yshklarov

You are correct if you mean a 2-sphere, but a spherical shell in space-time would be a 3-sphere, which gives quite a lot more information. To make things a bit simpler we could consider a 2-sphere × an interval -- the boundary of a 4-dimensional cylinder -- which is to say, your spherical shell at all points in time from t_0 to t_1, and also the entire interior of the spatial region at both the initial time t_0 and the final time t_1.

Indeed. A "violation of logic and geometry"? Reading the author's own description, it's hard to see what the big deal is:

"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.

Thanks!

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.

Great article, but the lack of sentence capitalization makes it unnecessarily difficult to read.

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.

We love to do work that is useful and valuable to others, and we often form our identities around this. But identities are in large part socially constructed, so many of us need the recognition of others for our contribution. And it can be very painful when we perceive that the credit for our life's work got "stolen". Naturally, we fight against this. There's nothing shameful there. Sure, you can hold onto an ideal of egoless service. There's nothing wrong with that, either. But it's misanthropic to pass such harsh judgment on people for behaving in such a normal and natural manner.

That observed fatality rate, 2, is too low to give a precise estimate of the mean. If we assume fatalities follow a Poisson process, then it's plausible (at 5% significance level) that the true expectation is only 0.36 deaths, not 2.

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

It has nothing to do with being easier to work with (at least, not in this day and age). The biggest reason is that minimizing sum of squares of residuals gives the maximum likelihood estimator if you assume that the error is iid normal.

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 <predictor>"). 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.

We have no evidence that the lead in solder makes its way into the body of the person doing the soldering (and we've been at this for quite some time!). The concerns about lead in solder are due to the environmental hazards of electronics waste, and the hazards associated with mining and smelting lead.