KvanteKat

Deepseek is a private corporation funded by a hedge fund (High-Flyer). I doubt much public money was spent by the Chinese state on this. Like with LLMs in the US, the people paying for it so far are mainly investors who are betting on a return in the long to medium term.

Sure, but the alternative is not really any better: if the choice is between being the guy who got it wrong vs. being the guy who got it wrong _and_ being the guy who persisted in throwing good money after bad, surely the former is prefereable. As far as I see, the fact that they keep going indicates that they genuinely still believe Copilot could pan out and become profittable in the long run.

You can think of it like this:

- The characteristic function of a random variable X is defined as the function that maps t --> ExpectedValue[ exp( i * t * X ) ]

- Computing this expected value is the same as regarding t as a constant and integrating the function x --> exp( i * t * x) with respect to the distribution of X, i.e. if X has the density f, we compute the integral of f(x) * exp( i * t * x) with respect to x over the domain of f.

- on the other hand: computing the Fourier transform of f (here representing the density of X) and evaluating it at point t (i.e. computing (F(f))(t) if F represents the Fourier transform) is the same as fixing t and computing the integral of f(x) * exp( -i * t * x) with respect to x.

- Rearranging the integrand in the previous expression to f(x) * exp( i * -t * x), we see that it is the same as the integrand used in the characteristic function, only with a -t instead of a t.

Hope that helps :)

For those interested in looking slightly more into the characteristic function, it may be worth pointing out that the characteristic function is equal to the Fourier-transform (with the sign of the argument being reversed) of the probability distribution in question.

In my own experience teaching teaching probability theory to physicists and engineers, establishing this connection is often a good way of helping people build intuition for why characteristic functions are so useful, why they crop up everywhere in probability theory, and why we can extract so much useful information about a distribution by looking at the characteristic function (since this group of students tends to already be rather familiar with Fourier-transforms).

The variable n comes out of nowhere in theorem 3.3, and they do not refer to it in the proof itself as far as I can tell. Is this just an editing error (I think the formula 3.4 needs the variable n if f is multidimensional and we are integrating over R^n, but since f is in L^1(R) I'm not sure what it signifies. I am however worried that there's something I'm missing).

What exactly is the argument that corporations are incapable of unbounded exponential growth contra a possible future AI? Is there just something magic about computers, or am I missing something obvious?

How is "The circumferance of an idealized circle divided by its diameter" not a finite expression of π? Saying something cannot be expressed finitely in an integer-based numeral system, and saying that it admits no finite representation are two radically different statements.

Despite it being a non-starter from a pragmatic standpoint, we could for instance easily imagine a novel numeral type that encodes the set S = {a + b·π where a and b are integers} (we can encode integers quite easily and all we need to reposesent such a number in silico is to encode a and b). Using such a numeral type, we are able to do exact arithmetic if our operations are restricted to addition and subtraction (and if we are content with fractional representation of numbers as being considered "exact", we can also do division and multiplication although we would have to work within the larger set S' = { (a + b·π) / (c + d·π) where, a, b, c, and d are integers and c·d ≠ 0} rather than within S).

Part of the issue is that after a while we tend to forget that the cases that turned out to be true were dismissed as conspiracy theories at the time. In recent memory for example, a lot of claims about the capabilities and application of the US signal intelligence apparatus abroad (especially in allied coununtries) were dismissed as conspiracy theories prior to Snowden. If you talk to a lot of people today, they will tend to remember it more as a "we kinda' always knew, but just didn't have confirmation" situation than a "I'm sure the NSA is doing _something_, but there is no way it would be this extensive" situation.

I suspect OP may have been going for a variation on the old "Programmer returns with zero eggs and 12 gallons of milk after having been asked to get one gallon of milk and if they have eggs to buy a dozen"-joke, but it falls flat in this instance since it relies on an interpretation bordering on deliberate misconstrual (i.e. applying the modifier "for each year of service" to the whole phrase "16 weeks plus two additional weeks" rather than just to the latter fragment "two additional weeks").

Without knowing the exact approval history in the US, I doubt that it is a lax approval process as much as it is an absence of better alternatives.

There are not really any known effective clinical interventions (be they in the form of medicine, therapy, or things like more exercise), and a 10% improvement is better than nothing (clinical therapy (notably Cognitive Behavioral Therapy) is generally believed to be more effective but not by that much and it is financially out of reach for many people who are able to afford medication).

> The problem with treating depressed people is to get them to actually do the things that will help them. That can be incredibly difficult without medication.

The problem with talking about doing "things that will help them" is that we don't really have a lot of effective clinical interventions. Even the most common interventions (SSRIs, Congnitive Behavioral Therapy, physical exercise, etc.) are not really that effective at treating depression and have little to no effect in large parts of the affected population. That being said, these treatments _do_ work for some people so they should definitely not be dismissed out of hand (although it may in some cases be regression to the mean more than anything else, i.e. if you get better after a while on your own but have undergone treatments of one form or another you may erroneously believe your most recent treatment was effective).