The Shannon number

What is the basis for reason? And mathematics?

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Walker
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The Shannon number

Post by Walker » Thu Mar 22, 2018 4:23 am


wtf
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Re: The Shannon number

Post by wtf » Thu Mar 22, 2018 7:12 am

Walker wrote:
Thu Mar 22, 2018 4:23 am
It hardly seems possible.
I'll see your Shannon number and raise you Skewes's number.

Atla
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Re: The Shannon number

Post by Atla » Thu Mar 22, 2018 7:25 am

Can I play? I guess the next one in the line is Graham's number

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Arising_uk
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Re: The Shannon number

Post by Arising_uk » Thu Mar 22, 2018 2:57 pm

Walker wrote:
Thu Mar 22, 2018 4:23 am
It hardly seems possible.

https://en.wikipedia.org/wiki/Shannon_number
Except it was brute force search that beat the GM's?

Walker
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Re: The Shannon number

Post by Walker » Fri Mar 23, 2018 5:47 am

Arising_uk wrote:
Thu Mar 22, 2018 2:57 pm
Walker wrote:
Thu Mar 22, 2018 4:23 am
It hardly seems possible.

https://en.wikipedia.org/wiki/Shannon_number
Except it was brute force search that beat the GM's?
That implies that a super computer can tag every atom in the observable universe, but not necessarily win a chess game against a GM from the unobservable universe. Not yet. And considering night light-pollution, just how extensive were Shannon's powers of observation?

Walker
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Re: The Shannon number

Post by Walker » Fri Mar 23, 2018 5:58 am

Atla wrote:
Thu Mar 22, 2018 7:25 am
Can I play? I guess the next one in the line is Graham's number
“But even the number of digits in this digital representation of Graham's number would itself be a number so large that its digital representation cannot be represented in the observable universe.”

I think this means that if you write out the number then the number itself would take up all the available space in the universe, but maybe I’m just boggled.

Atla
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Re: The Shannon number

Post by Atla » Fri Mar 23, 2018 6:42 am

Walker wrote:
Fri Mar 23, 2018 5:58 am
“But even the number of digits in this digital representation of Graham's number would itself be a number so large that its digital representation cannot be represented in the observable universe.”

I think this means that if you write out the number then the number itself would take up all the available space in the universe, but maybe I’m just boggled.
Yeah something like that. And so if someone could accurately imagine Graham's number, that person's head would immediately collapse into a black hole. :)

As far as I know the last famous number is the tree(3) number. (There are even bigger numbers people have come up with of course, but they are too artificial imo.)
Graham's number is really pathetically small compared to tree(3). So even if we had a Graham's number of people, and we would split tree(3) equally between them, each of them capable of imagining just that tiny little fraction of tree(3), they would still all of them have their heads collapsed into black holes (ok this is a very stupid and meaningless comparison). :)

Impenitent
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Re: The Shannon number

Post by Impenitent » Fri Mar 23, 2018 11:59 am

the number of crackers in a box is not that daunting

-Imp

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Arising_uk
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Re: The Shannon number

Post by Arising_uk » Fri Mar 23, 2018 3:32 pm

Walker wrote:That implies that a super computer can tag every atom in the observable universe, but not necessarily win a chess game against a GM from the unobservable universe. Not yet. And considering night light-pollution, just how extensive were Shannon's powers of observation?
No idea what you are talking about but the computers that beat GM's did use brute force calculation so Shannon appears to be wrong in this respect.

Walker
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Re: The Shannon number

Post by Walker » Fri Mar 23, 2018 7:24 pm

Arising_uk wrote:
Fri Mar 23, 2018 3:32 pm
Walker wrote:That implies that a super computer can tag every atom in the observable universe, but not necessarily win a chess game against a GM from the unobservable universe. Not yet. And considering night light-pollution, just how extensive were Shannon's powers of observation?
No idea what you are talking about ...
That means you’ve comprehended all you need to know, which is perhaps a safety valve to keep your head from collapsing into a black hole.

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Arising_uk
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Re: The Shannon number

Post by Arising_uk » Fri Mar 23, 2018 7:34 pm

And this relates to the claim that Shannon's number meant computers won't beat GM's by brute force with the fact that they have beaten them by brute force how?

Walker
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Re: The Shannon number

Post by Walker » Fri Mar 23, 2018 8:01 pm

Arising_uk wrote:
Fri Mar 23, 2018 7:34 pm
And this relates to the claim that Shannon's number meant computers won't beat GM's by brute force with the fact that they have beaten them by brute force how?
:D

Well, I was headed down the philosophical road of an example of conscious energy being a lightning bolt that follows the choiceless path that it knows it must follow, given the conditions at the moment its existence crosses the line from potentiality to manifestation, which is the instant when thought becomes action and decision tags along saying, hey, I did that.

However, brute force.

Brute force references the raw number crunching power to calculate all the possible permutations of a move.

Shannon proved that there are more moves than atoms in the observable universe, which is a lot.

However, his powers of observation are limited. He had a planet under his feet blocking a chunk of the universe, not to mention the fog of night light-pollution around metro areas of Michigan and the Northeast corridor from MIT in Boston to DC, and beyond.

So, it’s possible that there’s a chess move out there beyond the observable universe that some GM has cooked up to collapse Big Blue into a black hole.

I know, I know. We’re talking abstract numbers, I’m struggling with humour, but blame Shannon. He introduced “observable,” with all its assumptions. Or maybe just Wiki did that.

Atla
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Re: The Shannon number

Post by Atla » Fri Mar 23, 2018 8:12 pm

A perfect database and brute force are two totally different things.

Btw Super GMs might still score a few draws against engines every now and then, in a few openings where most pieces get traded in the first few moves, but otherwise they can't do shit and always lose. Top GMs have like 2750-2850 ELO, engines have like 3300. Alpha Zero probably even more.

Walker
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Re: The Shannon number

Post by Walker » Fri Mar 23, 2018 8:52 pm

A perfect database and brute force are two totally different things.
Money is being placed elsewhere: NSA, Facebook, et al.

Btw Super GMs … check

might still score a few draws … check

against engines … uh, check

every now and then, … check

in a few openings … check

where most pieces get traded in the first few moves,… I’ve been teaching a grandkid how to play with another younger one hanging around and watching, and I’ve found the best way to teach a kid is to refrain from capturing their pieces. The light dawns brighter when the child sees the capture and makes the decision, and with more pieces there’s more practice for basic footwork. We’ve played about five slow games that took a long time. Good progress.

but otherwise they can't do shit and always lose. … check

Top GMs … check

have like 2750-2850 ELO, … lost *

engines have like 3300... lost

Alpha Zero probably even more ... lost

But that’s okay, considering the chance of implosion.

* could be chess rankings for tournament players.

1x0
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Re: The Shannon number

Post by 1x0 » Sat Mar 24, 2018 7:30 pm

I wonder if we would use mathematics 4D instead of 2D could the expression be easier.

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