Recent content by LeoYard

Do you have a linked article to mathematical proof? I'm looking for an article that explains the importance of proofs in mathematics.

I'm also wondering about what you wrote: "... this particular symmetry gives rise (through Noether's theorem) to intrinsic spin...". Sure. But what does it mean? From a strict physics point of view, how can an intrinsic property act in the same way as a motion, without being motion itself? Very...

Can anyone explain why does an electron have intrinsic spin? Pauli and Dirac matrices show the existence of spin, but this doesn't really explain the physical origins of the spin.

Let's consider an image of a natural scene ;we 've got some individuals (pixels) that may differ one from another (different colors). the entropy E of the system is E=sigma(-p.logp), where the sum is computed over the colors and p is the probability of occurence of a given color. the issue...

a) What is the modern definition of the time unit and the length unit? b) How people actually Materially realize these units ? (a) in the wiki, it reads: Second: Under the International System of Units, the second is currently defined as the duration of 9,192,631,770 periods of the...

Three scientists at the Santa Fe Institute, an interdisciplinary institute in northern New Mexico, took up this question a few years ago and discovered that if you compare elephants to lions to housecats to mice to shrews, you discover that heartbeats vary in a precise mathematical way. The...

Thank you, genneth. Coulomb's law states that the electric field from a point charge drops as the square of the radius. Put two charges at the same place and you get zero electric field, so the two charges need to be slightly displaced. However, as you go to large radii, the separation between...

What is the basis for the sixth root dependancy on the inverse of the distance between the dipoles (in any dipole-dipole interaction)? Is it empirical or can it be mathematically derived?

Thank you for the links. So, we can't be more specific than that. I thought of excluding solids. But, still the way substance (gas or liquid) behaves depends very much on its temperature in non-trivial ways.

How does heat capacity relate (mathematically) to density? I imagine first relating entropy to density, it will depend on the molecular structure and everything, but is there a general formula ? http://en.wikipedia.org/wiki/Volumetric_heat_capacity I found this link, and it deals with...

Bertrand Russell stated : "To choose one sock from each of infinitely many pairs of socks requires the Axiom of Choice, but for shoes the Axiom is not needed." The idea is that the two socks in a pair are identical in appearance, and so we must make an arbitrary choice if we wish to...

Can we quantify synchronicity and randomness ?

I'm somewhat familiar with fuzzy logic, and i came across complementary logic at this link http://www.geocities.com/complementarytheory/CompLogic.pdf I've never heard about it. I don't understand it. Can anyone explain it ? Thanks

The following is a well-known unsolved problem : If n is an integer larger than 1, must there be integers x, y, and z, such that 4/n=1/x+1/y+1/z? A number of the form 1/x where x is an integer is called an Egyptian fraction. Thus, we want to know if 4/n is always the sum of three...

Let R be a convex region symmetrical about the origin with area greater than 4. Show that R must contain a lattice point different from the origin. This is the 2-D case of Minkowski's theorem, right ? How about the n-dimensional version ? The n-dimensional version is : Given a convex...