Conway's Life, seebs

[Michali]

Step one: show that the initial state of a closed system is (essentially) its endstate. (3+3=6)

Step two: describe an end state as an infinite loop on a closed-finite grid, and explain oscillation via means of static extra-dimensional value.

Step three: postulate the universe is a closed and finite system, and what that means about our present circumstances.

[Kael]

Step four: Profit.

[seebs]

Originally Posted by Michali

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

Nope.

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

It does. Precisely.

But the function does not make the inputs and outputs the same thing.

For one thing, there are many functions.

Imagine, if you will, a function "fry". Applied to bacon, it gives you crispy bacon; applied to eggs, it gives you fried eggs. Applied to a cat, it gives you jail time.

That doesn't mean that a cat is jail time, or that all bacon is crispy. It means that bacon can become crispy.

Now, what if all bacon is always fried. Thus, no matter what, every piece of bacon will one day become crispy.

Your argument is that this means that all bacon is ALREADY crispy, we just don't know it. My argument is that if it's floppy, soggy, and full of uncooked fat, it's not crispy, even if it may later become crispy.

For some reason, you seem totally, blindly, devotedly, fixated on the notion that, if something will eventually undergo a transformation, that it's already undergone it and no prior state matters. This is bullshit. This is stupid. It makes no sense at all.

By your argument, the inevitability of dying means that everyone is already dead, we just don't "perceive" it yet. But that's fucking stupid. Not just stupid; fucking stupid. We can distinguish between life and death. We can talk about whether death is imminent or may be some time away yet. We can do things between now and then.

The mere fact that states may at some point resolve to an outcome does not mean that they already have. It does not mean they are just the same as if they had. It just means that they will, later, resolve to that outcome. So what? The destination is not the journey.

[seebs]

Originally Posted by Michali

Step one: show that the initial state of a closed system is (essentially) its endstate. (3+3=6)

But you haven't done this. At all. You haven't even begun to hint at a thing which could be the outline of a schema for describing a way in which one could explore the question of whether there might be evidence leading to such a conclusion.

You've just assumed it, declared it, asserted it, repeated it, and occasionally said that, since it's true, something else must be true which proves your assumption.

You haven't offered a meaningful definition, or an explanation, or anything which would lead to an explanation of why this would be true. In fact, you haven't even really explained what it would mean to say this was true. You've just said it's true.

Okay, let's try going at this from a different angle.

Let us assume that the claim "the initial state of a closed system is (essentially) its endstate" has meaning.

For this to be true, I think we have to be able to describe what it would mean if it were false. So, let's call the statement above statement E (for "endstate"). And let's consider statement ~E: "the initial state of a closed system may not be (essentially) its endstate."

Now, if E has meaning, you should be able to describe some kind of difference between a world or system or something in which E is true, and a world or system or something in which ~E is true.

Let me give an example.

Let's say I take the statement "for any line on a plane, and any point not on that line, there is exactly one line containing the given point which does not touch the first line." (We'll call this P, for Parallel Postulate.) Now, consider a contrary statement; "for any line on a plane, and any point not on that line, there is no line containing the given point, which does not touch the first line."

I can show you how each of these systems differs. I can even give you examples of both; the first is classical Euclidean plane geometry, the second is geometry on the surface of a sphere. On a sphere, any straight line (which turns out to be a great circle of the sphere) through a point must necessarily intersect any line that doesn't contain that point. There are no "parallel" lines in the sense we normally understand them. (Latitude lines aren't straight; they're "curved" with respect to the geometry of the sphere. By contrast, note that longitude lines always intersect at the poles.)

See, this makes it possible to discuss the hypothesis, because we can talk about how we'd tell whether it is true or not.

So, let's take, say, Conway's Life.

You claim that for a "closed" system (what's "closed" mean? What makes something a "system" or "not a system"?), the initial state "is (essentially)" the end state.

So. How would we tell whether this were true or not? Show us what it would mean to say that it were false; what would have to be different about Conway's Life for it not to meet your description?

[Farren]

Originally Posted by Michali

Step one: show that the initial state of a closed system is (essentially) its endstate. (3+3=6)

I just don't get your basis for doing this.

For a start, your arithmetic rendering above doesn't match your words or the system being discussed . The Game of Life follows a rule of the general form Staten = f[Staten-1]*. In your simpler way, it might be rendered as 6=f(3) for a given iteration or even the translation from first to last state in a finite step Game of Life, but not 3+3=6.

One state leads to one state, if you wish to put it in those terms, so the extra "3" implying an extra state in your formulation above is already just cause for confusion. If you consider the two "3"s above to represent entire states, well, any given state of Conways life is not a function of two other states, but one. So I'll take the above as a rough analogy to entire states and assume its a flawed analogy, with my restatement of the calculation being more correct.

Now 6=f(3) does not imply 6=3. Yet thats exactly what you're implying. The word "is" in my mind maps most closely to the symbol "=" in math. If 6 is considered to be the "end state" and 3 the "initial state" then, since 6 is not equal to 3, the statement "the end state is the initial state" is simply wrong. 6 is a function of 3. It is not 3.

In light of this, it looks like you're using some other, hermeneutic definition of "is" which is opaque to the rest of us. And using uncommon definitions of words that no one else is privy to effectively amounts to communicating nothing. And I think it arises more from equivocation in your own mind than any deeper meaning actually existing. What do you mean by "is" if not "="?

*If you're not familiar with this kind of pseudo-code rendering of formulas f(state) means "some function of states" and staten/f(staten-1) is shorthand "any given state in an ordered set"/"some function of the prior state in the same ordered set" respectively.

[S.Vashti]

And what does one call an end state when Conway's Life shows a stable oscillating series (like 10 across)? This is one of the reasons why it's not a reasonable claim to make, that the end state is equivalent to the initial state.

I point out the 10 cell across initial state, because the stable end state never again displays the initial 10 cell across position, but instead oscillates between 16 different iterations.

[seebs]

The other interesting case (which does require an infinite grid, of course) is the case where there's no stable oscillation or final state, but a continuous development.

[Michali]

Originally Posted by seebs

Nope.

Bi-conditionals are obviously to blame for equalities in value. Just think of the problem:

a.) 3+3=6. (6 is the value of 3+3, if and only if 6 is the value of 6)
b.) 1+5 <=> 6
c.) even if its x+y=6 (x+y is the value of 6, if and only if 6 is the value of 6)

So why can't I, in light of knowing a,b,c, say that 3+3 is the value of six if and only if 1+5 is the value of six if and only if x+y is the value of six if and only if 6+0 is the value of six?

Originally Posted by seebs

It does. Precisely.

But the function does not make the inputs and outputs the same thing.

I don't get this. Causeway's life, you'll agree, is at least deterministic. If its deterministic its operating using bi-conditionals. Well what do you mean when you say the function of the input which determines the output, does not have the same value as the output?

Originally Posted by seebs

For one thing, there are many functions.

Imagine, if you will, a function "fry". Applied to bacon, it gives you crispy bacon; applied to eggs, it gives you fried eggs. Applied to a cat, it gives you jail time.

That doesn't mean that a cat is jail time, or that all bacon is crispy. It means that bacon can become crispy.

Now, what if all bacon is always fried. Thus, no matter what, every piece of bacon will one day become crispy.

Your argument is that this means that all bacon is ALREADY crispy, we just don't know it. My argument is that if it's floppy, soggy, and full of uncooked fat, it's not crispy, even if it may later become crispy.

For some reason, you seem totally, blindly, devotedly, fixated on the notion that, if something will eventually undergo a transformation, that it's already undergone it and no prior state matters. This is bullshit. This is stupid. It makes no sense at all.

By your argument, the inevitability of dying means that everyone is already dead, we just don't "perceive" it yet. But that's fucking stupid. Not just stupid; fucking stupid. We can distinguish between life and death. We can talk about whether death is imminent or may be some time away yet. We can do things between now and then.

3+3=6 ... the "3+3" is input. The 6 is the output. Method is something that we do because we don't know the value of something, it isn't a fact about what we're dealing with.

You're purposely thinking of input only in terms of something like F(x) in "3+x"=6. That is totally not what I'm referring to and I never used a variable when explaining this phenomenon. Obviously our input into Causway's Life is that of an entire grid. We don't have input coming along via means of our little brother pushing us out of the way and plotting a whole bunch of random points in my scenario.

I've been saying over and over that all the variables, if known, (AKA if the grid cannot be interfered with and the entire given grid is taken into account) then the input is the output. Saying it will be the output is only what you would say if you needed to work it out.

This is the form of equality I'm talking about. This is absolutely no different than us saying "3+3" is "6". "3+3"... That is 6, but it appears as 3+3 because you haven't added them together yet.

Originally Posted by seebs

The mere fact that states may at some point resolve to an outcome does not mean that they already have. It does not mean they are just the same as if they had. It just means that they will, later, resolve to that outcome. So what? The destination is not the journey.

The answer is, a "state" of a system is coming directly from not understanding the value of that system. You see a sequence of states because you are trying to figure out what it is that you are observing. Its apparent to me, now, that "states do not work themselves out" (as you suggested), and whether or not you're conscious of it, you, observer, is working them out.

[seebs]

Originally Posted by Michali

I don't get this. Causeway's life, you'll agree, is at least deterministic.

Conway's. But yes, it's deterministic.

If its deterministic its operating using bi-conditionals.

What does this mean?

Well what do you mean when you say the function of the input which determines the output, does not have the same value as the output?

I mean that they're different things.

Imagine the function f(x) = x+1.

f(2) = 3. f(3) = 4.

This does not mean that "2 equals 3". It means that "2, modified by f(), equals 3."

3+3=6 ... the "3+3" is input. The 6 is the output. Method is something that we do because we don't know the value of something, it isn't a fact about what we're dealing with.

The method also exists.

It is one of the inputs!

You're purposely thinking of input only in terms of something like F(x) in "3+x"=6. That is totally not what I'm referring to and I never used a variable when explaining this phenomenon. Obviously our input into Causway's Life is that of an entire grid. We don't have input coming along via means of our little brother pushing us out of the way and plotting a whole bunch of random points in my scenario.

I'm thinking of inputs and outputs as separate, because they are separated by an operation.

I've been saying over and over that all the variables, if known, (AKA if the grid cannot be interfered with and the entire given grid is taken into account) then the input is the output.

Yes, you have been saying that all along.

It's still wrong.

You can say it over and over and over, and it doesn't become right.

Saying it will be the output is only what you would say if you needed to work it out.

No, it's what I would say if there were a PROCESS by which A becomes B.

A is not B.

If "f(x)" is "the next letter after x", then f(A) is B. But that doesn't make A the same as B.

This is the form of equality I'm talking about. This is absolutely no different than us saying "3+3" is "6". "3+3"... That is 6, but it appears as 3+3 because you haven't added them together yet.

But they are totally different.

The states in life are like a function. Imagine f(x) = x + 3.

f(3) = 6.

f(4) = 7.

But that doesn't mean 3=6. It means that there's a function involved.

Conway's life gives a function from input states to output states. They aren't the same.

The answer is, a "state" of a system is coming directly from not understanding the value of that system.

This is meaningless.

You see a sequence of states because you are trying to figure out what it is that you are observing.

No, I see a sequence of states because there is a sequence of states, each of which is different, and results from a process.

Its apparent to me, now, that "states do not work themselves out" (as you suggested), and whether or not you're conscious of it, you, observer, is working them out.

Please take a week off from the wacky baccy and come back to this.

[Michali]

Originally Posted by seebs

The other interesting case (which does require an infinite grid, of course) is the case where there's no stable oscillation or final state, but a continuous development.

I'm inclined to think that stability is achieved via even higher levels of dimensional explanation on an infinite grid.

No oscillation means no static third dimensional representation, unless that oscillation is recorded in non-finite ways.

So, explosion A oscillates continuously while the oscillating factors are sustained closer to the center of the explosion. Relatively speaking, the center of the explosion will repeat more towards the center than on the fringes, in most explosions, since containment will act as a temporary finite grid. Explosion B is far away and is also maintaining oscillation at a further distance with emptiness in between. So we have relatively 3 dimensionally related "macro-cells" operating at a distance until they end up meeting. This extra dimension is now a time component allowing for 3-d cells to interact on a macro level.

This must ultimately stabilize if this "time-grid" is finite. And such a picture of a what the stable thing would look like, I don't know.

[Michali]

Seebs, I really can't argue with you any clearer about this. The input of "3+3" to "arithmetic" is 6.

f(x) = x under arithmetic laws... aka put into a calculator

f(3+3) = 6.

The input "3+3" can't be reasonably be put into non-arithmetic, seebs. Saying it can will be like, f(x)= x as an image. f(3+3)= the image of "3+3"

Ok yeah stick 3 in a system where its being added by 3, you get 6. That is not as easily put in Conway's life. Conway's life is a set of laws about cells and what they do. But what if there's only one law? There aren't any need for multiple states.

f(x)=x changes under the conditions of Conway's rules.
f(lone blue square)=grey square

What is that equals sign doing, seebs?^^^

Isn't that saying that the function of a lone blue square is a grey square? If the output is "turns into a grey square", how could the simulator possibly work?

And don't say that's what it means if its a joint action, like, its sensibly turns into a "grey square" if you calculated a few states ahead, because thats exactly the reason a complex grid could be interpreted as its end state.

Dude, you are stubborn something else if you think this isn't understandable. Even Hume questioned what causation actually was when all we have is correlation.

[Michali]

-edit- Er actually its:

f(x)=x changes under the conditions of Conway's rules.
f(lone blue square)=grey square in the next generation.

The question about whether the equals sign can be interpreted as "is" is still a question for you.

The function of the "lone blue square" equals "the grey square in the next generation" in Conway's life.

We input a "lone blue square", and this is not the output of "a grey square in the next generation."<-- is what you're thinking is making your point.
We input "the function of a blue square", and this is the output of "the grey square in the next generation" <--- is what you think I'm thinking.
The initial state which is the "function of a lone blue square" is the "grey square in the next generation" <--- is actually what I'm thinking

[Joshua Adams]

I can't really make head or tail of this argument (since nothing you say even vaguely supports the conclusions you want), but you seem to be trying to say that function inputs equal function outputs, because "f(x) = x" and "f(3+3) = 6".

Well, those are examples where the input equals the output, but that doesn't mean it's true generally. In fact, f(x) = x is the unique function in which that property holds true for all x. You seem to be trying to generalize from specific examples from arithmetic to claim that mapping things means they're "the same".

We can model a state in Life as an array of booleans. In arrays, we define equality component by component; if aij = bij for all i and j, then grid A = grid B. That's pretty basic stuff. So, these two are not the same:


since a12 does not equal b12. This is clearly a valid way to define equality of two states. Any other definition we come up with has to be consistent with this definition.

We can, of course, define a mapping between two states. But simply having a mapping does not imply equivalence. Indeed, we can map anything to anything else. We can even give an extensional definition of the mapping, without stating any rule.

Suppose S is the set of all states. Let φ:S→S by "φ(x) has one more grey cell than x". Then inequality is built right into the function, since no grid has one more grey square than itself. φ cannot be an equivalence relation since it's not reflexive. It also fails the tests of transitivity and symmetry. So, not every function has the property that the inputs equal the outputs.

Suppose we instead consider the set T, of all states which lead to termination. Define the relation ~:T→T to mean "leads to the same end state in Conway's Game of Life as". That is, A ~ B means that A and B eventually lead to the same state in Life. You can check easily that this one is an equivalence relation, but it has some odd consequences that don't seem to be at all intuitive. Suppose you had distinct states α, A, B, C, D, ... , Z. (distinct as in, component by component, their cells do not match up exactly).

Suppose if the initial conditions are A, this happens:
A, C, E, ... , U, W, Y, α, α, ....
B, D, F, ..., V, X, Z, α, α, ....

This is possible to achieve in practice (As a trivial example, suppose you took a non-symmetrical state A that terminated in all dead cells; just flip the grid around some axis to get a different chain that results in the same thing).

Now, obviously, A~α. But also, B~C~D~...~Z~α. So, you have states which don't even appear in the same history as each other being considered "equivalent" under this arrangement. This doesn't seem right. It seems obvious that in the chain starting with A, things unfold totally differently than when they start with B. The fact that they both happen to end in α doesn't justify calling them the same. I already stipulated that they're not the same, by the definition discussed earlier. So the two definitions are inconsistent.

And it brings up another point. If the final state is the "reason" for the preceding states, then we're in a quandary. Because if we're at α, well, α can't decide between A, ..., Y and B, ..., Z. So if we ask "why did Q happen and not R" then α tells us precisely nothing. Actually, if we want to know the answer, we have to look at the beginning, not the end. Which is what one would expect, I guess.

[Michali]

Joshua Adams, thank you very much for your post. I am not that familiar with arrays and I am interested in this concept. Most of your post (after the mentioning of arrays) I could not grasp, but it does seem to rest on arrays. Let's see if I understand arrays correctly:

When you said, "In arrays, we define equality component by component" I'm going to assume that's the reason I could be wrong in claiming all function inputs are equal to their function outputs. My first question is, "Is this the only reason?" Also, I just recently managed to pin point my intuitions towards the argument that I believe a function input must always equal (and I would go so far as to say it is identical) to its function output, so I apologize for the confusing thread.

On arrays, I don't know how to use the term exactly, but it seems to refer to a group of elements. Two arrays can have different elements, and yet have the same function output. Thus, we can have different function inputs with the same function output? What I don't see, is how it defeats the argument that a function input does not equal its function output. Is this due to the transitive equality this would entail between the two different arrays?

If this is the case I would have to say that there may be a difference of arrays, but there isn't a difference of function input. Consider the case of this 3 x 3 grid where a lone blue cell is in the center, and then consider a different array where a lone blue cell is top-center. The arrays are different but the function input should only require the relevant aspects of their elements. The relevent aspect could be as specific as the function input "a lone blue cell" or as general as "any possible state that will turn the grid all grey".

This seems similiar to something you said about flipping the axis on the grid. I'm not sure what you were saying, but it would seem to suggest that elemental properties of an array do not matter when the function input could be the same in the way I mentioned above. Imagine we input "A" and saw output "B". If we stood on our head, so it appeared flipped upside down, and we input "a" and saw output "B", would we really come to think "A" is not equal to this "a"?

[Michali]

Originally Posted by Michali

I'm inclined to think that stability is achieved via even higher levels of dimensional explanation on an infinite grid.

No oscillation means no static third dimensional representation, unless that oscillation is recorded in non-finite ways.

So, explosion A oscillates continuously while the oscillating factors are sustained closer to the center of the explosion. Relatively speaking, the center of the explosion will repeat more towards the center than on the fringes, in most explosions, since containment will act as a temporary finite grid. Explosion B is far away and is also maintaining oscillation at a further distance with emptiness in between. So we have relatively 3 dimensionally related "macro-cells" operating at a distance until they end up meeting. This extra dimension is now a time component allowing for 3-d cells to interact on a macro level.

This must ultimately stabilize if this "time-grid" is finite. And such a picture of a what the stable thing would look like, I don't know.

I'm going to expound on this idea of temporary oscillation, and point out that gliders exhibit very good structure oscillation with very temporary cell-specific oscillation. Analyzing the glider, I noticed there is a structurally-central cell which seems to occupy a cell longer than the others. The glider travels in the direction that the outlying cells remain in longest. After these "forward cells", the central cell moves forward, and the back of this structure has a "tail" which seems to only occupy a cell which has been grey atleast once.

Large scale explosions could also sustain their structural oscillation via this means of grid travel on an infinite grid. I think what determines whether explosion A or B survives an intersecting event, is in which way the resultant structure continues to move. I hypothesize that, depending on their individual structures, they could create these outcomes:

cancel
pass through eachother (if there is a significant difference in power, "power" being relative length of time a cell is occupied, in which case, theoretically, small and quick macrocells could pass relatively intact)
merge for more momentum (and or average direction for a diagonal intersections) and or more or less power)
overrun at the expense of momentum (and or more or less power)
or become destroyed in full reversal.

We could actually get justification for postulating an infinite time span or a finite time span on this infinite grid with this reasoning:

Either there are no interactions between macro-cell structures or there are interactions. Time would not exist (relevantly) if there are no macro-cell interactions left. For this to be the case the grid would appear as either all grey cells or the input state on an infinite grid allows for no interaction via means of radial seperation (away from eachother in all directions, or around eachother via some means of circular movement). If time is infinite, interactions will have to take place, and some structures will acuire "averaging characteristics" via means of interaction. Some structures will continue to move away from these interacting types. The ones that will never interact will cease to exist in relevance to time, and thus we are left to consider the relationships between the averaging macro-cell structures as the next dimension.

-edit- We already find a template for the nature of the relationship between these averaging macro-cell structures, and we seem to be able to, not only differentiate, but also stratify, these enities in terms of closeness to the average power, direction, and momentum of all entities that exist. An entity approaches a perfect average via transactive interaction with other entities. The closer to the average, I can only suspect, the higher up in the stratefication we can place the entity. I suspect that the closer to the average they become, the more like a group entity they can become. Those which either do not transact, or overexagerate transactions will decrease in averageness and will fall outside this grouping effect. Thus this next dimension is something about this grouping effect, with these un-averaged entities falling out of relevant existence with respect to this next dimension.

In this next dimension of the grouping-transacting entities, we could see a stratefication here in terms of averageness to other averaging-groups on the infite grid. Interaction with these much farther away groups will require locally grouped-entities to behave in a communicative way over large distances with eachother. Those entities' behavior which are interruptive of this process of increasing communication for far-group transaction will become irrelevant to this next dimension of cross-group averaging and will ultimately be weeded out and thus not exist. This next dimension is somehing like good behavior.

Dimensions:

Cell
Line-grid (rule of cell relations founded here)
Plane-grid
Oscillation
Time
Averaging
Grouping
Good-behavior
(something dealing with the connection of all the groups in an infinite grid)

[Raven_poe]

Originally Posted by Michali

-edit- We already find a template for the nature of the relationship between these averaging macro-cell structures, and we seem to be able to, not only differentiate, but also stratify, these enities in terms of closeness to the average power, direction, and momentum of all entities that exist. An entity approaches a perfect average via transactive interaction with other entities. The closer to the average, I can only suspect, the higher up in the stratefication we can place the entity. I suspect that the closer to the average they become, the more like a group entity they can become. Those which either do not transact, or overexagerate transactions will decrease in averageness and will fall outside this grouping effect. Thus this next dimension is something about this grouping effect, with these un-averaged entities falling out of relevant existence with respect to this next dimension.

Here's my problem with this. I don't claim to be a rhodes scholar, but on average I can usually keep up pretty well. All of those words, by themselves, I can understand. But when arranged in that particular arrangement, I just have to ask. What?

[seebs]

Originally Posted by Michali

I'm inclined to think that stability is achieved via even higher levels of dimensional explanation on an infinite grid.

Do any of these words have any kind of meaning here? Because I'm sure not picking any up.

No oscillation means no static third dimensional representation, unless that oscillation is recorded in non-finite ways.

So, explosion A oscillates continuously while the oscillating factors are sustained closer to the center of the explosion. Relatively speaking, the center of the explosion will repeat more towards the center than on the fringes, in most explosions, since containment will act as a temporary finite grid. Explosion B is far away and is also maintaining oscillation at a further distance with emptiness in between. So we have relatively 3 dimensionally related "macro-cells" operating at a distance until they end up meeting. This extra dimension is now a time component allowing for 3-d cells to interact on a macro level.

This must ultimately stabilize if this "time-grid" is finite. And such a picture of a what the stable thing would look like, I don't know.

What on earth do you think the word "dimension" means?

[seebs]

Originally Posted by Michali

Seebs, I really can't argue with you any clearer about this.

I've noticed.

The input of "3+3" to "arithmetic" is 6.

This doesn't even mean anything. It is, in the immortal words of Wolfgang Pauli, not even wrong. To be wrong it would have to have some kind of semantic content.

f(x) = x under arithmetic laws... aka put into a calculator

f(3+3) = 6.

The input "3+3" can't be reasonably be put into non-arithmetic, seebs. Saying it can will be like, f(x)= x as an image. f(3+3)= the image of "3+3"

What is "as an image"? I have no idea what you think those words mean.

Ok yeah stick 3 in a system where its being added by 3, you get 6. That is not as easily put in Conway's life. Conway's life is a set of laws about cells and what they do. But what if there's only one law? There aren't any need for multiple states.

But there are multiple states. We can tell them apart because the descriptions of them are not equivalent or interchangeable.

f(x)=x changes under the conditions of Conway's rules.
f(lone blue square)=grey square

Okay.

What is that equals sign doing, seebs?^^^

Describing the relation of a function, an input, and an output.

You can't say "therefore there's no input". Take away the input and the output is gone too.

Isn't that saying that the function of a lone blue square is a grey square?

No, because the original is coherent, and the sequence of words "the function of a lone blue square is a grey square" is not coherent.

If the output is "turns into a grey square", how could the simulator possibly work?

Correctly.

And don't say that's what it means if its a joint action, like, its sensibly turns into a "grey square" if you calculated a few states ahead, because thats exactly the reason a complex grid could be interpreted as its end state.

No, it couldn't. It's different. It is a thing which later-becomes its end state.

Okay, let's try this.

Given knowledge of a series of fairly predictable events, such that you can safely assume that just about anyone you meet will be dead in a hundred years, start buying people sympathy cards for the deaths of all their loved ones. After all, since there's no such thing as "hasn't happened yet, but will" in your philosophy, they're already dead, we just haven't "perceived" it yet.

Dude, you are stubborn something else if you think this isn't understandable.

No. You're writing incoherently. You're stringing words together without any concrete or coherent definitions, and either what you're saying is batshit insane, or you're not using most of these words correctly.

Even Hume questioned what causation actually was when all we have is correlation.

And this is a total and complete non-sequitur.

[Raven_poe]

Michali has been trying to explain his theory to me over aim. Since I want to go to bed, he's agreed to let me post the chatlog of it here. Maybe you guys can make sense of it for me. I've attached it as a .txt to this post, so as to not spam those who don't want to read it with a wall o' text.

[Michali]

Seebs. Let's close our argument. I'll quote wikipedia.

The function of the input is always the function of the output. I'm sure you'll agree.

This is how this relates to Conway's Life:

"and the discrete moment at which this happens is sometimes called a tick. (In other words, each generation is a pure function of the one before."- (Conway's life wiki)

It is not the normal sense of time or causation because:

"Time is also discrete, and the state of a cell at time t is a function of the states of a finite number of cells (called its neighborhood) at time t − 1"- (Celluar automaton- wiki)

and

"Discrete time is non-continuous time. Sampling at non-continuous times results in discrete-time samples....In contrast to continuous-time systems, where the behaviour of a system is often described by a set of linear differential equations, discrete-time systems are described in terms of difference equations."- (Discrete time, wiki)

There's no need to have input because:

"The "game" is actually a zero-player game, meaning that its evolution is determined by its initial state, needing no input from human players."- (Conway's game of life, wiki)

Now that you know you are completely wrong, how ridiculous did I sound? I didn't even research until now.

[Michali]

Oh shit I think I pwnz0rd the world.

-edit- and just to top it off, which I will repost to close my last thread, thermodynamics are reversible because:

"If a deterministic process is time reversible, then the time-reversed process satisfies the same dynamical equations as the original process, AKA reversible dynamics; the equations are invariant or symmetric under a change in the sign of time. Classical mechanics and optics are both time-reversible. Modern physics is not quite time-reversible; instead it exhibits a broader symmetry, CPT symmetry." - (Time reversibility, wiki)

and that just means it can be done with:

"In physics, the laws of motion of classical mechanics have the above property, if the operator π reverses the conjugate momenta of all the particles of the system, p -> -p . (T-symmetry).

In quantum mechanical systems, it turns out that the weak nuclear force is not invariant under T-symmetry alone. If weak interactions are present, reversible dynamics are still possible, but only if the operator π also reverses the signs of all the charges, and the parity of the spatial co-ordinates (C-symmetry and P-symmetry)." - (Rversible dynamics, wiki)

[Farren]

Its apparent you don't have the math, programming, or physics knowledge to even express yourself properly, but you're repeatedly telling a bunch of programmers, mathematicians and physics nerds that they're wrong when you barely understand their terms. That's clear from the fact that you keep using these terms in the wrong way.

I'm a programmer and software architect and a bit of a science geek. Seebs writes books on programming. Believe me, you haven't pwnz0red anyone. You're still just stringing together terms in a manner that makes no sense to anyone.

The function of the input is always the function of the output. I'm sure you'll agree.

Here's what you just said, in more formal terms:

If output=f(input) then input=f'(output)

Now this is actually true, but it doesn't mean what you think it means, in fact in many cases it means exactly what Seebs has been trying to communicate.

By way of illustration, lets say you have a system that evolves by squaring its previous state (squaring is the "function") and presume an initial state represented by the number -2. Three iterations of the system will produce the following ordered set of states:

{-2,4,16,256}

Pretty clear so far. 4=square(-2), 16=square(4) and 256=square(16). So looking at that set one can infer that, for any single element of the set (statet),

statet=square(statet-1)

So the output is a function of the input.

OK now lets examine the second half of your statement. To wit, that the input must always be some function of the output. One would assume that, since the output is always a square of the input, the input is always the square root of the output.

So, for any given element of the set (statet), we would expect that

statet = squareroot(statet-1)

Which is saying that the input is a function of the output.

Only problem is, all positive numbers have not one but two square roots, and the square roots of negative numbers are irrational.

squareroot(16) = {4,-4}
squareroot(4) = {2,-2}
squareroot(-2) = squareroot(-2) (this can't be reduced to a rational number)

So you can see that the relationship between set elements from left to right in the set is not the inverse relationship going from right to left in the set. If we tried to use a squareroot function to predict the initial state from the end state (256), we'd get a different set:

{{{{-2,2},squareroot(-4)}, squareroot(squareroot(-16))},{{4,-4},squareroot(-16)},{16,-16},256}

which is not the same as

{-2,4,16,256}

In fact, There isn't a function of the form

statet = squareroot(statet-1)

for each element of the set, to describe the set going from right to left (backwards in time, if you will). Instead there are a set of branching possibilities, because inverse of the function that clearly informs to evolution of the set from left to right produces a set of two outputs for any positive number.

Which is another way of saying in our simple system above you can infer, with certainty, the future (the next element) from the past (the current element), but not the past from the future.

So there's an implied direction in the relationship between the elements of the set, implied by the direction in which a single function explains the progression of elements.

There's no need to have input because:

"The "game" is actually a zero-player game, meaning that its evolution is determined by its initial state, needing no input from human players."- (Conway's game of life, wiki)

Now that you know you are completely wrong, how ridiculous did I sound? I didn't even research until now.

Michali it seems you've convinced yourself but no-one else. The rest of us, in contrast, understand each other but can only make out shreds of coherence in what you're saying.

Lets dig through what you've just posted and try to figure out whether it has any bearing on anything

"and the discrete moment at which this happens is sometimes called a tick. (In other words, each generation is a pure function of the one before."- (Conway's life wiki)

It is not the normal sense of time or causation because:

"Time is also discrete, and the state of a cell at time t is a function of the states of a finite number of cells (called its neighborhood) at time t − 1"- (Celluar automaton- wiki)

and

"Discrete time is non-continuous time. Sampling at non-continuous times results in discrete-time samples....In contrast to continuous-time systems, where the behaviour of a system is often described by a set of linear differential equations, discrete-time systems are described in terms of difference equations."- (Discrete time, wiki)

And? Do you remember how this discussion started? Seebs gave Conway's life as an example of a sequence of events which, when taken together, have an implied direction. He then suggested that our universe may be similar in that respect. And nothing you've said so far contradicts that.

In fact the idea that time may have minimum, discrete units in our universe is present in several physical theories. There is no certainty that time in our universe is not discrete. Going a step further, cellular automata similar to Conways Life have actually been suggested as models for how the universe operates, by physicists.

So what, exactly, did you establish above?

There's no need to have input because:

"The "game" is actually a zero-player game, meaning that its evolution is determined by its initial state, needing no input from human players."- (Conway's game of life, wiki)

This is one of those arguments that the rest of us just look at and say "what the fuck is he actually saying?".

By definition, the input for a given iteration of Conways life is the output of the previous iteration. Whether a human sets the initial state or its randomly generated is irrelevant. Every iteration has an input. To wit, the output of the previous iteration. So, uh, there is a "need" for input, because otherwise you aren't talking about Conways Game of Life.

Now that you know you are completely wrong, how ridiculous did I sound? I didn't even research until now.

LOL. I'm glad you convinced yourself. Now try convincing the rest of us.

[Joshua Adams]

Originally Posted by Michali

Joshua Adams, thank you very much for your post. I am not that familiar with arrays and I am interested in this concept. Most of your post (after the mentioning of arrays) I could not grasp, but it does seem to rest on arrays. Let's see if I understand arrays correctly:

Arrays are ordered, indexed lists. I'll give you a one dimensional array with 5 elements:
A = {5, 76, 0, 9, 14}.
We index the array elements as follows: A1 = 5, A2 = 76, A3 = 0, etc. (Sometimes we start at 0 instead of 1 with the indices, but that makes no difference).

What I showed you before was a two dimensional array. This is also known as a Matrix. Each component needs two indices (subscripts) in order to specify its row and its column within the matrix. Actually, a two dimensional array is an array of arrays if you think about it. Each column, for instance, is just a 1D array in itself.

Three dimensional arrays are easy to visualize; imagine a 2D array, where each cell is actually a stack of elements instead of just one element. Hence, a 3D array is an array of 2D arrays. We can extend to higher dimensions by applying this "array of arrays" concept over and over, but it's impossible to visualize what they'd look like.

When you said, "In arrays, we define equality component by component" I'm going to assume that's the reason I could be wrong in claiming all function inputs are equal to their function outputs. My first question is, "Is this the only reason?" Also, I just recently managed to pin point my intuitions towards the argument that I believe a function input must always equal (and I would go so far as to say it is identical) to its function output, so I apologize for the confusing thread.

The reason you are wrong in claiming that function inputs equal function outputs, is because they don't, in general. As I said, there is exactly one function for which this holds true for all x: f(x) = x. Other functions map certain inputs to themselves but not all. For example, f(x) = x2 maps 0 and 1 to themselves, but everything else gets mapped to something different. Still other functions map everything to something different. For instance, f(x) = x+1. Clearly, if x+1 were equal to x, then 1=0. Which is absurd. So f(x) does not equal x in this case.

On arrays, I don't know how to use the term exactly, but it seems to refer to a group of elements. Two arrays can have different elements, and yet have the same function output. Thus, we can have different function inputs with the same function output?

It depends on the function. For example, you could define a function on a set of arrays, g(X). And suppose g(X) = 0 for all X. Then clearly every input has the same output, for that function. Other functions will yield different outputs

Important observation: You can map things together that come from completely different sets! So I just mapped an array to the number 0. These are clearly two entirely different species of mathematical object, but here they are in a function together.

What I don't see, is how it defeats the argument that a function input does not equal its function output. Is this due to the transitive equality this would entail between the two different arrays?

It is due to innumerable counterexamples that we have given you. We've given many functions whose inputs don't equal their outputs. So your idea is false. Period.

If this is the case I would have to say that there may be a difference of arrays, but there isn't a difference of function input. Consider the case of this 3 x 3 grid where a lone blue cell is in the center, and then consider a different array where a lone blue cell is top-center. The arrays are different but the function input should only require the relevant aspects of their elements. The relevent aspect could be as specific as the function input "a lone blue cell" or as general as "any possible state that will turn the grid all grey".

Sure, you could come up with a [b]specific[/i] function that maps the two grids to the same thing. You could have a piecewise function which specifies what the output would be for any grid with a single blue square. What of it? The only limit to what a function can do is your imagination.

This seems similiar to something you said about flipping the axis on the grid. I'm not sure what you were saying, but it would seem to suggest that elemental properties of an array do not matter when the function input could be the same in the way I mentioned above. Imagine we input "A" and saw output "B". If we stood on our head, so it appeared flipped upside down, and we input "a" and saw output "B", would we really come to think "A" is not equal to this "a"?

Yes, since A and a are different. Their components don't line up.

[Michali]

Originally Posted by Joshua Adams

Yes, since A and a are different. Their components don't line up.

Thank you, and let's see. What if I hung upside down from the cieling, and my brother sat straight up. We begin the simulator of the top-center blue cell. Was it "A" (right side up) or "a" (upside down) that we input?

If its one or the other, whats the reason? Is it relativity? If its relativity, isn't that suggestive that this is a result of my relationship to it, and not what it actually is?

[Joshua Adams]

Standing on your head doesn't actually change anything, if you're feeding the grid into a computer program. Obviously. Then if you're upside down and you perceive the blue square to be in row 3, column 2 instead of row 1, column 2, you're simply wrong. The problem arises because you are numbering the squares according to their relative position to you, whereas actually the program has a well-defined internal ordering.

Because of this, there's a difference between flipping the grid and flipping yourself. Flipping the grid means actually feeding the computer the grid that would result from such a flip. It would recognize this as a different initial condition.