Is there a level of mathematics where symbols are created or interpreted spontaneously?

Question

Intuitive Mathematics? Can symbols be constructed and later analyzed for application/design?

Answer 1

On the level of mathematical research, mathematicians often use lot of creativity to invent new symbols or new uses of symbols. These are the constraints:
- the symbols must be defined
- they must make things easier to read
- they must be available in the character set of the type writer/printer

Of course, if it is not necessary, we stick to traditional symbols because people are used to it.

But in set theory, for instance, the Hebrew letter Aleph is used for the first infinite cardinal number, and I have seen papers where the letters Beth and Gimel are thrown in.

Also, in one of the books of my shelf the author suddenly uses a Russian letter.

In formal symbolic languages used in theoretical computer science, such as Z, many new symbols are devised so that every concept has a unique symbol.

However, in all these cases the symbol must be defined. Mathematics does not work with strings of symbols that "look" nice and only get a meaning afterward. The symbols are meaningless and irrelevant unless they are defined.

Answer 2

1) In a sense, Chaos Theory fits the above description. The random objects in question could be interpreted as representative of symbols whether in nature or mathematics.

Can't help but think of the geometric designs often used to illustrate Chaos Theory. Often, photos representing CT also have repetitive representations in nature as well as other symbolic pictures resulting from Fractal Geometry. I believe Mandelbrot intuitively stumbled upon Chaos Theory and that it will be extremely significant when man does learn to travel in space/time...especially the time dimension.

It is only by interpreting the PATTERNS in the symbols that Chaos Theory can be analyzed to an infinite degree. Chaos Theory does have its roots in mathematics since it is based upon statistical probability as well as Fractal Geometry.

2) It has also been said that certain great works of classical music can be reduced to mathematical terms resembling the musician's intuitive response to particular states.

For example, one classical funereal musical piece (can't remember which one) is said to be identical mathematically with the molecular structure of cells in a particular disease state. I believe I heard it said that it was a type of cancer. Anyone recall having heard this? In essence this would be another level of mathematics where the symbolism of music has been subconsiously drawn out by the composer, resulting in an exact mathematical representation of the molecular structure of that which inspired the work of art.

Answer 3

Most of the symbols used in mathematics are greek letters, like a delta, sigma, theta and so on... They are given meaning by the equations or calculations they represent. It seems at times like they're just random symbols, though.

Answer 4

This sounds like a question for graphic design.

Mathematics is a language of precision, and it is built to communicate a very precise idea from one person to another.

In order to do that its symbols, as strange as they are, have very (sometimes excruciatingly) specific meanings.

Spontaneous symbols with new/nonstandard meaning in math is like saying your car can be any color you like as long as its black. Its not math.

Answer 5

Yes, Quantum Mechanics.

Answer 6

algebra