3 ms·
>> "What is truly stunning about the fact that modern science and mathematics are formulated through a sequence of marks is its exclusivity: nothing other than
by sdenton4 4y ago
>> "What is truly stunning about the fact that modern science and mathematics are formulated through a sequence of marks is its exclusivity: nothing other than these finite sequences of symbols is ever found in modern mathematical reasoning."
Well that's simply not true. We draw pictures all the time. But putting that aside...
Written mathematics is a serialized form of mathematical understanding, meant to be decoded by other mathematicians. The understanding itself is often very non-textual, and the process of serialization and deserialization can be extremely difficult. And the reasoning process itself often proceeds in non-textual ways, prior to the process of serialization.
- NoToP 4y agoYou kind of just described the language faculty as well.
- tgv 4y agoEveryday language is an entirely different thing. I don't think we can "serialize" maths at a speed of 3 symbols per second. I also think your OP is quite wrong. What (s)he calls serialization, is attempting to formulate and test an idea in a "proof language", where a successful and correct string determines the validity. A normal sentence has an entirely different use. Math is (much) more like programming than speaking.
- kevinventullo 4y agoThat said, much of modern mathematics is still fairly informal, with “the proof is left to the reader” implicitly showing up in nearly every written sentence for the sake of brevity.