In case anyone else is wondering why the meter is so awkward: It turns out that in the original this passage was prose, not poetry. Source: https://www.universitychurch.ox.ac.uk/sermons/devotions-upon...

"Put a box around any region of space (space-time, really, but I’m going to drop time throughout this essay for ease of visualization, as physicists often do). The holographic principle asserts that no matter what’s going on inside — from gas molecules pinging around to black holes colliding — you can decipher the entire contents of the box just by repeatedly measuring points on the surface."

Well, if we're bounding a region of space-time then, in a purely classical universe governed by deterministic ODEs or PDEs, the statement reduces to a triviality: having information about the boundary amounts to knowing all boundary conditions. Of course I understand that this isn't really the statement of the holographic principle, but the article's formulation is rather underwhelming.

To expand a bit: It's clear from the writing that the formatting is an intentional stylistic choice. My point wasn't about aesthetic preference. I meant precisely what I wrote. Language evolves and orthography evolves. We've been capitalizing less and less for centuries now. But (until very recently) it was a universal rule to capitalize the first letters of sentences. I believe this is partly because (again, until very recently) people read in large quantities and, to a fluent reader, sentence capitalization serves an important purpose: it helps the eye recognize where one sentence ends and the next begins. Periods alone can be easy to miss, or confuse for commas, when the eye is moving quickly.

Anyway, this is all a very minor point. You have a cool site and I enjoyed your article. I hope you keep writing.

Apologies if this comment is off-topic, but it really is quite egregious, and since the article was submitted by the author I presume they are open to the feedback.

So it's more useful to look at serious injury statistics as a proxy. For those, Waymo says that there is a significant reduction.

Comments URL: https://news.ycombinator.com/item?id=47200641

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https://math.stackexchange.com/questions/2140493/counterintu...

If your model is different (y = Ax + b + e where the error e is not normal) then it could be that a different penalty function is more appropriate. In the real world, this is actually very often the case, because the error can be long-tailed. The power of 1 is sometimes used. Also common is the Huber loss function, which coincides with e^2 (residual squared) for small values of e but is linear for larger values. This has the effect of putting less weight on outliers: it is "robust".

In principle, if you knew the distribution of the noise/error, you could calculate the correct penalty function to give the maximum likelihood estimate. More on this (with explicit formulas) in Boyd and Vandenberghe's "Convex Optimization" (freely available on their website), pp. 352-353.

Edit: I remembered another reason. Least squares fits are also popular because they are what is required for ANOVA, a very old and still-popular methodology for breaking down variance into components (this is what people refer to when they say things like "75% of the variance is due to "). ANOVA is fundamentally based on the pythagorean theorem, which lives in Euclidean geometry and requires squares. So as I understand it ANOVA demands that you do a least-squares fit, even if it's not really appropriate for the situation.

Comments URL: https://news.ycombinator.com/item?id=45646540

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Comments URL: https://news.ycombinator.com/item?id=45135659

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In any case, they are a bit more advanced, and out of scope for the undergraduate course I linked to.

This lecture by Dennis Freeman from MIT 6.003 "Signals and Systems" gives an intuitive explanation of the connections between the four popular Fourier transforms (the Fourier transform, the discrete Fourier transform, the Fourier series, and the discrete-time Fourier transform):

https://ocw.mit.edu/courses/6-003-signals-and-systems-fall-2...

How do you compute the fractional FT? My guess is by interpolating the DFT matrix (via matrix logarithm & exponential) -- is that right, or do you use some other method?

I also once made my own variant of this (just like gregfjohnson's idea): A "lucky minesweeper" where luck can be toggled on/off at any point during the game: https://github.com/yshklarov/minesweeper

"From the point of view of software engineering, the rapid spread of C represented a great leap backward. It revealed that the community at large had hardly grasped the true meaning of the term “high-level language” which became an ill-understood buzzword."

Source: Niklaus Wirth, A Brief History of Software Engineering, 2008 (https://people.inf.ethz.ch/wirth/Miscellaneous/IEEE-Annals.p...)

In my view, having a single lingua franca is nice. It better facilitates knowledge transfer. I wouldn't want to see a fracturing where each area of knowledge (or, say, every specialization/application programming) is best treated in a distinct linguistic community. That would be bad for everyone.