The creativity and range of newgrounds content was mind blowing. The focus on fun as opposed to money making was really clear to me even as a kid. I've always had this little conspiracy theory that they killed flash because it was a threat, too easy for us to make our own culture and fun without a wealth extraction step in the middle. I know it's not true but it's just a weird little feeling I have.
Probably best to avoid the word ring in a mathematics discussion unless you're talking about the algebraic structure. It's very much a mathematical `keyword`.
I was just referring to one of the early sentences saying breakfast is a vector space. If you allow arbitrarily many (say) eggs so that two eggs and one egg are different breakfasts, you get a cone inside R^d. If you normalise and consider the ingredients as fractions of a whole (so that 1 egg and 2 eggs are both represented by the 1.0 egg breakfast) you get this simplex structure and the coordinate system you mentioned. But that's still not a vector space as there are not inverses in general. At best it can be embedded in R^d.
Someone else may have said this but strictly speaking breakfast is something like a cone in a vector space, unless you want to explain to me how to eat negative eggs.
Amazing that when ai "solves" an erdos problem by finding the solution in an existing paper it gets hundreds of points and comments, but when ai fails a more rigorous test designed by practitioners (i.e. a much better test of the claim that ai will soon do research level mathematics) it gets zip.
C is the only way to make a field out of pairs of reals. Also (or rather just another facet of the same phenomenon) we might be interested in polynomials with integer coefficients, but some of those will have non integral roots. And we might be interested in polynomials with rational coeffs but some will not have rational roots. Same with the reals but the buck stops with the complex numbers. They are definitely not accidental they are the natural (so to speak) completion of our number system. That they exist physically in some sense is "unreasonable effectiveness" territory.
In my experience, the so-called 1% are mostly just thinkers and researchers who have dedicated a lot more time from an earlier age to thinking and/or researching. There are a few geniuses out there but it's 1 in millions not in hundreds.
So what if we are quite predictable. That doesn't mean we are "trying" to predict the next word, or "trying" to be predictable, which is what llms are doing.
Over a large population, trends emerge. An LLM is not a member of the population, it is a replicator of trends in a population, not a population of souls but of sentences, a corpus.
People like to, ahem, parrot this view, that we are not much more than parrots ourselves. But it's nonsense. There is something it is like to be me. I might be doing some things "on autopilot" but while I'm doing that I'm having dreams, nostalgia, dealing with suffering, and so on.
The thing about norman doors is that it's not really a design flaw, not in every case. Like handles on push doors. It's tempting to think of that as a design flaw but more likely it's designed to be mass produced and reversible, the cost of making two (or more) configurations being much higher than the occasional confused user. You could argue this only enhances the metaphor as a lot of design issues occur when things are optimised for the company and not the user.
Can you give an analogous example for data science? I confess ignorance here, and always took the term at face value. Is the issue that "data science" tries to be agnostic about the source of the data? (I'm not claiming that that is true, just guessing)
Are you an expert? Not gatekeeping here but I have no intuition for what is easy or hard to formalise. A lot of very simply stated graph theoretical results are apparently extremely hard to formalise.
I just asked chatgpt about 72 hour preparedness kit. I said what I had already and asked it about the best way to store it first. It said something to the effect of "good, you are thinking about this in exactly the right way -- make sure you have the containers in place and then get the exact contents right later" not exactly the wording but you get the picture and can probably guess where I'm going with this.
When I asked again, this time I asked about the items first. I had to prompt it with something like "or do you think I should get the storage sorted first" and it said "you are thinking about this in exactly the right way -- preparedness kits fail more often due to missing essentials than sub optimal storage"
I can't decide which of these is right! Maybe there's an argument that it doesn't matter, and getting started is the most important thing, and so being encouraging is generally the best strategy here. But it's definitely worrying to me. It pretty much always says something like this to me (this is on the "honest and direct" personality setting or whatever).
I think your objection regarding future governments is valid. The others I don't think are valid. For the record I agree with your conclusion that any effort like this is doomed to fail. But we already enforce point of sale age checks at scale across multiple domains. And as for perverse incentives, part of the proposal is more or less identical to how scratch cards for gambling work. There probably is a black market for these and there probably have been attempts at fraud. But they aren't very large, not enough to tank the system anyway.
Yeah it's insulting. It would be very long and boring to list all the things I thought of and discarded, just to ward off such attempts at help. If someone doesn't ask your advice, don't give it.
It's obviously of more interest as a piece of outreach than as a piece of mathematics. Nevertheless I've always wondered about the e^ipi + 1 = 0 formulation. It seems ugly and ad hoc, and the connection between the "5 constants" is not all that meaningful.
That e^ipi = -1 is related to the much more profound observation that the complex numbers represent a sort of rotation into a previously unknown dimension of numbers.
There was a lot of hubris around microwaves. I remember a lot of images of full chickens being roasted in them. I've never once seen that "in the wild" as it were. They are good for reheating something that was produced earlier. Hey the metaphor is even better than I thought!