User talk:2600:1700:F90:7D10:7581:3A71:D8CF:EC77

I find the idea that the distinction between a number and its representation as "fetishistic" to be fatuous. There is a powerful connection between number representations and human progress. That connection lies in the fact that the ability to efficiently keep track of large numbers of things is vital to maintaining any sort of organized civilization.

Denominational numbering systems (Roman, Babylonian, etc) marked a big improvement over the use of tally marks. The Mayans created a denominational system that was actually a modified base numbering system based on the number 400. Their denominations were 1,5 and 20. These numbering systems enabled the creation of significant infrastructure that fostered progress and public health. On the evil side, they enabled the organization and creation of large armies.

The modern base numbering system with place value (decimal being the earliest example) enabled modern science in that it allowed for the compact representation and easy manipulation of extremely large numbers (such as Avagadro's number) and extremely small numbers (Planck's constant which is of order 1e-34).

Modern computers use the binary numbering system and bundle it using octal and hexadecimal numbers.

What is number? It is an abstract concept based on this idea: two sets of objects have the same number if they can be placed into 1-1 correspondence. This notion of "same-sizeness" is what the notion of number is all about.