Donald Knuth: Surreal Numbers [video]

http://quantifiedself.com/2009/09/the-social-memex/

----

Relevant excerpt from The Mars Trilogy by Kim Stanley Robinson:

"Actually, now that he thought of it, losing his train of thought had been happening a lot. Or so he seemed to remember. It was an odd problem that way. But certainly he had been aware of losing trains of thought, which seemed, in their blank aftermath, to have been good thoughts. He had even tried to talk into his wrist pad when such an accelerated burst of thinking began, when he felt that sense of several strands braiding together to make something new. But the act of talking stopped the mentation. He was not a verbal thinker, it seemed; it was a matter of images, sometimes in the language of math, sometimes in some kind of inchoate flow that he could not characterise. So talking stopped it. Or else the lost thoughts were much less impressive than they had felt; for the wrist recordings had only a few phrases, hesitant, disconnected, and most of all slow – they were nothing like the thoughts he had hoped to record, which, especially in this particular state, were just the reverse – fast, coherent, effortless – the free play of the mind. That process could not be captured; and it struck Sax forcibly how little of anyone’s thinking was ever recorded or remembered or conveyed in any way to others – the stream of one’s consciousness never shared except in thimblefuls, even by the most prolific mathematician, the most diligent diarist."

Among authors alone, I would imagine we've lost a great many brilliant books because brainstorming is tricky and variable. Some days you get nothing, some days you get a dozen ideas and only one makes it out to the rest of the world.

I can't think of a good answer. Meditation and memory training might help, but are not silver bullets. Typing tends to be flow breaking (though I'm sure smartphones have improved matters) and vocalization is slow and awkward. It's hard to imagine anything short of EEG-translation removing the I/O limits on the mind.

I've been using the voice recorder on my phone to capture inspiration for years now (plus journals, ambient recordings, etc). I've got 1,700 recordings now, and whenever I dive deep into a new project I listen through the relevant ones for help.

Imagine that you have a high resolution, high fps camera. To record its feed requires a memory card that is capable of handling the data rate that the camera produces. Otherwise, the events captured by the camera are lost forever as they are flushed away by the forthgoing frames. Essentially, the problem boils down to the ability to encode the information at least as quickly as the lifetime of the information.

I believe the same thing happens in thought. We have a state of mind, an idea, that we want to share. Because we can't simply transfer whole brain states between each of us, we first need to serialize our ideas in writing or speech. That process is lossy, and possibly lengthy (or at least longer than your train of thought). In the mean time, a variety of new thoughts come to your mind, flushing the original idea.

So following this analogy, a solution to the problem of lost ideas would be to have higher bandwidth means of expressing and recording ideas. Personally this problem annoys me quite a lot in a variety of incarnations, and I think advances in Human Computer Interactions will directly address this.

For instance, consider a program. Sometimes I have a full blown picture of the program I want to build in mind. Then along the many hours it takes to serialize this into a programming language, I battle myself, attempting to keep the idea fresh. There many steps along the way that contribute to the serialization cost:

    - The abstractions of the programming language.
    - The step from "programming language" to "abstract syntax tree".
    - The letters I have to type.
    - The movement of my fingers on the keyboard.
    - The translation of my brain from program construct, to
      structure, to sentences, to words, to tokens, to letters,
      to movement of my fingers, to keypresses.

   * * *

This total order is also very useful. Namely one can associate surreal numbers to positions of a large class of two-player games. The sign of the associated surreal number (whether it's positive, zero, or negative) then tells you which player possesses a winning strategy. See https://en.wikipedia.org/wiki/Surreal_number#Application_to_... for more information on this point.

A mix of real and complex numbers is just a set of complex numbers, because every real number is a complex number. And complex numbers do not possess a total ordering: https://proofwiki.org/wiki/Complex_Numbers_cannot_be_Totally...

Actually surreal numbers have a well-defined partial order despite the dimensionality concerns; keep in mind surreal numbers are a class, not a set. (They contain as a strict subclass the transfinite ordinals, so it must be a class).

Moreover I think the form <:> is best considered an operator (or generator) than a cartesian product. You can put a set of surreals on one side of <:> and out pops another surreal.

> In mathematics, the surreal number system is an arithmetic continuum containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals share many properties with the reals, including a total order ≤ and the usual arithmetic operations (addition, subtraction, multiplication, and division); as such, they form an ordered field.

https://en.wikipedia.org/wiki/Surreal_number