Cosmological "pure" numbers

[The "forces" of nature arise from various media operating on various scales.] -EBTX

MM would appear to distinguish scale from medium. A scale not independent from medium is suggested at www.fractalcosmology.com as associated with a candidate for a cosmologically "pure" number of 10^30. See site.

>Logic is invariant because it does not depend on existence. If we found our universe failing to obey the rules of logic, we could safely conclude that our universe was not reality, but a sophisticated "holo-deck" created by some intelligence to present us with an artificial reality where the rules can be changed at the whim of the programmer. -|Tom|-

I'm not sure that I agree with this. Logic is a thought process conceived by human beings that seems to have relevance to what we observe, but I would argue it only has relevance because the said "logic" is inherent to the physical universe. Our brains are made of substance that is part of the universe and we are constrained by physical law to only conceive thoughts allowable by those rules. We cannot conceive of a mathematical priciple that does not have in some sense a "physical" counterpart. If the universe obeys Euclidean geometry does that mean hyperbolic geometry is a conception outside the box? No. You will observe hyperbolic geometry in M.C.Escher artwork. This is the basic reason why mathematics is applicable to the outside world, we cannot conceive things outside the laws of the substance of what we ourselves are made of. I would agree with the 2nd part of your statement though because if the rules of the universe changed our very thought processes would change along with it and we would never observe a logical contradiction because logic itself would change.

There are some issues surrounding the acceptance of true infinity in a physical theory that I find interesting to contemplate. Here are a few:

1. The MM predicts matter substance at all scales of size. Let us use a mathematical analogy here. Conventional science can be viewed as believing in a number line that begins suddenly at 0, proceeds by integer marks and ends at some finite number. The MM basically says now that the number line goes from - to +infinity with all the real numbers inbetween. Mathematicians recognize now that there is an infinite heirarchy of infinities starting with aleph 1. The MM recognizes aleph 1 as being physically real, Tom have you given any thought to the notion that physical substance actually extends to the higher levels of aleph also?

2. If infinite amounts of matter extend to infinity than any physically realizable organization of matter must exist somewhere at any time. In fact, by PURE PROBABILITY alone life must arise out of matter and do so an infinite number of times. It then seems to me that the MM in effect takes the Many Worlds hypothesis and simply moves them all into the currently existing one that we experience, anything imagineable is actually occuring somewhere. Is this a fair assessment?

3. A truly infinite universe could explain the Fermi paradox. Intelligent aliens haven't gotten to us yet because we happen to live in a subsection of the universe where intelligent aliens are simply too far away to run into us.

4. If there are micro entities infinitely below the ones we know of in the atomic realm then it seems that there exists in priciple no end to Moore's Law of computer circuitry. The universe would have an infinite amount of information and an infinite storage capacity. Imagine computers being able to simulate worlds down to the atoms in real time.

5. Does the MM have any prediction about the speed of entities on different scales? Electromagnetic waves are far slower than gravitation, are sub-micro waves moving slower than electromagnetic and super-galactic waves moving far fast than gravity or is there no relation between scale and media velocity?

Food for thought.

>[Jeremy]: Logic is a thought process conceived by human beings that seems to have relevance to what we observe, but I would argue it only has relevance because the said "logic" is inherent to the physical universe.

Logic is the process of reasoning. It should not be confused with the laws of physics or the nature of the universe. The rules of logic do not depend on anything physical or even on existence.

>[J]: Our brains are made of substance that is part of the universe and we are constrained by physical law to only conceive thoughts allowable by those rules.

Humans did not invent logic. The marvel is that we are evolved enough to discover and understand it.

>[J]: We cannot conceive of a mathematical priciple that does not have in some sense a "physical" counterpart.

Let's not mix math into this subject. I made no statements here about math. That's a whole other question.

An example of logic is "If A implies B and B implies C, then A implies C". That is a general, absolute truth and does not need a physical counterpart.

> [J]: 1. have you given any thought to the notion that physical substance actually extends to the higher levels of aleph also?

The MM has five dimensions, each of which ranges from infinitesimal to infinite. At a given time and scale, the universe would have aleph-3 units of substance.

> [J]: 2. the MM in effect takes the Many Worlds hypothesis and simply moves them all into the currently existing one that we experience, anything imagineable is actually occuring somewhere. Is this a fair assessment?

The ordinary meaning of "universe" is everything that exists. So yes, MM is in a sense like the Many Worlds hypothesis. But there are no "parallel universes". That is probably one of many examples of things, such as dream worlds, that we can imagine, yet that are physically impossible.

>[J]: 3. A truly infinite universe could explain the Fermi paradox. Intelligent aliens haven't gotten to us yet because we happen to live in a subsection of the universe where intelligent aliens are simply too far away to run into us.

The "Galactic prime directive" or some equivalent of it seems a sufficient reason for why we are not in contact with other intelligences.

>[J]: 4. Imagine computers being able to simulate worlds down to the atoms in real time.

Imagine that we are the computer simulation for some much larger scale reality.

>[J]: 5. Does the MM have any prediction about the speed of entities on different scales? Electromagnetic waves are far slower than gravitation, are sub-micro waves moving slower than electromagnetic and super-galactic waves moving far fast than gravity or is there no relation between scale and media velocity?

Real speed is not a function of scale, but apparent speed is. Things seem to happen fast on small scales and slowly on large scales. Gravitons move so fast that collisions are mostly destructive. So there is a wide gulf between gravitons and the next largest things we know of -- "light-carrying medium" (LCM) entities. This gulf then explains why gravitons can travel so far between collisions. LCM particles are essentially everywhere we can see, but are part of a contiguous medium and therefore relatively stationary. So assemblages are easy, and we have a whole zoo of particles just above that scale.

>[J]: Food for thought.

Yummy. -|Tom|-

>An example of logic is "If A implies B and B implies C, then A implies C". That is a general, absolute truth and does not need a physical counterpart.

I have no trouble with the logical statement but I do not see how realization of such a statement can occur without interaction with a physical universe. Mathematicians have argued about this for centuries as to whether logic is just "out there" somewhere separate from the universe or not. Ultimately the beginning axioms of logic are articles of faith that one simply has to accept, they cannot be proven themselves and to my mind are only "logical" because they seem to agree with what we observe. If before you were born we removed your brain and put it into a jar and nourished it without any sense of hearing, sight or touch do you think you would still be able to conceive of logic or even be concious without interaction with the universe?

>Let's not mix math into this subject. I made no statements here about math. That's a whole other question.

I thought logic WAS a branch of mathematics.

>Logic is the process of reasoning. It should not be confused with the laws of physics or the nature of the universe. The rules of logic do not depend on anything physical or even on existence.

But from whence comes this process of reasoning? And what process of reasoning was used to come up with the first process of reasoning? This is fundamentally why I believe logic cannot be compartmentalized totally away in some mysterious metaphysical realm away from our interaction with the surrounding universe. Logic MUST be a part of the laws of physics because we could not successfully apply that process of thinking unless the physical laws happened to go along with it. You say that if the universe suddenly disobeyed logic that we would know that we were in a simulation, but this position is relative, I could just as easily say that everyone's thinking process had suddenly become irrational. Unfortunately I know of no experimental way to settle this difference of opinion about the nature of logic, the question will probably continue be argued for centuries beyond us with no resolution.

> [Jeremy]: I have no trouble with the logical statement but I do not see how realization of such a statement can occur without interaction with a physical universe.

The logic exists without a realization. "If A implies B" is a supposition, and does not require that A or B exist.

> [J]: Ultimately the beginning axioms of logic are articles of faith that one simply has to accept, they cannot be proven themselves and to my mind are only "logical" because they seem to agree with what we observe.

This is a typical fatalist position. I do not agree. Pragmatism allows us to break the vicious circle of chicken before egg before chicken... with regard to premises. If a simulation of reality is very good, we may not be able to tell if this is reality or a simulation. But the only rational way to behave is in conformity with the reality presented to us because the consequences of doing otherwise is painful and deadly. We thus make a pragmatic decision to assume this is reality and not a simulation because the most likely alternative to any other assumption would be a cessation of existence.

We therefore are given certain premises that we must accept for purely pragmatic reasons. Those get us started with reasoning to other conclusions. We still have the possibility of detecting that we are in a simulation if something logically impossible were to happen. The rules for reality testing distinguish objective events from hallucinations or the products of irrational minds.

> [J]: If before you were born we removed your brain and put it into a jar and nourished it without any sense of hearing, sight or touch do you think you would still be able to conceive of logic or even be concious without interaction with the universe?

Probably not. But that doesn't make logic any less compelling. It just means I would never be cognizant of it. This is starting to sound like :If a tree falls in a forest but no one hears..."

> [J]: I thought logic WAS a branch of mathematics.

Logic is a field of study unto itself. Mathematics has co-opted logic as one of its many tools, especially useful for theorem proving and the like. But as evidenced by paradoxes and occasional inconsistencies, mathematics is not always as rigorous as pure logic.

> [J]: Logic MUST be a part of the laws of physics because we could not successfully apply that process of thinking unless the physical laws happened to go along with it.

You prefer to suppose that logic would not exist if humans and intelligences did not exist. I suppose otherwise. This difference of opinion is really about the nature of logic. You seem to think of it as sets of words like "If A implies B...". But I think of it as concepts that do not require discovery to nonetheless be true. Truth can exist without consciousness to appreciate it. Beauty might be argued to exist only in the eye of the beholder, but not truth and not logic.

> [J]: the question will probably continue be argued for centuries beyond us with no resolution.

Again, I am not so pessimistic. I present my solution to the logic of truth and reality in chapter 20 of "Dark Matter...". -|Tom|-

>[T]This is a typical fatalist position.

I would say it is a REALISTIC position. I know of no one that claims axioms themselves can be proven with logic. They must be ACCEPTED, how can they be accepted completely devoid of the consequence of OBSERVING that they work?

>[T]This is starting to sound like :If a tree falls in a forest but no one hears..."

This is not my position at all. The forest exists if SOMEONE, SOMEWHERE exists, they don't have to be right next to the tree. If I go around the universe with a pistol, shoot every sentient being and then shoot myself then in what sense does the universe (or logic) continue to exist unless I invoke an outside observer (god) to perceive it in some way? Or how about this, let's get rid of the forest. I wave a magic wand and the whole universe disappears except for Tom V floating in an empty, black nothingness. You are now free to indulge in any logical system that you might devise, what evidence would you now use to argue that the other system was not valid compared to your previous one except that it conformed with a memory only or produced a contradiction from beginning premises? This is the sense in which I don't think logic exists extant of something to beat it against.

>[T]You prefer to suppose that logic would not exist if humans and intelligences did not exist.

I suppose I do. I do not see in what sense the universe, logic or anything else can be said to exist unless there is a minimum of one conciousness to observe it.

>[T]I suppose otherwise. This difference of opinion is really about the nature of logic. You seem to think of it as sets of words like "If A implies B...". But I think of it as concepts that do not require discovery to nonetheless be true. Truth can exist without consciousness to appreciate it. Beauty might be argued to exist only in the eye of the beholder, but not truth and not logic.

I do not think of logic as strings of words. It is precisely the fact that it seems to take sentient beings to discover or acknowledge it that makes me suspicious of the notion that it is "just there". I don't know for a certainty that you are wrong but you still not have given me the location of where or in what form other than metaphysical this pure logic of yours can exist. If you put it in a realm of conciousness somewhere, that might be metaphysical but I could wrap my head around it. But I get the impression (perhaps wrongly) that you are advancing a completely clockwork universe that obeys mindless principles that just somehow "exist".