Saturday, October 01, 2011

on why computers are not as complicated as you think.

with apologies to my friends who have heard me rant about this before, i nevertheless think that computers are fundamentally 1-dimensional, even painfully so.

those of you who know what a turing machine is [1] will think the idea is perfectly natural. as for the rest of you, you will have to suffer my usual amount of complaint ..

if you use an old-school text editor to compile LaTeX like me [2], then the cursor blinks at you when you stop typing. it's not as if it ever stopped blinking ..

 .. well, that i can't be sure, but it certainly blinks when you stop typing.

in fact, if you stare at it long enough, then it looks like someone is winking at you, over and over .. as if laughing at you, knowing that you don't know what to write or how to explain yourself, even though you know how to prove it mathematically forwards, backwards, and sideways.  

well, fvck you, computer.

so i found myself, having to start a research plan which is the bulk of an Academy of Finland grant application. i had ideas, but they were without structure at all, and the combination of a blank screen and a winking, subversive cursor was too much for me ..

.. so, 2 weeks ago, i pressed the off button.

a piece of paper is a pretty intuitive thing to us humans, if only because we are familiar with it from school. if you think about it as the analog version of a potential digital device .. an advanced version of a tablet or an iPad, perhaps .. then it is an incredibly flexible interface. for one thing, i can write anywhere on a page, and organize the information later.
i may start with a paragraph of text, but being stuck, start drawing a diagram in one corner, then realise that i should estimate something, and write out a computation in another corner, decide that, having understood what i mean to express mathematically, then i'll return to finishing the paragraph that i started earlier.
the reason why this is harder on a computer is twofold:
  • alphabetic languages are inherently linear, which means that you must impose an order on your thoughts .. at least, if you're unwilling to cut-&-paste or delete. not every thought or series of thoughts of mine is orderly, which makes typing out ideas hard.
  • the human eye is a wonder of processing power. perhaps in the near future, image processing will advance to such an extent that a computer can see and recognise images as well as a human .. but until then, if i doodle something, then my friend can see that i was thinking abot linear homotopy. a computer has no such flexibility.
at any rate, i found that most of my recent grant application was initially written in ink and longhand. for me, it was far more helpful to include an additional dimension's worth of freedom, if only to fully express myself.

[1] and, of course, believe in the church-turing hypothesis.

i say believe, because -- let's face it: you can never prove a statement like "everything computable is Turing computable." you can only disprove it, by constructing a fundamentally different architecture that is backwards compatible with standard digital software.

honestly, when i first heard the church-turing hypothesis, i was quite impressed. then again, i was quite young then and had no taste. as for now, i view it as the computer science version of a peano curve .. in the sense that a ticker-tape (i.e. a real line) can be mapped injectively to a 2-D microchip (i.e. the coordinate plane). in that sense, it's not clear to me if there is anything mathematically interesting in applied computer science. theoretical computer science, from what little i've seen, looks quite cool. any science that will take metric-space embedding problems seriously is a fine science, in my book!

[thumbs up]
well, at least it's better than intelligent design, which seems to me utterly untestable.

[2] i was visiting a colleague once, and stopped by departmental tea. like the hapless nerds that we are, we started talking about graphics via latex. one guy was complaining about this one package and i had no idea what it was, so i asked him to explain it to me (how i can download it, etc). when he asked me what i used, i told him "pstricks" and then he paled

apparently i'm a masochist, by mathematical standards and otherwise.

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