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What fascinates me is that if you had enough cotton candy, it would be a black hole. I don't mean it would collapse into a black hole, I mean even at a uniform
by jon_richards 2y ago
What fascinates me is that if you had enough cotton candy, it would be a black hole. I don't mean it would collapse into a black hole, I mean even at a uniform density of 0.05 grams per cubic centimeter, it would already be a black hole.
We're so used to surface area scaling at r^2 and volume scaling at r^3 and the weird effects that can have (never scale up an exothermic reaction), but the maximum amount of matter that can exist in a volume without creating a black hole scales by r^1. Even with cotton candy, that r^3 is going to out-scale r^1 at some point.
It's an interesting thought experiment for algorithm complexity as well. Can you actually retrieve an element from an array in constant time regardless of the size of the array? In the extreme case, the drive containing the array must have r proportional to the size of the array to avoid becoming a black hole. Assuming the query and element travel along the drive at the speed of light, retrieving the element still takes time proportional to the size of the array.
- lainga 2y agoI have struggled to find an established name for this value. I thought it would be something called the "Schwarzschild density", but no luck. Famously, the [someone's name??]-density of the observable universe just happens to be very close to the density that would tip the universe over into being a very large black hole
- littlestymaar 2y agoBut given that the universe is expanding, if we're close to this density doesn't that mean that the density used to be higher than the threshold at some point?
- pixl97 2y agoThis is why when talking about the big bang physicists talk about the inflation field at the start of it. The primitives in the pre microsecond universe have to be different from a black hole otherwise there's no way to un black hole yourself.
- jon_richards 2y agoWouldn't it just be the inverse of the Schwarzschild radius? https://en.wikipedia.org/wiki/Schwarzschild_radius https://en.wikipedia.org/wiki/Schwarzschild_radius
- dTal 2y agoWorth noting that even setting aside weird black hole physics, in the real world the amount of storage available given some information density and some maximum constant access latency is bound in r^3 by the speed of light, and therefore array access is not really constant time but O(∛n). This isn't some abstract ivory tower thing but the way computers actually work - due to cache hierarchies you will find that working with a 100 byte array is much faster than working with a 100 megabyte array, which is much faster than working with a 100 terabyte array. Every time the data gets larger, it gets further away...
- adrianN 2y agoThe TLB also adds some log factors to array access, which dominate for arrays that fit within a few dozen centimeters of your CPU.