| > Mathematics is a language, but then why are you saying there was no Mathematics before Pythagoras? Obviously Pythagoras didn’t invent language! He did invent the language. When Pythagoras used to teach some folks the division (mathematical operation required for Trigonometry which is required for building Egyptian Pyramids) he faced with un-understanding of "why we should learn this silly useless numbers?" Then Pythagoras has invented a music (consonance and dissonance at least) and everyone started to learn Math because most of us can hear that numbers which may lead to either consonance or dissonance. > you are conflating the ability to exploit nature with the ability to understand it. Yes you are right, I do not see how can you understand Physics/Nature without exploiting anything. And if you are enough successful to exploit something so why not to claim that I have gained some understanding. > There would be no physics without humans inventing it just like there would be no language without humans inventing it. I think two instances of "humans" word are extra, that words don't add anything into the discussion of some mathematical and physical concepts. And I keep staying on my opinion that: if one fly can do something complicated in controllable experiments set by human (kind of pull this rope and get some sugar) and another fly can learn this queue of actions from the trained fly, that means that after the experiment both flies share some physical knowledge about Nature. |
I am happy to equate exploitation with understanding, but then I don’t see how you could possibly understand Mathematics without exploiting computation.
The pyramids were built at least 1000 years before Pythagoras was even born. If division and trigonometry was needed to build them then the Egyptians understood and exploited division trigonometry before Pythagoras invented the language to explain/teach division and trigonometry.
It is not at all surprising that nobody else could understand (exploit, compute with) a language Pythagoras made up, but eventually he taught (indoctrinated?) some students on how to use his invention.
To compute with; and exploit any language first you must comprehend its grammar and semantics.
Still! The Babylonians could compute the square root of 2 (in practical terms, obviously they didn’t call it “square root of 2”) to arbitrary precision even without having numbers in their Mathematics.
Overall I don’t think we are disagreeing over anything substantial either way. Computation is the controlled manipulation of matter. Manipulating symbols to do useful things is a form of computation.
A fly may have some knowledge sufficient to exploit nature in the moment, but it doesn’t have the knowledge necessary to encode and communicate its knowledge to its peers. And it certainly can’t communicate its knowledge to generations 2500 (or more) years into the future.