Conway's Life, seebs

[seebs]

Originally Posted by Michali

Seebs, your counter argument is this, mister:

You don't use the terminology the way I do, therefore your wrong.

Largely, yes.

Specifically, every claim you make relies on terminology to have any meaning at all. And yet, if you use it wrong, all the meanings the terminology would give you don't work.

Well here is my final explanation:

f(x)
f(x)=y
y
~x

That's it. That's all I'm saying. If you can't understand that, then I'm done. f(x) = ~x. Yes, that's what I'm saying. Yes, that's my last word.

And it still ignores sequence.

x. then. y.

Monday, then Tuesday.

dayafter(Monday) = Tuesday.

Monday, then Tuesday.

Monday exists. Then, after Monday is over, Tuesday exists.

there is no input.

Of course there is!

There is no x if x is input. There is no blue square if blue square is input.

Maybe English isn't your native language.

Do you understand that "is" and "was" are different words, with different meaning?

[Michali]

was, is, doesn't matter. did you have x before f(x)?

[seebs]

Originally Posted by Michali

was, is, doesn't matter.

It does indeed matter!

It is Monday, but it was Sunday.

It can't be both Monday and Sunday at the same time (and in the same place, stupid date line), but it can be Monday now and Sunday yesterday.

did you have x before f(x)?

In the case of the simulator? Yes. We had t0, then we had t1, then we had t2. All of them existed in sequence. That's how Conway's Life works. If you don't have multiple sequences and transitions between them, you aren't playing Conway's Life.

Now, if all you show me is t1, I can't tell you the details of which state you had previously -- but if it's a state in a game of life simulator, that resulted from running the simulator, there was some previous state.

And if there wasn't, then this isn't an f(x) at all, because f(x) refers only to something produced by the function f.

[Michali]

look, if we have, y, we have f(x). If we had f(x), we had x+rules. Well x+rules is like "x under the rules of Conway's life" because "in Conway's life, its a rule that all lone blue squares are grey". So, in Conway's life, there are no lonely blue squares, because if there are lonely blue squares, they are grey squares. So if x is a lonely blue square, f(x) is not. Meaning x was never in Conway's life.

[seebs]

Originally Posted by Michali

look, if we have, y, we have f(x).

Nope.

Again, you're getting confused about equality.

If we had f(x), we had x+rules.

Yes.

Well x+rules is like "x under the rules of Conway's life" because "in Conway's life, its a rule that all lone blue squares are grey".

No, it isn't.

It's a rule that lone blue squares are replaced by grey squares in the next generation.

They aren't grey. They are inputs that produce grey outputs. That's not the same.

So, in Conway's life, there are no lonely blue squares, because if there are lonely blue squares, they are grey squares. So if x is a lonely blue square, f(x) is not. Meaning x was never in Conway's life.

But of course it was. It could have been the output from a previous input!

I think I'm beginning to see some more of your problems.

Domain and range are not interchangeable.

Since I posted explicit definitions of these terms, I can safely assume that you've already read those definitions and understand what I just said.

[Michali]

Originally Posted by seebs

Nope.

Yes we do. "Wherever you go, there you are." is analogous. With regard to your f(burningwood)=ash example, "f(burningwood)" is, the most super-general description that could entail that ash is simultaneously true.

If f(x)=y. f(x) is simultaneously true with y. If y is "being in the north pole" and f(x) is "buying a jet, flying to the north pole, parachuting down, and kissing the snow"... If f(x) is true, y is simultaneously true.

Again, you're getting confused about equality.

Yes.

No, it isn't.

It's a rule that lone blue squares are replaced by grey squares in the next generation.

They aren't grey. They are inputs that produce grey outputs. That's not the same.

Negative, Conway's life is a set of rules applied one state at a time. You used this to argue against me earlier about "end states" in Conway's life.

But of course it was. It could have been the output from a previous input!

I think I'm beginning to see some more of your problems.

Domain and range are not interchangeable.

Since I posted explicit definitions of these terms, I can safely assume that you've already read those definitions and understand what I just said.

[/quote]We are only dealing with one instance of one input and one output.

[seebs]

Originally Posted by Michali

Yes we do. "Wherever you go, there you are." is analogous. With regard to your f(burningwood)=ash example, "f(burningwood)" is, the most super-general description that could entail that ash is simultaneously true.

Not really.

If f(x)=y. f(x) is simultaneously true with y. If y is "being in the north pole" and f(x) is "buying a jet, flying to the north pole, parachuting down, and kissing the snow"... If f(x) is true, y is simultaneously true.

But again, values aren't "true" or "not-true" in general. They're just values.

Negative, Conway's life is a set of rules applied one state at a time. You used this to argue against me earlier about "end states" in Conway's life.

You didn't understand that, either.

In any event, while Life applies to one state at a time, it is a sequence of states, each handled in turn. No sequence, no Life.

We are only dealing with one instance of one input and one output.

And even then, you're still getting confused.

"lone blue square" is a valid input for Life, even though it can never occur as an output. The function's domain is substantially larger than its range.

[Michali]

Then I'm through with this, seebs.

"Wherever you go, there you are" is analogous.

f(You fly to the north pole)= you are at the north pole

That's how functions work to me. If they don't work like that to you, then we can't really argue any more.

[seebs]

Originally Posted by Michali

Then I'm through with this, seebs.

Okay.

"Wherever you go, there you are" is analogous.

Not really.

But let's say it were.

You are still totally fucking wrong, to such an extent that I cannot imagine you ever even said this once.

Wherever you go, there you are.

f(You fly to the north pole)= you are at the north pole

Well, no, but I know what you mean.

So.

You start in Minnesota. You fly to the north pole.

Then Michali says Minnesota never existed, you were never there, and you can't even talk about Minnesota. Because you are at the north pole.

That's how functions work to me. If they don't work like that to you, then we can't really argue any more.

I don't think we can until you learn what a fucking function is.

1. "f(you fly to the north pole)" is backwards. You're describing an operation as an input, but that's probably not what you meant. You probably ought to have spelled it as "fly_to_north_pole(you)". See how it works? You're the input, the function performs an operation, and the result is you-at-north-pole.
2. Even so, you keep offering examples in which it is quite clear that there is change between one stage and another. Before you call fly_to_north_pole(), you're somewhere else. Afterwards, you're at the north pole.
3. Furthermore, since there's not an airport there, we know you didn't start at the north pole; you started somewhere else. The operation "fly_to_north_pole()" implies locations other than the north pole.

The problem here is that you keep saying "you're at the north pole", and people grant that this is so, and you then say "therefore all other locations are nonexistent and you were never anywhere else", and people tell you it's wrong. And then... you keep arguing about the "at the north pole" part, which isn't even anything anyone disputed.

Everyone has granted that, if you feed a lone blue square into Conway's Life, you get out a grey square. That's not under dispute, any more than "flying to the north pole means you're at the north pole after you do it" is.

What's under dispute is your assertion that the origin never existed. That is the part where your argument is incoherent at best.

Your position, as repeatedly stated here, is more correctly analogous to "wherever you go, that's the only place there ever was, and there wasn't any kind of travel involved either because the existence of places other than where you are now is logically impossible."

[Kael]

You know, Mich, I love the way you ranted against the Dunning-Kruger effect while completely missing the point. Did you bother to read the original research, or just dismiss it after a cursory review of the Wikipedia article?

You know, let's just pretend you've convinced us. Yup, we believe you. We see the perfect and flawless logic of your arguments. Obviously there is no input. Now, it is time to get your work out there. The scientific community needs to hear this. Get it published in a scientific journal for all to see! I believe in you, Michali. Get to your local university and rub those stuffy professor's noses in your undeniable correctitude!

Gigantic wave of sarcasm aside, perhaps you should seek reputable publishing if you feel so strongly convinced about this. If it's as clear as you seem to think it is, I don't think you'll have much trouble.

[Michali]

Originally Posted by Michali

I guess its like you say the words "δύο αδέλφια" (which means two brothers in Greek.) Once you say them you ask me, "I just said something in Greek, what did I just say?" When I answer "'Two brothers' in Greek is what you said." you tell me, "No I said δύο αδέλφια, which happens to be 'two brothers' in English."

This seems to be one side of the problem.

Now imagine the same scenario and you say "δύο αδέλφια", except you and I do not know what "δύο" means (it means two). But if either of us know what "αδέλφια" means (brothers) then it would immediately enlighten us as to what "δύο" means. You say the phrase in Greek and then you ask, "What did I just say in Greek(this time)?" I, because I heard "αδέλφια" at the end, reply "Two brothers in Greek." Now you seem to be saying that even that was the wrong answer. You feel that "δύο brothers" is what you said in Greek, and it is only after I acknowledge this that I can then say "Two brothers is what you said in Greek."

Does "brother" exist in Greek?

[seebs]

Originally Posted by Michali

Does "brother" exist in Greek?

No...

But it does exist in an English<->Greek translator.

Actually, translation gives an interesting opportunity to explore this. Let's say we use the mythical language which has fifty words for "snow". And we put one of these words into a translator, and out comes the word "snow".

Your argument all along has been that the entire other language doesn't exist, only the English words it translates to.

My argument is that, while we don't know which of those fifty words was put into the translator, we know one of them was or the translator wouldn't have said "snow".

[Michali]

Originally Posted by seebs

No...

But it does exist in an English<->Greek translator.

Actually, translation gives an interesting opportunity to explore this. Let's say we use the mythical language which has fifty words for "snow". And we put one of these words into a translator, and out comes the word "snow".

Your argument all along has been that the entire other language doesn't exist, only the English words it translates to.

My argument is that, while we don't know which of those fifty words was put into the translator, we know one of them was or the translator wouldn't have said "snow".

Right, interesting assessment on your part. I also don't care if "brother" exists in the translator, mind you, I only care if it exists in Greek.

Lets say snishy is a kind of snow of Incas. When we put snishy in the translator it comes up snow in english, and so does a lot of other words, such as swishny. Snishy doesn't exist in english nor does swishny. And that's my point.

[Kael]

Your point is that the input doesn't exist in the output? OMG, you are a fucking genious.

You do realize that no one has been arguing against that premise, right? Only against your inane idea that because the input doesn't exist in the output, it must not ever have existed at all.

[Michali]

Originally Posted by Kael

Your point is that the input doesn't exist in the output? OMG, you are a fucking genious.

You do realize that no one has been arguing against that premise, right? Only against your inane idea that because the input doesn't exist in the output, it must not ever have existed at all.

Read the OP

[seebs]

Originally Posted by Michali

Right, interesting assessment on your part. I also don't care if "brother" exists in the translator, mind you, I only care if it exists in Greek.

But what you say is not "the output is not a blue square", but "the blue square doesn't exist".

Conway's Life is both English and Greek. Or, maybe, German and English.

Lets say snishy is a kind of snow of Incas. When we put snishy in the translator it comes up snow in english, and so does a lot of other words, such as swishny. Snishy doesn't exist in english nor does swishny. And that's my point.

Your point, as you have repeatedly and consistently asserted, over and over, is that "snishny" does not exist at all. You have very carefully said that you mean not just that it doesn't exist in the "end state" (the English translation) but anywhere at all, ever (the German original).

Conway's Life is a translator; it translates from one thing to another. "lone blue square" is one of the things it can translate from. (It is also one of the things it can translate to.)

Let's use a better example: "gift". The word "gift" is a German word, meaning a toxic or fatal substance; it is also an English word.

Now, when you put "gift" into your German->English translator, it comes out "poison".

Your argument, all along, has been that "gift" doesn't exist, there's no such thing as gift, and if you think there is it's because you're crazy. In fact, you're wrong.

1. "gift" is a perfectly valid word in the domain of the German->English translator.
2. "gift" is a perfecttly valid word in the range of the German-English translator.

You keep saying crazy stuff like "the state is the next state", which seems to imply that you think that we can never just run the function once, or choose not to run it, but that the moment anyone mentions a function we have to run it over and over and over until it stops. That's not how functions work.

[Kael]

Hmmm? Oh, yes. That. The prequel was better.

Lemme try something. Is this your argument? ---> Because we cannot derive past states from only the current one, they must not have existed, and the system is, was, and will always be in its final state. The earlier states are merely the final state waiting to happen.

Any corrections you'd like to make?

[Joshua Adams]

Originally Posted by Kael

Hmmm? Oh, yes. That. The prequel was better.

Lemme try something. Is this your argument? ---> Because we cannot derive past states from only the current one, they must not have existed, and the system is, was, and will always be in its final state. The earlier states are merely the final state waiting to happen.

Any corrections you'd like to make?

What he doesn't seem to get is that sets have an existence independent of whether we're running them through a function.

We can talk about S = {all possible square matrices of Boolean variables}. Its members amount to states that can be input to, or output by, Conway's Life. The function Conway(x) is defined in such a way that it maps S into S. S is a mathematical object that doesn't go away no matter how many times we think about what happens when we run an element of it through Conway(x).

You'd think that taking his logic and applying it to another situation to show the absurdity would get him to reconsider his position. But no. Apparently, 0 doesn't really exist because there's some expression in x for which f(0) = 5. Never mind the fact that g(5) = 0 for some g(x). If I do f(x) and you do g(x) at the same time, does 0 exist or not exist?

Try another example. Suppose we had a function dim(x) mapping S to the integers, where x is a member of S, and the function returns the number of cells in one row of S. So, if s is a 4x4 grid, then dim(s)=4. Now, did s "turn into" 4? Sweet Jesus Fuck, no. The function is telling us, in this case, how big s is; it doesn't replace it.

Consider the Euler Phi function. You give it an integer and it tells you how many integers less than or equal to the input are relatively prime to the input. Do the inputs go away after we obtain this information? Think, man!

Conway(x) tells us this: If we seed the Game of Life with state x, what will come in the next generation? That's all. It doesn't friggin' destroy x.

[Michali]

Sorry I haven't been posting much on this, I've been finishing a final paper and this was the topic I was writing on. "Flabbergab"

Ok anyway, lets see I think I found out something interesting as I was writing the paper. I think I have a formula for what we mean by "representation"

Lone blue squares, I think, are representations of the output of a grey square in Conway's life... Am I saying that right, by the way? English is to Greek, as Our world is to what? with regards to Conway's life.

[Michali]

Originally Posted by Joshua Adams

Conway(x) tells us this: If we seed the Game of Life with state x, what will come in the next generation? That's all. It doesn't friggin' destroy x.

Right yeah, but let's talk about the role of a variable real quick.

Now in:

(1+2)+3=x "x" is going to stick around for the next couple steps
3+3=x ...
6=x ...
6 And then, we don't need x anymore.

Well isn't that the roll of a lone blue square in the simulator? The same lone blue square in the input is never in the output. So we represent an actual grey square with a lone blue square in the input, and in the output, the lone blue square turns grey.

We no longer need the representation and that's why there's this elimination effect: x inputs and f(x)=y, so a part of this output has to do with this: ~x.

[seebs]

Originally Posted by Michali

Lone blue squares, I think, are representations of the output of a grey square in Conway's life... Am I saying that right, by the way?

If you're saying it correctly, it's wrong.

Since I have no idea what you might think you're saying, I can't really say.

English is to Greek, as Our world is to what? with regards to Conway's life.

I have no idea which relationship you're looking for. I just plain have no clue what you mean.

Right yeah, but let's talk about the role of a variable real quick.

Okay.

Now in:

(1+2)+3=x "x" is going to stick around for the next couple steps
3+3=x ...
6=x ...
6 And then, we don't need x anymore.

So?

That's purely notation.

Well isn't that the roll of a lone blue square in the simulator?

No. The role of "x" in the above is purely notation. There's no point at which "x" has any meaning other than "placeholder for another value".

By contrast, the role of the lone blue square in the simulator is actual input which is used to calculate results. That the results might be the same as results you could get from something else doesn't matter.

The same lone blue square in the input is never in the output.

So what? The output and the input are different things.

So we represent an actual grey square with a lone blue square in the input

Wrong.

There is a blue square in the input.

, and in the output, the lone blue square turns grey.

So? The output is different from the input.

We no longer need the representation and that's why there's this elimination effect: x inputs and f(x)=y, so a part of this output has to do with this: ~x.

So what?

You keep saying this as though the inputs didn't exist. Of course they did; they were what we used to generate the outputs.

Again: Your argument is that ash proves that there was never wood at all. That's stupid.

[Farren]

Michali, it seems obvious to me that the crux of your argument is that the tangible thing, the grid, is only ever in one state, so the past states don't materially exist at any point of observation. Which is true in the sense that past states don't currently, materially exist at any instant in which we observe Conways Grid.

But that strikes me as a trivial observation that's self-evidently true. And an aspect that's been conspicuiously absent from the discussion thus far is the observer's role in our hypothetical Conway's Life universe. Specifically, the fact that an implicit requirement of imagining Conway's Life as an analogy for the universe necessarily demands that the observer is a construct within that universe, some pattern in the grid itself.

Such a pattern can only have any conception of a past if it has memories of past states. Naturally, those memories describe parts of the grid, not the whole grid. A pattern within the grid cannot encode memories of the entire grid, because encoding memories of the entire grid would always require more configuration space than the entire grid can represent.

So the only conceivable way our game of life can be an analogy for the universe and our role as observers in it, is if it is viewed as a universe within which one pattern (you, me) encodes a history of itself and surrounding patterns using some system of representation. Which I would intuitively say equates to some kind of fractal, as an aside.

Now if we imagine ourselves as a pattern, with memories of the past, we can arrive at a limited number of possible conclusions from that:

1. That our memories are false.

To wit, that there has only ever been this state and no process has taken place to produce these memories. Instead, we are simply experiencing an awareness of an unchanging present moment configured in such a way that it seems, in this present moment, that there was a past.

This is akin to saying "There were always 271 posts on this thread. No process occurred that led from one post to another until we arrived at this point. The content of the present thread only gives the illusion of a dialog having taken place"

In this scenario, there is only the instantaneous awareness of an illusory past and nothing else. Neither is there a possible future in which things will be different. There is no argument taking place. There is no question of why we seem to experience time passing and infer causes and consequences. There is no Conways Life.

2. That our memories are a description of actual "past states", and are causally produced by past states

In this scenario, there is a necessary past (which doesn't, as Popper has pointed out, imply a necessary future), a place, if you like, in which states other than the present one exist, which have some procedural relationship with the present that can be expressed as a function.

In this scenario, we are having a debate. This thread has grown. Time has passed. A past logically "exists" where there are states that have a procedural relationship to the present state.

3. That our memories are a description of actual "past states", but all future states already exist

In this scenario, the universe is again static. The entire history of states is a single ordered set, where each element exists simultaneuosly.

A necessary implication of this is that there is some kind of moving eye outside of the system which for reasons unknown moves forward through the set under its own steam and can only observe the interactions of a particular pattern within each element of the set (the pattern that represents your corporeal form), observing the set one element at a time.

If the first scenario is the true state of affairs, there is no argument. You do not have a perspective. No-one is right and no-one is wrong. There is only a single, eternal, unchanging state in which this discussion appears to have taken place. You cannot add to it because there is no future, etc, etc.

So in effect its just a species of reductio ad absurdum. A self-defeating argument that reduces itself to nonsense from its own premises.

If the second scenario is the true state of affairs there is a logically necessary past that exists, containing states that exist in that past. Causality requires tense, so we can say something "existed", meaning "it exists in the past".

If the third scenario is true there is a logically necessary past that exists and a logically necessary future that exists. The universe isn't simply the present state of a variable but an ordered set which an unexplained outside awareness steps through sequentially, aware only of components of each element (the interactions of the pattern in each element representing our corporeal form)

None of these scenarios allows us to say of past states "they never existed", even the first one, which makes observation and inference meaningless by its very nature. It even renders a large portion of the sentences on this thread, including yours, meaningless, since tense is so deeply ingrained in our language.

[seebs]

Even if we allow for an observer outside the universe, I think we still find that the analysis essentially applies. If we allow for any discussion of comprehension or patterns or future states, we have to allow for past states as well.

[beyelzu]

I haven't bothered to way through all the bullshit, but in regards to conrad's life as being some sort of model for the universe, i think that the argument is fundamentally flawed, the universe is simply not deterministic. It seemed that way before modern physics but with quantum mechanics came the realization that we know exactly fuckall about what particular particle is going to do. It's a statistical thing, and thus the universe is simply not deterministic.


Now, farren and seebs, I have enjoyed reading some of your posts in this thread, but I think that yall are getting bogged down in the minutia of an argument. Since it is impossible to know what states lead to what other states on a particle by particle basis, the universe isn't just unknowable in that way in practice it is also unknowable in principle


In short, god absolutely loves to shoot the craps.

[Kael]

Not that I personally disagree with you, bey, but saying it's not just because we don't understand it isn't right. It is possible we simply don't know all the rules yet, rather than there being any truly random elements in the universe.