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Get technical proof reading, lots of technical proof reading. I'm no expert in anything and I can see so many flawed or incomplete or inappropriate arguments.

Get technical proof reading, lots of technical proof reading. I'm no expert in anything and I can see so many flawed or incomplete or inappropriate arguments. This might be okay for an interesting coffee table book but not for anything serious. I'll list a few examples of where my shallow understanding differs. My biggest beef is "I've already tipped my hand and told you that (my hypothesis is that) mathematics is the study of possible models of objective reality." This is where I stopped reading altogether. That's not what most of mathematics is, such as those areas you listed. They are largely axiomatic systems of logic. That they correspond to such a degree with our experience of the 'real' world is the shocker. Another one is the Banach-Tarski "paradox", the paradoxical part isn't that there's two from one. We can do this with only the real number line between 0 and 0.5 and fill the line from 0 to 1. That this defies our experience of the world isn't surprising as we don't deal interactively with uncountable infinities of any degree. A final example is Church numerals--they encode numbers, just the numbers with no associated nouns. Something that might not make sense in our world but does in lambda calculus.

lisper 2y ago
> the paradoxical part isn't that there's two from one What do you think the paradoxical part is then? > We can do this with only the real number line Actually you don't even need the reals. You can do the same trick with just the rationals. Half of aleph-zero is still aleph-zero. > Church numerals--they encode numbers, just the numbers with no associated nouns. That's debatable. I would say that a Church numeral's noun is an action (actions are nouns), specifically, function application. [UPDATE] > My biggest beef is "I've already tipped my hand and told you that (my hypothesis is that) mathematics is the study of possible models of objective reality." I guess I didn't make it sufficiently clear that I'm not claiming this is an accepted consensus, this is a hypothesis that I am advancing and prepared to defend. Maybe I should be more explicit about that. > They are largely axiomatic systems of logic. I don't deny that. But not all axiomatic systems of logic are mathematically interesting. Chess, for example, can be axiomatized, but it's not particularly interesting from a mathematical point of view. You're not going to win a Fields medal for finding interesting chess puzzles. > That they correspond to such a degree with our experience of the 'real' world is the shocker. Yes, exactly. That is one of the facts that supports my position.

lisper 2y ago

> the paradoxical part isn't that there's two from one What do you think the paradoxical part is then? > We can do this with only the real number line Actually you don't even need the reals. You can do the same trick with just the rationals. Half of aleph-zero is still aleph-zero. > Church numerals--they encode numbers, just the numbers with no associated nouns. That's debatable. I would say that a Church numeral's noun is an action (actions are nouns), specifically, function application. [UPDATE] > My biggest beef is "I've already tipped my hand and told you that (my hypothesis is that) mathematics is the study of possible models of objective reality." I guess I didn't make it sufficiently clear that I'm not claiming this is an accepted consensus, this is a hypothesis that I am advancing and prepared to defend. Maybe I should be more explicit about that. > They are largely axiomatic systems of logic. I don't deny that. But not all axiomatic systems of logic are mathematically interesting. Chess, for example, can be axiomatized, but it's not particularly interesting from a mathematical point of view. You're not going to win a Fields medal for finding interesting chess puzzles. > That they correspond to such a degree with our experience of the 'real' world is the shocker. Yes, exactly. That is one of the facts that supports my position.