By inspection

by James Somers, September 9, 2009

Mathematicians will sometimes say that a result follows “by inspection,” meaning roughly that its proof is so straightforward that to work it out would almost be patronizing. [1]

It’s a useful phrase to have in mind, and it’s led me to a somewhat strange idea—that science, and I mean this quite generally, has developed as though one of its goals was in fact to make more and more things provable that way, “by inspection.”

Consider, for example, how thousands of years ago one needed all kinds of clever arguments to convince someone that the Earth was round, whereas today you can just send them to space and have them look. Or how a student on his laptop can now brute-force a problem that once required tricky mathematics. Or how IBM can take 3D pictures of atomic bonds whose structure was always deduced, never seen.

New technologies, then, seem to serve twin purposes: one, to generate more inputs to an inferential model, like telescopes do for cosmologists and accelerators do for physicists, and two, to replace these models with simple pictures of the truth.

So we can imagine a future in which doctors see diseases, rather than teasing them out based on patients’ symptoms or history; where chain-termination DNA sequencing is replaced by high-resolution radiography; where we explore the deep oceans instead of just guessing what’s there.

Think of how J. Craig Venter’s team discovered tens of thousands of new organisms in a barrel of seawater that marine microbiologists said would be empty. [2] The difference was that he had tools—for rapid DNA sequencing, mostly—that they didn’t. He could see more. [3]

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[1] Example: suppose we’re playing a game of chess, and we inform our opponent—we claim—that he has been checkmated. We could be highly rigorous and say, “in particular, you cannot move here because of X, nor here because of Y, nor here…”, but we would be insulting his intelligence. So instead we just leave it to him to inspect each of the possible moves until he sees, quite plainly, that there is no way out.

[2] See p. 40 of this awesome book of conversations / talks about life (think biology, not philosophy) [PDF, via].

[3] In the same way, individual minds have a way of moving from slow, heavily (and cleverly) deductive inferential procedures to a kind of rapid inspection. That is, when you learn a great deal about something, you are in some sense just building highly defined manipulable mental objects, ones that you can look at, bend, and combine at will. It’s like how expert chess players, instead of meticulously playing out lines, “see the whole board” and fluidly explore it, or how expert coders feel like they can “hold the program in their head.”

This ability is hard-earned. Which is why it’s probably not a good idea to, say, forget about mathematics because we can now compute so quickly, or rely on imaging machines at the expense of clinical expertise. If we look for shortcuts we’ll likely get lost.

But it’s worth recognizing the power of richer mental pictures—that they are worth more than just the work put in to build them.