Skip to main content
MathOverflow

Return to Question

minor typos
Source Link
Martin Sleziak
Martin Sleziak
  • 4.7k
  • 4
  • 35
  • 40

There are meaningful questions we can ask about Euclidean geometry which could not have been posed in the time of Riemann or even of Hilbert, and which would have made no sense at all to Euclid. For example,  does two-dimensional Euclidean geometry emerge as the large-scale limit of a quantum geometry? The fact that we are able to ask this question today demonstrates that the relevant constellation of absolute presuppositions, scene of inquiry, disciplinary matrix, or however you wish to phrase it, has simply changed.

pg-7, Towards a Philosophy of Real Mathematics

I'm trying to understand the highlighted line. What exactly is Quantum Geometry supposed in this context? Better, if the whole bolded question could be explained.

What I found so far:

  1. This wiki confuses me more since explanations assumes physics context I think.

  2. This MSE thread gives conflicting opinions, in particular, of one user saying this maybe an ambigousambiguous question to ask.

There are meaningful questions we can ask about Euclidean geometry which could not have been posed in the time of Riemann or even of Hilbert, and which would have made no sense at all to Euclid. For example,does two-dimensional Euclidean geometry emerge as the large-scale limit of a quantum geometry? The fact that we are able to ask this question today demonstrates that the relevant constellation of absolute presuppositions, scene of inquiry, disciplinary matrix, or however you wish to phrase it, has simply changed.

pg-7, Towards a Philosophy of Real Mathematics

I'm trying to understand the highlighted line. What exactly is Quantum Geometry supposed in this context? Better, if the whole bolded question could be explained.

What I found so far:

  1. This wiki confuses me more since explanations assumes physics context I think.

  2. This MSE thread gives conflicting opinions, in particular, of one user saying this maybe an ambigous question to ask.

There are meaningful questions we can ask about Euclidean geometry which could not have been posed in the time of Riemann or even of Hilbert, and which would have made no sense at all to Euclid. For example,  does two-dimensional Euclidean geometry emerge as the large-scale limit of a quantum geometry? The fact that we are able to ask this question today demonstrates that the relevant constellation of absolute presuppositions, scene of inquiry, disciplinary matrix, or however you wish to phrase it, has simply changed.

pg-7, Towards a Philosophy of Real Mathematics

I'm trying to understand the highlighted line. What exactly is Quantum Geometry supposed in this context? Better, if the whole bolded question could be explained.

What I found so far:

  1. This wiki confuses me more since explanations assumes physics context I think.

  2. This MSE thread gives conflicting opinions, in particular, of one user saying this maybe an ambiguous question to ask.

Became Hot Network Question
Source Link
Brian
Brian
  • 1.5k
  • 1
  • 12
  • 22

What is Quantum Geometry supposed to be about?

There are meaningful questions we can ask about Euclidean geometry which could not have been posed in the time of Riemann or even of Hilbert, and which would have made no sense at all to Euclid. For example,does two-dimensional Euclidean geometry emerge as the large-scale limit of a quantum geometry? The fact that we are able to ask this question today demonstrates that the relevant constellation of absolute presuppositions, scene of inquiry, disciplinary matrix, or however you wish to phrase it, has simply changed.

pg-7, Towards a Philosophy of Real Mathematics

I'm trying to understand the highlighted line. What exactly is Quantum Geometry supposed in this context? Better, if the whole bolded question could be explained.

What I found so far:

  1. This wiki confuses me more since explanations assumes physics context I think.

  2. This MSE thread gives conflicting opinions, in particular, of one user saying this maybe an ambigous question to ask.