How Do Zero and Infinity Influence Our Understanding of Physics?

[Mr. Robin Parsons]

Thank you, for the clarification...

 

[Antonio Lao]

Addendum to this Thread

To anyone who still wants to know the purpose of this thread,

Maybe I wasn't clear at the beginning, but the point I am trying to get across is that zero and infinity are ordinal numbers. They could not really be used to do any calculation.

But in actual calculations they become the limits to be approached.
This is how differential calculus is built that some argument of the domain approaches zero but the range of that function is never zero or infinite.

In integral calculus, the limits of integration usually start from negative infinity to positive infinity but the actual result is in between.

The key to understanding zero and infinity is the theory of limits.
How we can use mathematical arguments to show the logical existence of a limit at zero and at infinity hence show that a series will converge to a limiting value. If the series diverge then it not useful and nobody wants it. Nobody wants infinity.

The theory of infinite series can very well shed some light on the meaning of zero and infinity.

I think I can now rest my case.

Antonio

 

[Antonio Lao]

Belated Reply

Mr. Robin Parsons,

This is a belated reply to your post about Emmy Noether. Yes, I am referring to her symmetry theorem. But the one that bothers me is the symmetry in time for conservation of energy. This symmetry says that energy does not depend on the progress of time. But in real life, we know it does, increase of entropy, thermodynamics tells us that energy does depend on time. So the CPT theorem cannot be true for our universe. The other problem is that these symmetries hold only for a closed system but there is no way at this point of our knowledge in science to show that out universe is closed. The big bang theory says it can go on expanding forever unless we can find the dark matter (energy) to hold back the expansion. We have not found this dark matter. There are many hypotheses but no consensus agreements just yet. To make matter worse, cosmologists are now saying the expansion is accelerating.

Antonio

 

[Mr. Robin Parsons]

Originally posted by Antonio Lao
(SNIP)[/color] This is a belated reply to your post about Emmy Noether. Yes, I am referring to her symmetry theorem. Antonio (SNoP)[/color]

O.K. Thank you...and, it is wrong!

 

[matt grime]

Originally posted by Antonio Lao
To anyone who still wants to know the purpose of this thread,

Maybe I wasn't clear at the beginning, but the point I am trying to get across is that zero and infinity are ordinal numbers. They could not really be used to do any calculation.

But in actual calculations they become the limits to be approached.
This is how differential calculus is built that some argument of the domain approaches zero but the range of that function is never zero or infinite.

In integral calculus, the limits of integration usually start from negative infinity to positive infinity but the actual result is in between.

The key to understanding zero and infinity is the theory of limits.
How we can use mathematical arguments to show the logical existence of a limit at zero and at infinity hence show that a series will converge to a limiting value. If the series diverge then it not useful and nobody wants it. Nobody wants infinity.

The theory of infinite series can very well shed some light on the meaning of zero and infinity.

I think I can now rest my case.

Antonio

You should not talk of infinity as either a cardinal or an ordinal. There are obviously infinite cardinals and infinite ordinals but there are many such and to imply some uniqueness is incorrect. This seems to be a common misconception in this forum: the difference between infinite and infinity.

In particular, there seems to be this idea that there is this unique object we call infinity. That that infinity is what we mean in a sequence tending to infinity, and for it to be the cardinality of the Natual numbers.

 

[Mr. Robin Parsons]

Originally posted by Antonio Lao
(SNIP)[/color] but the point I am trying to get across is that zero and infinity are ordinal numbers. (SNoP)[/color]

Ahem as the post above (perhaps) concurs, 'Infinite' (and/or Infinity) is NOT a number!

 

[matt grime]

Absolutely: infinity is not a number. The clarity of the exposition got lost in the impotent rage felt at the repeated misunderstanding of a very simple object/concept.

 

[Radic]

Simply

There is difference between math which is used by mathematicians and physicists.Infinitely small in physics means very small which cannot be measured,but not aproximately small!

 

[Antonio Lao]

Infinity in Binary

To everybody who still wants infinity to be a number,

In the binary number system that of 1's and 0's, used in digital computers. infinity can be written as

infinity = ...1111111111111111111111111

where the dots to the left are all 1's but I would not live long enough to finish placing all the 1's. But infinity minus 1 is simply given as

infinity - 1 = ...1111111111111111111111110

and

infinity - 2 = ...1111111111111111111111101

and

infinity - 3 = ...1111111111111111111111100

Antonio

 

[Mr. Robin Parsons]

If Infinity (and or infinite) is a number, well, please:
insert here -->

As for the mention of the Noether work, as being wrong, do they now know that it is wrong and will, as a result of that knowledge start re-examining the work as to see if they can "arrive there first" (either Back there, or pehaps, to me, ahead there...as I come upon it for the Second time...) OHH! but wait, this is the statement/testimony/attestiment of ONLY ONE MAN, just one Guy's opinion! That's all.

Will Y'all watch as this goes on, are "They" Now! cornered, by this posting? will "They" go out and start looking, re-viewing, Emmy Noether's works to see if they think that Now "They" have missed something, or made a mistake? better Yet Who the Heck are "They"!? (I want to KNOW! only that (this one --> ) statement, the rest of 'the above', is NOT a joke... )

And as a simple serious question, is it acceptable to allow one persons 'opinons' to have more weight, then anyone elses? WHY?

 

[Hurkyl]

infinity = ...1111111111111111111111111

Actually, this is -1.

(I'm assuming that you intend arithmetic to be defined on these infinite strings as the natural extension of arithmetic on binary strings of finite length)

 

[chroot]

Originally posted by Hurkyl
Actually, this is -1.

You mean, in 2's complement notation?

- Warren

 

[Hurkyl]

You could call it that! Why the "Blah!" face? Arithmetically, it is indistinguishable from -1. *shrug*

 

[chroot]

Originally posted by Hurkyl
Arithmetically, it is indistinguishable from -1. *shrug*

Only if you're doing 2's complement arithmetic. You could just as well be doing signed-magnitude arithmetic, in which case it is *not* -1.

- Warren

 

[Hurkyl]

Try it. Add one to ...111111. Multiply it by 10. Subtract 1 from 0. The only assumption I'm making is that you are extending ordinary binary place notation arithmetic to infinite strings of binary digits.

(unlike the finite string case, where you are either assuming some sort of modulo arithmetic going on, or have some overflow condition making some operations invalid)


Still, I should make the point (which Chroot may have been making) that this is an extension; not part of the standard thing we call the natural numbers (or integers, or whatever you want to use)

 

[Antonio Lao]

Hurky,

Thanks for the math prep talks. You are the mathematician and I'm not.
Whatever you say I have to agree with you. When it comes to math, I'm just an amateur and an onlooker from the outside.

Antonio

 

[Organic]

Hi Antonio,

Please look at this:

http://www.geocities.com/complementarytheory/RiemannsBall.pdf


and this:

http://www.geocities.com/complementarytheory/CQ.pdf

 

[8LPF16]

Hurkyl,


Are there any infinite numbers that are used as contants besides Pi, Phi, and e ?

Also, is there a name for infinite numbers that have repeating numbers for a certain # of digits? ie .788699788699...?


LPF

 

[chroot]

SLPF,

There are an infinite number of irrational numbers, whose digits do not repeat or terminate. (Please don't call them "infinite numbers.")

The numbers with repeating digits (any number of them) are called rational numbers.

- Warren

 

[8LPF16]

chroot,

so the 3 contstants I gave are irrational, but not infinite? (I realize they don't represent an infinite value, but do "go on forever")

and, to confirm, no special name for numbers that have patterns in their repitition that has no end.

what is "the problem with infinite numbers" I hear mentioned regularly? ie re-normilization?

LPF

 

[chroot]

Originally posted by 8LPF16
so the 3 contstants I gave are irrational, but not infinite? (I realize they don't represent an infinite value, but do "go on forever")

They are irrational, which means their decimal expansions do not repeat or terminate. Do not use the word "infinite" when describing them, as that is not proper usage. There is no such thing as an "infinite number." There are numbers, which are not infinite, and there is infinity, which is not a number.

and, to confirm, no special name for numbers that have patterns in their repitition that has no end.

The special name is "rational."

what is "the problem with infinite numbers" I hear mentioned regularly? ie re-normilization?

Those problems do not deal with "infinite numbers," which, again, don't exist. Those problems are with infinities that are predicted by various formalisations like quantum electrodynamics. The theory sometimes predicts infinite results, which are not physically possible. Renormalisation is a procedure -- a sort of "trick" -- which can defuse some of those infinities, allowing the theory to produce non-infinite results.

- Warren

 

[Mr. Robin Parsons]

Personally, I have no problem with the methodologies of mathematics, the use(s) of Imaginary numbers, Rational Numbers, etc. as it does make sense, in it's mathematical applications, and some of those, correspond with reality, and/or a description thereof, hence exceedingly useful, as is the concept of 'Use of Infinity' in mathematics, just that, at that particular point, personally, I would diverge, and go with, in respect of Principals of Physics, the realities 'projection', which, as I understand it, precludes us from any "View" of the infinite, or mathematical expression of the actual truth of what infinite could/would/is be(ing).

 

[Hurkyl]

Antonio:

The main point I (and others) are trying to make is that it's a matter of definition (and the consequences of said definition), not a matter of trying to explore the properties of some vague idealized concept of infinity.

I couldn't resist bringing up the "...1111 = -1" thing because it is one of the oddities I found fascinating when I was younger. I might start exploring this type of representation again, actually.

(Oh, and exploring a vague concept isn't necessarily a bad thing, if your goal is either to assist finding a more rigorous approach, or to lay the foundation for coming up with an unambiguous definition for said concept)


8LPF16:

The two concepts "infinite string of digits" and "infinite number" are different concepts. It is true that, for instance, that the decimal representation of \pi is an infinite string of digits, but \pi is a finite number.

Also, is there a name for infinite numbers that have repeating numbers for a certain # of digits? ie .788699788699...?

We call this a repeating decimal expansion (or repeating decimal for short).

It is a fact that a (real) number is a rational number if and only if its decimal expansion is eventually repeating.

what is "the problem with infinite numbers" I hear mentioned regularly? ie re-normilization?

If I understand correctly, what happens here is that a particular scheme for approximating things has bad properties (it "converges" to something like \infty - \infty + \infty - \infty + \ldots) so you have to modify the scheme somehow (renormalization) so that it doesn't develop these bad properties.

 

[Mr. Robin Parsons]

"Renormalization" is what Fenyman used in his work "getting the infinite, out of the electron", ended up with a 1 I'd heard. (read, actually)

Useful tool of calculus too, I've heard/read.

 

[8LPF16]

chroot,

So, what is standard procedure for dealing with a non-terminating rational number? Is it essentially "pick a place to stop"?

Also, are you aware of any theories on particles (or anything) using non-terminating rational numbers as a format to exchange information or interact? Very much like computers using 1 and 0, except more complex, and naturally occurring.

LPF

 

[chroot]

Originally posted by 8LPF16
chroot,

So, what is standard procedure for dealing with a non-terminating rational number? Is it essentially "pick a place to stop"?

Standard procedure? What do you want to do?

Also, are you aware of any theories on particles (or anything) using non-terminating rational numbers as a format to exchange information or interact? Very much like computers using 1 and 0, except more complex, and naturally occurring.

No.

- Warren

 

[8LPF16]

chroot,

In part, what I'm trying to do is work with a series, or set of these numbers, and, depending on when "the calculation ends" (what digit of the repeating #), the calculation gets thrown off. When a computer, by its limitation, ends the calculation, it rounds up.

This reminded me of the problem in last post. Because these numbers do not terminate, I thought they might be similar to dealing with "infinities".

LPF

 

[chroot]

8LPF16:

Use arbitrary-precision arithmetic.

- Warren

 

[Antonio Lao]

Godel's Successor

Hurkyl,

As I said I am agreeing with whatever you say about math.

As a matter of fact I will vote for you as the next successor to Kurt Godel.

Thanks for all your enlightenments on math.

Antonio

 

[8LPF16]

post on page 2

Antonio,


You were saying that time zero would have infinite mass or energy?

By my breathing lung analogy, the oxygen comes in as pot. E, lungs full = pot. mass, then they exchange. CO2 and oxygen simultaneously exchange while lungs are full. Now pot. E is in blood, kin. E in lung (exhaling). The same switch for pot. mass to kinetic. Time values are not used.

The point is, in a closed loop, or cyclicle system, where do you define time zero? (even the values most likely never reach zero, and are exchanged at ratios >0/<100%).

It is easier to state it as the beginning of the cycle (frequency?) rather than a particular moment.

Also, I was trying to draw a comparison with 0/infinite to the prismatic expreriment. Black (darkness) being zero light, and magenta being "infinite". They are actually neither 0/infinite because of pure definitions - in a close system (Universe), where can the values of darkness be said to begin or end? (same for light) Only with something known as grayness, can these two super-forces be mediated (simultaneously). Only in this "transition" period, does simultaneity exist.


LPF