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July 8, 2015

Mary Shelley on Invention

Posted by Tom Leinster

From the 1831 introduction to Frankenstein:

Invention, it must be humbly admitted, does not consist in creating out of void, but out of chaos; the materials must, in the first place, be afforded: it can give form to dark, shapeless substances, but cannot bring into being the substance itself. […] Invention consists in the capacity of seizing on the capabilities of a subject, and in the power of moulding and fashioning ideas suggested to it.

She’s talking about literary invention, but it immediately struck me that her words are true for mathematical invention too.

Except that I can’t think of a part of mathematics I’d call “dark” or “shapeless”.

Posted at July 8, 2015 12:54 PM UTC

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Re: Mary Shelley on Invention

The dark and shapeless are those parts of mathematics yet to be defined. Newton faced this when formulating his method of fluxions. And we face this today in pondering the proper mathematics for quantum gravity.

Posted by: Metatron on July 8, 2015 2:06 PM | Permalink | Reply to this

Re: Mary Shelley on Invention

“I have traversed this bottomless night, which extinguished all light and the joy of my life; I entreat you my son, leave the science of parallels alone. You should detest it more than lewd intercourse.” -Wolfgang Bolyai “I have created a new world out of nothing.” -János Bolyai

speaking of the dark.

Posted by: joez johnsmith on October 30, 2015 10:56 PM | Permalink | Reply to this

Re: Mary Shelley on Invention

“Chaos” and the “dark and shapeless” could be identified with “contradiction”.

A mathematical truth should hover at the edge of contradiction. It should contain enough to avoid it but nothing more.

Posted by: RodMcGuire on July 8, 2015 2:23 PM | Permalink | Reply to this

Re: Mary Shelley on Invention

Given the set of all “Post canonical systems” - which strikes me as pretty random and formless - why mathematicians concern themselves with a narrow subset seems perhaps an interesting question.

Posted by: tryggth on July 12, 2015 2:54 AM | Permalink | Reply to this

Re: Mary Shelley on Invention

Expanding on RodMcGuire’s identification of “chaos” with “contradiction”, I think the fundamental essence of the “dark and shapeless” is raw, untyped, arbitrary, meaningless computation. The gods, nature, whatever, give us the ability to compute anything, but don’t tell us what we should compute.

Of course, to turn the ability to compute into something practical, for both scientific and engineering purposes, we must carefully select a subset of those computations that we can relate to useful meanings. Mathematical structures were invented precisely for this purpose: to give meaning to some (necessarily not all) computations.

This, in my view, makes clear why a foundation of mathematics must put the notion of mathematical structure at the forefront (category theory, type theory), rather than leave it as an exercise to the user (material set theory).

Posted by: Eduardo León on July 12, 2015 2:44 PM | Permalink | Reply to this

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