was a callow youth: M.M. Botvinnik, One Hundred Selected [Chess] Games (trans. Stephen Garry, Dover ed. 1960).
• This English translation was originally published in 1951 by MacGibbon & Kee.
Clarification 1: Well, I guess I didn't buy the same book, exactly. How should I put it? Should I have said, "I bought another copy of Botvinnik's book." But this is all so tedious. I will let the IP people worry about such things.

Clarification 2: I am no longer a callow youth. Now I am instead a callow adult.

• Several months ago I vowed finally to learn the game of Go. (The board and pieces, elegant though they are, lie largely unmoved and unused on my dining room table.) Getting the Botvinnik book more recently -- just a few days ago -- moved me to wonder if he would have been a masterful Go player. Botvinnik was probably the greatest positional player that the game of chess has ever seen -- or, in any event, Botvinnik's mastery of pawn structures was astonishing: he built elaborate pawn forts and then moved them, move by move.

### Weird Life

Space scientists are now urging a search for weird life, weird forms of life. See NYTimes (July 7, 2007).

I must be an advanced scientist: I found weird life here on earth long ago.

N.B. Perhaps scientists also misspoke when they said they were hard on the heels of a theory of everything. (This claim raises the William-Clinton-like question: What is "everything"?)

## Monday, July 02, 2007

### Relevance and Causality

What is the relationship between causal relations among events (or causal explanations or hypotheses) and the relevance of evidence? I have been wrestling with this question for a long time. I have found an excellent book that sheds much light on this question. See James Woodward, Making Things Happen (Oxford University Press 2003).

Woodward has useful comments about Nancy Cartwright's intriguing skeptical attitude toward causal explanations. See, e.g., Nancy Cartwright, The Dappled World: A Study of the Boundaries of Science (Cambridge University Press 1999) and her more recent book (which I have not yet read) Hunting Causes and Using Them: Approaches in Philosophy and Economics (Cambridge University Press 2007).

Woodward professes to be an admirer of Judea Pearl -- and Woodward's approach in some particulars does follow Pearl's. But Woodward (I am pleased to say) emphasizes more than Pearl has (I think) that rational relevance judgments are possible (and common) even in the absence of anything that might resemble a full-blown theory (or even a half-baked theory) of causal connections in a particular situation.

James Woodward uses nice examples (mostly from the sciences) to illustrate his points.

• Amazon.com's "book description" of Cartwright's 2007 collection of papers (see citation above) suggests that Cartwright uses her latest book to make a counterattack against critics such as Woodward:
Hunting Causes and Using Them argues that causation is not one thing, as commonly assumed, but many. There is a huge variety of causal relations, each with different characterizing features, different methods for discovery and different uses to which it can be put. In this collection of new and previously published essays, Nancy Cartwright provides a critical survey of philosophical and economic literature on causality, with a special focus on the currently fashionable Bayes-nets and invariance methods – and it exposes a huge gap in that literature. Almost every account treats either exclusively how to hunt causes or how to use them. But where is the bridge between? It’s no good knowing how to warrant a causal claim if we don’t know what we can do with that claim once we have it. This book will interest philosophers, economists and social scientists.
•