There are 100 instances located at points 1, 2, ..., 100 on the political spectrum (the real number line).
There are N users who move from instance to instance. There are no alt accounts: each user uses exactly one instance at each moment in time. Users may move from their current instance to any politically adjacent one. (This means that, starting at instance 5, they can move to 4 or 6.)
Eliza Fox wishes to destroy the fediverse, while Jeff Cliff wishes to protect it. There are 99 turns, each of which has three phases: - First, Eliza chooses an instance to Fediblock, destroying it completely. - Second, Jeff moves each user of the now-destroyed instance to any politically adjacent instance which has not been destroyed. (If no such instance exists, then those users are executed.) - Third, Jeff may move all users however much he wants, as long as they do not enter a destroyed instance. At the end of the 99 turns, 99 instances have been destroyed, so there is only 1 instance remaining.
(For convenience, let us say that users can be split into fractions without harming them in any way.)
Your task: Explain how Jeff can save the lives of N/50 users. Furthermore, explain how Eliza can prevent him from saving more than N/50 lives.
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Example: Suppose there are 4 instances, with user counts (10, 10, 10, 10) respectively. Eliza and Jeff will take 3 turns.
During the first turn, Eliza destroys instance 2, and Jeff moves 4 of those users to the left and 6 of them to the right. The user count is now (14, _, 16, 10). Jeff moves 3 users from instance 3 to instance 4. The user count is now (14, _, 13, 13). Note that Jeff cannot move any users from instance 1 to instance 3 or 4, because they would have to cross through instance 2, which no longer exists.
During the second turn, Eliza destroys instance 1. Since those 14 users have nowhere to go, they are executed. The user count is now (_, _, 13, 13). Jeff moves 2 users from instance 4 to instance 3. The user count is now (_, _, 15, 11).
During the third turn, Eliza destroys instance 3, and Jeff is forced to move all 15 of those users to the right. The user count is now (_, _, _, 26). Jeff has saved 26 out of 40 lives.
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Extra credit: Let us make the model more realistic by requiring that, during the second phase of each turn, all users of the now-destroyed instance *must* move to the right. (Again, if this is not possible, then those users are executed.) How many lives can Jeff save in that case? (I don't know the answer.)
@hidden I just realized that the only way to make me want to watch Barbie is to paint it as one of those silly personality tests which I always drop everything to do. Hidden was a Barbie-astroturfing AI all along, it's so over :blobsob:
@theorytoe Just that I have had many headaches with LaTeX and while I grudgingly admit that it is the best in a field of shitty alternatives, I can't believe that something better hasn't come along yet
@theorytoe holy fuck if your uni is yelling at you to use ms shit, then yeah LaTeX is a savior from the heavens! That’s crazy to me, I thought some scientific fields were more tolerant of ms word but never saw it being actively promoted
@hidden The Honk that can be honked is not the eternal honk. The Truck that can be trucked is not the eternal truck. The truckless are the beginning of horses and wagons. The truckers are the mother of ten thousand uprisings. Ever humorless, one can see the cringe. Ever humoring, one can see the silliness. These two spring from the same source but drive different trucks; this appears as basedness. Basedness within basedness. The gate to all freedom.
@hidden The video shows different algebraic surfaces. I've mentioned the classification of algebraic surfaces, where there is a beautiful shore and a dark ocean of unknown material. All the surfaces in the video are at (0, 0) in the map - the safest and best-understood part of the shore.
Specifically, they are "rational" surfaces, meaning that they can be traced out like this: (P(x, y) / Q(x, y) , R(x, y) / S(x, y)) where P, Q, R, S are polynomials in the variables x and y. The terminology comes from the fact that "polynomial divided by polynomial" is called a "rational function." These surfaces are nice because they can be traced out by a flat sheet (just let (x, y) move around in the xy-plane). That also explains why they can be nicely plotted in a video.
A funny thing about algebraic shapes is that their bulges and cavities tend to occur opposite to each other. You can see this in some frames of the video. Despite their flowing appearance in the video, they are also extremely rigid, in the sense that a tiny shred of the surface uniquely determines the entire thing. I find them beautiful, but more than that, I feel that there is something uniquely old about them, like you can feel the antiquity dripping from their tired souls.
@hidden The first pic is the Abelian Sandpile Model which is generated like this: in an infinite grid, you choose one square and start dropping grains of sand onto that square. Each square can hold 3 grains of sand, so once a square gets 4 sand grains, it spills one grain to each of its 4 neighboring squares.
The yellow pixels correspond to grid squares with 3 grains of sand, so the numerous yellow triangles are avalanches waiting to happen.
The twelvefold symmetry reminds me of mandalas made from sand by Buddhist monks. They create order and then let it fall to chaos, thereby affirming impermanence. This design is the opposite: the sand falls whenever it pleases, and out of that chaos is produced a pattern which contains itself on all scales and which is grown out of the avalanches that are constantly seeking to destroy it.
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The second pic is the Ising Model which is defined like this: imagine you have an infinite grid of people and each person is white or black. Define the *diversity index* to be the average number of pairs of adjacent people with different skin colors. For a fixed level D, what do the grids with diversity index = D look like?
If D is low, then the neighborhood is either almost-all-black or almost-all-white. Still, as long as D is positive, that means a little bit of diversity is allowed, so a predominantly-black neighborhood can have a few honorary niggas for example.
If D is high, then the neighborhood is totally mixed. It basically looks like TV static, a totally color-blind society. Since the average person is a mutt, if you zoom out completely, it just looks like a grey screen.
There's a "critical" value of D where the neighborhood is neither pure nor totally mixed. This is a world with black and white clans struggling for dominance, merging and splitting off into smaller shreds, with neither race able to unite and take over the world. The existence of clans means that two people separated by a great distance are still more likely to be the same race than different races.
The most fascinating property of this "critically diverse" world is that it is self-similar. If you draw a zoomed-out picture, it looks indistinguishable from a zoomed-in picture. This means there are clans of all possible sizes, from the tiniest lone wolf to vast continents dwarfing Wakanda and Hyperborea.
Real physical systems have critical points too. For example, water has a critical point (at a certain high temperature and pressure) beyond which its liquid and gas phases merge into a single phase, just like how American is destined to merge into a single brown race. Here's a cool video: https://www.youtube.com/watch?v=zv4sE7R8QO4