Exploring Zero and Infinity in Physics

[Mr. Robin Parsons]

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

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

 

[Mr. Robin Parsons]

This is your conversation from the other thread, extended, isn't it?

 

[Antonio Lao]

8LPF16,

The breathing cycle is the same as time cylce. Time is always implicitly defined as a periodic function. Each cycle of the lung's motion in-out is one period. This lung's period is related to the heart beats and to the pulse. Our heart beat is a chaotic nonliear system yet it is what keep us alive because there is order out of the chaos. The unit of period is time in seconds for one cycle, frequency is defined as the number of cycles per second of time. frequency is the inverse multiple of the period.

The electromagnetic spectrum includes the visible prismatic light (light that we can see). What we cannot see by our eyes beyond the color red are the infrared light (heat light), the microwave light, the mm waves light, the radio waves light,
and beyond the other end of magenta are uv lights, the x-rays light, and the gamma rays light. They are all lights, they all move at the speed of 300,000 km/s. Their speeds are always the same but their wavelengths and frequencies are different and if you multiply the wavelength and frequency of one particular light it is always equal to 300,000 km/s.

c = wf = 300,000 km/s for all lights mentioned above.

w is the wavelength, f is the frequency

Antonio

 

[8LPF16]

Antonio,


I think the bottom line is that in any 2 component system that you can think of (that are existing in duality/polarity) a third component must also exist. Sometimes the third party exists in simultaneity (ie. - N.& S.), and sometimes it operates on distinct intervals (of the 2 polarities) described as "gray". The intervals are always determined by the ratio of polarities, not by time. The intervals can be described by whole integers of ratio.

So, in terms of your original question, WE (and all things that exist for us) are what exist in between zero and infinity.

LPF

 

[Fromfiretolife]

Hello there for all that don't know me My name is Ike. I don't know much about physics and advanced math but here is my theory.


My theory is that Where is a a place where the face of zero would exist because we have to take into consideration everything when we say the phrase zero and the universe is far to vast to say zero. To my knowledge the phrase absolute vacuum is unobtainable because we have infinity in the universe as far as size and where we have infinity as in size there will always be a object small enough to enter such a space and if there were such a space where would we place particles like photons and neutrinos that like any particle could be the subject of a polarity change thus attaching itself to the original particle at hand inside such an environment through static because to my knowledge everything in our universe is moving around something.

 

[Mr. Robin Parsons]

Originally posted by Mr. Robin Parsons
This is your conversation from the other thread, extended, isn't it?

And thank you for your responce "starter" of the thread, "Ignorance is Bliss" (apparently)...

 

[Antonio Lao]

Mr. Robin Parsons,

I gathered you were asking me whether this thread is somehow an extension from other threads?

To tell you the truth, all the threads that I posted in this physics forum are all connected in some ways. Now they are all so convoluted and I seem to lose track of the main purpose when I started to answer some of the questions from other replies, they are now disconnected!

----------------------

8LPF16,

I am going to start from square one. The starting point that I going to use is the history of math. You can see for yourself if you look into the following books:

1. Michael J. Crowe 'A History of Vector Analysis'
2. Morris Kline's 3 volumes set 'Mathematical Thought from Ancient to Modern Times'

The study of two components system started where math started within the context of two broad traditions: (1) math for the sake of math itself (just for the mental fun of it), (2) math for the physical sciences (serious problem solving in real life).

These two traditions became separated as time goes by. Now the gap is very wide. Mathematicians are losing touch with reality and the physical scientists are trying their best to find "the math" that they can used in solving serious problems in the real world.

One of the serious problems we are having now and maybe in the near future is the harness of energy. Globally speaking, our energy source (fossil fuels) is depleting at an accelerated rate. Indirectly this might have causes the conflicts between nations. In a deeper sense, it is just a question of survival. Do we want to survive as a group?
Or do we want to survive as an individual? But we cannot survive without the helps of others. This is a fundamental dilemma of mankind. But we must be thankful that so many have given up their lives so others can live because of what they believed to be the right thing to do.

Back to math, the natural number system has only one component and this component is the positive integers from zero to infinity. Then math became two components by adding negative integers to the number line from zero to negative infinity. This was for the purpose of finding roots to algebraic equations. Still some equations cannot be solved by +/- numbers. so math has to invent the imaginary numbers. So the complex numbers are a higher two components system, the combination of real and imaginary numbers. Yet this complex number system is still not capable of solving all the real world problems.
Sir William Rowan Hamilton started quaternions, quaternions are hypercomplex numbers. They are the two components of scalar and vector. later, others like Gibbs and Heaviside separated the scalar and the vector for each to have its own algebras. Still vectors cannot completely model the real world problems. So Tensor calculus was invented. Tensors can solved most problems in general relativity but not quantum mechanics so again spinors were invented to solve GM.

If we look closer at all these number systems, they are all composed of two-component systems. Each component has its own definitions and properties. The two components are magnitude and direction. The property of magnitude is that it is a scalar or absolute value of a number. Direction is a component that can best be modeled by the definition of angles. But angle is related to distance by the trigonometric functions. And within the sine function, zero and infinity are implied to exist. sine 90 degrees is the ratio of one over zero which is infinite, cosine 90 degrees is ratio of zero over one which is really zero. The existence of triangle, in this case, the existence of a right triangle, circumvented the problem of zero and infinity. Right triangles can only exist in plane Euclidean geometry but not in non-Euclidean geometries as used in GR hence the need of tensor calculus, vector analysis of higher dimensions.

Antonio

 

[Mr. Robin Parsons]

Thank you...

 

[Antonio Lao]

Mr. Robin Parsons,

You are more than welcome.

Antonio

 

[Antonio Lao]

Fromfiretolife,

What you said about the vacuum is very similar to one of the major philosophical problems that Aristotle was studying.

Zeno's paradoxes were also used to clearup the idea of a vacuum. So we can say that the problem of vacuum was a major preoccupation of all ancient philosophers even up to our modern time's thinkers.

I am also one of the people who study the vacuum. There are now many books on the subject directly or indirectly discussed by each author. One book came to mind is John D. Barrow's 'The Book of Nothing.' The main theme of this book is to relate vacuum to the origins of the universe.

For me, the vacuum contains an infinite amount of something. I cannot describe this 'something' by use of our current knowledge of math because to me our current math is deficient since math deals with numbers. The question that numbers can answer is 'how much and where?' answering the 'where?' needs the definition of an origin, a starting point. but to solve the problem of vacuum, we do need to answer 'when?'. This 'when?' question is related to the definition of the physical concept of time. This definition gives meaning to the word 'before' and 'after' and 'first', 'second', and 'third.' The natural numbers used for these words are the ordinal numbers. The cardinal numbers are used for 'how much?' and 'where?' The mathematicians don't feel the need to make this distinction but as a physicist, I need the distinction to describe the physical concept of 'direction.'

The 'infinite something' in the vacuum cannot be static. They are constantly in some sort of local movements. One point moves here to there, another point replaces here from there. So the vacuum is full in this sense although the points are always moving here and there.
Associated with each movement is a 'direction.' Since there are infinite points, there are infinite 'directions.' Each point has its own direction and one point will never try to change to another 'direction' because all the other 'directions' already been taken by other points. So each point keeps its own 'direction' for all eternity. This is the principle of directional invariance.

When the points group together they formed two distinct objects which for now we call them the potential mass and the kinetic mass. By doing these distinction, it's unavoidable that two directions of time must exist. One for the potential mass and one for the kinetic mass.
This is simplification at the utmost. Reality is much more complicated. But by defining the physical concept of directional invariance we have a good start to finally answer the question of the vacuum.

Antonio

 

[8LPF16]

Antonio,

I appreciate your depth of information provided, it is nice to see a wider base of knowledge than just "formula memorization".

I appologise to you for my regular "abuse of terminology" through generalization. I typically speak in the broadest terms, this is not illogical, as the goal in mind will require just that to bring Unification into reality. I do not have much interest in math theory, just the practical side. It needs to be as simple as possible, and some paring down and generalizing is required. I have arrived here with you (trying to solve GR/QM gap) from an entirely different place. The history of man, and symbols used to communicate quantity for the last 10 to 20 thousand years. We lived for 90% of this time with very simple "math". From this study, I developed an evolutionary profile of the beginning of the need to symolize quantity, and the seeds of civilization, and the pattern of human thought. This lead me to developing a "Trinary Math Sytem", which just means 3 symbols/values that can be traced to the creation of any number, or natural value. It can be used as a scale (music term) in that "definitions" can be represented by the 3 symbols (numbers, words, or concepts). Dualities have a third value of "that which is neither", which I stated before, can be all at once (a fine line) or gradual (gray staircase).

In applying this to our current theory of "color", it became apparent that the 3 overlapping circle model is fine, but the values assigned to them are wrong. They can not produce all colors. Period. So, here is a place to change. A tight model will work in all situations - that is Science. This same approach brings the duality of mass/energy, dark/light, and electron/proton into a common arena, where we can all find a set of symbols (language) that we agree on.

Zero and Infinity fit into this system in a philisophical way, but I do not think you will ever find an equation that uses these as actual values (math)to solve the problem at hand. I think that using terms like "ALL/NOTHING, or BEGINNING/END" are better suited for the philisophical side of this problem. (certainly, the Specialists following this conversation will be happier if those terms are not used when using the numbers approach to the solution)
The philisophical side of unification is, to me, understandable. Therefore, I turn to "those who specialize in the measuring and defining of systems in nature with numbers", in order to bring about a set of values that we can all agree will work in describing the set of rules that allowed creation.


LPF