Conway's Life, seebs

[Michali]

Originally Posted by fragment

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?

Sorry I missed this. When I use the words "actually a grey square" I'm not meaning (obviously) that its actually grey in its appearance to you in color. In fact, the reason we have such a hard time conceiving this is due to the fact that I am asking you to imagine that this 3 X 3 grid, and the rules of Conway's life, are the only things that exist.

Because the state where it appeared blue is useful to us in this argument (i.e., thus blue square is functioning in our Universal system), its hard for me to say that it is "actually a grey square" when it should be described as "its actually a grey square if all there was was the 9-cell grid and the laws of Conway's life."

I am also attempting to lay out why I have an inclination to believe this, and like I said earlier, it is only "relevantly a blue square" if it has something to do with its contribution to the state at which the system stabilizes. So the reason its not actually a blue square in my example is due to the fact that the entire grid is acting under a single law. Just like when someone hallucinates and sees a pink elephant, and then they realize that they are hallucinating one, they know that their mind is reporting "there is a pink elephant in your room" but this is ultimately false. He can report the pink elephant, and be justified in saying a pink elephant is appearing in his mind, but he can't say one exists in reality. And we do say things like this... "there isn't actually a pink elephant", or "there isn't really a pink elephant". Now, I could use that pink elephant for other tasks, such as entertaining myself, or a good story for later, but it isn't real on the basis that on some important universal level it isn't relevant in the same way other things in my room are.

The difference between the use of the terms "actual cell color" and "relevant cell color" in the context of the simulator is that "actual cell color" can be used to interpret the immediate next state and "relevant cell color" is used to interpret at least two states forward. Even if we had an extremely complex initial state, it is imaginable that if you ran the system and saw how it stabilized, you could look at the initial state and "interpret the actual state" as the stabilized state. You do not have to have the individual processes to figure this out, because those processes are used due to the fact that we aren't aware of the law that dictates the initial state is (and not "will become") the stable state. Just like a grid the size of a small law, exampled before, is almost the same thing we use to describe the law.

So, someone says "Hey, how do I play Causway's life?" I say, "A blue cell by itself will become grey in the next generation". Am I giving him an experience of this 3 x 3 grid and two generations, or am I telling him how a lone blue square should be interpreted? I am inclined to think that I am telling him how it should be interpreted in the system so he can work it out.

[Michali]

I'm sorry I know there were a bunch of responses and I'll get to them sometime today.

I looked up "rule" "principle" and "law" and there do not seem to be any adequate explanations for these terms. So, my confusing all of you is not without justification.

At its core I'm saying is that a conditional law is another way of saying what something "really is" in the context of that condition. If a whole grid can be a conditional law just by saying "this is what this means", then all whole grids can coherently be a conditional law on the same justification of "this is what this means".

Please refer to post 26 until I reply to the others.

-edit- also, I'm sure all finite grids will at least oscillate. Oscillation, to me, is a form of stabilization.

[seebs]

But Michali, "there used to be X but isn't now" and "there was never X" are not the same.

The pink elephant didn't exist. But if it was sunny yesterday and now it's cloudy, the sunny day did.

[Raven_poe]

Originally Posted by Michali

I'm sorry I know there were a bunch of responses and I'll get to them sometime today.

I looked up "rule" "principle" and "law" and there do not seem to be any adequate explanations for these terms. So, my confusing all of you is not without justification.

I'm curious as to where you looked these up. But I'll offer what help I can. Casually speaking, these three words are synonyms, and can be interchanged within a sentence. More precisely, a law in a scientific field refers to an observed phenomenon in which a certain set of conditions will always result in the same outcome. The phrase "conditional law" is then redundant, because law implies conditions. Laws are also often represented mathematically, because the conditional nature means they can be easily modeled in a mathematical system.

A rule, once more in everyday conversation, can be used in place of a law, but more precisely is often used to define the parameters that the law occurs within. Just like you would use the word to explain the rules of a game.

Principle (again, interchangeable in common usage) is usually used to more strongly emphasize a rule, or to describe a set of rules.

Originally Posted by Michali

At its core I'm saying is that a conditional law is another way of saying what something "really is" in the context of that condition. If a whole grid can be a conditional law just by saying "this is what this means", then all whole grids can coherently be a conditional law on the same justification of "this is what this means".

I already pointed out the redundancy of a conditional law. Laws by nature are conditional. But laws aren't universal truths. A law does not explain a phenomenon, it DESCRIBES a phenomenon. You're confusing law with theory. Take for example the phenomenon of gravity. The law of gravity (which made Newton famous) is a mathematical model that can be used to very accurately calculate the amount of attraction between two bodies, given their mass and distance apart from each other. But this does nothing to explain what gravity is. The THEORY of gravity does that, which I will leave for you to look up on your own, as it isn't relevant to this discussion.

Originally Posted by Michali

-edit- also, I'm sure all finite grids will at least oscillate. Oscillation, to me, is a form of stabilization.

If oscillation is an equivalent to stabalization to you, then I'd be curious to know what part of the oscillation is your end state? At which snapshot of the oscillation do you draw your conclusion to say that it was always this way, and do the previous parts of the oscillation exist? If so, then why don't non-repeating processes that lead to this exist? And if not, then why not?


my own edit- Also, hi. I'm a personal friend of Michali's, the one he quoted previously in the AIM log.

[seebs]

Hey, ravenpoe!

[fragment]

Originally Posted by Michali

Sorry I missed this. When I use the words "actually a grey square" I'm not meaning (obviously) that its actually grey in its appearance to you in color. In fact, the reason we have such a hard time conceiving this is due to the fact that I am asking you to imagine that this 3 X 3 grid, and the rules of Conway's life, are the only things that exist.

Because the state where it appeared blue is useful to us in this argument (i.e., thus blue square is functioning in our Universal system), its hard for me to say that it is "actually a grey square" when it should be described as "its actually a grey square if all there was was the 9-cell grid and the laws of Conway's life."

Yes, I realise that you're arguing about what things look like from within the system, but that doesn't answer my question. I'll try restating it.

Say there is a given stable state - all grey squares. There are several hypothetical earlier states, including lone blue square, that could lead to this end state. You are saying that all of these are equivalent to the all grey square state. Fine, I'll grant that for this discussion. But that also means that the all grey squares state is equivalent to all of those other states too. Within the system I see no reason to prefer "all grey squares" to any of these other states as a way of describing the "actual" state. Rather, it appears that you've made an unsupported assumption that "grey" is a default state for a square, and that "blue" is only to be used when it is necessary. You are treating "blue" and "grey" differently without giving a reason for doing so.

[Iacchus]

Hey, I just bought a copy of SimCity Societies and have been playing that for the past few days and, it is kind of fun ... but, as for this Conways's Life game? I have no idea what you folks are talking about. Is this something you can buy and play on your computer? Is it anything like Spore? which, somebody was just telling me about last night.

[Raven_poe]

Originally Posted by Iacchus

Hey, I just bought a copy of SimCity Societies and have been playing that for the past few days and, it is kind of fun ... but, as for this Conways's Life game? I have no idea what you folks are talking about. Is this something you can buy and play on your computer? Is it anything like Spore? which, somebody was just telling me about last night.

I'm new around here, so I could be walking into this one... but if you're looking for an actual -game- based on Conway's Game of Life (which is itself a computer program which acts as a simulator) then I direct you to http://www.kongregate.com/games/squi...argame-of-life

[S.Vashti]

Originally Posted by Iacchus

Hey, I just bought a copy of SimCity Societies and have been playing that for the past few days and, it is kind of fun ... but, as for this Conways's Life game? I have no idea what you folks are talking about. Is this something you can buy and play on your computer? Is it anything like Spore? which, somebody was just telling me about last night.

These are flash "games" you play on different web sites.

John Conway's Game of Life

Conway's Game of Life

[Michali]

Originally Posted by seebs

But Michali, "there used to be X but isn't now" and "there was never X" are not the same.

The pink elephant didn't exist. But if it was sunny yesterday and now it's cloudy, the sunny day did.

(1+2)+3=6
Ok, what is "3" being added to?

Is it being added to (1+2) or is it being added to (7-4)?

If you say its being added to another 3, and not these provided, what do you mean if you say there was a 2? Was there a seven? Was there always another 3?

I'm inclined to say thats all just our method of writing "6", and we are trying to simplify it via means of basic arithmetic.

There never is or was a -4, 1, 2, 3, or 7. There was always "6 of something". Also, your example of cloudy and clear fails, because I am reffering to completely closed systems via means of the universe (or "everything") and entire-grid (in Causway's life). I am not saying I am a dead body right now. I'm saying the end state of the universe is the only thing that is right now.

In the equation, "(1+2)+3=6". The "1" only exists relative to the "2"... but that relationship is existent because of their relationship to the "3" and the "3" only exists because of its relationship to the six.

So "6" is the end of the systemic processes of basic arithmetic, but if there isn't a "6" (and this is the hard part) on both sides of the equation in the first place, then there's nothing here.

6=
(1+2)+3 <---- there is definately "only a 6" in that even though we don't see one.

[Michali]

Originally Posted by fragment

Yes, I realise that you're arguing about what things look like from within the system, but that doesn't answer my question. I'll try restating it.

Say there is a given stable state - all grey squares. There are several hypothetical earlier states, including lone blue square, that could lead to this end state. You are saying that all of these are equivalent to the all grey square state. Fine, I'll grant that for this discussion. But that also means that the all grey squares state is equivalent to all of those other states too. Within the system I see no reason to prefer "all grey squares" to any of these other states as a way of describing the "actual" state. Rather, it appears that you've made an unsupported assumption that "grey" is a default state for a square, and that "blue" is only to be used when it is necessary. You are treating "blue" and "grey" differently without giving a reason for doing so.

So, yes, very good. If you grant me all of those, then you're right in raising this question. Why shouldn't I just say that the initial state is really what the stable state is? I'm not going to argue that, and for my purposes this is fine. So long as we admit that the same could be said in reverse. Namely that, the stable state really is what the initial state is. They all mean one thing, and its this one thing that makes them equal. Its interesting to us in the latter case because we live in a system that we do not consider to be its end state. Even if you said, well the universe really is 1942, I'd be like, ok, but its also really every other state too. More importantly, its the stable state that can be reffered to with accuracy. You could say, "its really 1942 and this means Hitler is still alive", but I would say, "oh but your reffering to an unstable state where he is dead in 2008, and I believe the universe is in 2008".

Suppose some pattern explodes and in 50 generations it stabalizes at all grey cells. Now, all 49 states are equally a grey state. Except, to us, we find them incrimentally closer to a grey state based on how many more steps till we get there. Another completely different system explodes and in a different 50 generations comes to all grey cells. All of these are equal in that they are all grey states, and each is equal to the other different explosion. Even as you work this new one out, imagine 40 frames down the line you think "hey they are all grey states anyway" and you switch a frame out with the the second frame from the other explosion... you haven't changed anything at all. Your still dealing with something that will stabilize at all grey states. The only thing you've changed is how much work you'd end up doing to get there.

[seebs]

Originally Posted by Michali

(1+2)+3=6
Ok, what is "3" being added to?

Is it being added to (1+2) or is it being added to (7-4)?

It's being added to (1+2).

If you say its being added to another 3, and not these provided, what do you mean if you say there was a 2? Was there a seven? Was there always another 3?

The 1+2, in this context, happens to have the same value as "3".

I'm inclined to say thats all just our method of writing "6", and we are trying to simplify it via means of basic arithmetic.

Then you're inclined to be wrong. It's not a way of writing 6. 6 is an outcome.

You're just asserting, over and over and over, saying it different ways, that the initial state and process ARE the outcome. You keep saying it. You don't offer a reason to believe it. You don't show us a problem we have that this way of viewing things solves. You've been offered dozens of problems that we currently have excellent, working solutions for, which your way of viewing things unsolves.

What's the point? It doesn't get us anything. It appears to be neither useful nor true.

[Michali]

Originally Posted by seebs

It's being added to (1+2).

The 1+2, in this context, happens to have the same value as "3".

Then you're inclined to be wrong. It's not a way of writing 6. 6 is an outcome.

You're just asserting, over and over and over, saying it different ways, that the initial state and process ARE the outcome. You keep saying it. You don't offer a reason to believe it. You don't show us a problem we have that this way of viewing things solves. You've been offered dozens of problems that we currently have excellent, working solutions for, which your way of viewing things unsolves.

What's the point? It doesn't get us anything. It appears to be neither useful nor true.

See I think your being hard headed. Ok fine, "(2+1)" is not "3". Next time I see "3+(2+1)", I'll make sure I explain how I added one and two together before I tell someone its "3+3". What if the equation had some unknown variable like "§"? 3+§=6. What's "3" being added to, seebs?

Ok, fine, you admit its the same value as 3. That's really all I'm saying. When you say "§" is the same value as "3", and 3+3 is the same value as six... that's what I mean when I say there is ""really"" 6 and not 3+3 or 3+§.

So, by your lead, for any state in Conway's life, that state has the same value as its end state. Would you agree to this? Would you agree to the use of the identical term "value" in both arithmetic situations and states in Conway's life?

[fragment]

Originally Posted by Michali

The only thing you've changed is how much work you'd end up doing to get there.

Actually, by allowing states that end up in the same stable state to be switched at will with no effect, it seems you've eliminated all possibility of discovering, from within the system, the causal processes involved in getting from one state to another state. Without those you don't have the means of evaluating which states will lead to the same stable states.

[seebs]

Originally Posted by Michali

So, by your lead, for any state in Conway's life, that state has the same value as its end state. Would you agree to this? Would you agree to the use of the identical term "value" in both arithmetic situations and states in Conway's life?

No.

"Value" is specific to arithmetic, it doesn't work for causality.

[Michali]

Originally Posted by fragment

Actually, by allowing states that end up in the same stable state to be switched at will with no effect, it seems you've eliminated all possibility of discovering, from within the system, the causal processes involved in getting from one state to another state. Without those you don't have the means of evaluating which states will lead to the same stable states.

Oo, this is a good argument.

So I go, "Hey they are all equall." And switch them out disjointedly.
He says, "You aren't playing Conway's life if what you did is a valid move. If you spliced in, say, a single state of one system into another that both end the same way, here you should be breaking the rules because the states do not lead to eachother."

But the thing is, I didn't splice them in random places in order to lead them to eachother. I spliced them because they all lead to the same thing. Splice is a bad word, as its more like shuffle. I shouldn't have even mentioned that. In other words, if I splice state 2 so that it appears to come immediately after state 48 in a sequence, they are still equal in their respective stability-functions (new concept I'm going to explore) and the splicing wasn't a way of going, "hey this comes after this", its more like, "what the hey, its going to do the same thing, so big deal if it appears to come after this one." The reason it doesn't matter in which way you splice them is because they only sequence if you need them to sequence. All the states represnt the same stability-function, and so they all "mean" the same thing. So it wasn't so much a splicing as it was a shuffle, and showing that a sequence of events is based on our need to use them in order to calculate the stability-function.

[Michali]

Originally Posted by seebs

No.

"Value" is specific to arithmetic, it doesn't work for causality.

Does value work for logical coniditionals? Like, in A if and only if B. Does A have the same value as B?

Wikipedia explains "value (mathematics)" as

In mathematics, value commonly refers to the 'output' of a function. In the most basic case, that of unary, single-valued functions, there is one input (the argument) and one output (the value of the function).

So why can't value ("the output of a function") apply to Conway's life?

[Kael]

Aren't you supposed to be demonstrating how Causality is reversible, rather than how all states are the same? You've really switched tracks here. Conway's Life came up as an example of a system where you cannot deduce past states from present ones, to which you reply "well it doesn't matter because they all mean the same thing." This does NOT support your original assertion, that in a perfectly deterministic system one CAN deduce past states just as easily as future ones from any given state.

Even granting your equally spurious assertion that all states in a completely closed system are essentially equal, this does not in any way support your original claim. Can you sort yourself out and decide what it is you're really after here?

[Michali]

Originally Posted by Raven_poe

I already pointed out the redundancy of a conditional law. Laws by nature are conditional. But laws aren't universal truths. A law does not explain a phenomenon, it DESCRIBES a phenomenon.

What's a Universal truth? In conway's life, in a 3X3 grid, is it not a "universal truth" that a lone blue square will ultimately turn grey? Why can't it also be a universal truth that a more complex system will ultimately become its output? We wouldn't normally consider this to be a rule because of how specific this application would be.

Originally Posted by Raven_poe

If oscillation is an equivalent to stabalization to you, then I'd be curious to know what part of the oscillation is your end state? At which snapshot of the oscillation do you draw your conclusion to say that it was always this way, and do the previous parts of the oscillation exist? If so, then why don't non-repeating processes that lead to this exist? And if not, then why not?


my own edit- Also, hi. I'm a personal friend of Michali's, the one he quoted previously in the AIM log.

Ok, this is obviously the next step, if we ever get past this first step. I am not sure, but I'm inclined to say that a stable blue block is still appearing state by state by state. If a line of 3 blue cells oscillate for the rest of their states, then those cells which appear to change from blue to grey are only half blue. In a stability achieved state, the oscillating factor does not play a role in any un-predicted interference.

Honestly, I think this is the presence of an exra dimension in the grid. So, those cells which remain blue most often are "higher" out of the grid then those that only appear blue half of the time. Imagine a finite grid which is completely chaotic, and will never completely stablize in the common sense. It should, or so I believe, repeat states, and doing so it will determine how often a cell is turned blue during a cycle. If you could record a gradiation of those cells which turned blue from most often to least often, and then 3 dimensionally raised those cells upwards, the height of which, depends on how many times it turns blue in the cycle. You would get a terrain-like formation. This is what the stable state looks like.

[Michali]

Originally Posted by Kael

Aren't you supposed to be demonstrating how Causality is reversible, rather than how all states are the same? You've really switched tracks here. Conway's Life came up as an example of a system where you cannot deduce past states from present ones, to which you reply "well it doesn't matter because they all mean the same thing." This does NOT support your original assertion, that in a perfectly deterministic system one CAN deduce past states just as easily as future ones from any given state.

Even granting your equally spurious assertion that all states in a completely closed system are essentially equal, this does not in any way support your original claim. Can you sort yourself out and decide what it is you're really after here?

I switched threads because I felt this issue was off-topic from the last one, and I suspected this would end up being more fundamental and settle my intuitions better. What I came to realize is, it doesn't matter what the system is. It's not "backwards causation" I want to argue for any more, its something like systems existing because of their function.

[Kael]

Ok, so we'll just set your 'backwards causation' on the junk heap then, and talk about why State A is NOT State B, regardless of the fact that State A causes State B. Really, I don't see where you're getting this from.

Here's a more brutal example than the ones above:

Let's say you get a limb cut off, then die of bloodloss, in a completely closed system. We have three states, you normal and healthy, you with a limb cut off, and you dead. Certainly one state leads to the other in this closed system, mostly with the last two. Do you not see, however, that these states are far from equivalent? Sure, there's still the same amount of mass in all three, but in one you're alive, in another you're in agony, and in the third you're dead. They are not the same.

[Michali]

This 3rd dimensional aspect is becoming more apparent to me now as the answer. The reason all the different initial states are equal in Conway's life is because they all represent a stable state of infinitely imprerssioned cells. Among these infinitely impressioned cells, they can, with relation to eachother, be plotted as to how often they are impressioned, and this three dimensional form we come up with is the function of our input.

[Michali]

Originally Posted by Kael

Ok, so we'll just set your 'backwards causation' on the junk heap then, and talk about why State A is NOT State B, regardless of the fact that State A causes State B. Really, I don't see where you're getting this from.

Here's a more brutal example than the ones above:

Let's say you get a limb cut off, then die of bloodloss, in a completely closed system. We have three states, you normal and healthy, you with a limb cut off, and you dead. Certainly one state leads to the other in this closed system, mostly with the last two. Do you not see, however, that these states are far from equivalent? Sure, there's still the same amount of mass in all three, but in one you're alive, in another you're in agony, and in the third you're dead. They are not the same.

You mean there are more than three states but your only considering three? Your going to need to use a better example because I dont understand what rules your using. What you might ask is, "hey the universe might be a system, you will probably turn 38 sometime in the future, why aren't you really 38 right now?" I'd have to say this isn't the laws of the system of the universe. For all I know the stablility-function is the only thing that exists, and thats all that I can be sure about. I'm not 38 because that's probably not the best description of the stability-function.

[Raven_poe]

Originally Posted by Michali

You mean there are more than three states but your only considering three? Your going to need to use a better example because I dont understand what rules your using. What you might ask is, "hey the universe might be a system, you will probably turn 38 sometime in the future, why aren't you really 38 right now?" I'd have to say this isn't the laws of the system of the universe. For all I know the stablility-function is the only thing that exists, and thats all that I can be sure about. I'm not 38 because that's probably not the best description of the stability-function.

Wait, you seem to be flipping back and forth in respect to time. In your hypothetical systems within conway's life, time doesn't exist, and you define everything by its end state, saying that the lone blue square doesn't exist because it "stabalizes" into a constant grey square. And then when describing yourself, you say you aren't a provided end state, and postulate that the reason you aren't currently is because that's not the best example of stabalization?

It can't work both ways. Either you currently exist, in which case you admit your conway's life theory to be incorrect, or you're already dead, because you are equal to your end state. We -do- know enough of the rules of our universe to know that death is an inevitability. And so given this, if what you theorize is true, then you're already dead.

So which is it?

[Michali]

Originally Posted by Raven_poe

Wait, you seem to be flipping back and forth in respect to time. In your hypothetical systems within conway's life, time doesn't exist, and you define everything by its end state, saying that the lone blue square doesn't exist because it "stabalizes" into a constant grey square. And then when describing yourself, you say you aren't a provided end state, and postulate that the reason you aren't currently is because that's not the best example of stabalization?

It can't work both ways. Either you currently exist, in which case you admit your conway's life theory to be incorrect, or you're already dead, because you are equal to your end state. We -do- know enough of the rules of our universe to know that death is an inevitability. And so given this, if what you theorize is true, then you're already dead.

So which is it?

The problem is, you don't know enough about the universe to know what its end state is. Your probably thinking heat death but you still don't know that. Not only that, on the subject of what I am in the midst of all this, you don't know that I'm dead at the end state. So you can't make me choose.

All I'm saying is, the only thing that can truly be reffered to in a closed-finite system, is its function.

I'm not a closed-finite system, and death isn't my only function, in other words. If you pull your hand away from the stove and I asked why you pulled it away, you'd say the stove burned you. But if you reflected on it, you could more accurately describe the reflex in terms of evolution and biology. Well escalate this method appealing to better explanations until your thinking about how that functioned on a Universal level.