I was pondering whether to cut the quote at this point, or to include the rest of the dialogue between natural philosopher Daniel Waterhouse and alchemist Enoch Root. I decided to cut the quote here firstly because otherwise it would be too long, and secondly because the rest of the dialogue does not have the same stirring, “yay science!”, “yay modernity!” feeling of Daniel’s tirade. But it is thought-provoking, so I include it below, with some reflections after it:
″ ’Tis a noble pursuit and I wish you Godspeed,” Root said, “but remember the poles.”
“The poles?”
“The north and south poles, where your meridians will come together—no longer parallel and separate, but converging, and all one.”
“That is nothing but a figment of geometry.”
“But when you build all your science upon geometry, Mr. Water-house, figments become real.”
Daniel sighed. “Very well, perhaps we’ll get back to Alchemy in the end—but for now, no one can get near the poles—unless you can fly there on a broom, Mr. Root—and I’ll put my trust in geometry and not in the books of fables that Mr. Boyle and Sir Elias are sorting through below. ’Twill work for me, for the short time I have remaining. I have not time to-night.”
How do you interpret this? The best interpretation I can make for what Root is saying is that when you describe Nature in abstract, mathematical/geometrical ways, you will end up confusing your abstraction for reality—and then anything which does not fit with your abstraction (like the pole does not fit in the Cartesian grid) will seem inherently mysterious, even though its mystery is an illusion of your abstract description and it is not more inherently mysterious than the pole is inherently different from other points on Earth.
This resonates with the view some philosophers have on the hard problem of consciousness and how to dissolve it: the idea goes that modern science describes nature in quantitative terms and pushes everything qualitative to the subjective realm (e.g., light is “in reality” electromagnetic waves defined as such and such equations, and color is the subjective perception of it and exists only “in the mind”) and then qualia seem inherently mysterious and not-fitting with the rest of nature, but this is only because we have confused our abstractions for reality. The more recent Putnam has said things along these lines, as well as several “neo-Aristotelian” philosophers. But I wouldn’t have associated Stephenson with such views, and yet Root seems to be speaking for him here, so I am a bit confused.
Hunh? It’s just an allusion to non-Euclidean geometry and the Gauss-Bonnet theorem, which prevents any Cartesian grid system from working on the sphere.
Yes, that is the surface meaning, but it seems to me there must be a secondary one. Daniel’s tirade in the previous comment is not just saying “we will be able to draw accurate maps using a Cartesian grid” (otherwise, why say “that will be the end of Alchemy”? what does that literal meaning have to do with alchemy?). Notice that he is responding there to Root’s assertion that there is little contrast between alchemy and “the younger and more vigorous order of knowledge that is associated with your club”, i.e. modern science (the club is the Royal Society). So I take him to mean that the new scientific method, which relies on precise, mathematical thinking as opposed to the qualitative, semi-mystical thinking in alchemy (this is what “Cartesian grid vs dragons” stands for), will carry the day and eliminate alchemy. So I think that Root’s reply that “you will leave out the poles” must have a hidden interpretation that fits in this broader argument, besides the surface one you point out.
That there must be a second meaning is also supported by Daniel saying with a sigh “Very well, perhaps we’ll get back to Alchemy in the end”—you wouldn’t need alchemy to draw a map with a different projection that includes the pole!
Well, it’s been pointed out on occasion that modern physics did get back to alchemy—in the sense of transmuting elements (radioactivity). Personally, I took Root as referring to what the alchemists did achieve: apparent immortality, given his presence in Cryptonomicon. The younger order achieved a great deal, but just as map projections always have difficulties caused by mapping 3D to 2D, the younger order has difficulties with a few singular parts of the territory, if you will.
I was pondering whether to cut the quote at this point, or to include the rest of the dialogue between natural philosopher Daniel Waterhouse and alchemist Enoch Root. I decided to cut the quote here firstly because otherwise it would be too long, and secondly because the rest of the dialogue does not have the same stirring, “yay science!”, “yay modernity!” feeling of Daniel’s tirade. But it is thought-provoking, so I include it below, with some reflections after it:
How do you interpret this? The best interpretation I can make for what Root is saying is that when you describe Nature in abstract, mathematical/geometrical ways, you will end up confusing your abstraction for reality—and then anything which does not fit with your abstraction (like the pole does not fit in the Cartesian grid) will seem inherently mysterious, even though its mystery is an illusion of your abstract description and it is not more inherently mysterious than the pole is inherently different from other points on Earth.
This resonates with the view some philosophers have on the hard problem of consciousness and how to dissolve it: the idea goes that modern science describes nature in quantitative terms and pushes everything qualitative to the subjective realm (e.g., light is “in reality” electromagnetic waves defined as such and such equations, and color is the subjective perception of it and exists only “in the mind”) and then qualia seem inherently mysterious and not-fitting with the rest of nature, but this is only because we have confused our abstractions for reality. The more recent Putnam has said things along these lines, as well as several “neo-Aristotelian” philosophers. But I wouldn’t have associated Stephenson with such views, and yet Root seems to be speaking for him here, so I am a bit confused.
Hunh? It’s just an allusion to non-Euclidean geometry and the Gauss-Bonnet theorem, which prevents any Cartesian grid system from working on the sphere.
Yes, that is the surface meaning, but it seems to me there must be a secondary one. Daniel’s tirade in the previous comment is not just saying “we will be able to draw accurate maps using a Cartesian grid” (otherwise, why say “that will be the end of Alchemy”? what does that literal meaning have to do with alchemy?). Notice that he is responding there to Root’s assertion that there is little contrast between alchemy and “the younger and more vigorous order of knowledge that is associated with your club”, i.e. modern science (the club is the Royal Society). So I take him to mean that the new scientific method, which relies on precise, mathematical thinking as opposed to the qualitative, semi-mystical thinking in alchemy (this is what “Cartesian grid vs dragons” stands for), will carry the day and eliminate alchemy. So I think that Root’s reply that “you will leave out the poles” must have a hidden interpretation that fits in this broader argument, besides the surface one you point out.
That there must be a second meaning is also supported by Daniel saying with a sigh “Very well, perhaps we’ll get back to Alchemy in the end”—you wouldn’t need alchemy to draw a map with a different projection that includes the pole!
Well, it’s been pointed out on occasion that modern physics did get back to alchemy—in the sense of transmuting elements (radioactivity). Personally, I took Root as referring to what the alchemists did achieve: apparent immortality, given his presence in Cryptonomicon. The younger order achieved a great deal, but just as map projections always have difficulties caused by mapping 3D to 2D, the younger order has difficulties with a few singular parts of the territory, if you will.