Life In 19x19

some comment on your paper:

on your paper, way you define terms are more confusing than actual term.
if you are the only one understanding the terms you use what is the point of your paper? (dont ask me for example because every terms you defined are confusing)
i for one understand perfectly many many mathmatical terms and proofs so dont blame me for not understanding your paper.
i am sure there are few who tried to read your paper. i am curious if i am the only one who feels that way.

Magicwand, I guess you are referring to my ko definition paper. I needed months to write it, so I'd expect an educated reader to understand it within about 2 weeks of reading. Alternative estimate: the definition part of the paper should be read like a maths journal text, i.e., spending 30 minutes per text line (this was my somewhat advanced maths study experience at university, e.g. for algorithm and complexity theory 3rd semester). If you spend less, then I am not surprised that you have difficulties with understanding. OTOH, the name of the terms help. E.g., would you recognise "strategy" if it were called "nut"?:) Readers familiar with similar definitions such as in my rules research texts have a chance of faster understanding. The examples can help, but I understand if you take the hard way and want to understand the definitions before entering the examples section or reading something related:

http://home.snafu.de/jasiek/j2003com.html

BTW, when visiting a go player who is a professor for functions theory, he showed be an "introductory" book for it. My comment: I would need two months to understand it. I.e., if he had shown me some of his "easier" research, I would have had to educate myself first, because I had not had any functions theory as a student.

Your maths study enables you to educate yourself if necessary to understand with much time and effort, but I think you should not expect contents to fly to you with only little effort.

John, two questions.

1. You say that the virtues of the East Asian-language Go literature is abundantly proved by the virtues of East Asian players. I'm not sure this follows. Would we say this about chess, or other games - that the countries with the strongest players have the best books? Would we say that within any game, when one country eclipses another in international competition, we should infer that the former's literature had previously eclipsed the latter's?

(I'm not denying the conclusion, by the way. The relative quality of translated Japanese books and new English creations settles that for me.)

2. Some of the best go research in Japan is in shogi journals? Intriguing; please say more.

Self-contained minor interlude that needs no replies: The complexity Jasiek's ko paper does not exceed that of Euclid's Elements, which used to be taught in many high schools (it may still be). I get the feeling that reading comprehension (and perhaps an aversion to definitions in general) may be a greater barrier to reading it than anything else. If a person has completed high-level math courses and still feels that Jasiek's ko paper is too complex, than perhaps that person has only applied math skills and little pure math ability.

lemmata wrote:Self-contained minor interlude that needs no replies: The complexity Jasiek's ko paper does not exceed that of Euclid's Elements, which used to be taught in many high schools (it may still be). I get the feeling that reading comprehension (and perhaps an aversion to definitions in general) may be a greater barrier to reading it than anything else. If a person has completed high-level math courses and still feels that Jasiek's ko paper is too complex, than perhaps that person has only applied math skills and little pure math ability.

How many definitions are there in Elements, and how many of them contain technical terms that are left undefined?

lemmata wrote:Self-contained minor interlude that needs no replies: The complexity Jasiek's ko paper does not exceed that of Euclid's Elements, which used to be taught in many high schools (it may still be). I get the feeling that reading comprehension (and perhaps an aversion to definitions in general) may be a greater barrier to reading it than anything else. If a person has completed high-level math courses and still feels that Jasiek's ko paper is too complex, than perhaps that person has only applied math skills and little pure math ability.

and what percent of High schools teach using the elements, and what percent of high school students graduate understanding geometry?

John Fairbairn wrote:Counter-example 1: "Thinking techniques of professional go players" (Seeing the overall position and the ability to evaluate) by Yoda Norimoto. Over 200 pages of solid text (three diagrams).

That sounds awesome, I hope it gets translated!

RobertJasiek wrote:The two books are light day and night. Calling good theory results "obvious" is the third stage of great findings (after the stages "everything flawed", "nothing new").

This is a basic conceptual error. Theory must be useful in order to be good in this context.

When we discuss the paper, do we mean this one: http://home.snafu.de/jasiek/ko.pdf? I confess, I sometimes find it hard to find the most important things on your site, Robert.

palapiku wrote:

John Fairbairn wrote:Counter-example 1: "Thinking techniques of professional go players" (Seeing the overall position and the ability to evaluate) by Yoda Norimoto. Over 200 pages of solid text (three diagrams).

That sounds awesome, I hope it gets translated!

It's this book for those interested.

http://www.amazon.co.jp/%E3%83%97%E3%83 ... 534&sr=8-8

I have it at home, but I haven't opened it up yet. I've just been a fan of his for a while, so I want to have it around when I have some time.

jts wrote:How many definitions are there in Elements, and how many of them contain technical terms that are left undefined?

There are probably no more than 200 definitions (it's been a while), but more than 100. I can't really answer the second question, but there are certain important things that are not defined explicitly but implicitly by their assumed properties such as the notion of length.

speedchase wrote:and what percent of High schools teach using the elements, and what percent of high school students graduate understanding geometry?

The "it may still be" in my post strongly suggests that I don't know what they teach in high schools today. However, I begrudgingly teach some university classes from time to time, where it becomes apparent that many college students didn't graduate high school with an understanding of geometry. Perhaps they don't teach Elements in high school anymore? I can't imagine that college students would have such poor understanding if they had studied Elements.

For a couple of centuries, one could not be called an educated person without having studied Elements, and the students of the first universities would definitely have been familiar with it.

Now, I am in no way suggesting that the quality of Jasiek's paper is comparable to that of Elements, which is truly a masterpiece of masterpieces. However, from an analysis of the syntax, the arguments in Elements are fairly low in complexity. Of course, part of the beauty of Elements is that it uses elegantly simple arguments to prove some very nice things.

The domain of the logic being applied in Jasiek's paper is finite. This is pretty much as simple an environment as you can get in mathematics. It might have a great number of simple things written in succession, which makes it look intimidating. Jasiek's word choices probably make things a bit worse, but he's not trying to sell the paper for money, so he might have put zero effort into making it more fluidly readable.

I actually think that Jasiek's writing style would benefit a lot from additional mathematical training. Introducing just a sprinkle of symbolic notation in the right places might make his definitions and arguments more concise and clear.

Also...

When I say that the complexity of Jasiek's ko paper is no more than that of Elements, I am saying the arguments in both would look similarly complex if we removed the parts relevant to giving the arguments meaning and left only the parts necessary for making logical inferences. What is meant by this?

Consider the following paragraph: All swans are white. Any animal that can produce viable offspring by mating with a swan is also a swan. Ann the Swan at the local zoo is a swan. Bob the Bird at the local zoo mated with Ann the Swan and produced viable offspring. Therefore Bob the Bird is a swan and is white.

Now try to ignore the meaning of those sentences and look at isolate the parts that are relevant to the argumentation by replacing some terms (here's one crude approximation): Any object x that has property S also has property W. For any objects x and y, if object y has property S and the pair (x,y) taken together has property PVO, then x has property S. Specific object A has property S. The pair (A,B) taken together has property PVO, where B is a specific object. Therefore B has properties S and W.

These statements have no discernible meaning, but their logical structure and correctness are the same as those in the plain English version from which they were constructed.

A small but not insignificant part of the reason that Elements is easier to read than Jasiek's ko paper is that most people already have some familiarity with and intuition about the many objects and properties (line, point, angle, circle, parallel, etc.) that are defined in the former (in the same way we are familiar with swans, mating, offspring and white) whereas we have very little familiarity with the objects and properties being described in the latter. This is nothing that cannot be overcome with some patience and time.

Lastly...

I'm not saying that Jasiek's paper is correct. I'd have read it carefully to say that (and like most people, ko rule theory isn't something that interests me). However, if we're just talking about it's complexity, then I only need to scan its syntactical structure, which can be done fairly quickly.

Now...

I believe y'all were discussing something far more interesting than this ko paper.

PS: The bit-width thing was ridiculous... Some people started posting moves by their coordinates in their Malkovitch games (instead of entire diagrams), presumably to save bits. This shows that people trust the admins quite a bit. That trust might have been slightly compromised.

lemmata wrote:PS: The bit-width thing was ridiculous... Some people started posting moves by their coordinates in their Malkovitch games (instead of entire diagrams), presumably to save bits. This shows that people trust the admins quite a bit. That trust might have been slightly compromised.

I am the guilty one. my work computer was taken away and my android is only source of internet. and it is not easy posting entire diagrams with android.

Actually, people post coordinates in Malkovich games because they are posting from mobile phones, or from work.

So I believe Euclid prove nearly 500 propositions with 140 definitions, none of which contain any previously undefined term more complicated than "greater than". The first and best known book is 23 definitions and 48 propositions, including the Pythagorean theorem.

RJ's ko paper contains 36 defined terms, of which 5 are actually "defined elsewhere". Of these some are not felicitous (e.g., "prevent" is defined as "force to fulfil not"), some depend in unfortunate ways on undefined terms ("basic-ko-intersection" is defined as "the intersection of a basic-ko": perfectly intuitive and perfectly useless, given that basic-ko is defined elsewhere and intersection is undefined... presumably he means set-theoretic intersection, but how would one know?)

Now, how many propositions about ko are proved using these 36 definitions?

Magicwand wrote:

lemmata wrote:PS: The bit-width thing was ridiculous... Some people started posting moves by their coordinates in their Malkovitch games (instead of entire diagrams), presumably to save bits. This shows that people trust the admins quite a bit. That trust might have been slightly compromised.

I am the guilty one. my work computer was taken away and my android is only source of internet. and it is not easy posting entire diagrams with android.

I see. I guess you didn't fall for it then.

I don't know if you saw the bit-width thing, but you should go check it out. Jasiek's user name (and only his) was shortened by the admins (an admin?). That was a particularly passive-aggressive action on the part of the admins to infringe upon a forum member's dignity. Of course, it might be said that Jasiek was damaging his own dignity without the admins' help, but doing so should be his right (and not the admins').

jts wrote:Actually, people post coordinates in Malkovich games because they are posting from mobile phones, or from work.

So I believe Euclid prove nearly 500 propositions with 140 definitions, none of which contain any previously undefined term more complicated than "greater than". The first and best known book is 23 definitions and 48 propositions, including the Pythagorean theorem.

RJ's ko paper contains 36 defined terms, of which 5 are actually "defined elsewhere". Of these some are not felicitous (e.g., "prevent" is defined as "force to fulfil not"), some depend in unfortunate ways on undefined terms ("basic-ko-intersection" is defined as "the intersection of a basic-ko": perfectly intuitive and perfectly useless, given that basic-ko is defined elsewhere and intersection is undefined... presumably he means set-theoretic intersection, but how would one know?)

Now, how many propositions about ko are proved using these 36 definitions?

You are missing my point, which was about the level of cognitive ability necessary to make sense of the arguments with time and patience, and not about their efficiency.

Also, do you realize that you are complaining that Jasiek's work isn't half as elegant and efficient as Euclid's? Why are you holding Jasiek to what is probably the ultimate (and impossible) standard?

Finally, we frequently talk about placing stones on intersections of lines on the go board. That seems to be the obvious interpretation here, and not the set-theoretic one. Also, when you complain of basic-ko being defined elsewhere, I think you should consider the hypothesis that the target audience for this document already knows what is meant by a basic-ko as Jasiek uses it. You might rightfully complain that not providing a link to where the definition may be found is a bit sloppy, but that's about it (EDIT: He does provide his e-mail in the document, so there is implied possibility of asking the author directly). You would be surprised how often this happens even in published mathematics articles if the definitions are familiar enough to the target audience. Sometimes a paper might contain a term which is defined in two slightly different ways in the literature and the author assumes that you know the one he's talking about, much to the reader's chagrin. This is obviously bad practice, so I am not defending the practice itself. However, I do think that it is harsh to lash out at Jasiek for the kind of incompleteness of presentation that even professional mathematicians are guilty of...especially when he likely wasn't aiming to achieve the standard of peer-reviewed mathematics when sharing that document online. EDIT: I also would give him credit for acknowledging that those definitions are not in the document proper at the beginning. That's more than I would have expected of a layman.

jts wrote:How many definitions are there in Elements, and how many of them contain technical terms that are left undefined?

jts wrote:So I believe Euclid prove nearly 500 propositions with 140 definitions, none of which contain any previously undefined term more complicated than "greater than". The first and best known book is 23 definitions and 48 propositions, including the Pythagorean theorem.

I missed this earlier, but it's not nice to ask questions that you already know the answers to... It makes people paranoid. If you were trying to make a point rhetorically, why not just make it directly, like you did later?