hey, Lets start some math discussion!

[lindagarrette]

consistent sequences in nature are physical phenomenon we can visualize if we examine them numerically. There is really no such thing as a particle or an instant in time. We like to think in terms of static conditions because they are easier to work with. Pandora

[lindagarrette]

Here is a site on fascinating numbers in nature: http://www.brantacan.co.uk/fibonacci.htm


"So the whole Fibonacci thing is an accident. The rule is that the leaves or florets grow for maximum space. The rest - Fibonacci numbers, spirals, pretty patterns - follows automatically.

In this context, the Fibonacci numbers are like the magic numbers in nuclear physics. The difference is that if plants had never existed, the Fibonacci numbers would still have interesting properties, whereas the values of nuclear magic numbers are dependent on the properties of nuclear forces, and are not in themseleves interesting. Very far from the floor of the valley of stability the values may even be slightly different from the normal ones.

Furthermore, if the universe could have been created with slightly different fundamental constants, the nuclear magic numbers could have been different, but any life-form that could grow like plants would still show the GS and Fibonacci numbers.

Perhaps the whole of physics is like the plant numbers. Perhaps the many elegant laws that so many people have struggled for so many years to create are just an accidental reflection of a few deep rules that we do not know. For example, from the use of the Lagrangian function, many laws can be recovered. The laws of refraction and reflection can be deduced from the simple rule - light takes the path of least time. " Pandora

[Freethinker]

Originally posted by: lindagarrette
consistent sequences in nature are physical phenomenon we can visualize if we examine them numerically. There is really no such thing as a particle or an instant in time. We like to think in terms of static conditions because they are easier to work with. Pandora

Uncertainty, just like Zeno's Arrow paradox 2500 years before, shows that we can know EITHER the instant or the motion. A solid arrow can be examined at any time. It will be the same solid arrow whether stationary or moving. We will never know it to be an object in motion. But we will know it's motion. So we think in EITHER static or motion, but not both.

[lindagarrette]

I'm trying to figure out if there is such a thing as a particle, or mass, for that matter (so to speak). Superstring theory seems to indicate there are only waves at the bottom of it all except perhaps for 'branes' which may be something solid. Any clues? Here's a brief description from a math web site. Pandora
Distinction between waves and particles.

It is essential that one understand the distinction between waves and particles. A classical particle is something that has: position, momentum, kinetic energy, mass and electric charge. A classical wave has the attributes of: wavelength, frequency, velocity, amplitude of the disturbance, intensity, energy and momentum.

The most distinctive difference between the two is that a particle can be localized, whereas a wave is spread out and occupies a relatively large position of space. There is one important difference between photons and massive objects in the way their waves and particles are related. Because for a photon, only one rule is required to get both wavelength and frequency from a photon's particles of energy and momentum. A massive object, on the other hand, requires separate rules for its wavelength and frequency.

There is some conflict between previous classical ideas and those of the theory of matter waves. For example, the concept of a classical trajectory of a particle must be discarded and replaced by a probability distribution spread over a large region of space. But, with the application of Freire's enunciated that major flaw in the development of the wave theory of matter, no need the probability to find out the particle position in a certain region.

Because the wave is spread out and occupies a relatively large position of space, I would say equivalent to an expansion of (nq*Y) in the space. That is why it is need to find out the particle through the probability. http://www.jfreire.com/extend_html/extend3.htm

[Tim_Lou]

.................................................. .........

i should've realized that this forum is mainly about science....
math is.....
well, this topic somehow changed back to physics........
anyway, keep going....

just ignore me....keep going...

[GAHD]

"Do numbers exist because we want them to? Or did we discover numbers because nature is broken into discrete units?"

Would have to say discreet units. best example being the solar system; the planets, moons, sun, all are distinct (though some are amorpherous).

This " odd unit" (singular meaning odd) thinks that numbers exist because we discovered them, and gave them names. Odd to discover something that doesn't exist in any physical sence.

[Freethinker]

Originally posted by: Tim_Lou
.................................................. .........

i should've realized that this forum is mainly about science....

math is.....

well, this topic somehow changed back to physics........

anyway, keep going....

just ignore me....keep going...

Sorry Tim. When I was around your age I also enjoyed working with equations. I remember "doscovering" quadrtic equations. I'd solve them just for kicks.... I know, I was a strange kid.... I was a teacher's aid in College, but that was primarily treaching slide rule.... ya THAT long ago. Back when you had the THINK... lol

Now I seem more interested in the philosophy behind it. That math is not just about working with symbols that represent quatities and functions, but why and from where.

But it will not help you to keep a topic in the area you want by promoting an inferiority complex, you just need to find an equation that catches.

[Tim_Lou]

lets ask:
what is the meaning of numbers?

i personallly believe that humans create numbers.
back in the acient day, the early humans see that there is a sheep, a cow, an apple....they start to realize the meaning of one...

hmm....one thing weird is that why is it 9+1=10?
what not something like A? why do we use "10" as standard?

the nature is making some sort of sense out of numbers, hmmm....what if we all use another system like
oct, hex.....
how about this, make it that c=1, maybe the world would come out with some nice numbers!

think about this, does other animal know the meaning of numbers? do they have an idea of 1~10? i know some mammels do understand them.....so, is number "natural", or "artifical"?
(any comments?)

[Bo]

as for the pure linguistics: The meaning of a number is exactly what semantics tells you what it is. So we can easely from now on call all 10's A (or X to use the latin number system).
As to what a number means: in my opinion a number is just some property you can give to an object. For example: 1 apple is green (sort of). round (sort of) and we have 1; 2 apples have the same properties, but then we have 2 of them (that means:1 apple and 1 apple). So a numbering system is just a system to order the imaging of the world in our perception (or something like that)
i thnik the above definition is also unconsciously known by most intelligent mammals.
As for calling c=1 (i suppose you mean the speed of light): That is something which we in high energy physics do all the time (we also take h, planck's constant, equal to 2pi). You can easely do this, because physical observables (as c or h) are dependent on the scale you use. Take for example the difference between meters and inches, or Celsius, Fahrenheit and Kelvin. The main point is that the scale you choose doesn;t change your physics (as long as you're consistent).
There are however some numbers which we just *cannot* change. e.g. pi, e (the base of the so called 'natural logarithm'), gamma (the euler constant) and probably there are some more.
what these numbers 'mean' or where they come from is as far as i know still a mystery...
Bo

[Bo]

And also to say something about the formula you gave: i wondered how did you derive this? There is a general formula for these kind of problems (the so called Faulhaber's Formula see e.g: http://mathworld.wolfram.com/FaulhabersFormula.html) But that's quite hard to derive in general.

I tried to prove your formula myself and after some work (considering (n+1)^5 - n^5 for all n) i got an expression of the fourth power problem in 3, 2, and 1 power sum problems. These can eventually by the same technique be expressed in the well known (and easy to derive) 1st power sum sollution: [sigma( K=1...n)]K = 1/2(n*n+n)
substituting all gives your (and mathworld's ) formula

is this anything near your proof? or have you just done this by trial and error?
if you want the complete written out proof: just ask me and i'll write it down.

Bo