Right, like in math, not all infinite sequences contain every finite subsequence. For example, a non-repeating sequence of 2's and 7's contains no sequence "4". The further condition is that the number be normal[1].
Also, TIL we don't know whether π is normal thus the popular claim that "every string of numbers eventually occurs in π" is not known to be true
Nice post. With respect to maximizing future options, I find the ideas expressed in the following quotes are interesting counter-points.
From '4,000 weeks': "Not only should you settle; ideally you should settle in a way that makes it harder to back out, such as moving in together, or having a child. The irony of all our efforts to avoid facing finitude -- to carry on believing that it might be possible not to choose between mutually exclusive options -- is that when people finally do choose, in a relatively irreversible way, they're usually much happier as a result."
From 'Zero to One': "When people lack concrete plans to carry out, they use formal rules to assemble a portfolio of various options. ... A definite view, by contrast, favors firm convictions. Instead of pursuing many-sided mediocrity and calling it "well-roundedness," a definite person determines the one best thing to do and then does it."
It hasn't worked perfectly though, as the vaste majority of American bisons (all but 4 herds in fact) aren't true bisons but have cattle genes due to hybridation.
There are second hand accounts from indigenous people, excavated bone sites with tools and spear tips, but reportedly no first hand recorded observations from Europeans of buffalo running off cliffs.
Buffaloes aren't exactly Main Battle Tanks you know: it's not that difficult to build fences that are able to stop them (it just won't be the light fences you have in mind).
Also, not voluntarily pushing the beasts to your fences is going to help a bit, since buffaloes don't run to cliff on their own…
I had similar thoughts on this. It looks polynomial because he classified errors into certain groups and spread them across an axis which we implicitly think is a dimension. But it's not... as he says, "Along any one dimension we might have a combination of issues (i.e. multiple implementation bugs)". So looking at the grid and thinking you're at a single point is wrong... but so is thinking you could be any configuration of locations (you couldn't be at points (1, 1) and (2, 2), you also need to be at points (1, 2) and (2, 1), i.e. the set of points you're at is transitive). Thus this is a bad way to "enumerate the failure cases" and makes his notion of "adding a dimension" pretty unintuitive. It makes more sense to see every point of his dimensions as itself a dimension. Each of these dimensions could be either correct or incorrect, 1 or 0. So you're configuration could be visualized as a string of 1's and 0's. Thus, the number of possible configurations grows exponentially (2^n).
Also, TIL we don't know whether π is normal thus the popular claim that "every string of numbers eventually occurs in π" is not known to be true
[1] https://en.wikipedia.org/wiki/Normal_number
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