- 10 Jul '08 19:33 / 2 editsIf you could be the designer of a "universe", how would you go about it?

I apologize for the metaphysical nature of this thread. Think of it as candy for the soul, and not as "Science to live by".

I would design a single irreducible ongoing computation that would begin and work toward a state that could not be known. The purpose of "existence" would be to reach that final state.

This would imply evolution. The mandate would be to change... forever change -- searching for the final "mystery" state. The only force needed in this universe could be called "change". Time and entropy and conservation would be it's children.

In this engineered universe, one would view the process as mysterious and planned, but unknowable. Any being that resulted (through evolution) as a means of pursuing the unknowable outcome, would ask "What is the meaning of existence?" and the ever changing computation would reply :

"If I knew the meaning then existence would be pointless. For if the end of the universe were present in it's beginning -- if we are merely in the middle of a deterministic unfolding of a set of initial conditions -- then the universe would be a pointless exercise. I am not pointless. You are not pointless. Everything has partial meaning. Nothing has full meaning until the computation is complete."

What kind of a universe would you engineer in this grand scheme? What mechanisms would you use for genesis?

I would invoke "a prime law" to embed math as the prime mover. Then I would use math/geometry to design a "rack" upon which matter/space/time could be installed. Then I would use higher maths to build space/time/energy/consciousness and hang it on the rack of space/time. This entire mechanism would be called "reality".

So the mechanism is mathematics. The very essence of space/time/matter and indeed the underpinning dark energy/matter??? that is the framework would all be part of the initial irreducible computational engine/problem/... slash "What"?

It is at this initial point of genesis that my imagination fails me. Some "force" so mighty that it builds "Integer" into "something" and proceeds to invest all of space time with "realness"...

The problem is this "prime law". My imagination can't even begin to envision the beginning. How would the "prime law" invent math? And "invent" implies intelligence, which is not logical, as we are trying for a "beginning of a universe" here. How would math create time? Or Space? Or .... anything. Which came first? Geometry or Curved Space/Time? My "prime law" must act in some way to give math physical reality. Math must be able to "fold" or "act upon" something in order to create the dark matter rack of reality.

The big bang obviously holds a truth, in as much as it seems to have happened. But in a universe where time is so weird... does "begin" have any force of "realness"? - 10 Jul '08 21:02

And the final question, who invented the 'prime law', which opens up an unending quest, for if you find that out, then what invented THAT, etc...*Originally posted by StarValleyWy***If you could be the designer of a "universe", how would you go about it?**

I apologize for the metaphysical nature of this thread. Think of it as candy for the soul, and not as "Science to live by".

I would design a single irreducible ongoing computation that would begin and work toward a state that could not be known. The purpose of "existence" wou ...[text shortened]... .. does "begin" have any force of "realness"? - 10 Jul '08 21:16 / 1 edit

Same question really. What was before...*Originally posted by FabianFnas***Okay, I have the opportunity to create a Universe from the beginning.**

Then, in which universe do I belong? Outside the universe I'am in verge to create?

So, before my creation, where am I?

It's the big pyramid scheme in the sky - 10 Jul '08 23:28 / 1 edit

lol*Originally posted by sonhouse***And the final question, who invented the 'prime law', which opens up an unending quest, for if you find that out, then what invented THAT, etc...**

You hit upon the question that is "not knowable". For the task you set the equation/function/engine (whatever) is to discover the "prime law".. inducing an eternal loop you see.

That puts the meaning of "existence" into the same condition that we find ourselves in... in this "real" universe.

from original post... "I would design a single irreducible ongoing computation that would begin and work toward**a state that could not be known.**" - 10 Jul '08 23:39

Well, all you need to do for that is to have a computer try to figure the exact value for PI, 3.14159......... Seems that satisfies your quest.*Originally posted by StarValleyWy***lol**"[/b]

You hit upon the question that is "not knowable". For the task you set the equation/function/engine (whatever) is to discover the "prime law".. inducing an eternal loop you see.

That puts the meaning of "existence" into the same condition that we find ourselves in... in this "real" universe.

from original post... "I would design a single i ...[text shortened]... computation that would begin and work toward [b]a state that could not be known. - 10 Jul '08 23:49

It can be done by making a world, drawing a perfect circle of diameter 1m and saying pi is the length of the edge of the circle.*Originally posted by sonhouse***Well, all you need to do for that is to have a computer try to figure the exact value for PI, 3.14159......... Seems that satisfies your quest.** - 11 Jul '08 02:19

Not to burst your bubble but that is the circumference. PI is the ratio between the diameter and the circumference. It doesn't matter if you make the circle the size of the solar system, you won't find an exact number for PI.*Originally posted by flexmore***It can be done by making a world, drawing a perfect circle of diameter 1m and saying pi is the length of the edge of the circle.** - 11 Jul '08 02:47 / 1 edit

Erm, yes you will. Presumably if you are the Uber-Engineer, you can make perfect little Archimedean circles, and thus specify pi, although you won't be able to write it down in positional notation (and it's a little bit anthropomorphic, for this metaphysical thread, to predicate your notion of exactness on positional notation).*Originally posted by sonhouse***Not to burst your bubble but that is the circumference. PI is the ratio between the diameter and the circumference. It doesn't matter if you make the circle the size of the solar system, you won't find an exact number for PI.**

Actually, this is interesting -- I've assumed the Uber-Engineer capable of perfect Euclidean feats, but said "writing a decimal expansion of pi that is exact is so impossible that even God can't do it". This distinction exposes some assumptions about the Uber-Engineer.

EDIT What is wrong with flexmore's post? When the diameter is 1, the circumference is pi. - 11 Jul '08 06:05

What if, if you were a über-Über-engineer and constructed a circle with a diameter the same as that of the Universe - is pi still the ratio between the circle's diameter and its circumference?*Originally posted by sonhouse***Not to burst your bubble but that is the circumference. PI is the ratio between the diameter and the circumference. It doesn't matter if you make the circle the size of the solar system, you won't find an exact number for PI.**

Actually, in this case, I would say no. I think pi is not a constant in big scale in practical sense, but it varies with the diameter.

If you have a circle large enough you can actually measure the curvature of the space. Only if Space is Euclidic, pi is the conventinal one, but is Space really Euclidic? - 11 Jul '08 06:21 / 1 edit

I misread flexi's post. I see what you mean now. But the circumferance is still not going to be able to be pinned down in terms of the diameter because they are like different units, like meters on one hand and you need fathoms on the circumference or some such. If you try to measure the circumference you just run into the problem of scale, you have a microscope on the circumference ruler and you need bigger and bigger magnification to see that each time you try to measure it, when you go to a larger magnification it has slid out of the way a bit, so you do that again and go to yet a higher magnification and it has slid out of the way a little bit again and so forth.*Originally posted by ChronicLeaky***Erm, yes you will. Presumably if you are the Uber-Engineer, you can make perfect little Archimedean circles, and thus specify pi, although you won't be able to write it down in positional notation (and it's a little bit anthropomorphic, for this metaphysical thread, to predicate your notion of exactness on positional notation).**

Actually, this is i DIT What is wrong with flexmore's post? When the diameter is 1, the circumference is pi.

It would be interesting as Fab says, to see what PI is around the whole universe. Also what is PI even around a planet, since the gravity of the planet will change space-time a bit. It would seem you would get a different value for PI when you are on the ground vs when you are a thousand miles up in space. A very slight difference I would say. - 11 Jul '08 14:05 / 2 edits

That's all true. What I was getting at is that saying "The circumference of this circle of diameter 1 is pi" is giving an exact value for pi -- the ability to do arithmetic with exact values doesn't really require that we write down some numbers. Euclid was doing arithmetic with exact values with no knowledge of modern number notation.*Originally posted by sonhouse***I misread flexi's post. I see what you mean now. But the circumferance is still not going to be able to be pinned down in terms of the diameter because they are like different units, like meters on one hand and you need fathoms on the circumference or some such. If you try to measure the circumference you just run into the problem of scale, you have a micro ...[text shortened]... the ground vs when you are a thousand miles up in space. A very slight difference I would say.**

EDIT Besides, if I were the Uber-engineer, gravity would be first to go (as in, the last part of your post is an interesting point, and in my universe there would be no pesky interesting little bits of physics to get between me and my perfect circles ). - 13 Jul '08 03:26 / 1 edit

If gravity were to go, it would seem to me no accretion could take place so no stars would form and no planets.*Originally posted by ChronicLeaky***That's all true. What I was getting at is that saying "The circumference of this circle of diameter 1 is pi" is giving an exact value for pi -- the ability to do arithmetic with exact values doesn't really require that we write down some numbers. Euclid was doing arithmetic with exact values with no knowledge of modern number notation.**

EDIT Besides ...[text shortened]... be no pesky interesting little bits of physics to get between me and my perfect circles ).

I was thinking about that PI thing in various gravity fields, it seems to me if you draw the circumference around a planet and then were able to draw a line straight across to be the diameter ( you would of course be stabbing a needle through the planet but we are using a planet with a magic hole right through it that doesn't touch our line).

So going though a higher gravitational field would seem to me the geodesic would make the line length longer than if a mass were not present, so the 3.14159... would go down slightly, 3.14158... Heck, with the right size field, PI might not even be an irrational # any more. Maybe at some point it would be exactly 3.000000000000000000000000.

I wonder what PI would be like if you were at the event horizon of a black hole, talk about extremes!

IF PI changes near a black hole, then the exact # would depend on which direction you drew the circumference, like tangent to the singularity, it would be symmetrical but if it were drawn down and up from the singularity it would effect the circumference AND the diameter. - 13 Jul '08 06:02

This has me wondering, but here are some things, mostly in case I have time to think about this again and catch on to what you're saying:*Originally posted by sonhouse***If gravity were to go, it would seem to me no accretion could take place so no stars would form and no planets.**

I was thinking about that PI thing in various gravity fields, it seems to me if you draw the circumference around a planet and then were able to draw a line straight across to be the diameter ( you would of course be stabbing a needle through th ...[text shortened]... were drawn down and up from the singularity it would effect the circumference AND the diameter.

Given a 2-dimensional Riemannian manifold M, let a "circle" in M be the set of points at a given distance (wrt the Riemannian metric) from a given point. It's almost 2 am and it's been some months since I messed with anything like this, but I'm pretty sure this circle is a nice 1-submanifold of M. It's circumference is just its length, and its diameter is the length of any maximally long geodesic segment with endpoint on it. In general, the ratio of circumference to diameter will vary from circle to circle within the manifold, so pi is not constant in general, like you say.

Conjecture 1: There are manifolds of constant curvature in which pi is not constant (the motivation here is that pi defined differently, as the sum of the angles in a triangle, is not constant in the hyperbolic plane, say).

Conjecture 2: The two definitions of "pi" given above are somehow locally equivalent.

Task for geometers: Let pi be defined pointwise on M by stating that pi at a point is the pi (as defined above) for the unit circle centred at that point. Then the pi map is a smooth map from M to the positive reals. Write it down explicitly -- what different values can it take? What if M is something gravitationally realistic?

Speculation: The triangle angle-sum definition is way better than the circumference/diameter definition, for sonhouse's purposes.