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I studied maths at uni 30 years ago and have forgotten it all and I love how completely uncomprehensible all of these examples are if you're not in the field:
by codeulike 3y ago
I studied maths at uni 30 years ago and have forgotten it all and I love how completely uncomprehensible all of these examples are if you're not in the field:
The Busemann-Petty problem (posed in 1956) has an interesting history. It asks the following question: if K and L are two origin-symmetric convex bodies in Rn such that the volume of each central hyperplane section of K is less than the volume of the corresponding section of L, does it follow that the volume of K is less than the volume of L: Voln(K)≤Voln(L)?
Its such a dense avalanche of concepts. If you coded up a few examples using actual values to run the calculations in the much-less-dense format of code (say js or python or fortran) how many lines of code would it be? Fifty? Hundreds?
- jayd16 3y agoAren't you comparing the code for calculations with the jargon of the question? I feel like the proofs would be quite long.
- snovv_crash 3y agoSurely the example which disproves the hypothesis would be smaller than the proof that it is valid for all values?
- foota 3y agoCould be, but sometimes the description of an object can be quite involved if it's constructed in some bizarre form (e.g., the intersections of some already complicated objects, for instance)
- bigbillheck 3y agoIf you read the actual text of that mathoverflow answer you'll see that it was first disproved for dimensions >=12 and that all the rest of the work was in dimensions 3 thru 11.
- klyrs 3y agoI absolutely love this question. It cannot be answered!
- codeulike 3y agoJust trying to think of what the equivalent in code would be, and so calculating actual values seems like the closest analogue, but I know its not really comparable. I'm grasping for ideas of how can we compare the concept-density of mathematical notation with the concept-density of code?
- teraflop 3y agoThat depends very much on how K and L are defined. The code to calculate whether any possible cross-section of K is greater than the corresponding cross-section of L is trivial if they are both (hyper)spheres. If they are polyhedra (polytopes), then it would be a lot more involved. And if their boundaries are defined by even more complicated surfaces, it could be fiendishly difficult. The relationship between declarative statements about infinite families of continuous objects, and imperative code that can be implemented on a discrete computer in finite time, tends to be very very non-trivial.
- layer8 3y agoUnless you are programming in Python, it should be possible in one line.