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Old 7th April 2017, 03:51 PM
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Darwinsbulldog Darwinsbulldog is offline
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Default The Sudoku universe as a "model' for the real one. [Warning, puppy woo!]

Well, not a model exactly, but an analogy. I am not trying to prove nothing, just speculating really.

Ok, now that is understood. The Sudoku universe has some rules, analogous to the physical laws of the universe in a rough way. There are several versions of the game, where we have numbers, letters or symbols and a matrix of various sizes.

For the moment I want to concentrate on the 81 square matrix, and for convenience, just use numbers. [The numbers are symbols for physical laws: gravity, weak force, strong force etc]. I am not saying that they are real forces, just constants in the universe.

OK, so now the rules.

1. The numbers [constants] are from 1 to 9.

2. Every nine square box must contain only 1 to 9, no repeats and none missing from the set [1-9].

3. Every row [of the 81 box matrix] must contain the numbers 1-9

4. Every column [of the 81 box matrix] must contain the numbers 1-9.

As far as I know, the minimum known numbers to solve any puzzle is at least 26. 26/81 is roughly 32%

So one can obtain all the positions and numbers to solve the puzzle via logic if your data on the constants is 32% or better.

Putting it another way, one can obtain a posteriori omniscience in each game using the evidence supplied and applying logic.

The number of combinations? 81! [factorial] I think, but I am prepared to be corrected.

So, theoretically, a society could obtain omniscience of the Sudoku universe provided we played all the variations.

The other interesting fact is that there are many possible universes in Sudoku-land that don't violate the rules. Eighty-one factorial, if my guess is correct. Anyway, a shit-load.

Seems to me, at least, that there could be many ways a viable universe could be "put together", using a number of rules and constants. This suggests to me that a real multiverse is possible. In other words, many universes, all self-consistent within themselves, but incompatible and compartmentalised from each other. [The Sudoku "boxes" representing geometry which separates the universes from each other.]

it seems likely that observers in each universe [should they exist] would be unable to contact or detect any other universe, unless there happened to be very similar universes adjacent to each other, but perhaps not even then. It depends what the rules are of course, but if they were Sudoku-like in any way, they would tend to be mutually exclusive.

Thoughts?

And I prefer you not to knit-pick*, just talk about any MAJOR glitches. And remember, we are talking about in imaginary universe, not the real one. Of course I want to make it as real as possible, but not yet.

I want to know if my notions are basically on-track

* Of course, nit-pick away, and am not ordering you to do or not do nuffing. But I would prefer constructive criticism, ie, try to help me make the model work.
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Old 7th April 2017, 05:11 PM
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Default Re: The Sudoku universe as a "model' for the real one. [Warning, puppy woo!]

Well 81! is definitely wrong... that would be the number of ways of arranging 81 different symbols in a sudoku grid.
Apparently the real solution is
6,670,903,752,021,072,936,960
http://stackoverflow.com/questions/7...sudoku-puzzles

Although any solution to that problem is probably going to depend on whether you regard puzzles as the same if one can be obtained from another simply by swapping some of the symbols... e.g. if you take a valid puzzle and replace all the 1s with 9s and all the 9s with 1s the logic to solve it is exactly the same - is that the same puzzle? Depends on your point of view.

Anyway, the model is fun and I don't really have any nits to pick as long as the analogy doesn't get stretched too far. But at the risk of doing just that, may I invite you to consider an extension to it. Imagine a self-aware entity that exists in just one column of a Sudoku puzzle. It can explore it's own column, and discover in what order the 9 numbers appear, but would be incapable of identifying that the reason for that arrangement is due to constraints imposed in dimensions that it is just not aware of. And even if somehow this entity somehow could postulate the existence of the 8 other columns, it might still be totally incapable of identifying what overall puzzle it's column forms part of, or even which column it is existing in.
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Old 7th April 2017, 05:43 PM
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Default Re: The Sudoku universe as a "model' for the real one. [Warning, puppy woo!]

I've often thought of Sudoko as a way to demonstrate how knowledge of one piece of information can prove or disprove assumptions in a different area, but my approach was 'smaller'.
Consider the central 3x3 grid, (let's call it the local area). If we know the complete solution for this area, we have direct information about vertically and horizontally adjacent 3x3 blocks. We know something of what can't be possibe in some of those squares. But we know nothing about diagonal blocks.
But if we can somehow determine a value in the horizontal or vertical plane, we can extrapolate that to the diagonals.
What happens when the knowledge of our own local area is incomplete, but we have information about other blocks, much like a real Suduko puzzle? We can develop theories on what values go in certain squares, and as long as there is no contradiction, the theory holds, as soon as we find a contradiction, the theory is discarded.
Also, the only block really bound by this Suduko is the 'Local Area' centre block. All blocks on the edges can be part of totally different Sudukos, even though their own values remain the same.

To complicate things a little, I'm pretty sure 3x3 is a limitaion we put on ourselves, 4x4, 5x5, 1000x1000 Sudukos are surely possible?
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Old 7th April 2017, 06:10 PM
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Default Re: The Sudoku universe as a "model' for the real one. [Warning, puppy woo!]

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Svadifari said View Post
To complicate things a little, I'm pretty sure 3x3 is a limitaion we put on ourselves, 4x4, 5x5, 1000x1000 Sudukos are surely possible?
Yes... 4x4 puzzles at least are available recreationally. There are all manner of other variations too, like interlocking grids (e.g. where the bottom left set of 9 cells of one puzzle form the top right 9 of another) or with additional constraints layered over the top.
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Old 7th April 2017, 08:28 PM
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Default Re: The Sudoku universe as a "model' for the real one. [Warning, puppy woo!]

Quote:
virphen said View Post
Well 81! is definitely wrong... that would be the number of ways of arranging 81 different symbols in a sudoku grid.
Apparently the real solution is
6,670,903,752,021,072,936,960
http://stackoverflow.com/questions/7...sudoku-puzzles

Although any solution to that problem is probably going to depend on whether you regard puzzles as the same if one can be obtained from another simply by swapping some of the symbols... e.g. if you take a valid puzzle and replace all the 1s with 9s and all the 9s with 1s the logic to solve it is exactly the same - is that the same puzzle? Depends on your point of view.

Anyway, the model is fun and I don't really have any nits to pick as long as the analogy doesn't get stretched too far. But at the risk of doing just that, may I invite you to consider an extension to it. Imagine a self-aware entity that exists in just one column of a Sudoku puzzle. It can explore it's own column, and discover in what order the 9 numbers appear, but would be incapable of identifying that the reason for that arrangement is due to constraints imposed in dimensions that it is just not aware of. And even if somehow this entity somehow could postulate the existence of the 8 other columns, it might still be totally incapable of identifying what overall puzzle it's column forms part of, or even which column it is existing in.
Is that all-small number of combos! :-) ? No wonder the puppy can find Sudoku solutions!
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Old 7th April 2017, 08:31 PM
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Default Re: The Sudoku universe as a "model' for the real one. [Warning, puppy woo!]

Quote:
Svadifari said View Post
I've often thought of Sudoko as a way to demonstrate how knowledge of one piece of information can prove or disprove assumptions in a different area, but my approach was 'smaller'.
Consider the central 3x3 grid, (let's call it the local area). If we know the complete solution for this area, we have direct information about vertically and horizontally adjacent 3x3 blocks. We know something of what can't be possibe in some of those squares. But we know nothing about diagonal blocks.
But if we can somehow determine a value in the horizontal or vertical plane, we can extrapolate that to the diagonals.
What happens when the knowledge of our own local area is incomplete, but we have information about other blocks, much like a real Suduko puzzle? We can develop theories on what values go in certain squares, and as long as there is no contradiction, the theory holds, as soon as we find a contradiction, the theory is discarded.
Also, the only block really bound by this Suduko is the 'Local Area' centre block. All blocks on the edges can be part of totally different Sudukos, even though their own values remain the same.

To complicate things a little, I'm pretty sure 3x3 is a limitation we put on ourselves, 4x4, 5x5, 1000x1000 Sudukos are surely possible?

Sure, I only did the ( 9x9 =81 squares) as an example.

As for the values, we can play with them as we wish. Make the speed of light a half or twice the "real" value or whatever. Make gravity, stronger, weaker etc......
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Old 8th April 2017, 07:39 PM
wadaye wadaye is online now
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Default Re: The Sudoku universe as a "model' for the real one. [Warning, puppy woo!]

I just reduce it to a binary choice in any one square and from there its simply a matter of following each choice pathway and the one which doesn't work disappears leaving the other choice as the correct one, ignoring errors
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Old 8th April 2017, 08:03 PM
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Default Re: The Sudoku universe as a "model' for the real one. [Warning, puppy woo!]

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wadaye said View Post
I just reduce it to a binary choice in any one square and from there its simply a matter of following each choice pathway and the one which doesn't work disappears leaving the other choice as the correct one, ignoring errors
Would't that universe be a bit too simple?
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Old 8th April 2017, 10:09 PM
wadaye wadaye is online now
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Default Re: The Sudoku universe as a "model' for the real one. [Warning, puppy woo!]

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Darwinsbulldog said View Post
Quote:
wadaye said View Post
I just reduce it to a binary choice in any one square and from there its simply a matter of following each choice pathway and the one which doesn't work disappears leaving the other choice as the correct one, ignoring errors
Would't that universe be a bit too simple?
Sudoku is probabaly vlike protein combinations, and a very simple one at that. Think of a 9 base set in three dimensions of minor boxes, horizintal and vertical.
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Old 9th April 2017, 11:08 AM
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Default Re: The Sudoku universe as a "model' for the real one. [Warning, puppy woo!]

Of course, we are playing the role of a god-like observer that can see the whole universe, and are able to fill in any gaps with a priori values and the rules.
Knowing just one of the 3 X 3 boxes in the greater (9x9) multiverse is more like the real case, but we get peeks of all nine (3X3) boxes in the Sudoku games.

Of course, in the real universe, we do not know all the rules [eg quantum gravity] and we only know of the single universe, and are ignorant of any others [if they exist].

Perhaps there is some quantum entanglement phenomenon or something else, too subtle for us to know yet, that would help us to know the values in the other boxes. Would the rules be universal though, as in Sudoku?

The inflationary idea, which is basically a phase change, is accepted, but really it is only a deux ex-machina technique to get around the speed of light limit.

What other phases of reality are there? [Assuming inflation is actually real, and not a misunderstanding of some process we are not yet aware of].

IMHO, the universe MUST make sense, even if we do not yet know the logic behind it all. If there is a multiverse, then the "bridges" between them, and perhaps the creative power behind it all, must be at the quantum level.

Because at the macro-level, eg 'worm-holes" doesn't seem to have enough explanatory power. In other words, one goes through one universe into another via a worm hole, but all you get is that int he new universe, everything is time reversed. You go into the worm hole, and emerge through an expanding singularity on the other side[I am ignoring "spaggettisation", of course].

That contradicts my notion of what a multiverse would look like, because, if the multiverse exists, it will be a sort of dynamic, foamy place. Universes being born, growing old and dying. The most logical [self-compatible universes last the longest, and the illogical ones are still-born. or so I imagine.

Of course, this is all puppy-poo, but to me the universe must have been thorough a process of natural selection of some type. In the absense of a creator, there must be a creative process. Some way of cycling through possible universes, and the most logical universes surviving long enough for life to emerge. Something of that kind is the only type of naturalistic explanation possible, IMHO.

Shitty though it is, it is far better than any magical, creator-god set up that makes even less sense.
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