Zero and Infinity

[Antonio Lao]

Zero and Infinity

In mathematics, we see these two numbers appear almost always as the end points of some limiting processes. We see zero in the definition of a derivative in calculus. We see infinity in the math of infinite series. In this discussion, we will try to see these extreme numbers in physics. These will be used to give some insights into the following statements: (1) The mass is zero, (2) the mass is infinite, (3) the time is zero, and (4) the time is infinite.

The mass is zero. Since mass is equivalent to energy, the statement is same as “the energy is zero.” Zero energy does have a meaning in quantum mechanics. It is the energy of the vacuum equals half a quantum (Planck’s constant over 4 pi). This is associated to a point particle at the absolute temperature of zero. Because of Heisenberg’s uncertainty principle, this energy can never be exactly zero. This gives meaning to the quantum vacuum as a complex structure. This structure was verified by experiments to detect the Casimir effect.

This structure of the quantum must necessarily give meaning to an infinitesimal volume. In mathematics, we can define volume in any given dimension of space. And if the geometries are that of a sphere or a cube, there exist formulae to calculate their volumes.
It can be shown that the volume of 1-sphere is equal to the volume of a 1-cube. The different in volume becomes worse and worse at higher dimensions. This volume is static. In order to make the volume dynamic, it must be associated with a vector, in this case, an infinitesimal vector. This is called a local infinitesimal motion (LIM). For volumes to have any physical meaning, it must be a closed volume. The closure of one-dimensional volumes forms closed one-dim loops. And there are two distinct types. The LIMs are all conserved and there is infinite number of them. Here again we have reached infinity by not going as far as the next LIM. In mathematics, a line segment or a loop (closed line segment) contains in itself infinite number of points. We can take away the end points of a line segment, and still there remain an infinite number of points. It is useless to keep removing end point, the number of points will never be less than infinity.
But in the loop, the LIMs have started from a begin point and have passed infinity and back to the same begin point without really knowing it, just in the blink of an eye. And it continue to cycle through these infinite points forever and ever holding on to the same bearing of travel. This is the principle of a directional invariance.

If we attempt to visualize this volume in two-dimension, we get the limiting problem resulting in a Sierpinski carpet, which area is zero, and while the total perimeter of the loop is infinite. In three dimensions, we get the Menger sponge, whose volume is zero, while its surrounding area is infinite. Only in one dimension does the volume of the loop make any little sense. And it is in this one-dim that we can justifiably defined eight invariant properties for the principle of directional invariance.

The time is zero. This is just to give a linear definition for time. Taking the line segment again, zero time is surely at one end. The other end might be when time equals infinity. But in a closed loop, time just keeps flowing, from time zero, passes infinity and back to zero, on and on. Since in principle, there are two distinct types of closed loops from a 360 degrees twist of a Moebius strip, there are two directions of time. These two directions can only make any sense if viewed in one dimension. If we attempt to view time in three dimensions, we get the senseless image of Escher’s Waterfall. The validity of most of Escher’s images is true only if we live in the one dimension. For the one dimensional Waterfall, it is logical to have two directions of flow. In three dimensions, the water (time) has to flow uphill fighting against the forces of gravity making it only natural for water (time) to flow downhill.

We have discussed the concepts of 1-dim volume and the possibility of two directions of time. By so doing, without even realizing what we have done, we have actually separated the space-time structure of special and general relativity and came up with a bonus of an extra time’s direction than can most benefit the description of antimatter, which was not part of relativity but is a big equal participant in quantum field theories.

[8LPF16]

Antonio,

This thread deserves more life.

On the point of a closed loop, you could still have the beginning at 1 (or any other small number) rather than "absolute" zero. Such as I've mentioned before - .0618033..., which is "less than zero" in loose terms. I think that sometimes, we need to think in loose terms because the numbers that we use are our invention. Nature just deals in quantities - and sometimes this appears loose to our rigid math.

LPF

[Antonio Lao]

8LPF16,

I agree with you 100%. The zero that I am driving at is the zero of time. This zero time is called the temporal intersect of two mirror worlds. One world is contracting in space and one is expanding in space. The total energy of both worlds is conserved. The zero time is the connection or bridge between these mirror world. The flow of time for each world is opposite in "direction" as that of the other. This different direction of time flow becomes my justification for the existence of antimatter and consequently also justified the CPT Theorem of physics.

Antonio

[Organic]

And if we have 3 connected worlds?

[Antonio Lao]

Organic,

The temporal intersect only takes two worlds at a time (time=0). This does not mean that there is only one temporal intersection, there can be many and in fact infinitely many. Each intersect takes two mirror worlds at a time in order for conservation of the CPT Theorem (total energy cannot be destroyed or created).

Antonio

[Mr. Robin Parsons]

Didn't have time yet to digest all of what you have written, but...
Originally posted by Antonio Lao
(SNIP) This is associated to a point particle at the absolute temperature of zero. Because of Heisenberg’s uncertainty principle, this energy can never be exactly zero. (SNoP)
Heisenberg's principal speaks (Only!) of our inability to measure, (at atomic scales..) it does NOT dictate, in any way, shape, or form, how the universe (or atoms) operate(s)

[8LPF16]

Just think, we can't measure the atomicly small, or the Universely big. Personally, I think we are a millenium from knowing when/where the Universe started. We will have to travel the far reaches, and gather vast data to even begin. I don't really care how old the planet is or our Universe, it doesn't have relevancy in my everyday life. Until we have a better grip on when/where we came from, and how our world works (and how to work in harmony with it), I think it's energy spent in the wrong direction.

I thought Heisenburg was more of a ratio of uncertainty - knowing place and time simultaneously. Which, I will add, if you know the path an object takes then this Herculean task becomes rather simple.
(ask a detective)

The reason I still shy from zero - even with time ... I look at the expansion/contraction of the Universe to be analogous with my lungs. They are never empty, even as a fetus, there were fluids inside, and at some point, exchanged with oxygen from Mom's blood.
All things are cyclical, a "breathing" Universe needs no beginning or end.

LPF

[Antonio Lao]

8LPF16 and Mr. Robin Parsons,

Time zero is not a quantitative thing that I can measure.
It is just another name for the qualtitative directional meaning of time. Time zero means that there is no way we can measure or determine which directions time will take, growing older or growing younger.

But in Heisenberg's uncertainty principle, time is measureable but only if it is related to the energy of the vacuum. Energy can be borrowed from the vacuum but the more energy you borrow the shorter time that you can keep this energy to useful purpose. If you borrow infinite amount of energy from the vacuum it can only keep it for zero time which is no time at all. If you borrow zero energy then you can keep it forever.

Antonio

[russ_watters]

Originally posted by Mr. Robin Parsons
Didn't have time yet to digest all of what you have written, but...

Heisenberg's principal speaks (Only!) of our inability to measure, (at atomic scales..) it does NOT dictate, in any way, shape, or form, how the universe (or atoms) operate(s) That's a common misinterpretation (due largely to laymans' descriptions like that found in "A Brief History of Time"). It was actually first proposed by Heisenberg himself. It is not correct. http://en.wikipedia.org/wiki/Uncertainty_PrincipleThe uncertainty principle is sometimes erroneously explained by claiming that the measurement of position necessarily disturbs a particle's momentum. Heisenberg himself offered this explanation initially. Disturbance plays no part, however, since the principle even applies if position is measured in one copy of the system and momentum is measured in another, identical one. It is more accurate to say that the particle is a wave, not a point-like object, and does not have a well-defined simultaneous position and momentum.

[Organic]

Hi Antonio Lao,

I am talkin about any odd number of worlds where their time balance = 0

[Antonio Lao]

Organic,

Is infinity an odd or even number? If I assume that there are infinite number of universes, is this number odd or even?

But we don't have to answer the question if all we wanted is to say something about the connection between two worlds, by doing some kinds of binary operations such as addition and multiplication.

So we just taking two things at a time, do some analyses, and then go ahead and make generalization. It might turn out that all these worldly connections might be just relative and where the absolutes is at zero and infinity. These two extremes can only be approached but never be reached exactly. So we all have our journey to follow but we can never say that we have finally at the destination (the end of eternity). To think about our average lifespans and compare to infinity, our lifespans are just zeros, as if we never existed at all.
Our awareness of our existence is a gift given by higher collective awareness that at the moment I don't have any answer.

Antonio

[matt grime]

Originally posted by russ_watters
That's a common misinterpretation (due largely to laymans' descriptions like that found in "A Brief History of Time"). It was actually first proposed by Heisenberg himself. It is not correct. http://en.wikipedia.org/wiki/Uncertainty_Principle

I don't see how your correction corrects what was posted. Heisenberg's principle is *just* a manifestation of a fairly straightfoward result of some integration you might come across in, say, an advanced course on Fourier Analysis.

The post by Mr Robin Parsons didn't mention anything about *disturbances* by measurement, but merely talks of our inability to simultaneously measure these two quantities. It doesn't state any reason for this inability.

[Antonio Lao]

Matt Grime,

Are you addressing your post to me or other? Maybe i did not understood what was the question.

As far as Heisenberg's Uncertainty Principle goes, there are most likely many interpretations. For me, I am not an authority on it, I am just using it to say something about zero time and infinite energy.
Time and energy are conjugated into another form of the principle. The other is momentum and position.

Antonio

[8LPF16]

Also to Matt,

It seems logical to me that, depending on what your using to measure, that at the atomic scale, the tool would disturb the thing being measured. Is this not accepted now?

LPF

[Antonio Lao]

8LPF16,

The disturbance of the obsevers was never questioned by the authorities of quantum physics. So you are correct. They were trying to come up with a good explanation for the double slits experiment of interference patterns. Feynman was able to resolve this mystery with his sum of histories - path integral methods.

Antonio

[8LPF16]

Antonio,

My idea on the double slit experiment: the slit disturbs the normal path of the wave of potentials, they are at first scattered about, but will eventually regroup. The difference (from Feynman) is I don't think they travel all potential paths simultaneously, I think they know them all previous to going through the slit, and the experiment does not allow them enough distance to regroup into one slit. Given enough distance, the image on the back wall would be what is predicted by particle definition - 1 slit.

What is the standard distance from the slit to the back wall in this experiment?

Any record of someone doing a sideways slit experiment?

As I stated before, when doing even the simple prismatic experiment that Newton did, if you change the distance, you get different results. If you change position (I call it anti-slit, in which, the color is examined before it hits the wall, not after), then you will get different results as well. I thought scientific experiments were supposed to eliminate these discrepancies by testing other locations, conditions, etc.?

It is my very strong belief, after doing these tests, that the slit itself throws the results. It creates a dark-light-dark condition that forces a change to the natural dark to light flow (vector forward in time).

LPF

[Antonio Lao]

8LPF16,

Feynman used the principle of least action. This principle states that nature will never waste time or energy on purpose. For every possible path, nature will always choose the path that takes the least amount of time and the least amount of energy. On an Euclidean plane, this is the straight line. On a spherical surface, this is the geodesic curve. The standard distance should be the same for both surface. What is summed are the probability amplitudes, which is the normalized product of the wave function and its conjugate.

Distance for the slit experiment is arbitrary. It can be any distance you want as long as the apparatus can be fitted into the room.
Another thing I need to mention is that the width of the slit cannot be larger than the wavelength of the radiation going into the slit.
The radiation can be light, or x-ray (use crystal lattice as slit), or a stream of electrons, or a stream of apples.

Antonio

[8LPF16]

Antonio,

The path of least resistance dominates all my ideas. This is why I say the photon would never travel all paths, because it knows the paths already, through color memory. The gamma portion of the wave acts as a "scout", and directs the wave like a laser sight on a gun. So, it "knows" what is on the other side before the "visible" portion comes through.

I understand the need for contol of the width of the slit, how could they possibly have missed the need to control and record different distances?

Here is the slit through prism:

[DARK]red/yellow..[LIGHT]..cyan/violet[DARK]

the "cone" extending from the controlled slit to the wall is mediated by the distance. Only when it is "squeezed", through improper distance, do you see:

[DARK]red/orange/yellow..GREEN..cyan/blue/violet[DARK]

what they missed is the constant of attraction of red and violet to darkness, and yellow and cyan(turquoise) to lightness. This is critical to unifying electro-weak and gravitio-strong.

This is confirmed by the anti-slit experiment. You will see:

[LIGHT]yellow/red..[DARK]..violet/cyan[LIGHT]

upon final calibration for distance you will see:

[LIGHT]yellow..magenta..cyan[LIGHT] (magenta has maximum attraction to darkness, and apparently, optimal communication with gamma)

By decreasing the distance, magenta is "squeezed" apart into red and violet. You can watch this happen as you change distance.

The rainbow can be more easily explained this way. The Earth =[DARK]..clear area=[LIGHT]..rain cloud=[DARK], the long distance "squeezing" green (and other tertiary colors) into the picture.

My theory puts the primaries at C-M-Y, and R-G-B as secondary. A fairly minor change, with major ramifications.

LPF

[Mr. Robin Parsons]

Originally posted by Antonio Lao
(SNIP) Time zero is not a quantitative thing that I can measure.
It is just another name for the qualtitative directional meaning of time. Time zero means that there is no way we can measure or determine which directions time will take, growing older or growing younger.
(SNoP) Time, equalling zero, equalls infinity, respective of energy, not a new, or unknown, thought.

Heisenbergs uncertainty principal as I learned of it tells of 'light' being 'shined' on the outer valence shells of electron orbitals, to make measurements, it is the act of shining the light (EMR probe of any kind/type of EMR) that excites the electron, and therefore we cannot determine it's position, prior to our investigative light shining having adulterated the event we are attempting to observe.

This DOES NOT imply, nor state, that the electron is not observable, nor that its position and momentum are NOT, Both, simultaneously knowable, just that we have not a method to achieve that outcome, due to the constraints that the physical reality imposes upon us, by it's very nature, and makeup/arrangement.

[Antonio Lao]

Mr Robin Parsons,

The nature that limits us from knowing the quantum world is the inherent symmetry of the structure.

A point looks the same from any angle, any distance, any time.

Antonio

[Mr. Robin Parsons]

Originally posted by Antonio Lao
Mr Robin Parsons,
The nature that limits us from knowing the quantum world is the inherent symmetry of the structure.
A point looks the same from any angle, any distance, any time.
Antonio Are you refering to the work of Emmy Noether as per your reference to symmetry?

[8LPF16]

Antonio,

I forgot to ask - do you have a prism?

LPF

[Antonio Lao]

8LPF16,

I do have a prism.

Antonio

[Organic]

Antonio,

You wrote:

Our awareness of our existence is a gift given by higher collective awareness that at the moment I don't have any answer.

If 0 is the balance of infinitely many worlds, then each awareness is limited to some world, but when we try to be aware to more then one world at a time, we get 0.

Form 0 point of view infinitely many worlds become one.

So, through this point of view, we have:

1) 0 aware to global 1.

2) Local 1 aware to 0.

By (1) we get infinitely many worlds that never destroy each other.

By (2) each world gets its possibility to fulfill its own uniqueness.


The hidden divinity is 0 aware to 0.

[Antonio Lao]

Organic,

I could never have said it better than you. Thanks.

Antonio

[Mr. Robin Parsons]

Once again Mr. Robin Parsons ASKS...
Are you refering to the work of Emmy Noether as per your reference to symmetry? If you would prefer NOT to respond, fine, but it ends the discussion for me...

[Mr. Robin Parsons]

Originally posted by Organic
Antonio, You wrote: If 0 is the balance of infinitely many worlds, then each awareness is limited to some world, but when we try to be aware to more then one world at a time, we get 0.
Form 0 point of view infinitely many worlds become one.
So, through this point of view, we have:
1) 0 aware to global 1.
2) Local 1 aware to 0.
By (1) we get infinitely many worlds that never destroy each other.
By (2) each world gets its possibility to fulfill its own uniqueness.
The hidden divinity is 0 aware to 0. Humm could it just be that 'zero' is simply the distinguishing/distinguishment between 1 and -1 AKA that which separates them as to allow us to see 1 and -1, otherwise we have no distinction between negative values and positive values, no midpoint....

[matt grime]

Originally posted by 8LPF16
Also to Matt,

It seems logical to me that, depending on what your using to measure, that at the atomic scale, the tool would disturb the thing being measured. Is this not accepted now?

LPF

Ask a physicist. my post was merely to point out that robin was being misrepresented.

[Mr. Robin Parsons]

Originally posted by matt grime
Ask a physicist. my post was merely to point out that robin was being misrepresented. How, please....

[matt grime]

I seem to recall russ watters claiming you had misrepresented heisnberg's principle in respect of 'disturbing' things when measured. I pointed out that you hadn't used the word disturbed, or even alluded to it.

[Mr. Robin Parsons]

Thank you, for the clarification...

[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

[Antonio Lao]

Mr. Robin Parsons,

This is a belated reply to your post about Emmy Noether. Yes, I am refering 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 concensus 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) This is a belated reply to your post about Emmy Noether. Yes, I am refering to her symmetry theorem. Antonio (SNoP) 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) 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]

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]

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 wanna KNOW! [6)] only that (this one --> [6)] ) 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? [g)]

- 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 occuring.

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 occuring.
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]

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]

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 exhange 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 vaccum 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 modelled 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

[Antonio Lao]

8LPF16,

Thanks for telling me where you stand in your quest for understanding of the world.

If I can be of help any further in your quest, don't hesitate to ask. I will help you if I know the answer.

I think you already have the answer to your quest, just a matter of communicating to others?

Antonio

[8LPF16]

Antonio,

When I thought that your origial post deseved more time, I had no idea this would happen!

You have already hepled very much, and I will hope to continue receiving some help from you from time to time.

Like the British, we speak english as a common language, but are still culturally different. The course of my education is quite different than Western. Some translation will be required occasionally to have effective communication.

LPF

[Fromfiretolife]

Hi antonio,

Thank you for your response to my problem, Let me tell you a little about the use for perfect vacuum that I am trying to resolve. I am trying to better understand the whole light speed and how to achieve it just for my personal satisfaction. I heard a rummor that there have been experiments conducted to try to reach the speed of light I do not know if this is true but according to the teller of the story, the reason the speed of light was not achieved was because the object in which they were trying use kept on gaining mass and thus gaining weight and thus slowing down or staying at a speed not reaching the speed of light. I believe if a man made box or space with perfect vacuum were created this object would be able to reach such a speed. I really am not sure if this was true about the experiment I am eager to find out but I don't know who conducted the experiment or nothing. I have been thinking that a way to harvest such a box might be to create a self inteligent matter capable of becoming a different state and size diminishing in size surrounded by a reverse electromagnetic field coupled with an antistatic field to eliminate the possibilities of any matter wanting to reach the absolute vaccum environment coupled with a vaccum to continously suck out by product with a series of one way valves/magnets. All coupled with a detector that would detect particles like neutrino's and would pull them to the apparatus waste site. Although the whole apparatus would be covered with a liquid nitrogen wall to keep any microorganisms and or matter frozen. the inside of the apparatus kept at extreemly low temperatures. In addition the way to suck out the debris and or matter would include many other similar vacuums surounding this dome of space or box of space with the one-way valves in series and the original dome where you would want the absoulute vacuum to be would have to be at a higher pressure but still in a sense a absolute vaccum. In addition to the one way valves in a series between every one way valve you would have sort of a reservoir to put the byproducts/microorganisms/gasses and so on divided by a openable valve not operated by vaccum in itself. What do you think of this particular model? This is just a little something I was thinking about last night and I decided to write it down. And by any means if someone else has some input please feel free to help I am just trying to learn and understand more. Thank You

Ike...

[Antonio Lao]

Fromfiretolife,

What you describe in your post is similar in many ways to the accelerators in Europe at CERN in Geneva, Switzerland and Fermilab in Batavia, Illinois. These have been in operations for a while. And they were responsible for the discovery of many particles. The people involved have received Nobel Prizes already. They did accelerate particle at nearly 99% the speed of light what holding them back to exactly the speed of light is Einstein's equation. When matter and antimatter collide at high speed and high energy, matter does transform to pure energy in the form of photons and photons does travel at light speed. The phenomenon of vacuum fluctuations are cases in point that this change of matter-antimatter to energy is constantly being realized in the infinitesimal domain of the vacuum.
The process that the labs did is to accelerate electrons in one direction and positrons in the other direction. Once they reached energy 99% light speed the particle beams were made to collide. Pure energy in the form of photons are produced profusely. The fact is we don't need high speed to create pure energy, all we need is to keep matter in one bottle and antimatter in another bottle then mix the two bottle, the result is pure energy, just that simple, really! The problem is how to keep antimatter in a bottle. For the scientists, they use something similar to the Penning traps as pioneered by Dehmelt. It is some sort of electromagnetic trap. Dehmelt and other received the Nobel Prize for this work in 1989.

FYI: The chambers were the electrons and positrons reside are perfect vacuum as far as our current technology can create. In other words, the experiments are done in a 'perfect' vacuun.

The superconducting supercollider that was supposed to be built in Texas was designed to operate at superconductor's temperature which necessarily needed liquid nitrogen to cool the machine. But this was too expensive. The whole project was scrapped by U. S. Congress.

Antonio

[Fromfiretolife]

Antonio,

Thanks antonio for the response I will keep that into consideration when I start to think about new ways, do you know any places to get more information about where to get information on the project at CERN and the project that was scrapped at texas to evaluate it and learn about them in detail.

Ike...

[Fromfiretolife]

Wow I can kinda see how the particles would accelerate moving the electrons in one way and the positrons in the other way it is in deed a very nice design, that is very interesting.

Ike.