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DoktorGreg
2005-Feb-02, 01:53 AM
If the universe is finite in size it would see that all the number systems are wrong. Numbers do have a maximum value. If you were to construct a perfectly efficient computer utilizing all the matter in the cosmos, it would still have a finite maximum value, that number would be really big, but a definite maximum value.

How am I wrong? Also is this a Cosmology, Math or a Computer Science problem?

Russ
2005-Feb-02, 02:17 AM
If the universe is finite in size it would see that all the number systems are wrong. Numbers do have a maximum value. If you were to construct a perfectly efficient computer utilizing all the matter in the cosmos, it would still have a finite maximum value, that number would be really big, but a definite maximum value.

How am I wrong? Also is this a Cosmology, Math or a Computer Science problem?

Hello DoktorGreg: I don't think I've had the pleasure of posting with you before. Please accept my belated 'Welcome aboard the BABB.'

How are you wrong? IF the universe is in fact finite, then I don't thing you are wrong.

Question #1: Who said the universe is finite?

The Supreme Canuck
2005-Feb-02, 02:18 AM
Number systems are theoretical constructs. If the Universe is finite, it has no bearing on these theories. Hence, there is no maximum number.

Bad jcsd
2005-Feb-02, 02:19 AM
Mathd is an entirely abstract subject and is not constrained by reality (and number systems are dependent only on their axioms which have no dependence on reality), so no physical fact ever makes anything in maths wrong.

01101001
2005-Feb-02, 02:22 AM
If the universe is finite in size it would see that all the number systems are wrong. Numbers do have a maximum value. If you were to construct a perfectly efficient computer utilizing all the matter in the cosmos, it would still have a finite maximum value, that number would be really big, but a definite maximum value.
How does a concrete computer constrain the maximum size of an abstract set?

Kristophe
2005-Feb-02, 02:27 AM
I'm more curious about if there is a maximum number, what happens if we add one to it?

um3k
2005-Feb-02, 02:31 AM
I'm more curious about if there is a maximum number, what happens if we add one to it?
Everything blows up.

DoktorGreg
2005-Feb-02, 03:15 AM
If the universe is finite in size it would see that all the number systems are wrong. Numbers do have a maximum value. If you were to construct a perfectly efficient computer utilizing all the matter in the cosmos, it would still have a finite maximum value, that number would be really big, but a definite maximum value.
How does a concrete computer constrain the maximum size of an abstract set?

For example, say we set about computing PI to the ultimate precision on this cosmos computer. We would reach a point where, the computer simply has no more space to store another digit of precision. Is that the End of PI? Or does PI continue beyond that? If it does continue beyond that, you can never know what it is.

Granted this is just a thought experiment...

On adding one to the maximum number.

Say the entire universe were arranged into a 10 to the infinity -1 (is the the correct notaion for the maximum number?) power bit accumulation register that supported a single instruction. We will call that instruction INC......... When we reach the maximum value that this register holds, and execute INC one more time, It would.... probably explode as the entire univere switched from an on state to a off state during the same clock cycle resulting in the biggest billable hours debacle of all time.... But I digress, if it performed as expected, it would simply roll over to zero.

think

unsigned int i;
unsigned universe c;

Finally...

Russ, here is hoping it is infinate, I see no reason to think that the universe is finite in size. Here is hoping it isn't, because that means all things are possible. I really hope all things are possible.

01101001
2005-Feb-02, 03:21 AM
If the universe is finite in size it would see that all the number systems are wrong. Numbers do have a maximum value. If you were to construct a perfectly efficient computer utilizing all the matter in the cosmos, it would still have a finite maximum value, that number would be really big, but a definite maximum value.
How does a concrete computer constrain the maximum size of an abstract set?

For example, say we set about computing PI to the ultimate precision on this cosmos computer. We would reach a point where, the computer simply has no more space to store another digit of precision. Is that the End of PI? Or does PI continue beyond that? If it does continue beyond that, you can never know what it is.

You've only said the ultimate concrete computer has finite precision. HOW does that constrain the maximum size of a set? HOW does it limit the number of digits of pi?

skrap1r0n
2005-Feb-02, 03:46 AM
I thought they found the last digit in Pi about 2 years ago

DoktorGreg
2005-Feb-02, 03:48 AM
If the universe is finite in size it would see that all the number systems are wrong. Numbers do have a maximum value. If you were to construct a perfectly efficient computer utilizing all the matter in the cosmos, it would still have a finite maximum value, that number would be really big, but a definite maximum value.
How does a concrete computer constrain the maximum size of an abstract set?

For example, say we set about computing PI to the ultimate precision on this cosmos computer. We would reach a point where, the computer simply has no more space to store another digit of precision. Is that the End of PI? Or does PI continue beyond that? If it does continue beyond that, you can never know what it is.

You've only said the ultimate concrete computer has finite precision. HOW does that constrain the maximum size of a set? HOW does it limit the number of digits of pi?

Im not saying it constrains it, all I am saying is, you can never know what that next digit is, there is no functional way to approach it. Sort of like, you can only get really close to the speed of light, you can never actually go C. Just like the universe has a maximum speed, there is also a maximum number. Thats all.

01101001
2005-Feb-02, 04:28 AM
Just like the universe has a maximum speed, there is also a maximum number. Thats all.
That doesn't follow from your assumptions. HOW do you get there?

I'm quite willing to agree that the finte number of particles in a finite universe can only take on a finite number of states. HOW does that mean there are no larger numbers just because they cannot be represented?

Maddad
2005-Feb-02, 04:33 AM
If you were to construct a perfectly efficient computer utilizing all the matter in the cosmos, it would still have a finite maximum valueYou just described one possible difference between a really big number and infinity. The number system goes on forever because it is infinite. All the matter in the universe is not.


you can never know what that next digit isWhether that is true or not does not mean that this next digit cannot exist. Because I do not see the traffic cop hiding behind the billboard does not mean that I cannot get a speeding ticket.

DoktorGreg
2005-Feb-02, 05:29 AM
Just like the universe has a maximum speed, there is also a maximum number. Thats all.
That doesn't follow from your assumptions. HOW do you get there?


I'm quite willing to agree that the finte number of particles in a finite universe can only take on a finite number of states. HOW does that mean there are no larger numbers just because they cannot be represented?

I guess we call em 01101001's Number set, which includes all numbers greater than the maximum expressable number.

Evan
2005-Feb-02, 07:09 AM
What the heck is going on? Anyone ever study number theory? Between any two rational numbers are an infinite number of irrational numbers. Any set of numbers is a member of a superset.

kucharek
2005-Feb-02, 07:47 AM
One of the questions here is, if there may be a time where we can't compute any more digits of Pi because our computer can't hold the number. Do methods to compute Pi require the whole result so far be stored in it, or are there algorithms which produce new digits of Pi all the time with a limited memory size?

Kristophe
2005-Feb-02, 08:07 AM
I'm not sure I understand how a finite amount of computer memory is supposed to limit anything, especially the maximum number. You can always add one to any finite number to produce another, larger finite number. And you can invent new notation to keep the expression for such numbers compact. We can represent numbers unthinkably large with a few strokes of a pen.

And isn't infinity - 1 still infinity? Infinite => unending, right? Or did I skip that lecture?

01101001
2005-Feb-02, 09:29 AM
One of the questions here is, if there may be a time where we can't compute any more digits of Pi because our computer can't hold the number. Do methods to compute Pi require the whole result so far be stored in it, or are there algorithms which produce new digits of Pi all the time with a limited memory size?
David H Bailey (http://crd.lbl.gov/~dhbailey/)


This formula, now known as the "BBP formula for pi", permits one to compute the n-th binary or hexadecimal digit of pi, without computing the first n-1 digits, by means of a simple scheme that requires very little memory and no multiple precision software.
I think you still need arbitrary precision, more properly arbitrary space, to compute an arbitrary nth digit.

01101001
2005-Feb-02, 09:46 AM
I'm not sure I understand how a finite amount of computer memory is supposed to limit anything, especially the maximum number.
I think he abandoned it.

If he didn't, I'd like to ask him: in a nearly evacuated glass bottle that holds but a single particle having 2 possible states, must the value of pi inside the bottle equal 1?

joema
2005-Feb-02, 12:43 PM
If the universe is finite in size it would see that all the number systems are wrong. Numbers do have a maximum value. If you were to construct a perfectly efficient computer utilizing all the matter in the cosmos, it would still have a finite maximum value, that number would be really big, but a definite maximum value.
Numbers do not have a maximum value. Despite popular phases like "the universe is too big to calculate", math (and computers) can easily express numbers far bigger than ANY physical reality.

The smallest known particle is the quark with a diameter of possibly 10E-17 meters. The distance to the farthest object is about 14 billion light years, or 1.3E26 meters. If the entire volume of the universe was filled with quarks, that would be about 1.12E126 quarks. No problem with computers expressing that. Even my old HP calculator handled that with no sweat.

Math can easily express numbers vastly beyond any physical reality. E.g, consider the number 9^9^9 (nine to the ninth to the ninth). 9^9 = 387420489, so it's 9^387420489, which is a number with 360 million digits.

Argos
2005-Feb-02, 01:09 PM
As to a finite computer, you could still have a virtually infinite number of operations, so you would not be constrained by the size of the universe when handling information.

jofg
2005-Feb-02, 01:56 PM
A very wise person once told me that at the upper end of "numbers", they role back to zero again - creating a continous loop (visualize the infinity symbol).

Of course you can take this with a grain of salt since this wise person was my son (then 3). But I thought it was an interesting theory none-the-less!

:)

Swift
2005-Feb-02, 01:59 PM
I thought they found the last digit in Pi about 2 years ago
I think it's 4 (my lucky number).
Hey, I have a 1 in 10 chance of being right! :wink:

JohnW
2005-Feb-02, 04:06 PM
I thought they found the last digit in Pi about 2 years ago
I think it's 4 (my lucky number).
Hey, I have a 1 in 10 chance of being right! :wink:
I'll take 0. :D

skrap1r0n
2005-Feb-02, 04:12 PM
The thing is, you can take any number and add one to it. I seriously doubt there is a number that the universe will not let you add One to it.

Mathematics is a TOOL of science, not necessarilly a science itself. I am gonna get yelled at for saying this but the fact is, you cannot create something with formulas, you can only represent things with that formula. It's not like some guys will be working on an obscure formula and and just blink into another dimension or create a singularity or something.

for some reason I am reminded of the extra credit question in my last college math final.


"How long is a piece of string"

There are 2 correct ways to represent the answer.

Ilya
2005-Feb-02, 05:37 PM
If the universe is finite in size it would see that all the number systems are wrong. Numbers do have a maximum value. If you were to construct a perfectly efficient computer utilizing all the matter in the cosmos, it would still have a finite maximum value, that number would be really big, but a definite maximum value.
Numbers do not have a maximum value. Despite popular phases like "the universe is too big to calculate", math (and computers) can easily express numbers far bigger than ANY physical reality.

The smallest known particle is the quark with a diameter of possibly 10E-17 meters. The distance to the farthest object is about 14 billion light years, or 1.3E26 meters. If the entire volume of the universe was filled with quarks, that would be about 1.12E126 quarks. No problem with computers expressing that. Even my old HP calculator handled that with no sweat.

Math can easily express numbers vastly beyond any physical reality. E.g, consider the number 9^9^9 (nine to the ninth to the ninth). 9^9 = 387420489, so it's 9^387420489, which is a number with 360 million digits.

My understanding is that in a finite universe there is a finite number of objects/events/states. That does not make a "maximum number", for numbers are abstract concepts independent of physical reality, but it does make for a "maximum number which refers to something in existence". Which is what DoktorGreg seems to mean.

John Dlugosz
2005-Feb-02, 08:45 PM
If the universe is finite in size it would see that all the number systems are wrong. Numbers do have a maximum value. If you were to construct a perfectly efficient computer utilizing all the matter in the cosmos, it would still have a finite maximum value, that number would be really big, but a definite maximum value.

I was just reading in New Scientist about the possibility of executing an infinite number of instructions in a finite amount of time, called a "Supertask". Under some models of the universe supertasks are possible; in others not.

What is the largest number that can be represented in our Universe? Counting how many quarks fit in all space is rather small, as noted earlier in this thread.

What about using the quarks, not to count outright, but to encode a number? If there is room for N quarks in the universe, and each position can be one of M types/flavors/states/whatever, then you have a way to represent numbers up to M**N in size.

Then again, I just represented that same number, in a much smaller space! It makes sence to ask if there is a limit to the information content of the universe, but that is different from asking what is the largest number that can "exist".

--John

Russ
2005-Feb-02, 09:14 PM
So is there any rule excluding a number that is say 10^100,000,000^100,000,000? If I did my arithmetic right, that number should be bigger than the number of quarks in the universe. Of course we could increase the the exponents by several million orders of magnitude and get bigger numbers yet. It's just that we wouldn't be able to stack up any barrionic matter to represent the numbers. Or have I missed the subject concept totally?

joema
2005-Feb-02, 09:31 PM
...in a finite universe there is a finite number of objects/events/states. That does not make a "maximum number", for numbers are abstract concepts independent of physical reality, but it does make for a "maximum number which refers to something in existence". Which is what DoktorGreg seems to mean.
I agree except it wasn't clear to me what he meant. Several times he stated "numbers have a maximum value". The normal interpretation of that is maximum magnitude -- how large the number can be.

But then he changed and started talking about irrational numbers like Pi, and whether a theoretical universe-size computer could store Pi to limitless precision.

Then he said the universe was not finite in size.

The answer to his 1st statement is there's no limit to the maximum value a computer can express. Just as you can express a number on paper vastly larger than any physical construct, so can a computer.

The answer to his 2nd statement is OF COURSE you cannot store an irrational number to infinite precision -- by definition they are unending. Nothing new about that.

The answer to his 3rd statement is the universe as we currently understand it is very finite. The farthest object is "only" 14 billion light years away (maybe 28 billion if you consider comoving radial distance). Relative to sizes math can express the universe is tiny.

As a side point what is the largest describable number without resorting to tricks like "infinity minus one"? That's sometimes a fun exercise.

Maddad
2005-Feb-02, 09:36 PM
in a nearly evacuated glass bottle that holds but a single particle having 2 possible states, must the value of pi inside the bottle equal 1?It will approximately equal 3.

skrap1r0n
No way I'm gonna yell at you.


"How long is a piece of string"Gotta be one Skinner long. Skinner's the guy who invented Skinner's Constant, the recipricol of the Fudge Factor. It's that value which when added to, subtracted from, multiplied by, or divided into the number you have gives you the answer that you're supposed to get.

Evan
2005-Feb-02, 11:36 PM
The farthest object is "only" 14 billion light years away

Waitaminute. It was 14 billion years ago.

joema
2005-Feb-02, 11:47 PM
It's probably more accurate to say about 28 billion light years (comoving radial distance):

http://www.badastronomy.com/phpBB/viewtopic.php?p=53334&highlight=#53334

Kaptain K
2005-Feb-03, 08:34 AM
The farthest object is "only" 14 billion light years away

Waitaminute. It was 14 billion years ago.
Actually, no!
That is the distance that the light has travelled, which is neither the distance it was then nor the distance it is now!

Toutatis
2005-Feb-03, 12:07 PM
In response to Dr. Greg's evocative post :)

First I'll address Aleph(0)

The universe may indeed be finite howbeit potential space is transfinite... (potential space being the non-entity which 'becomes' space while occupied by, or intervening, physical phenomena) - Of course time would need extend to infinity were physical phenomena to 'create' space at infinite distance. Note: *time is a dimension of space*!!! - hence 'potential time' is fair! ;)

And Aleph(1);
All distinct positions are separated by an infinite number of interstitial positions. "Having at least one dimension = 1/Aleph(0)" do I hear you say? Careful! That'd be shaking the 'tree' of the 'cerebraphobes' rather violently!!! [evil grin]

To cut to (as I see it) the crux of your question: Tis a matter of 'Apples and oranges'! (i.e. the 'concrete' [CIP physical quantities] and the 'abstract' [Pure mathematics]) :D

You may be interested in the work of Georg (sic) Cantor (to wit 'Transfinite Algebra') -- The very nature of your question suggests you would find it a fascinating study... Also, although marked by definite emphasis upon utilitarianism, a study of 'infinitesimal calculus' is well worth the time! :D

A brace of closing thoughts;

1) Realities - like universes, despite definition - are not necessarily entirely 'closed' systems...

2) I assert that physical reality is neither the sole nor, necessarily, the most important reality.


Enjoyed your question! :)

Best regards
Sarandon

PS --- Time constraints precluded my review of other responses - My reply is a direct response to the OP -- Please accept my apologies should I have repeated material or accidentally insulted anyone!!! All too often academicians endeavor to tailor reality (whatever that means) to their comfortable perception thereof (or to their pet theories) --- as opposed to the converse --- hence my ‘kludged’ epithet "cerebraphobes"... I know I've 'been there' and on more than a single occasion. http://www.badastronomy.com/phpBB/images/smiles/icon_redface.gif

joema
2005-Feb-03, 05:25 PM
...All distinct positions are separated by an infinite number of interstitial positions...
While true from a mathematical standpoint, from a physical standpoint there's a finite number of interstitial positions, according to current physics.

The smallest possible physical space is called "Plank length", and it's 10E-35 meters. It's small -- about 20 orders of magnitude smaller than a proton, which is 10E-15 meters. It's 17 orders of magnitude smaller than a quark, which is about 10E-18 meters.

However math can easily express that value, or even the number of possible 3D "Plank positions" in the universe. The probable diameter of the universe is 156 billion light years http://www.space.com/scienceastronomy/mystery_monday_040524.html, thus 2.2E54 cubic meters. There are 10E108 Plank positions within a cubic meter, so the total number of possible physical positions in the current universe is 2.21E162. Admittedly the universe is expanding, so is constantly creating more space.

But there is a limit to physical position at the small scale. Although we picture positions in space as infinitely continuous, apparently at the quantum level it becomes quantized and discrete.

Evan
2005-Feb-03, 05:30 PM
If we allow that the universe is expanding at least at the speed of light and we then begin to enumerate we will be able to enumerate infinitely as space is expanding infinitely at the same time. So, there is no limit.

joema
2005-Feb-03, 06:28 PM
Good point -- whether infinite or not depends on the definition. There's a limit at any one instant.

The normal interpretation of "how big is it" implies right now, at this moment.

If you wait for x expansion, then it's larger but limited at that point.

The rate of expansion actually doesn't matter -- it could be expanding at 1 mm per eon, and if you just wait long enough it's bigger.

Assuming an open universe where expansion continues, it would only be infinite size after infinite time elapsed (regardless of the expansion rate).

Grey
2005-Feb-03, 06:58 PM
Assuming an open universe where expansion continues, it would only be infinite size after infinite time elapsed (regardless of the expansion rate).
Assuming an open universe, it's already infinite in size and always has been.

joema
2005-Feb-03, 07:10 PM
...Assuming an open universe, it's already infinite in size and always has been...
I don't understand that. Why does an open universe (meaning expansion will continue) imply size has always been infinite?

Grey
2005-Feb-03, 07:27 PM
I don't understand that. Why does an open universe (meaning expansion will continue) imply size has always been infinite?
If the geometry of the universe is flat or open, then it's infinite in size, just like a plane or a hyperbola is infinite in extent. Only a closed universe would be finite in size.

The geometry of space used to be understood to be tied to its fate, with an open universe expanding forever, and a closed one eventually contracting again (and flat balanced between the two). However, with the addition of a cosmological constant into the mix, that's not necessarily the case. It's possible, at least in principle, to have a closed universe that expands forever, or an open one that eventually collapses again.

[edit to add:]
As I look more closely, you said "an open universe (meaning expansion will continue)", so you may be just using the term "open" to mean a universe that keeps expanding. However, that's not the standard use of the term in cosmology, where "open" and "closed" always refer to the geometry. The confusion may arise since, as I mentioned, without a cosmological constant term the two are necessarily linked, and we've only recently realized that there actually needs to be such a term. If that's what you were thinking, just consider my comment to be a small correction of terminology usage. :D

Bad jcsd
2005-Feb-03, 07:27 PM
...Assuming an open universe, it's already infinite in size and always has been...
I don't understand that. Why does an open universe (meaning expansion will continue) imply size has always been infinite?

An open unievsre is a partciualr geometry, due to the constraints on the topology of spacetime, in this case the geometry automatically implies the universe is infinite.

joema
2005-Feb-03, 10:12 PM
...you said "an open universe (meaning expansion will continue)", so you may be just using the term "open" to mean a universe that keeps expanding. However, that's not the standard use of the term in cosmology...
I'm still confused. If you query on the phrase "open universe", thousands of places it's defined as meaning expansion will continue, namely critical density < 1. This includes the sci.astro FAQ, various encyclopedias, etc. It was in that sense I used it.

I know there's also a topological definition to "open" vs "closed".

However how can an expanding universe be infinite in physical size? How can it expand to something larger, if the physical size is already infinite? What's larger than infinite size? Was it also infinite in size (say) 1 femtosecond after the big bang? Just trying to understand this.

Evan
2005-Feb-03, 10:20 PM
There are different classes of the sets of infinite numbers. The set of rational numbers is an infinite set. Between any two rational numbers lie an infinite number of irrational numbers. The set of all numbers, rational and irrational is infinitely larger than the set of rational numbers.

Grey
2005-Feb-03, 10:29 PM
I'm still confused. If you query on the phrase "open universe", thousands of places it's defined as meaning expansion will continue, namely critical density < 1. This includes the sci.astro FAQ, various encyclopedias, etc. It was in that sense I used it.
I fear that the fact that the geometry and ultimate fate are linked if there's no dark energy in the mix, as was thought until just recently, has confused the issue. The value of Omega always referred to the curvature, and we now know that whether it keeps expanding or not is not determined only by that geometry.

If I do a Google search for "open universe", the first site is for Celestia, an orbital simulator, the second gives the definition you're familiar with, but it's from The New Dictionary of Cultural Literacy, probably not the most scientifically up-to-date publication. :) The third is a lecture from a Cornell University course, and if you scroll down, you'll see a diagram showing just what I'd said, that it's possible for the universe to expand forever or not whether it's open or closed.


However how can an expanding universe be infinite in physical size? How can it expand to something larger, if the physical size is already infinite? What's larger than infinite size? Was it also infinite in size (say) 1 femtosecond after the big bang? Just trying to understand this.
Yes, when I say always infinite, I really mean it. I have a terrible time visualizing something infinite expanding, too, so I'd have an easier time conceptualizing things if the universe turns out to be closed. Still, that doesn't mean it's not the way it is. Just because something is infinite doesn't mean it has to be static. In this case, the expansion would be simply that the average density is going down as everything moves away from everythig else.

joema
2005-Feb-03, 11:03 PM
I have difficulty picturing a 3 dimensional unbounded universe, but that's different from infinite physical size. The globe is unbounded but finite in size.

Infinite physical size means whether 1 femtosecond after the big bang, or today, the diameter of the universe was/is infinite.

By that understanding, there's not a finite physical size, rather only a finite OBSERVABLE size. All statements about universe size, whether 28 billion light years, 80 billion light years, or 160 billion light years are wrong -- the size is infinite.

If the universe is infinite in size, doesn't that raise a gravitational version of Olber's paradox? Since gravity has infinite range, wouldn't a universe of infinite size and non-zero density have infinite mass?

I'll keep thinking about it and maybe it will sink in.

Evan
2005-Feb-03, 11:44 PM
Inverse square law.

Silent Knight
2005-Feb-04, 12:20 AM
I thought they found the last digit in Pi about 2 years ago

Pi. (http://mathworld.wolfram.com/PiDigits.html)


In December 2002, computer scientists Kanada, Ushio and Kuroda computed to a world record (more than one trillion) decimal digits, besting their previous world record of digits, set in 1999. The computation consumed more than 600 hours of time of a Hitachi SR8000 supercomputer (Peterson 2002, Kanada 2003)

It is not known if is normal (Wagon 1985, Bailey and Crandall 2001), although the first 30 million digits are very uniformly distributed (Bailey 1988).

Fortis
2005-Feb-04, 03:29 AM
I thought they found the last digit in Pi about 2 years ago

Pi. (http://mathworld.wolfram.com/PiDigits.html)


In December 2002, computer scientists Kanada, Ushio and Kuroda computed to a world record (more than one trillion) decimal digits, besting their previous world record of digits, set in 1999. The computation consumed more than 600 hours of time of a Hitachi SR8000 supercomputer (Peterson 2002, Kanada 2003)
Can you imagine the temptation for "just one more digit..." ;)

Toutatis
2005-Feb-04, 03:50 AM
Joema commented...


The smallest possible physical space is called "Plank length"

Exactly!!! :D - Inasmuch as Lp (i.e. ~ 1.6*10^-35 meters) <> (1/Aleph[0]) we see that Aleph(1) is inapplicable to physical quantities (as currently reckoned) BTW profound apologies to those disapproving of "1/Aleph(0)" I'm not crazy about it myself, Nor do I feel Cantor would have been 'amused' ;)


But there is a limit to physical position at the small scale. Although we picture positions in space as infinitely continuous, apparently at the quantum level it becomes quantized and discrete.

At the risk of being 'packed off' to ATMS I must make the following comment:

I seriously doubt the quantum paradigm represents the true nature of reality - Rather, it seems an ingenious 'patch' initially necessitated by the failure of Newtonian physics to properly address certain aspects of EMR induced phenomena (Classically the breakdown of the TEM model as applied to ‘photo-electricity’) --- But like its (now ‘subseted’) predecessor the quantum model appears both over-simplified and, at junctures, a bit "chipped 'round the edges" (as a trivial example please consider the ‘incompatibility’ of Quantum Field Theory to General Relativity) Hence the inception of String/Membrane Theory (Still another 'patch'?)

I submit that physical reality has neither the nature of the discrete nor the continuous (howbeit said paradigms work nicely within their respective scopes) --- That the 'truth' lies at a far deeper and horror of horrors non-'backward-compatible' level...

Without intent to proselytize (nor being so vain as to think I could) I would pose the question; What is the true aim of science?

1) Development of 'tools', and alternate sets of tools such that we have ‘something that works’ wherever needed despite possible ignorance as to the essential nature of ‘the work’.

_OR_

2) Attempting to glean the TRUE nature of reality despite practical consideration???

I can but hope for the latter, but sincerely, am I asking too much of science?

Apologies for the 'blasphemy' - If you'll be so kind as to overlook it -- I'll be back on my best behavior from now on! ;) And for the record; While mathematics is nearest and dearest to my heart – I profoundly respect science and the scientific process! The above is nothing like a ‘rant’ --- Just (less than eloquent) musing…

With utmost respect to all concerned
Dan Sarandon :D

Grey
2005-Feb-05, 01:07 AM
By that understanding, there's not a finite physical size, rather only a finite OBSERVABLE size. All statements about universe size, whether 28 billion light years, 80 billion light years, or 160 billion light years are wrong -- the size is infinite.
Correct. Every estimate I've seen of the universe's size (other than the observable size) has either explicitly assumed a closed universe or been an estimate of the lower bound of the size.


If the universe is infinite in size, doesn't that raise a gravitational version of Olber's paradox? Since gravity has infinite range, wouldn't a universe of infinite size and non-zero density have infinite mass?
Also correct. In addition to the inverse square law, which Evan mentioned, there's also the finite propagation time for gravitational interaction. That's also the speed of light, so anything we can't see can't affect us gravitationally either.