Whether we talk about correlated human, traceable human or detectable human, a prerequisite of the mere possibility of such a creature is the thoroughly mathematization of our life-world. It goes so deep that few of us even realize how mathematical it has become.
WARNING: this short text is a derivation of the ppt-presentation, drawings and pictures are missing and the style is nearly beyond comprehensibility
Thesis: it requires a "mathematized" world to let the idea of a correlated human function or work
Note 1: related to "everything is mathematizable" though not exactly the same
Note 2: rather different from "ecology of proofs and arguments"
Focus: "embodied" mathematics
The role of "what-if" stories to illustrate the thesis:
Is it possible to imagine a "non-mathematized" world (or only a little bit)?
Note: does the question make sense?
"necessary" knowledge
"biological number sense"
"necessary" development
Rough, very rough sketch!!!
* Imagine Egypt as an anarcho-socialist society … after flooding land is divided by mutual consensus: no need for right angles, no need for precursor of Pythagoras
* Imagine the Greeks without number symbolism and religion: no Pythagoras, no sacred architecture, no …
* If the gods are out, economy takes over: can you avoid the introduction of money?
* Side thought: if there is a kind of mathematical necessity (whatever it is), it is either because of the gods or because of the economy
* However, imagine: only locally tradeable stuff, no need for a general standard, so we are left with a bit of counting and a bit of measuring
* Intrat architecture. Imagine no temples, no sacred places, no stuff of that kind, nevertheless you not only want shelter, you want stable shelter
* Suppose you do not want to reach the skies (where pie/p is and pigs fly), stability problems can be solved empirically (I guess)
* Question: can you do "physics" and engineering (or what comes near) without maths? Answer: yes (just ask the Romans).
* Example
Vitruvius: De Architectura, around 27 BC
Principles of architectural.
History of architecture, and architectural materials.
Ionic temples.
Doric and Corinthian temples.
Public buildings, theatres, music, baths, and harbours.
Town and country houses.
Interior decoration.
Water supply.
Dials and clocks.
Mechanical engineering with military applications.
* Aha, warfare! The greatest inspiration for mathematics. Of course, linked to economy.
* Silly thought: in a peaceful, quiet world there is no need for mathematics
* Now the Renaissance has nothing to rely on (by the way, also imagine that the theologians did not keep logic and (bits of) mathematics alive)
* Who says Renaissance, says Art (or art). Does not mathematics enter there? Golden ratio, perspective, harmony, … Answer: not necessarily.
In short, we could have ended up in a quite different world that would have been hardly mathematized
Question 1: is that the kind of world to bring forth computers? Probably not.
Question 2: is that the kind of world to bring forth standardized measures? Probably not.
Question 3: is that the kind of world to bring forth mathematicians as members of a community? Probably not (cfr. China)
Now look back at our world: it is thoroughly mathematized:
Obvious examples: measures (DIN A4), back accounts (fundamental unit of comparison), numerals (platforms in stations), …
Less obvious examples: each time you listen to music (not just Bach!), each time you look at a painting (not just perspective!), each time you see a building (not just a church or renaissance palace!)
Non-obvious examples: walking in a park (imagine a view from the sky)
Non-obvious examples: the cloths you are wearing industrial patterns
To conclude:
If this story has had any power to convince you, then the following sentence must appear extremely mathematical:
"She took her bike, wearing her training outfit, but letting her watch at home, for a ride in the park, next to the King’s palace"