"Proportional Numbers" for Values In The Territory: Against Abuse of the Diametrical Real Number Line

Yesterday, Yudkowsky for the Nth time worked something really insightful into a response to someone asking, essentially, “how fucked are we?”

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I don’t know how to calibrate a scale of insanity either! A scale of sanity is conceivable enough, if I take the time to think about it [ fictional AIs and Warren Buffett at the top, unmedicated psychotics and toddlers at the bottom ]. But not a scale of ‘in-’. Is a fish “more insane” than a toddler? Is a rock?

I experience this sort of mental block around inverting concepts all the time. I used to think it was a problem with my thinking.

Lately, I’ve started noticing specific ways that allowing arbitrary real-valued attributes to have negative values is counterproductive. Eg:

[ this is me, Lorec is my Discord username ]

Now I’m starting to think our culture is just entirely in error here, and we would be better off talking about most qualities or attributes - eg ‘painfulness’, ‘blueness’, ‘sandwichness’ [ the amount something qualifies as a sandwich ], as though they have no natural opposite and cannot be easily inverted.

Negative numbers were invented to model debt. Now [ I’m told ] they pay fair rent in physics and computer graphics, as components of the complex plane. But debt, as an institution, is a questionably efficient allocation mechanism at best. And unless it proves itself elsewhere - which, to be fair, these things often do! - an invention or theoretical result is only as good as the purpose it was invented to accomplish.

I’ve been compiling my thoughts recently about the diametrical model of autism and schizophrenia. It’s been very satisfying to increasingly feel like I have the arguments to vindicate this theory, more than for most theories, and I think I can finally put a name to why.

Autism turned out to “have an opposite”, in schizophrenia.

Everything is supposed to have a secret opposite - that’s how we model the world when we talk as though something must be ‘the opposite of white’ - but for most things, I had been failing to perceive it. For autism, I had finally unearthed that missing secret opposite, proving that I’m capable of perceiving these diametrical spectra that are supposed to be everywhere! But the conclusion I’m drawing about diametrical spectra, on a gut level, is not what I would have expected. Now that I know what it looks like for two qualities to really be [almost] diametrically opposed to one another, I’m not thinking, “Oh, that’s what’s meant by the concept-inversion abstraction. Yes, now I see the inverses of qualities everywhere.” I’m thinking “Wait, almost nothing has this! If this is what it means for something to ‘have an opposite’, then almost nothing really does.”

I propose “proportional numbers” for the set analogous to the rational numbers, but radial - constructed out of ratios between only the natural numbers, not the diameter of integers. I think we should assume most in-the-territory qualities take values within this set, not the reals.