Why did this happen? A plausible answer follows.

First, neurotics are more likely to prefer math classes because they are terrified of being wrong. This is partly disposition and, I think, partly imprinting (maybe a response to lots of negative stimuli during development). Only math classes traditionally offer safety from getting wrong answers. Because of this, they are more likely to continue in math classes and work hard in them, and may study math to the detriment of other subjects, perhaps to the point of acquiring internal motivation to do so via fascination.

Second, neurotics who get advanced education in math are less likely to be capable of producing groundbreaking work of their own because neurosis means high latent inhibition, which means they are more likely to become educators. As educators, they are more likely to unduly punish small mistakes like missed minus signs with the same severity as big mistakes and incomprehension. This disincentivizes higher math education for equally high-IQ folks, ceteris pablum and such, who are not neurotic. They may argue that missing a minus sign is a really big deal because any amount of wrongness in an answer makes it wrong, which could have *disastrous consequences*, but the fact is that misplacing a minus sign on an exam that doesn’t matter, under a time limit, with no professional peer input, on material that a person learned last week, is not the same thing as bringing down the Challenger space shuttle.

I am not arguing in favor of incorrectness, I am saying come on people. Use your big dumb heads. Five point penalty *max* for that shit.

Third, as with many population dynamics a predominant personality type in a culture will eventually cause a tipping point, after which the personality feature becomes the default and deviance from the cultural norm is disincentivized at every step (even absent the gatekeepers in point #2). In cultures where people aren’t just plain mean, this manifests primarily as a communication problem. For instance, it is generally verboten (as I understand) to practice mathematical analysis outside of the French tradition because the French tradition gives the most exact definitions of the most abstract topics. You can’t define zero as “the integer between 1 and -1” or nobody will talk to you at math parties. You have to define it as the equivalence class [r, r], r ∈ ℕ. That’s how math people know you’re cool. You might get away with “the identity element of ℕ under addition” at work but you won’t get laid with any math groupies, no sir.

People who aren’t neurotic can still get by in math if they’re intelligent enough, because they will tend to make fewer errors for that reason, but sane folks have to be much smarter. The flipside of that is that the sane folks who make it through the grinder will tend to be much, much more creative and productive as working mathematicians. This is a simple result of intelligence and lower latent inhibition. They are also less likely to break down under the pressure of the singular professorial code of ethics: “Publish, yea, lest ye perish.” A neurotic person will be unable to publish anything except the most elementary extensions of existing theory, even if they can relax long enough to have an inspired idea. They’ll try to perfect that idea until they break down or die.

I mean, just imagine publishing an incorrect theory in a math journal. Your wife would leave you and your kids would disown you. Would your mother let you live secretly in her guest room? The oppressive shame would just be overwhelming, I can’t bear the thought even.

Good point about neuroticism. I pointed out some years ago that if you take a 1×10 strip of paper, twist and join it into a moebius strip, the surface area may indeed be 20, but if you reduce the thickness to infinitesimal, the surface area of the moebius strip should just be 10. Otherwise you are just counting the same infinitesimally sized 3d pixels twice.

I developed a whole area of infinite math separate from Cantor, based on interpreting powers of infinity as dimension. I never did figure out what the inverse was (negative dimension? what?) But the neurotics weren’t buying it.

So, a*inf^0 is a point on a line, a*inf^1 is a line segment, a*inf^2 is an area, like a square or circle, a*inf^3 is a volume, like a cube or sphere, a*inf^4 you get the picture.

Somehow, my “pixel” interpretation of infinitesimals really made the neurotics feel wrong on a deep level. All I was doing was extending the rules of arithmetic and powers etc, and treating 0 and infinity the way they decided to treat the square root of -1.

>I pointed out some years ago that if you take a 1×10 strip of paper, twist and join it into a moebius strip, the surface area may indeed be 20, but if you reduce the thickness to infinitesimal, the surface area of the moebius strip should just be 10. Otherwise you are just counting the same infinitesimally sized 3d pixels twice.

Yes, but I wonder if it runs afoul of the definition of a limit. Would like to work this out, or see it worked out.

>I developed a whole area of infinite math separate from Cantor, based on interpreting powers of infinity as dimension. I never did figure out what the inverse was (negative dimension? what?) But the neurotics weren’t buying it.

Theory is fun, but the real proof is in the pudding. “Does the theory provide solutions to problems?” You won’t get a neurotic to admit it, but this is how they are convinced of this sort of thing, just like everybody else who isn’t punting to authority.

>So, a*inf^0 is a point on a line, a*inf^1 is a line segment, a*inf^2 is an area, like a square or circle, a*inf^3 is a volume, like a cube or sphere, a*inf^4 you get the picture.

Indeed I do! You were rediscovering the Cartesian product set with visual intuition.

>All I was doing was extending the rules of arithmetic and powers etc, and treating 0 and infinity the way they decided to treat the square root of -1.

The thing about i is that it is a real thing, with real-life consequences, even if we call it “imaginary”. To wit, exp^(i*pi) = -1. Your visual treatment may eventually have turned out to be correct, and may not have.

You will probably enjoy this sort of madness, (H/T Heaviside for a different, related link): http://lymcanada.org/riemman-for-anti-dummies

Thanks, I’m really enjoying that Riemman link now. Have to set it aside or I won’t get any work done today. Engaging writing style too.

I grew up in a working class town with very limited access to books, computers, intellectuals. It did help my brain focus on fundamentals. I discovered the dot-product on my own too, then someone told me what it was. Now you’ve told me about the Cartesian product set as a name for my discovery. I was thinking it might be useful for simplifying calculus, and useful for computer graphics, but didn’t have brainpower to develop the work along those lines. It still might be, but in the current part of the civilizational cycle, we’ve passed the high water mark. The idea may never be developed.

Also, just as we don’t throw away i terms, I’m thinking when we come across zeros or infinities, we shouldn’t throw them away either. I hate throwing away information. I made software to visualize and move around in 4 dimensions. Almost broke my brain. :)

I was visualizing my infinitesimal “pixels” as something along the lines of the Planck constant, an irreducible tiny multidimensional building block that all other units are made from.

Funny, the kids from high school who graduated college and went to work in the City of London, still mock me for having investigated the square root of negative one. How does anyone graduate even first year college math without knowing about square root of negative one? Makes me fearful a bit; these university graduate peers are now in positions of power and influence, and they are that ignorant?

>Thanks, I’m really enjoying that Riemman link now. Have to set it aside or I won’t get any work done today. Engaging writing style too.

Only by relative comparison. It is amazing how boring academics can be in any subject. TMs are dropping the ball in propagating culture- it’s your job! You guys are natural propagandists.

Also, I came up with a good working definition of infinity: not necessarily the largest possible number, but “a number larger than we have the capacity to count or otherwise calculate with or deal with”

That is essentially the definition that is used. Basically, you can substitute lim x, x -> inf, for “infinity, the number” and get the correct result, if it exists. The “largest possible number” is not a good definition.

Aeoli… when you get too effective, if your narrative isn’t in the mainstream, the system will beat you down with underhanded and sneaky methods. The system will break its own rules to sideline you. Being a TM is like surfing; you have to identify and catch the wave. Nothing else works. TMs can televise the revolution; sometimes we even get lucky and get to catalyze the revolution because we recognized an opportunity at the right time and give things a tiny nudge. But that is all. We don’t have full melon powers.

Also, there is a chain of transmission that has to happen to propagate propaganda. And unless you can identify and get to those gatekeepers, you can’t catalyze things. Linus Torvalds was able to catalyze because he had an IQ of 160 and socially advanced parents, through them he cut his teeth on the inner politics of the Communist Party. My mental strength isn’t strong enough to do that. And strength is necessary. Maybe I can go out and make lots of money. But effecting social change? Takes a melon to do that.

Aeoli, a smart TM limits his exposure. You aren’t in a place where phone conversations suit your fancy, so I leave a lot unsaid. I communicate 10x more effectively by voice.