How Quantum Theory Is Inspiring New Math | Hacker News Reader

How Quantum Theory Is Inspiring New Math

quantamagazine.org

118 pointsdigital5526 comments

If anyone was wondering what that next number was in the sequence, the sequence for the problem given is https://oeis.org/A076912 and it is now known to begin,

    5, 2875, 609250, 317206375, 242467530000, 229305888887625, 248249742118022000, 295091050570845659250, 375632160937476603550000, 
    503840510416985243645106250, ...

If you want a few more details you might check out https://www.encyclopediaofmath.org/index.php/Clemens'_conjec... but of course mirror symmetries have whole textbooks devoted to them nowadays, one of which the Clay Mathematics institute has released to the public [PDF warning: http://www.claymath.org/library/monographs/cmim01c.pdf].

Thanks for the link. On page three this book refers to "high school vector calculus." Who studied vector calculus in high school?

This is a pretty common joke/expression among mathematicians i.e. "As you all know from kindergarten abelian groups are just monoidal groupoids with a single object" or whatever.

I understand "vector calculus" here as meaning "how to compute stuff with vectors", i.e. adding and subtracting vectors, computing the inner product etc.; not doing calculus with vectors. Obviously both interpretations are possible, but the latter is usually called multidimensional analysis.

Surely (multidimensional) analysis is the term used in mathematics for a more rigorous investigation of the basis of calculus. In physics, vector calculus is taught as a tool and the course is called vector calculus (or maybe multivariable calculus.)

The book uses "calculus" several times to mean "derivatives and integrals"

Europeans

Even African

People who grow up to attend graduate schoool in the study of mathematical methods of physics

AP courses have vector calculus.

It was the last unit in senior math at my high school.

Probably anyone who took a more than introductory physics class. Not me, though.

I did

That's numberwang!

Is there a simple explanation of what the GCI means?

Preferably without mathematical wording "for such a set that", "for a given function X where", "under a frobnobian measure if" etcetcetc

Bayes has simpler, word descriptions, for example.

If you have two convex shapes (like a circle and a rectangle) which have the same center, if you think of the center as a target, and throw darts at the target. The dart will be more likely to land in the intersection of the two shapes than would be derive by multiplying the probability of landing in one and the probability of landing in the other. If you were talking about independent events, like rolling 1s on two dice, you'd get the probability of both things happening by multiplying their independent probabilitis: so 1/6 * 1/6 = 1/36 probability for snake eyes. Another example would be the correlation between weight and height. If you took the median weight and median height, and took say the 10% of the population around that height and the 10% of the population around that weight, the overlap would be more than the 1% that would be calculated by taking 10% of 10%. The GCI says that for any reasonably distributed variables, this inequality (the probability of falling around the central tendency of all variable) will be greater than the product of the probability of falling around the center for each variable taken independently.

To be clear, this is presuming a (multidimensional) bell curve distribution for dart throws, or weights and heights, or for whatever. Let us be clear that the GCI is specifically about bell curve (i.e., normal, Gaussian, etc.) distributions, not about anything else.

Also, I believe the shapes must be not only convex, but symmetric under reflection through the center. But it suffices to consider only parallelepipeds.

what's "the GCI" here? I don't recognize that acronym, I couldn't find any term in the article it could be, and googling doesn't really turn anything up...

I think they must have commented on the wrong article by mistake. The "Gaussian Correlation Inequality" was recently proved, and discussed in this thread: https://news.ycombinator.com/item?id=13977554

Ah, you are right...

Second wikipedia link for CGI refers to computer-generated imagery. That or I didn't understand your question.

And hopefully no one uses the phrase "...therefore, it is trivial to say that..."

You want to understand mathematics without understanding mathematics?

I want an intuition of a concept in mathematics that isn't the same as the formal definition.

I gave a specific example (Baye's) - being able to juggle the symbols is entirely different from interpretation.

If you want the difference between an intuition and formalization, consider the "Copenhagen interpretation" which is non-mathematical, yet is based on mathematically formalised concepts.

Worth noting that all the results discussed in this article are 20+ years old. Bored reporter?

Bored... something: https://www.ias.edu/scholars/dijkgraaf

Reply on news.ycombinator.com