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If you try multiplying two numbers, say 4 digits each, using the standard grade school technique, you'll see that you end up writing the digit-wise product of each number, with a shift (adding a zero at the beginning) for each digit, followed by a sum. This is literally just a convolution operation over the digits (this is because secretly writing a number in base B is equivalent to expressing a polynomial evaluated at the integer B, and multiplying polynomials is a convolution over the coefficients). By the convolution theorem, this O(N^2) time operation can therefore be accomplished in O(N logN) time by doing multiplication in frequency space and then transforming back. This is because the Fourier transform is O(N logN), via the FFT, and multiplication is O(N).

I just looked up the answer to my original question - the Fourier trick is notionally only O(N logN), but because the FFT takes you from integers to floating points, as N gets larger you need to encode more and more bits to achieve enough precision to yield absolute errors <1 after doing both Fourier transforms. The need to encode those extra bits tacks on another logN, taking you to O(N log^2 N).

I was under the impression that because the grade school technique we learn is really just convolution over the digits, the fastest algorithms achieve o(n logn) via fourier transforms. Is that not the case?

I think the biggest (and, in my opinion, obvious) problem with this argument is that it relies on time having no value in the eyes of the consumer (or, equivalently, that the seller believes this to be the case). A consumer 5 years after a game's release may only purchase said game at marginal cost, but the consumer 1 day after release is willing to pay a premium to receive the product. There really doesn't seem to be any logical support for the component of the conjecture that says "because the price may eventually settle to the marginal cost, it must immediately settle to the marginal cost". There is obviously a time-constant present

> fully reusable rockets are going to be one of the most important engineering achievements in human history

The number of implicit biases, assumptions, and unsubstantiatable assertions packed into that extremely confident sentence is frankly kind of impressive.

We have no idea how important reusable rockets will end up being, because we have no idea of what the future potential (economical or otherwise) space travel will have. Even Musk’s oft repeated (supposed) personal motivation for space travel (“protection of the species”) will ultimately hinge far more on other, far more important (and as of yet unrealized) technologies than reusable rockets.

Not to mention your implicit comparison of reusable rockets to literally every other extant technology. I mean really - transistors? The written word? RF comms? Indoor plumbing??

Fyi the unscented Kalman filter is both easier to implement than the EKF, and also avoids several of the requirements that come along with the need to linearize (such as the differentiability requirement mentioned in the article). Also (to me, at least) the UKF is conceptually much cleaner, as the whole point is to place the approximation in the parameterization of the distribution, rather than on the function operating on that distribution.

https://groups.seas.harvard.edu/courses/cs281/papers/unscent...

That’s because, as the article explicitly states, this post is by walletwallet’s developer

> A Starlink satellite uses about 5K Watts of solar power. It needs to dissipate around that amount (+ the sun power on it) just to operate.

The “+ solar power” part is the majority of the energy. Solar panel efficiency is only about 25-30% at beginning-of-life whereas typical albedos are effectively 100%. So your estimate is off by at least a factor of three.

Also, I’m not sure where you got 5 kw from. The area of the satellite is ~100 m2, which means they are intercepting over 100 kw of bolometric solar power.

This still relies on a heat differential, as described in the Details section of your linked article: https://en.wikipedia.org/wiki/Thermophotovoltaic_energy_conv...

Useful, extractable energy comes from a temperature differential, not just temperature itself. Once your system is at temperature equilibrium, you cant extract energy anymore and must shed that temperature as heat

This argument assumes that you only need to radiate away the energy that the solar actively turns into electricity, but you also need to dissipate all the excess heat that wasn’t converted. The solar bolometric flux at the earth is 1300 w/m2, or 2600 for 2 sq m. That works out to an efficiency of ~20% for your home solar, and your assumed value of 750 w yields an efficiency of ~30%, which is reasonable for space-rated solar. But assuming an overall albedo of ~5% that means that you were only accounting for a third of the total energy that needs to be radiated.

Put another way, 2 sq m intercepts 2600 w of solar power but only radiates ~1700 w at 350 k, which means it needs to be run at a higher temperature of nearly 125 celsius to achieve equilibrium.

Thats not how big-O notation works. You don’t know what proportionality constants are being hidden by the notation so you cant make any assertions about absolute runtimes

In most places in the US (california being a notable exception) taxes are reassessed regularly based on market conditions. In some areas this can result in the property taxes rising to an appreciable fraction of the mortgage rate - or in the GPs case, what the mortgage would have been, if they hadnt paid it off already.

> Happiness simply comes from other things in life than 'my castle my kingdom'. I know its a typical US mindset (and far from US only) to have a house on your own, but its still an emotion

This is a frustratingly uninformed take. You are comparing apples to oranges by equating your decision-making process with that of someone in the US. The drive to own a house in the US is not just mediated by “emotion” - the calculus is fundamentally different than in many nordic countries. For instance, very few places in the US have rent control, which means that renting represents substantial risk of either experiencing a large increase in cost, or being forced to move at irregular intervals. On the other end of the spectrum, the US is one of the only places that offers 30 year mortgages, which means that (taxes and repairs aside) buying a home on credit still offers a high level of predictable cost over the long term. Also, at least historically, there are very many places in the US for which housing is very affordable, given that the USs overall population density is so much lower than the average European country.

This is of course not to suggest that buying is always a good call - but it is often a logical and financially sound one.

https://bopoolen.nu/en/laws-regulations/

Thats like saying the grocery store is ok with me eating some of the grapes while I shop so they must be ok with me walking out without paying for my groceries.

I’m not trying to be obtuse here. I really want to understand some sort of reasonable moral justification for actively avoiding paying for a service that you are using / circumventing the mechanism by which the business makes money.

Except in this case the only way the store makes money is either by you paying an entrance fee or by you looking at the products. You are being delivered a service (whose delivery costs money) while actively circumventing the mechanism the store employs to be compensated for that service.

You are using a service without paying for the service by actively circumventing the payment mechanism. Is that not stealing?

I would genuinely like to understand this perspective. Ads or paying for premium is how the underlying business makes money. The UX might suck but you have a choice - you can just not watch YouTube. The approach you describe (which i understand is a popular one) is equivalent to justifying robbing a store because their prices are too high.

A slightly stronger (and more relevant) statement is that the number of mutually nearly orthogonal vectors you can simultaneously pack into an N dimensional space is exponential in N. Here “mutually nearly orthogonal” can be formally defined as: choose some threshold epsilon>0 - the set S of unit vectors is nearly mutually orthogonal if the maximum of the pairwise dot products of between all members if S is less than epsilon. The statement of the exponential growth of the size of this set with N is (amazingly) independent of the value of epsilon (although the rate of growth does obviously depend on that value).

This is pretty unintuitive for us 3D beings.

That would also be an incorrect phrasing. This entire thread is a good illustration of the difficulty of speaking precisely about probabilistic concepts.

(The number of successes has zero uncertainty. If you flip a coin 10 times and get 5 heads, there is no uncertainty on the number of heads. In general, for any statistical model the uncertainty is only with respect to an underlying model parameter - in this example, while your number of successes is perfectly known, it can be used to infer a probability of success, p, of 0.5, and there is uncertainty associated with that inferred probability.)

> How much of a chance do you think we have of meaningfully changing a government, if they can guess with 80% degree accuracy how everyone voted, based on their chats and social networks

This doesnt really detract from your overall point, but you may be underestimating how easy it already is for the government to tell how you will vote, without use of networking information. Just knowing someone’s educational level and zip code is enough to guess their voting preferences to a high degree of accuracy (the latter component being the reason why gerrymandering is so effective).

Unfortunately I’m in the same boat. What appears especially telling is:

> tVNS applied for 30 min daily over 7 consecutive days increased VO2peak by 1.04 mL/kg/min (*95% CI: .34–1.73*; P = .005), compared with no change after sham stimulation (−0.54 mL/kg/min; *95% CI: −1.52 to .45*)

(emphasis mine) The 95% CIs for the case and control groups overlap. Seems borderline irresponsible to have a the abstract reporting a significant result.

I’m not sure what you mean by “higher population” but fyi what determines the required number of samples is a function of the full shape of the underlying distribution. For instance the Berry Esseen inequality puts bounds on the convergence rate as a function of the first two central moments of the underlying distribution. But the point is that the convergence rate to Gaussian can be arbitrarily slow!

https://en.m.wikipedia.org/wiki/Berry%E2%80%93Esseen_theorem

I’ve heard this statistic before and it always strikes me as basically a non-sequitor. You’re writing down two percentages as if they are meaningful with respect to one another, but they arent.

If we as a society agree that some sort of progressive tax system is good (based on the fact that the mere act of survival comes with fixed costs, that naturally impact low-wealth holders over high-wealth holders) then we presumably expect higher wealth people to shoulder a larger burden of the cost of maintaining society, relative to that wealth.

The top 1% hold >30% of all wealth in the US, which, by the logic I described above, makes your 40% figure sound not just not exorbitant, but possibly too low.

https://www.federalreserve.gov/releases/z1/dataviz/dfa/distr...

I would still say its completely wrong, given that this explanation makes explicit predictions that are falsifiable, eg, that airplanes could not fly upside down (they can!).

> Yep, for me it confirms all the reasons why I think python is slow

Yes, that is literally the explicit point of the talk. The first myth of the article was “python is not slow“

Very reasonable, I fully agree on that front

I thoroughly disagree with this sentiment.

In my experience, the most helpful approach to performing RCA on complicated systems involves several hours, if not days, of hypothesizing and modeling prior to test(s). The hypothesis guides the tests, and without a fully formed conjecture you’re practically guaranteed to fit your hypothesis to the data ex post facto. Not to mention that in complex systems there is usually 10 benign things wrong for every 1 real issue you might find - without a clear hypothesis, its easy to go chasing down rabbit holes with your testing.

Looks like your personal website isnt set up yet, its giving a wix error

I posted a very similar (perhaps more combative) comment a few months ago:

> Peoples’ memories are so short. Ten years ago the “well accepted definition of intelligence” was whether something could pass the Turing test. Now that goalpost has been completely blown out of the water and people are scrabbling to come up with a new one that precludes LLMs. A useful definition of intelligence needs to be measurable, based on inputs/outputs, not internal state. Otherwise you run the risk of dictating how you think intelligence should manifest, rather than what it actually is. The former is a prescription, only the latter is a true definition.

Not really. You can calculate the statistical significance of the difference of these measurements, which I’ve done here: https://www.mycompiler.io/view/4LA310YXZHO

For a null hypothesis of “their differences are consistent with zero”, the p-value is 17%, equivalent to a 1.4 sigma difference. That’s pretty far from a reasonable rejection criterion for the null hypothesis. I think most people would agree that that means these measurements are plausibly consistent.