Natural ChemE » November 7th, 2015, 2:27 pm wrote:Sigh. I keep telling people what I a genious I am - I even have a web blog with my IQ test scores which I've validated against two Quizilla tests - but no one listens, all 'cause I don't no do good in exams. Exams which, mind you, I'm quite certain are rigged to reinforce the liberal establishment because they're too afraid of my ideas. Personally I think that the Illuminati is involved.

LOL I totally agree with you! Most of what passes for our collective reality is an illusion driven by people with agendas. This I do believe. If we can't agree on Searle, can we at least agree on Chomsky? :-)

I get that you're smart. I'm trying to guide you to a modern understanding of abstract mathematics, so that you can use that information to support your philosophical ideas. At the very least, be able to speak the same language as everyone else.

At times I feel that you are in danger of falling into math crankery. One of my hobbies over the years has been the study of math crankery. I recognize the symptoms. The circle-squarers, the angle trisectors. And you know what? They're always engineers! I see this all the time. There is something about being extremely hands-on with numbers that makes it difficult for people to grok the abstract mathematical view. They are always the most brilliantly creative people, usually incredibly interesting people; but they just don't get math. And they're always brilliant engineers.

I am here to save you from that fate. I am trying to save you from becoming a math crank. I want you to consider learning a little mainstream abstract math, so that you can better achieve your own intellectual goals.

So you see how crazy I am. I'm trying to save your mathematical soul!

Natural ChemE » November 7th, 2015, 1:47 am wrote:Seriously though, is it truly classical math you love, or the beauty that emerges from what you can do with it?

I have zero interest in applications. I'm aware of the historical interplay between math, physics, biology, economics, and computer science. But when I see three rocks, I see the three, not the rocks. I've always had an abstract mindset.

There's a famous British mathematician of the 1920's named G.H. Hardy who wrote a book called A Mathematician's Apology; in which he states very clearly that his work is absolutely useless; and that uselessness is to be regarded as a supreme virtue in a piece of mathematics. And therefore, he needs to offer an Apology, in the sense of a justification for why he does his work. The kicker is that in the past thirty years Hardy's speciality, number theory, has become the foundation of public key cryptography, hence Internet security. I always wonder what he'd say if he found out that his beautifully useless subject had suddenly become useful. https://en.wikipedia.org/wiki/A_Mathema ... 7s_Apology

Natural ChemE » November 7th, 2015, 1:47 am wrote:

An honest question. I mean, personally, I used to say that I love math. However I had no real attachment to its particular form - I see programming, etc., as the same thing, just cooler. Is it different to you?

I studied math but earned my living as a programmer. I always regarded programming as easy. In math, if you're stuck, all you've got is pencil and paper. You have to fight through the limitations of your own mind. In programming you can always just type something. It's the dynamic aspect of typing and watching it run, over and over. Debugging. I really enjoy the mechanics and daily work of programming very much. I was born for it. But my soul is aligned with math in some way.

Natural ChemE » November 7th, 2015, 1:47 am wrote:

I guess that what I'm trying to say is that, as far as I can tell, this is math.

Right. And I'm trying to help you sort out what's important. If you are an expert in engineering math and an authority on numerical computation; and you are surfing Wiki pages on Lowenheim-Skolem and the hyperreals; I'm trying to put this stuff into historical and conceptual context for you. You can drive yourself nuts with that stuff if you don't have a context for it.

If you're interested in how math relates to the universe and physics and computation, I'm trying to point you in the right direction. And you keep wanting to go off into conceptual backwaters out of what ... opposition? Thinking you're smarter than all the professional mathematicians? You probably are! But they still know a lot more math than you. All I'm saying is learn the basic stuff before you try to improve on it.

Natural ChemE » November 7th, 2015, 1:47 am wrote:hyperreals are business-as-usual for me

Can you explain (clearly please!) what you mean by that? I know the hyperreals as a somewhat obscure construction in mathematical logic that allows you to have a model of the reals that contains infinitesimals. In which .999... = 1 is still a theorem, by the way, but let's not drive off that bridge right now.

Can you say what you are doing with infinitesimals in a practical sense? I'd be fascinated to know that there's an application. Now I do know that physicists and engineers like to think of derivatives in terms of infinitesimals. That I know about. But using actual nonstandard numbers in some application, I'd like to know about this.

Natural ChemE » November 7th, 2015, 1:47 am wrote: At least what math is now. I'm not blind to the fact that it's not what math was a hundred years ago, but.. isn't the fact that we've moved on really cool?

Yes, since 1840 we know that physics doesn't constrain math!! :-)