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,
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.)
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
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.
