This is one of those rare gems that one repeatedly comes back to. So many great points (many of which one wonders why they have not been raised before). And then an extremely spot-on Q&A where many possible objections are discussed. Thank you for sharing both with all of us.
Each leap in physics seems to depend on math invented within the preceding century. That puts decent odds on the computational/informational theories that are getting going now. Important talk! Who is 'pseudo'? I liked his question.
Great and interesting talk. I think every language, rich enough, is unreasonably effective in describing reality. I can, in practice, describe processes using english. Some other guy might describe it using chinese and even though these descriptions will not be totally accurate, as no description is, even with mathematics, both descriptions are valid(if we choose our words wisely). When mathematics is taken as another language like Korzybski did, the effectiveness of it becomes apparent and even necessary. It becomes the language of choice to talk about patterns in a way that is compressed and to the point with sharp syntax and no semantics.
The idea that cognition (which on some views contains math) is shaped by natural selection has been used both as an argument for (en.wikipedia.org/wiki/Evolutionary_epistemology) as well as against (en.wikipedia.org/wiki/Evolutionary_argument_against_naturalism) its epistemic power. Looking at neolithic structures, it seems obvious that we learned basic geometric facts (say, the Pythagorean theorem) from interaction with the physical world. But it is far less clear how either evolution or raw empiricism could lead to the notion that the number i^2 corresponds to -1. It was centuries later that we realized that this - by any means counter-intuitive - concept of i is helpful to describe nature.
Math is patterns. Why does nature obey patterns ? What does it mean to NOT obey a pattern ? Thermodynamics and information theory have investigated these ideas to some degree.
Seeing Lean4, it seems like we are closing in on a Virtual Machine, with an instruiction set. Not having this seems to be the root of disagreement and irreproducability. It may be the case that reality just IS mathematics, and everything that is mathematically consistent is what happens in some form. It might be nonsense to ask what it's made of.
This is one of those rare gems that one repeatedly comes back to. So many great points (many of which one wonders why they have not been raised before). And then an extremely spot-on Q&A where many possible objections are discussed. Thank you for sharing both with all of us.
Each leap in physics seems to depend on math invented within the preceding century. That puts decent odds on the computational/informational theories that are getting going now. Important talk!
Who is 'pseudo'? I liked his question.
Great and interesting talk. I think every language, rich enough, is unreasonably effective in describing reality. I can, in practice, describe processes using english. Some other guy might describe it using chinese and even though these descriptions will not be totally accurate, as no description is, even with mathematics, both descriptions are valid(if we choose our words wisely). When mathematics is taken as another language like Korzybski did, the effectiveness of it becomes apparent and even necessary. It becomes the language of choice to talk about patterns in a way that is compressed and to the point with sharp syntax and no semantics.
The idea that cognition (which on some views contains math) is shaped by natural selection has been used both as an argument for (en.wikipedia.org/wiki/Evolutionary_epistemology) as well as against (en.wikipedia.org/wiki/Evolutionary_argument_against_naturalism) its epistemic power.
Looking at neolithic structures, it seems obvious that we learned basic geometric facts (say, the Pythagorean theorem) from interaction with the physical world. But it is far less clear how either evolution or raw empiricism could lead to the notion that the number i^2 corresponds to -1. It was centuries later that we realized that this - by any means counter-intuitive - concept of i is helpful to describe nature.
Math is patterns. Why does nature obey patterns ? What does it mean to NOT obey a pattern ? Thermodynamics and information theory have investigated these ideas to some degree.
Seeing Lean4, it seems like we are closing in on a Virtual Machine, with an instruiction set. Not having this seems to be the root of disagreement and irreproducability. It may be the case that reality just IS mathematics, and everything that is mathematically consistent is what happens in some form. It might be nonsense to ask what it's made of.
Why justifies math using art. I couldn’t disagree more. And his definition of math as computation totally misses the point of math.