>there are other operations that aren’t quite involutions – “near-involutions”, one might call them2 – that nonetheless have the property that thrice is the same as once, four times is the same as twice, etc. ... Unlike mod-two arithmetic, which is about counting “zero, one, zero, one, zero, one, …,” the kind of counting that governs these operations goes “zero, one, two, one two, one two, …”
Interesting! Earlier I had a shower thought about "what would be an variant of idempotence?" That's where an operation has the same effect whether done one or many times.
One variant would be "has the same effect whether one two or many times". Another would be "can be in any one of two possible states after done one or many times" (as opposed to one possible state for idempotence). This looks like the latter!
>As it is we have a system of private "insurance" that can't consider the risk level of those being insured. All that means is the companies charge everyone else more to subsidize the cost of those who are more at risk.
That's what social insurance/welfare systems do throughout the developed world -- make sure everyone's covered at some minimal level even if it wouldn't be profitable when evaluated individually; it's just using insurance companies as an arm of the state to pull it off.
If, as it seems, your only objection is to labeling it "insurance", that's not a substantive objection to the merit of the policy, only how it's marketed.
What you're describing isn't insurance. There's nothing wrong with that and maybe (probably) its better than what the US has today, but if it claims to be insurance than it must be allowing the insurer to consider the risk of each policy it writes.
>It turns out that, aside from their common interest in antagonising Isaac Newton, Hooke and Leibniz also shared an interest in mechanising scientific reasoning through the invention of a universal language for science. Leibniz called his project the "Characteristica Universalis".
I'm surprised it doesn't mention Leibniz's famous "Let us calculate" quote:
>>In a 1679 letter to one of his patrons, Johann Friedrich, he described his project of the universal language as “the great instrument of reason, which will carry the forces of the mind further than the microscope has carried those of sight”. Later he wrote:
>>>The only way to rectify our reasonings is to make them as tangible as those of the Mathematicians, so that we can find our error at a glance, and when there are disputes among persons, we can simply say: Let us calculate, without further ado, to see who is right.[1]
I'm also kind of surprised that Hooke wrote the letter in English, since I assumed all academic communication across language barriers back then would have been in Latin. But ChatGPT tells me Leibniz was unusually multi-lingual.
> The only way to rectify our reasonings is to make them as tangible as those of the Mathematicians, so that we can find our error at a glance, and when there are disputes among persons, we can simply say: Let us calculate, without further ado, to see who is right.
And then Kurt Gödel forever permanently dashed those dreams.
He was ahead of his time, definitely, and binary logic is one critical step in getting there, but we're a long way from having a formal language to represent all claims that would ever arise in human argumentation to the point that it's simply a matter of calculation to resolve them.
Check out metamath.org I can't fathom any valid argument that couldn't be formalized to mathematical statements. There would still be disagreements on axioms and physical postulates, especially where there are conflicts of interest.
He didn’t actually base it on the Yiching, he just noticed that it could be expressed neatly in binary. But he had come up with binary code before that.
2) The use of the TLD .gouv.fr instead of .gov.fr, even though "gov" is a recognizable contraction of the intended French word "gouvernement".
(No, it's not a valid defense that "'gov' would be pronounced differently from 'gouv'": the English TLD .com is a contraction of "commercial", even though the "com" in "dot-com" is pronounced differently from the "com" in "commercial".)
Probably because of their proximity with the USA, the french-speaking community in Québec is far more attached to using French than actual French people.
That's why in France we use "Stop" and not "Arrêt".
On the other hand, ".gouv.fr" is something used in France.
gouv[ernement] is completely different than go[u]v[ernement]
Not only because of its pronunciation, but also because it's not a simple shortening of the original word.
We never use "aso" to talk about an "association", even though it would shorten it even more, because it just doesn't make sense.
You can remove the ending of a word, creating a kind of "prefix", bug it you remove multiple part of a word it just become something different.
>On the other hand, ".gouv.fr" is something used in France. gouv[ernement] is completely different than go[u]v[ernement]
How are they different? Contractions and abbreviations drop letters. That's the point. .gov would have been perfectly fine and matched other countries. It's a clear example of being different for the sake of it.
Oh wow, I had independently formulated that as the duality/parallel between corruption and cheat codes: "The more out-of-band information you need in order to be treated normally/fairly, the more corrupt the system is."
Right, for the OpenAI case to be analogous, they would have to switch to a system where your chats are homomorphically encrypted -- i.e. OpenAI does all its operations without knowing either the input or output plaintext. In that case, they'd only have encrypted chats to begin with, and would have to somehow get your key to comply with a warrant for the plaintext.
And note: the above scenario is not likely anywhere in the near future, because homomorphic encryption has something like a million times overhead, and requires you to hit the entire database on every request, when state-of-the-art LLM systems are already pushing the limits of computation.
Interesting! Earlier I had a shower thought about "what would be an variant of idempotence?" That's where an operation has the same effect whether done one or many times.
One variant would be "has the same effect whether one two or many times". Another would be "can be in any one of two possible states after done one or many times" (as opposed to one possible state for idempotence). This looks like the latter!
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