Everything is Unique !

[swansont]

I didn't say it was wrong Strange, I said it couldn't be proven conclusively mathematically, because math can't handle non-absolute values. The accuracy of the measurement is entirely dependent on the equipment one is using to take the measurement. The equipment itself is calibrated to an absolute standard, and will always yield an absolute result. They may be identical to that piece of equipment, but that certainly doesn't answer the question, does it? And to confound the problem, the more accurate we make the measuring devices, the less useful and less accurate it becomes in taking measurements, because it becomes too sensitive. Science approximates to an acceptable degree of accuracy and intentionally yields an absolute value that they can work with. You have to.

 

If I used a bathroom scale to weigh ping pong balls, can I claim all ping pong balls weigh 0? Of course not.

 

The only thing that has been proven is that science can make pretty damn accurate equipment.

 

What you say may be true for an analog system, but quantum systems provide the opportunity to discern small differences. Which comes up in the indistinguishability case — QM tells us that there must be some difference between fermions in a system — that can be their energy or their angular momentum, or some other quantum property that might be unknown, but the fact that chemistry works the way it does indicates that there aren't any other parameters than can be adjusted. Whether particles are in the same state or a distinct state is much more easily measured than a ping-pong ball on a bathroom scale.

 

http://en.wikipedia.org/wiki/Identical_particles

[imatfaal]

 

I think you're missing the point. We can only be as accurate mathematically, as the equipment we are using, or our patience in decimal places manually.

 

 

Math can only simulate reality to a finite point. Yes, it does many things very well, but we will always be limited to certain number of decimal places. In 99% of the cases it is good enough. Math only handles absolute values. We have to physically stop a computer from trying to solve problems before it errors out or fills storage.

 

And when it come to the speed of light, every decimal place becomes extremely significant.

 

No I think you are mistaking maths for emprical science. The equipment I use for maths is a pencil and paper - and if I want to be accurate I very rarely use decimal places.

 

What makes you think mathematicians use decimal places for accurate propositions - they use algebra, various notations, and arcane symbols; but once you actually start writing numbers down you are just doing sums (OK that's an exagerations - but hopefully you get the point). You seem to be confusing the limits of computation with the limits of mathematics. There is no limit to the accuracy of the ratio of the circumference to the diameter of a circle - and we use this ratio in untold diverse situations. We only use the numeric representation of pi to a certain number of decimal places when we are involved in computation.

 

In the model making, measuring, and computation side of things that you should be talking about then sometimes the numbers might become unwieldy - but we know the accuracy in measurement of physical properties (all decent scientific measurements, constants, and values are given with their known accuracy) and it is this inaccuracy that is the limiting factor in our calculations not the mathematics - not even the computational powers and memory size of our computers.

[andreasjva]

 

What you say may be true for an analog system, but quantum systems provide the opportunity to discern small differences.

 

I don't know Swansoot. No matter how I look at it, math is only capable of simulating reality. It can get pretty darn close the further we advance, but it is always limited to absolutes, and because of that simple fact, the results will always be absolute. The universe itself may be based on non-absolute values. We don't know. Is everything unique? Well, from one moment to the next it certainly is. Right? So the poster is at least partially correct at this point. Unless someone wants to argue that point, but I think that would be a futile argument, considering I'm a minute older (and everything that makes me up) than I was when I started writing this post.

 

The equipment I use for maths is a pencil and paper - and if I want to be accurate I very rarely use decimal places.

 

Then you're approximating the answer with fractions. Same difference. Do you know the precise fraction for pi? If you did, I think you'd have a Nobel prize under your belt.

Edited January 20, 2015 by andreasjva

[swansont]

 

I don't know Swansoot. No matter how I look at it, math is only capable of simulating reality. It can get pretty darn close the further we advance, but it is always limited to absolutes, and because of that simple fact, the results will always be absolute. The universe itself may be based on non-absolute values. We don't know. Is everything unique? Well, from one moment to the next it certainly is. Right? So the poster is at least partially correct at this point. Unless someone wants to argue that point, but I think that would be a futile argument, considering I'm a minute older (and everything that makes me up) than I was when I started writing this post.

 

As far as that goes, it's moot. QM is the best description we have of how systems behave at the atomic level and below, it works incredibly well, and it tells us we have indistinguishable electrons and atoms. Further, nothing we ever discover is going to change the fact that electrons filling up the orbitals in an atom, or atoms in a fermi gas, occupy distinct states. Hand-waving about some future undiscovered science isn't an argument.

 

As an aside, "absolute value" has a particular meaning in math, and not how you're using it. Besides, you're ignoring e.g. Boolean math and related concepts. You apparently have a very narrow view of what math is (math ≠ arithmetic), and that is a weak position from which to make your point.

[imatfaal]

 

...Then you're approximating the answer with fractions. Same difference. Do you know the precise fraction for pi? If you did, I think you'd have a Nobel prize under your belt.

 

No I am using a symbol - it is so much easier than dealing with numbers or fractions. And they don't do Nobel's for maths - and I am too old for a Field's.

[andreasjva]

 

Hand-waving about some future undiscovered science isn't an argument.

 

I'm not the one doing the hand waving, you are. Math is a simulation of nature, period. That simulation is only as good as the tool, and the tool we're using is limited to fixed values. We stop it at a certain point to continue the calculation. It's usable result must always be converted to a fixed value. We approximate by necessity. How tight we want the calculation depends on when we cut it off.

 

 

QM is the best description we have of how systems behave at the atomic level and below, it works incredibly well

 

I never disputed the worth or its useful accuracy. Science does some amazing things with the tools they've created.

 

 

As an aside, "absolute value" has a particular meaning in math, and not how you're using it.

 

You knew exactly what I meant of course. And yes, I know what else it can mean in mathematics. It terms of writing it is much easier to use absolute and non-absolute. You understood and I'm pretty sure everyone else reading was smart enough to figure it out as well.

 

 

 

No I am using a symbol - it is so much easier than dealing with numbers or fractions. And they don't do Nobel's for maths - and I am too old for a Field's.

 

Too old? Didn't know there were age limits on these things.

[Strange]

I didn't say it was wrong Strange, I said it couldn't be proven conclusively mathematically, because math can't handle non-absolute values. The accuracy of the measurement is entirely dependent on the equipment one is using to take the measurement. The equipment itself is calibrated to an absolute standard, and will always yield an absolute result. They may be identical to that piece of equipment, but that certainly doesn't answer the question, does it? And to confound the problem, the more accurate we make the measuring devices, the less useful and less accurate it becomes in taking measurements, because it becomes too sensitive. Science approximates to an acceptable degree of accuracy and intentionally yields an absolute value that they can work with. You have to.

 

If I used a bathroom scale to weigh ping pong balls, can I claim all ping pong balls weigh 0? Of course not.

 

The only thing that has been proven is that science can make pretty damn accurate equipment.

 

I don't know how any of that is relevant.

 

You knew exactly what I meant of course. And yes, I know what else it can mean in mathematics. It terms of writing it is much easier to use absolute and non-absolute. You understood and I'm pretty sure everyone else reading was smart enough to figure it out as well.

 

Actually, I was just about to ask what you mean by "absolute value".

 

But noe of that changes the fact that our current understanding (both theoretical and experimental) of electrons says that they have a limited number of possible states and, apart from those different states, they are identical.

 

The only argument presented for them not being identical is "what if they have all sorts of other variables we don't know about". Which is not a scientific argument. It is barely rational.

[swansont]

 

I'm not the one doing the hand waving, you are. Math is a simulation of nature, period. That simulation is only as good as the tool, and the tool we're using is limited to fixed values. We stop it at a certain point to continue the calculation. It's usable result must always be converted to a fixed value. We approximate by necessity. How tight we want the calculation depends on when we cut it off.

 

 

There's a whole slew of work that never uses actual numbers. It's also one of the great problems in teaching introductory physics that students want to put numbers in, when the manipulation of the symbols yields a better result.

 

if you bothered to read the link on Identical particles, you might notice the dearth of numbers in the calculations (aside from subscripts, which are integers anyway, so they are exact). It's all manipulation of variables and constants. The only calculated numbers are in a table, and those numbers could not be confused with one another (1/2 vs 1/3 vs 1/4)

[Strange]

Math is a simulation of nature, period.

 

Things are not that simple. The question of whether mathematics only exists because it reflects reality, or it exists independent of nature, or it is purely a human invention that we just-happen to be able to use to describe reality, or some combination of those, is a long-standing philosophical debate. There is no obvious answer. Period.

[andreasjva]

 

There is no obvious answer. Period.

 

There never is Strange.

 

 

Things are not that simple.

 

Math is simply a tool in describing the natural world, and as such, has obvious limitations in precisely defining specific problems. The universe would work just fine without it, and us.

 

That should be the simplest answers of all.

 

 

Actually, I was just about to ask what you mean by "absolute value".

 

Glad you were able to figure it out without a single mathematical calculation.

[cladking]

 

Math is a simulation of nature, period.

 

I don't believe this is really true. As soon as you accept your contention then the idea of two identical things becomes possible. If one equals one then two things can be alike. Numbers aren't "real" and each is a construct such that 2 is equal to one plus one and three is equal to two plus one. Rather math is simply quantified logic. You could do the same operations with words if they each had a single meaning but they don't. They have many meanings and nuances. Ideas can't be set to math even though math reflects the logic of nature so can be used to prove ideas. Our models of reality must be tied to reality through experiment where math is usually the tool to confirm or deny hypothesis.

 

Math is more like roadsigns to tell us where we are and where we might be headed. These signs must be interpreted correctly and the equations must be legimately applied to have meaning and to provide proper interpretation.

[andreasjva]

I don't believe this is really true.

 

I misspoke. Math is used as a tool to simulate and define natural phenomena; is more appropriate. Sorry for the confusion.

 

I do not disagree with your post.

 

 

math is usually the tool to confirm or deny hypothesis.

 

Edited January 20, 2015 by andreasjva

[Phi for All]

 

It isn't?

 

No. The aim of science is to develop the best explanation for a particular phenomenon. We use theory, not proof, to make sure we're constantly testing and improving our understanding.

 

Math uses "proofs" and "answers", and philosophy uses "truth", but not science. If we think something is "proven", we stop looking for a better explanation, and that's not how the methodology works best.

[hoola]

My post was hinged upon the idea that it is too soon to consider we have proper evidence as of yet to rule out substructure of the electron, since it and all other particles are not yet understood as to their source, of which the BB could have been a rather recent event in the process. Once we have the necessary facts worked out, we may have that evidence to rule out substructure of an electron in this universe, but not in others. It seems possible that hidden variables are indeed the major component of all "fundamental" particles, and the properties we can easily detect are the superficial ones supported by these variables...

Edited January 20, 2015 by hoola

[swansont]

My post was hinged upon the idea that it is too soon to consider we have proper evidence as of yet to rule out substructure of the electron, since it and all other particles are not yet understood as to their source, of which the BB could have been a rather recent event in the process. Once we have the necessary facts worked out, we may have that evidence to rule out substructure of an electron in this universe, but not in others. It seems possible that hidden variables are indeed the major component of all "fundamental" particles, and the properties we can easily detect are the superficial ones supported by these variables...

 

Except for the complete and utter lack of evidence of this, sure.

[hoola]

If it is determined a physical origin cannot be entirely explained by the BB, and ongoing analysis of the BB points to the existence of a pre-BB state, available physical evidence may only infer a possible pre-BB state, as physical reality is too coarse a structure to show more than superfical recent events.

Edited January 20, 2015 by hoola

[MomentTheory]

I would say that what you are describing is that perspective of form is always different, which would make more sense.

[Strange]

Math is simply a tool in describing the natural world

 

There are many areas of maths which have nothing to do with the natural world.

 

Glad you were able to figure it out without a single mathematical calculation.

 

I would still like you to explain what you meant by "absolute value", especially as you admit is not the usual meaning.

[Phi for All]

My post was hinged upon the idea that it is too soon to consider we have proper evidence as of yet to rule out substructure of the electron, since it and all other particles are not yet understood as to their source, of which the BB could have been a rather recent event in the process. Once we have the necessary facts worked out, we may have that evidence to rule out substructure of an electron in this universe, but not in others. It seems possible that hidden variables are indeed the major component of all "fundamental" particles, and the properties we can easily detect are the superficial ones supported by these variables...

 

This is a great example of why science prefers the best-supported explanations to "proof". We have some wonderful theories that explain most of what you think we don't yet understand. I guess that's because we didn't wait until all the "facts" and "proof" were worked out. We just observed reality, gathered the evidence, and developed a theory based on what we know, what we can observe, what we can predict will happen if we're right.

 

Where do you think all the variables are being hidden? Who is hiding them, and why are you ignoring reality based on a possibility that we're fundamentally wrong about it all?

[andreasjva]

 

"absolute value"

 

You could replace the adjective "absolute" with a number of alternatives, like:

 

complete, perfect, pure etc...

 

Probably should have opted for defined, specific, static, or fixed value. Absolute and non-absolute had a better ring to it. I took creative license in the writing.

 

ab·so·lute

ˈabsəˌlo͞ot,ˌabsəˈlo͞ot/

adjective

adjective: absolute

1. 1.

   adjective

   1.

   free from imperfection; complete; perfect:

   absolute liberty.

   2.

   not mixed or adulterated; pure:

   absolute alcohol.

   3.

   complete; outright:

   an absolute lie; an absolute denial.

 

There are many areas of maths which have nothing to do with the natural world.

 

Why certainly. I use a spreadsheet to keep track of my personal finances out to about 2 years. It simulates my bank accounts pretty well. Although, it's hard to factor in the wife all the time, but I take my best guess on her spending habits based on history.

 

Not sure what the comment has to do with the price of eggs in Egypt though....

[andrewcellini]

Math is simply a tool in describing the natural world

this leaves out all of pure mathematics and doesn't really begin to describe what math is.

[andreasjva]

As far as everything being unique on an individual basis, not likely. It's the large number of variables acting upon the many of the small that give the diversity of the larger. Much can happen over time that change the way things interact and combine with one another. Can science say with absolute certainty anything is precisely the same? No. But pretty much beyond a reasonable doubt most of these things they're talking about around here appear to be identical in nature. I've often looked at the universe itself as a copier of sorts, with no original required. It just does its thing over and over and over, and the complexity and diversity arises from sheer volume over time. The chance of a more substantial somethings being identical to another substantial something is about the same odds as everything being unique. That could be a little different when we're talking very large somethings. They could end up being a bit more identical in nature. I was thinking black hole in this instance, which is a critical mass point. Who knows though?

 

I just enjoy a good debate.

 

To answer the question though, no, it can't be said with absolute certainty. It would just be somewhat of a ridiculous avenue of research considering what they already know.

 

this leaves out all of pure mathematics and doesn't really begin to describe what math is.

 

The natural world was doing just fine before we invented numbers and then the mathematics to manipulate those numbers. The natural world is simply abiding by the laws of nature. Because nature follows rules, it follows the numbers. The universe came first, math came second.

 

I'm not exactly sure what you even mean by "pure" math. Sounds a bit esoteric.

[Strange]

The natural world was doing just fine before we invented numbers and then the mathematics to manipulate those numbers.

 

Invented or discovered?

 

 

I'm not exactly sure what you even mean by "pure" math. Sounds a bit esoteric.

 

It is a pretty standard term. You could look it up in a dictionary, if you are really unsure. This is somewhat different from you constantly using words in non-standard ways.

[hoola]

phi for all...I believe the variables are hidden in string theory, and the strings are composed of information, specifically mathematical information, as every possible (logical) form of information as expressed by PI. The logical component of the vast library of information as physical reality, the balance of illogical information as what can accessed only via sentience, hence an upper limit to free will...

[cladking]

 

Invented or discovered?

 

 

Invented.

 

Numbers don't exist in nature. They are a construct of the human mind.

 

Since no two individuals are alike we could count first apple, second apple, third apple, etc. "One", "two" and "three" have no existence outside their definitions. "Pi" has no existence either even though it is the the number of times per unit distance a nummolite might roll divided by its diameter. Nature is "logical" therefore math works. It is quantified logic.

 

Just as each of the apples differ, so too, do the nummolites and their individual math. Two humans who weigh about 117.3 pounds will balance on a teeter totter but they are not identical. If one gives birth before getting off the teeter totter they are not even two humans but "three". Numbers, counting, and math are all constructs with no independent reality. But so long as the logic is sound they work. Each apple retains its individual identity. The eight apple is different than the second apple.

Edited January 20, 2015 by cladking