Map of the chain

[Fred56]

The idea of increase and decrease leads to numbers and counting. Numbers lead to the idea of combination, of function within measure. Functions lead to “functions within functions”, and there is a projection, in both directions. Number maps to function, function maps to function within function (combination, transitivity, commutation), and on up the chain. Math is like a big chain.

 

Where do numbers come from?

We all understand “less”, “more”, and “same”, in terms of measurement. At first, human measurement of the environment was probably largely restricted to these ideas of (available) information. Gradually, a need would have developed to record information in ways other than storing it internally, and so language and the concept of oral records would have arisen, alongside the first use of other symbols and devices to “remember” something. Then as these systems extended, the concept of counting beyond the three basic "cocepts" (less, equal, more) -and after introducing symbol and language records,

would have produced ways of measuring the environment that became more useful.

Once the idea that measurement (less or more), could be represented (in markings, in language) by something; could be abstracted, Mathematics was born.

[the tree]

Where do numbers come from?

We all understand “less”, “more”, and “same”, in terms of measurement.

Whilst this is true in terms of history I guess. A surprising amount of maths can be derived without mention of less or more.

[Fred56]

Really?? With just equal/not equal? Like binary. I guess because we came with 10 things on the things at the end of those longer things, we ended up with base10. Numbers and number theory probably evolved once base10, at least, was used. There are still people (remote tribes) who don't count beyond three things, they have "more than" three, though.

[Bignose]

Numbers and number theory probably evolved once base10, at least, was used.

 

But, see, this wasn't true either. Ancient civilizations used all sorts of bases. Some used base 12, some used base 20, the Babylonians even used base 60.

 

I'm not sure that it is completely possible to recreate the origin of mathematics in hindsight. Things that are truly obvious to us -- from many years of schooling -- wouldn't be so obvious when they weren't taught every year. There are several books on the history of mathematics, you might enjoy reading through some of them.

[Fred56]

It's not meant to be a potted history, just how I think we developed the ideas, how abstraction of information became language and symbols.

 

Along with the ideas of change (increase/decrease), we would have had concepts like "with", "without" (inclusion/exclusion), and other basic ideas of measure (grouping/portioning) that project straight to numbers. There would have been a socio-structural pressure to develop symbolic forms of measure, and external, and oral, record-keeping came from this.

 

Once larger collections of people and larger organisation developed, along with the onset of things like agriculture and construction, our need to put numbers and their measuring to better use would have created greater pressures, for such things as the representation of distance, and volume, rather than just counting and recording quantities. A need for geometry would have arisen to better understand how to structure and calculate distance and area, to manage resources more effectively. Our understanding of the power numbers could give us to map, to abstract the world, would also have grown. Along with the concept of function within measure (itself some function), this led to more levels of abstraction.

 

The thing about this connection that math has back to "basic" ideas of measure or change, -difference; this projection, is that it goes all the way. All the way up the chain, past arithmetic, algebra, geometry (where you notice the chain starts to divide, to branch), on past a certain imaginary link which seems to connect to the chain in a lot of other places, but in a way that can't be seen directly. It's a link of pure logic, a product of our reason; you can see how much it supports the chain, holds it together, how many other real and imaginary reflections (of real links) to higher mathematical concepts there are, beyond the three dimensions, into a realm that exists because of our ideas of change, increase and decrease, and our logical minds. With numbers (imaginary and real), tagging along like trustworthy hounds.

 

...sorry about this to anyone with a non-artistic "clinical mathematical" pair of glasses on: I was thinking about numbers and how sometimes they "fly around" in your head, and this popped out (don't ask me)...

 

Twilight of our Reason

 

Soft light, green in the gathering of trees, a distant blue-emerald behind the grey clouds of evening.

The softening sussurus of bird wings, as they swift unnumbered through dying light to a shadowed shore.