Conway's Life, seebs

[Michali]

Conway's Life is a system where every state generates a fully deterministic next state. Its a grid of cells, each with values that change value depending upon the value of the cells adjacent to it. Sometimes stabilization occurs from an initial state, and sometimes it will never occur and the entire system (I'm guessing, will either oscillate or never repeat a prior state... not sure.) Because information can be lost, we cannot determine all past states from any usual future or end state.

When seebs mentioned this to me as a way to show how systems do not always exhibit retraceability since not all systems retain all their information, I realized something must be missing. The universe is meant to incorporate literally everything, and once again, I thought there might be lost factors going into play with these systems. I blamed it on the fact that what we were watching was the result of rules that the universe would ultimately causally play out, and that the system was dependant on them. When this was confusing, I spoke about an intuition I had regarding that there didn't seem to be a good reflection of "time" going on in this system, and I think I'm able to elaborate on what I mean now:

If its a rule, lets say:

((there is a grid of nine cells and a blue cell in the middle of (and surrounded by) grey cells will result in it turning grey))

Then I believe that we are inclined to believe that the first generation of the grid has one blue cell, and the second has no blue cells. I disagree, here, and I believe that because there is no possible way to interfere with this system (there is only 9 cells in the grid)...

there is no such thing as a blue cell in the center even though we can watch the generations on a simulation show a blue cell. In terms of the system (I know I need to better explain this) the apprent blue cell is actually a grey cell.

This is like:

-3+6-3=0=3x-4+12

This is just a complicated, but valid, way of signifying 0. Therefore, causality is not being shown here generation to generation, because there is really only one generation in Conway's life. The input state is the output state just like 3+-3 is 0.

[Farren]

That doesn't really make sense.

The state of the grid in Conway's game of life is not an arbitrary scalar derivative of its parts.

[seebs]

Er, no.

There are multiple states. They are distinct. We can usefully talk about these distinctions, because multiple start states could lead to a single result state. Thus, even if two states lead to the same state later, they were different previously.

Michali, the simple fact is, not everything is reversible. Trying to define the counterexamples away by claiming they aren't systems is crazy. When we say the universe "includes everything", that doesn't mean that any given single-time snapshot of it contains enough information to describe accurately all previous states.

You're begging the question something fierce, and I don't see why.

The input state is not the output state. They're different. We can show these differences in many ways, but the obvious starting point would be observing that multiple input states can yield the same output state.

[Michali]

Originally Posted by seebs

Er, no.

There are multiple states. They are distinct. We can usefully talk about these distinctions, because multiple start states could lead to a single result state. Thus, even if two states lead to the same state later, they were different previously.

Michali, the simple fact is, not everything is reversible. Trying to define the counterexamples away by claiming they aren't systems is crazy. When we say the universe "includes everything", that doesn't mean that any given single-time snapshot of it contains enough information to describe accurately all previous states.

You're begging the question something fierce, and I don't see why.

The input state is not the output state. They're different. We can show these differences in many ways, but the obvious starting point would be observing that multiple input states can yield the same output state.

Do you consider the input "state" to be a generation of the system?

-edit- also what I'm saying is all of those different input states that end up with the same end state are equal relative to the system... otherwise they aren't "states" at all. They are "states" relative to the system, because if there is no system in consideration, its just a grid of colors.

[Michali]

Originally Posted by Farren

That doesn't really make sense.

The state of the grid in Conway's game of life is not an arbitrary scalar derivative of its parts.

I am interested in what your saying, but can you explain what you mean?

[ceptimus]

If I can show you two different start positions that lead to exactly the same final position, will that invalidate your argument?

[Iacchus]

Notwithstanding that everything has its own trajectory?

[Michali]

Originally Posted by ceptimus

If I can show you two different start positions that lead to exactly the same final position, will that invalidate your argument?

No, see, that's the point. The suggestion your giving now was originally supposed to invalidate another argument I had, but what I'm trying to say is, those two "starting positions" are equal with respect to the system. This "Conway's Life" "system" is just a very complicated math problem, and not necessarily reflective causality. The "causal processes" we think we watch are just efficient calculations on the part of a problem solving computer or person.

The "initial state" that we plot is analogous to just randomly writting a math problem like "2X2-2+4/6"
The "end state" is analogous to whatever answer you work out "1".

This isn't causality, this is something like entailment (dealing with "if, then" conditional relationships). There is something about causality which occurs over time which is different than this. We say one thing causes another. So there are atleast two things involved in causality. This entailment relationship between states in Conways life, and mathematical problems and their solution deals with only one thing (the product of reasoning processes).

[Farren]

Originally Posted by Michali

I am interested in what your saying, but can you explain what you mean?

Basically what seebs said. There are multiple states. They are not the same.

[Michali]

Originally Posted by Farren

Basically what seebs said. There are multiple states. They are not the same.

Right, but like I said. They are equivalent.

[Farren]

Originally Posted by Michali

Right, but like I said. They are equivalent.

How? Its not apparent in your original post

[Michali]

Originally Posted by Farren

How? Its not apparent in your original post

read post 4 and post 8

[ceptimus]

But (in Life) we could run two grids side by side. One could be full of gliders - lots of action - and then eventually settle down to a static pattern. The second grid could just be that static pattern from the start. Are you really claiming that these two 'Life universes' are equivalent?

[Michali]

Originally Posted by ceptimus

But (in Life) we could run two grids side by side. One could be full of gliders - lots of action - and then eventually settle down to a static pattern. The second grid could just be that static pattern from the start. Are you really claiming that these two 'Life universes' are equivalent?

Yes, but they are equivalent in all respects to the Conway's life system. That we can see a more complicated version of one (non stable) is dependent on the fact that we have the ability to pause and suspend the rules.

Thus a blue square in the center of grey squares simply hasn't been figured out yet to actually be a grey square. Its suspended because the interactions of a large grid have an extremely complicated total solution. But, for instance, a grid as large as the rule itself, like the (grid of 9 squares one in the middle is blue) is another way of saying what it equals, not what happens next. It only matters "what happens next" if what happens next is some sort of interference such that it is no longer surrounded by grey squares. But because the entire grid is just these nine squares, no glider or anything is going to interfere.

Essentially what it boils down to is you could right a rule for the entire initial state of the grid, and that rule would be consistent with every rule of Conway's life.

[fragment]

Thus a blue square in the center of grey squares simply hasn't been figured out yet to actually be a grey square

Why do you say it's actually a gray square? If the two states are entirely equivalent, as you argue, what grounds do you have for preferring one over the other as the actual state?

[seebs]

Originally Posted by Michali

Right, but like I said. They are equivalent.

No, they're not. They're different. They lead to equivalent things.

Basically, your argument seems to be this:

Part 1:
Premise: All deterministic systems are reversible.
Conclusion: Given the final state of a deterministic system, all of its prior states can be deduced.

Part 2:
Observation: In Conway's life, you cannot deduce the earlier states of a game.
Conclusion: The earlier states must not exist, because they contradict the premise.

But they do exist, and the causality and generations exist and work just fine, and it's a system which is not reversible.

We're done here. There are irreversible systems. Move on.

[Michali]

I'm going to have to addrees your post in splices.

Originally Posted by seebs

No, they're not. They're different. They lead to equivalent things.

4+4 is equivalent to 8. It may not be identical, so I'll give you that. This lack of identity I don't understand, and I think it has to do with some potential reference to difference in the compositional parts. I'm going to say they are logically equivalent, and for all purposes, (4+4) may as well be identical to 8.

Originally Posted by seebs

Basically, your argument seems to be this:

Part 1:
Premise: All deterministic systems are reversible.
Conclusion: Given the final state of a deterministic system, all of its prior states can be deduced.

Not quite, its become now:

(assuming stable end states can be taken broadly in finite systems)
Premise: All deterministic systems have a definite end state.
Conclusion: Given an unstable state of a deterministic system, that system must ultimately give rise to its end state.

This conclusion is not just "the universe will end" but its that "this universe is because of its end".

In other words, either

Case 1: Conway's Life applies, and causality is like mathematical entailment, in which case, the universe as it is now is just an unstable, not-perceived-correctly, end state.

Or

Case 2: Causality is understood in the normal conservation of energy manner, and we could reverse it conceivably by working backwards from the end state. We might conclude that the disbursal of energy happened in such a way that it was because of the way it would end up, essentially. Or in other words, the end state is the reason for the entire causal chain. This seems similair to Case 1, for some reason.

I am inclined to say the end state is the reason for the universe as we see it.
I'm going to suspend that for now. What I mean to address is that Conway's life, and probably some other relevant examples, are not going to knock down the first premise you claimed I was making.

Originally Posted by seebs

Part 2:
Observation: In Conway's life, you cannot deduce the earlier states of a game.
Conclusion: The earlier states must not exist, because they contradict the premise.

But they do exist, and the causality and generations exist and work just fine, and it's a system which is not reversible.

We're done here. There are irreversible systems. Move on.

That was not my reasoning though. My reasoning was that your saying not all systems are reversible led me to believe that the causal processes of the physical simulator was ultimately to blame for appearance of generation to generation "states". Conway's life is like a cryptic message, a code for understanding it, and then understanding the actual message. You could understand it slowly, or if you understood the language that it was written in, you could understand it right away. Likewise, you could watch small local laws play out on one another for the end state, or you could calculate a law for the entire grid and the moment you run the simulator, it would show the end state. Either way, your not dealing with a necessary time component (cause and then effect) in this simulator.

I think this apparent time and causality factor is related to these illusions of unstable generations.

[Joshua Adams]

You could understand it slowly, or if you understood the language that it was written in, you could understand it right away. Likewise, you could watch small local laws play out on one another for the end state, or you could calculate a law for the entire grid and the moment you run the simulator, it would show the end state. Either way, your not dealing with a necessary time component (cause and then effect) in this simulator.

How is this different than the universe? If you knew everything about the state of the universe, and all the laws of physics, then under determinism, you could extrapolate all the way to the end of time. Thus, the present "equals" the future. It's the same thing as figuring out future states of Game of Life, except that the states are more complex to describe, and the rules aren't known.

Now, determinism appears not to be true, and it's impossible in principle (not just in practice) to know everything about a system precisely, so none of this really applies. But the Game of Life works conceptually just like a deterministic universe would, despite your objections regarding "time".

[Michali]

[22:27] NeonQuill: let me lay out a few lines and then Ill say end of line
[22:27] Raven : this is also why I don't like philosophy. Too much theory, too little evidence
[22:28] NeonQuill: the blue cell is there only if it can be interefered with
[22:28] NeonQuill: it cannot be interfered with
[22:28] NeonQuill: the blue cell is not there
[22:29] NeonQuill: end of line
[22:29] NeonQuill: yet we saw it
[22:29] Raven : What do you mean by interfered with?
[22:29] NeonQuill: it was never there
[22:29] NeonQuill: i know i know
[22:29] NeonQuill: ok
[22:29] NeonQuill: for instance
[22:29] NeonQuill: I could set a glider, right next to the 9 squares with a blue in the middle on a larger grid
[22:29] NeonQuill: in the next generation
[22:29] NeonQuill: the glider and the blue square will meet
[22:30] NeonQuill: and flip out in some way
[22:30] NeonQuill: and stabilize
[22:30] NeonQuill: thats what i mean be interfere
[22:30] NeonQuill: if it can be
[22:31] NeonQuill: a part of the processes that end up in the stabilization
[22:31] NeonQuill: thus
[22:31] Raven : conway's life, as I've come to understand the rules, is that there are certain rules of the game to define whether a cell lives or dies. Whether it's blue or grey. One blue cell by itself starts alive, but dies, becoming grey, because it's alone. Right?
[22:31] NeonQuill: we have this backwards causation via means of reason
[22:31] NeonQuill: right
[22:32] NeonQuill: or function
[22:32] NeonQuill: i mean via means of function
[22:33] Raven : But you can't say it was always grey. Or that it didn't exist. Because it did. Fourth dimensionally it exists in a moment of time. And mathematically you can't say that it is equal to the end state of being dead, because there are other beginning states that could lead to the same all grey squares.
[22:33] Raven : one blue square in the center, or four blue squares, one in each corner. Both of these will lead to all grey squares the next generation
[22:34] NeonQuill: right
[22:34] NeonQuill: these are all the same
[22:34] Raven : and so you're trying to say that one blue square = grey, and that 4 blue squares = grey. And both of these are true. Bue 4 blue squares does not equal 1 blue square, even though they arrive at the same output. Attempting to make them equal would be the same as dividing by zero, which was the point of the previous exercise I showed you
[22:34] NeonQuill: in other words
[22:34] NeonQuill: it "means" all grey squares... reading
[22:35] Raven : You have to see it as a passage of time, you have to see it 4th dimensionally. It's not just grey. It's a process by which one blue square died, or four blue squares died, that came to mean all grey squares.
[22:35] Raven : Two seperate possibilities, diverging at a similar conclusion, yet starting at different sources.
[22:35] NeonQuill: yeah but heres why not
[22:36] NeonQuill: lets say processes occured such that
[22:36] NeonQuill: we take the glider scenario
[22:36] NeonQuill: and it hits the sole blue ssquare
[22:36] NeonQuill: and lets say it all cancels out after 14 generations
[22:36] NeonQuill: and theres all grey suares
[22:37] NeonQuill: well that initial generation
[22:37] NeonQuill: thats all grey squares
[22:37] NeonQuill: but
[22:37] NeonQuill: lets say that we rewrote the rules
[22:37] NeonQuill: such that instead of
[22:38] NeonQuill: "one blue square adjacent to none or only one will be grey in the next turn"
[22:38] NeonQuill: etc
[22:38] NeonQuill: we wrote it to encompass the relevant cell-pattern of the glider and the blue lone cell
[22:38] NeonQuill: we wouldnt need to see the geerneations
[22:38] NeonQuill: we would know that it means all grey

[Michali]

Originally Posted by Joshua Adams

How is this different than the universe? If you knew everything about the state of the universe, and all the laws of physics, then under determinism, you could extrapolate all the way to the end of time. Thus, the present "equals" the future. It's the same thing as figuring out future states of Game of Life, except that the states are more complex to describe, and the rules aren't known.

Now, determinism appears not to be true, and it's impossible in principle (not just in practice) to know everything about a system precisely, so none of this really applies. But the Game of Life works conceptually just like a deterministic universe would, despite your objections regarding "time".

What I mean to show is that it doesn't matter what a given past state may look like, but that whatever it ends up as, thats what it is in the first place.

Here's why: If something appears to us in a system, but is irrelevant to the system's acheival of the endstate, then that thing is not as it seems. In other words, it has the appearance of a transacting subsystem... but it ultimately never transacts, and never was a transacting subsystem. I'll try to take snap shots of a simulator in a bit.

[seebs]

Originally Posted by Michali

4+4 is equivalent to 8. It may not be identical, so I'll give you that. This lack of identity I don't understand, and I think it has to do with some potential reference to difference in the compositional parts. I'm going to say they are logically equivalent, and for all purposes, (4+4) may as well be identical to 8.

Perhaps... But a process is not equivalent to its outcome.

Your argument is totally circular. You start with the assumption that the outcome states are all that matters. To prove this, you disregard every other state because you've already decided that outcome states are all that matters.

Premise: All deterministic systems have a definite end state.
Conclusion: Given an unstable state of a deterministic system, that system must ultimately give rise to its end state.

Okay. The premise is wrong. Not all deterministic systems have a definite end state. You might be able to get as far as "all deterministic and finite systems have either a definite end state or an eventual cycle of states".

This conclusion is not just "the universe will end" but its that "this universe is because of its end".

And that makes no sense to me.

Case 1: Conway's Life applies, and causality is like mathematical entailment, in which case, the universe as it is now is just an unstable, not-perceived-correctly, end state.

Incorrect.

A trip to California is not the State of California. Process matters.

Do you really think it doesn't matter at all whether a corpse died peacefully in old age or was brutally tortured to death? I mean, sure, wait long enough and it's all compost anyway... But I think it matters at the time that it's happening.

Case 2: Causality is understood in the normal conservation of energy manner, and we could reverse it conceivably by working backwards from the end state.

What do you mean "the normal conservation of energy" manner? This is a string of words with no obvious connection.

We might conclude that the disbursal of energy happened in such a way that it was because of the way it would end up, essentially. Or in other words, the end state is the reason for the entire causal chain. This seems similair to Case 1, for some reason.

It seems similar to me only in that both are, so far as I can tell, incoherent.

What about the end state makes it "the reason for" anything? Why is the outcome of something "the reason for" it? You haven't suggested anything to support this, that I've seen.

I am inclined to say the end state is the reason for the universe as we see it.
I'm going to suspend that for now. What I mean to address is that Conway's life, and probably some other relevant examples, are not going to knock down the first premise you claimed I was making.

But they have!

That was not my reasoning though. My reasoning was that your saying not all systems are reversible led me to believe that the causal processes of the physical simulator was ultimately to blame for appearance of generation to generation "states".

It's not an appearance. It's a reality. The states exist. We can observe them and measure them. They matter in many ways -- not least because the time it takes to reach a given state is also significant to us.

Conway's life is like a cryptic message, a code for understanding it, and then understanding the actual message. You could understand it slowly, or if you understood the language that it was written in, you could understand it right away. Likewise, you could watch small local laws play out on one another for the end state, or you could calculate a law for the entire grid and the moment you run the simulator, it would show the end state. Either way, your not dealing with a necessary time component (cause and then effect) in this simulator.

You're ignoring that necessary component, but it's absolutely there when you actually run the simulator.

I think this apparent time and causality factor is related to these illusions of unstable generations.

There's no illusion. They're real. We can observe them, by running the simulator.

You keep handwaving and saying they aren't real. What's not real about them? They're temporary, sure. So's everything else we know of.

[seebs]

Originally Posted by Michali

What I mean to show is that it doesn't matter what a given past state may look like, but that whatever it ends up as, thats what it is in the first place.

But you're not showing this. You're just asserting it.

Here's why: If something appears to us in a system, but is irrelevant to the system's acheival of the endstate, then that thing is not as it seems.

Why not? Furthermore, what do you mean "irrelevant to"? Those states may well have been necessary parts of how the system achieved a given state, instead of a different state.

In other words, it has the appearance of a transacting subsystem... but it ultimately never transacts, and never was a transacting subsystem. I'll try to take snap shots of a simulator in a bit.

Please define in detail the words "transacting" and "subsystem" as you're using them here. If you're defining them in terms of other things, repeat the request until you get to words you're using in their plain conventional English senses.

[fragment]

Originally Posted by seebs

Please define in detail the words ....... as you're using them here. If you're defining them in terms of other things, repeat the request until you get to words you're using in their plain conventional English senses.

Wow. Mind if I borrow this for other discussions?

In the meantime I'd kinda like Michali to answer my earlier question.

[Kael]

So you're asserting that all systems are their end states, they just don't know it yet? Do you not see the holes in this idea?

[Farren]

Michali you can represent the configurations of a Conway life grid as a single binary number. Lets say it has only 4 squares. In that case you would need four digits. The possible states of the grid would then be

0000
0001
0010
0011
0100
0101
...

And so on. Now you can clearly see 0011 is not equivalent to 0100. When the grid is in state 0100 it is not in state 0011. It may result from state 0011, but it is not state 0011. The grid can either be in state 0100 or state 0011. In fact if those two states represent an "oscillator", it can alternate between these two states endlessly, so you don't even have an "end state".

Lets assume, for the sake of argument that there is no time since that's what gave rise to this discussion, that time is simply an enfolding of past states in the present state to produce memory. One moment you say "I'm experiencing x" then the next "I'm experiencing y". Later, when you experience z you might say "z=f(x,y)" but that doesn't imply that you simultaneously experienced x and y, which is the same as experiencing z. It means you experienced x, then y, then z, then drew some inferences.

Put another way, 2 bottles standing on a shelf forever + 1 bottle standing on a shelf forever is the same as 3 bottles standing on a shelf forever. But 2 people having a baby is not the same as 3 people always existing.

You seem to be making the error of seeing numbers as concrete, whereas they are only abstractions used to draw inferences about concrete things.

In Conways life, the system takes the general form S=f(S0), where S is the present state and S0 is the previous state. Of course sequence is implied. The actual formula boils down to "the present state is a function of the previous state".