Which I found incredibly silly once I leaned about negative exponentiation and could now deduce the pattern.
Similarly, 0/0 became much more tractable to me once I learned L'Hôpital's rule https://en.wikipedia.org/wiki/L'H%C3%B4pital's_rule
1,879 karma · joined November 21, 2015
Which I found incredibly silly once I leaned about negative exponentiation and could now deduce the pattern.
Similarly, 0/0 became much more tractable to me once I learned L'Hôpital's rule https://en.wikipedia.org/wiki/L'H%C3%B4pital's_rule
Declaring 2x2=0+2+2, 2x1=0+2, 2x0=0 while 2xx2=1x2x2, 2xx1=1x2, 2xx0=1 seemed arbitrary.
What helped was learning about negative exponentiation and exponentiation simplification, so 2xx0 = 2xx2 x 2xx(-2) = 2xx2 / 2xx2 = 1.
That said, I clearly still take issue with unintuitive interpretations of "nothing" https://stackoverflow.com/questions/852414/how-to-dynamicall...
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}The first vending machine was actually first century and dispensed holy water. It was actually mechanized similarly to pre-electronic vending machines. https://www.logicvending.co.uk/history-vending-machines
If A is making $1001 and B is making $2000, A has to survive on 33% of what the economy produces.
Even if inflation could be exclusive to basic needs, causing A’s costs and B’s costs to both rise by $1000, the economy now heavily incentivizes more competition around satisfying basic needs. All rent going up equally regardless of unit size means it’s time to start building or converting luxury apartments to multiple low income apartments.
Huh, TIL.
Gurren Lagaan is surprisingly meta. One of the big problems with the fight-focused anime formula is that they constantly one-up themselves, eventually power spiraling to unsustainable levels. So Gurren Lagaan's plot revolves around an energy literally called "spiral power" and how unsustainable it is.
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Massively helpful, but also concerning how months later I still automatically try to go to the homepage every once in a while and run into my adblocker.
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.
I've been mulling over a sci-fi setting focused on keeping humans relevant in the context of advanced technology. One of the core ideas is that AIs decay without human interaction. State backups don't prevent it because noticing clues they've been out just makes it worse.