Millions, perhaps billions of humans have put food on the table and built machines with 100s of times the power or calculational ability of human individuals without ever needing to concern themselves with the breakdown of euclidean geometry. Perhaps there are machine designs that have failed due to this breakdown, but failure has so much entropy that it teaches us infitely (and I do not mean that literally) less than our successes do.
One idea I love in lesswrong is the “how do I code that in to an AI” bias in evaluating efforts. Even if there is some frontier where a deviation from euclidean geometry is necessary to understand in our design of the ultimate AI (or at least the last one built by humans)? Why would anyone be uninterested in the theory behind 99.99...% of the progress we are likely to make?
Millions, perhaps billions of humans have put food on the table and built machines with 100s of times the power or calculational ability of human individuals without ever needing to concern themselves with the breakdown of euclidean geometry.
Try sailing an ocean, as millions of humans have had to do (even just the ones doing so involuntarily like the Africa->America slave trade) with plain Euclidean geometry and then tell me how practical alternative forms of mapmaking, direction-setting, and locations are.
In addition to the object level mistake that gwern has pointed out, you’ve made a meta-level mistake.
I wasn’t arguing for the usefulness of Euclidean or non-Euclidean geometry. I was trying to shorten the inferential distance. Euclidean axiomatic mathematics is some of the first axiomatic mathematics anyone is taught in school in the West. The OP might not have understand what it was that his theory was missing in reference to infinite sets, so I used an example I expected him to be more familiar with, in an effort to make my point clearer to him.
You may not think my particular point is interesting in a practical sense, but pointing that out is quite rude unless you really think that I’m unaware that the difference between Euclidean geometry and real world geometry does not always make a practical difference.
It’s like asserting the difference between Newtonian and relativistic physics doesn’t make a practical difference. I don’t know how true that is, but saying something like that to Einstein or Hawking is just rude.
Millions, perhaps billions of humans have put food on the table and built machines with 100s of times the power or calculational ability of human individuals without ever needing to concern themselves with the breakdown of euclidean geometry. Perhaps there are machine designs that have failed due to this breakdown, but failure has so much entropy that it teaches us infitely (and I do not mean that literally) less than our successes do.
One idea I love in lesswrong is the “how do I code that in to an AI” bias in evaluating efforts. Even if there is some frontier where a deviation from euclidean geometry is necessary to understand in our design of the ultimate AI (or at least the last one built by humans)? Why would anyone be uninterested in the theory behind 99.99...% of the progress we are likely to make?
Try sailing an ocean, as millions of humans have had to do (even just the ones doing so involuntarily like the Africa->America slave trade) with plain Euclidean geometry and then tell me how practical alternative forms of mapmaking, direction-setting, and locations are.
As it happens, Nick Szabo is slowly blogging how exactly one does that: http://unenumerated.blogspot.com/2012/10/dead-reckoning-and-exploration-explosion.html and http://unenumerated.blogspot.com/2012/10/dead-reckoning-maps-and-errors.html
Just because many millions of people don’t need to concern themselves with that doesn’t mean there aren’t many other millions who don’t.
In addition to the object level mistake that gwern has pointed out, you’ve made a meta-level mistake.
I wasn’t arguing for the usefulness of Euclidean or non-Euclidean geometry. I was trying to shorten the inferential distance. Euclidean axiomatic mathematics is some of the first axiomatic mathematics anyone is taught in school in the West. The OP might not have understand what it was that his theory was missing in reference to infinite sets, so I used an example I expected him to be more familiar with, in an effort to make my point clearer to him.
You may not think my particular point is interesting in a practical sense, but pointing that out is quite rude unless you really think that I’m unaware that the difference between Euclidean geometry and real world geometry does not always make a practical difference.
It’s like asserting the difference between Newtonian and relativistic physics doesn’t make a practical difference. I don’t know how true that is, but saying something like that to Einstein or Hawking is just rude.