Chess will never be solved, here's why

Stand in the corner.

The Shannon number is not and never was intended to represent the number of all possible games. Not even under competition rules (it's obviously infinite under basic rules).

But with far less frequency in FIDE competition rules chess and ICCF chess if you count a position as reappearing only if the possible forward play is the same in both cases.

And where on Earth does 10^120 come from?

When you're trying to be clever it's better to get things right.

I didn't think I'd been asked again after the first time I gave my reason. Essentially, Cantor is positing the existence of finite numbers with special properties, in that they are finite but also infinite.

No. The DEFINITION of the adjective INFINITE is "NOT FINITE". This logically precludes any number from being both finite and infinite.

You need to first get enough understanding to avoid making obviously nonsensical statements.

I didn't think I'd been asked again after the first time I gave my reason. Essentially, Cantor is positing the existence of finite numbers with special properties, in that they are finite but also infinite. His mistake is that they are unknown finite numbers, since the series of infinite numbers is endless. It has a beginning but no end. If we choose to include negative numbers in the infinite series, again there is ambiguity, since we can choose to begin the series at zero.

Hence there are finite numbers within the infinite series which are unknown. He has chosen to call them "transfinite numbers" since they would be defined as any finite number outside the series of known finite numbers. Known finite numbers are considered to be normal (in that they have been used in calculations or whatever .... not a very good reason) and unknown ones are ambiguous and hence trans-finite. It's rather similar to Schroedinger's cat. Schroedinger originally invented the idea of a cat which is not known to be either alive or dead as a joke, intended to discredit speculation regarding superpositioning or ambiguously live states and dead states in the kind of primitive or childish interpretations of quantum theory which had started to become current. However, such interpretations have tended to gain currency, not because they have any merit, except that they appeal to some kinds of speculative creativity.

Cantor was merely using his imagination and attempting to demonstrate numerical hypothetical series. He was considered by many to be insane and ideed he did become certifiably insane. Also his ideas have absolutely no real use or no use in reality.

I'm very used to Elroch and others like him, trying to impose their will on the thoughts of various people here. I have no doubt that he will tell me that I'm wrong and that I don't understand a, b, c, and/or d. That kind of speculative dismissal is meaningless. Elroch habitually supports whatever he wishes to support and is usually unable to give coherent arguments. His qualification is in statistics and this is pure mathematics. You can make a set of anything, including of bananas, but someone who understands set theory is not an expert on bananas because of that.

Whether 10^120 is the exact number is not really important...what's important is the distinction between 10^44 unique positions and the (much) larger set of possible games, and whether Tygxc is properly applying his reductions or not. Not to say he isn't, but his cut and paste explanation that we've all seen several dozen times is not doing the job.

10^120 is a rough estimate of the game tree complexity. The wiki article gives 10^123.
When the game tree is a tree without considering the history of a move and when the leaf positions are unique, the game tree complexity is similar to the state space complexity (number of positions).

<<<No. The DEFINITION of the adjective INFINITE is "NOT FINITE">>>

Thinking that giving a definition of infinite makes your case is nothing more than an admission of your lack of ability.

If you were referring to the game tree complexity why did you call it the number of games?

You are entirely right that the two numbers are distinct in chess and I was wrong to conflate them. Thanks for drawing attention to this.

In games where there are no irreversible moves and no transpositions, the number of legal games is the number of leaf nodes. For example hex. These are the games where the idea that weak solution has the square root of the size of a strong solution makes best sense. But even here the game tree complexity is not the same as the number of leaf nodes, as I understand the definition.

I don't have access to the link you provide.

I linked it incorrectly, it seems. Here it is.

And the number for chess is later in the article, here.

Can you sketch an argument for why the game tree complexity would be 10^123 (presumably for basic rules chess since you quote 10^44 as the number of positions and that can only be understandable, if some way adrift, for basic rules chess). It could certainly be relevant to the thread.

I merely quoted the value from the article, having seen others previously. To me it cannot make sense for basic rules chess, since a tablebase has complexity ~10^44 and that strong solves the game. 

I think you missunderstand a few key details. I dont know what you mean with finite but infinite numbers. As for negative numbers its just a question of how we order them.

1= 1/1,

2 = 1/2 × -1,

3 = 1/2,

4 = 1/2 × -1,

5 = 2/1,

6 = 2/1 × -1

Do we agree that list contain all rational numbers, and that the list is infinitly large?

Now do we agree that at one point you come to number x = 3,14, and then later y = 3,15

Now you alternate between adding to this list, and a second list that contain all the real numbers. All the numbers of the first list will be on the second list so that x = 3,14 still on both lists. But when we come to y =3,15 on the first list the number pi will be on the second list so that on the second list y + 1 = 3,15

In this example there is no finite but infinite numbers. The list includes negative numbers. Both list are infinite, but one list is larger.

If all this is true then not all infinites are the same size.

<<<No. The DEFINITION of the adjective INFINITE is "NOT FINITE">>>

Thinking that giving a definition of infinite makes your case is nothing more than an admission of your lack of ability.

At the same time you define finite as not infinite.

Sometimes finite numbers are infinite they can overlap.

When there is infinite finite numbers (like let's say speed increases infinitely but the speed it is traveling is finite)

No you are wrong. Infinite is not a number, its a size.never said it was a number I just meant that finite numbers can exponentially increase infinitly 

Your example would then be: the list of all numbers is infinite, but every number on that line is finite.

Well you are correct, but you are talking about 2 different things.yes but I was trying to explain how they overlap ...

My position is that you are calling irrational numbers infinite numbers. An irrational number cannot be expressed as a simple ratio.

All I have been doing is having looked at the mapping plan regarding transfinite numbers, I understood that the plan was in effect an explanation rather than being the proof which it is held to be by some. I then looked up irrational numbers from several sources and all sources agree that many mathematicians disagree with Cantor. I then found that Cantor had literally gone mad, which can happen when a person invests himself in an untenable position and then finds it to be incorrect. All in all I am perfectly justified in assuming that Cantor was wrong to assume that irrational numbers can be held to exist, *as transfinite numbers* if they cannot be expressed as any series of digits.