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The thing that strikes me is how obviously nonsensical that is. It's not only a lie, it's someone straight up insisting that 2+2=5.

I'm frankly stumped by claims like those, I feel it's pointless to even debunk them (what is there to debunk? If you're willing to listen anybody qualified at all, you wouldn't believe it in the first place.)

Reminds me of this: https://en.wikipedia.org/wiki/Firehose_of_falsehood

HN post, just 14 hours ago: https://news.ycombinator.com/item?id=29773082

>> The thing that strikes me is how obviously nonsensical that is. It's not only a lie, it's someone straight up insisting that 2+2=5.

As Pauli said "It's not even wrong."

The article where they endorsed a presidential candidate for the first time in their history was pretty atrocious too - just based on out and out lying about what the US coronavirus response involved and how it compared to the rest of the world. It turns out that when you mix science and politics, all you're left with is politics that calls itself science and accuses its political opponents of attacking science.

I respected SA for that. And I think it was on topic for them given the anti-science sentiment transpired from one of the sides. And science will always be political.

> I respected SA for that. And I think it was on topic for them given the anti-science sentiment transpired from one of the sides.

One of the sides? Like Biden and Kamala saying they wouldn't trust the Trump vaccine?

The notion is that it was extremely fast delivery of a complex solution by an administration known to regularly stretch the truth when politically convenient (if not outright lie, c.f. inauguration crowd size and, now, response to the legitimate 2020 election).

The reality is that the mRNA vaccines were basically ready to go within a few weeks, and political dregs kept it from being approved even faster. But its inadvisable to change the bureaucratic infrastructure for disasters during disasters, and so here we are.

But yes, the crowd that Trump tends to seek support from is anti-science.

At risk of feeding the troll, but the vast majority of the US population are incompetent at science. There is a reason that science is the domain of people who are not only fairly smart but also carefully trained in how to make decisions based on evidence rather than social dynamics. While Trump's appeal is targeting people who are clearly scientifically-illiterate ... all politicians have messages crafted to appeal to scientific illiterates. There aren't enough scientifically competent people to even be a meaningful swing vote.

Every partisan is perfectly happy to claim that they are following science and usually fail to modify their behavior when confronted with actual science. That holds across the political spectrum. The Trump crowd aren't anti-science, they simply tend to anti-authority. I guarantee you that they're highly pro-science on the issues where the science agrees with them.

I’m baffled even pop pulp rag “editorial” leadership wouldn’t be familiar with the famous “stats don’t mean normal exists” examples dating back to the 1950s:

No “normal” man:

“Out of 4,063 pilots, not a single airman fit within the average range on all 10 dimensions. One pilot might have a longer-than-average arm length, but a shorter-than-average leg length. Another pilot might have a big chest but small hips. Even more astonishing, Daniels discovered that if you picked out just three of the ten dimensions of size — say, neck circumference, thigh circumference and wrist circumference — less than 3.5 per cent of pilots would be average sized on all three dimensions. Daniels’s findings were clear and incontrovertible. There was no such thing as an average pilot. If you’ve designed a cockpit to fit the average pilot, you’ve actually designed it to fit no one.“

And no “normal” woman:

“Before the competition, the judges assumed most entrants’ measurements would be pretty close to the average, and that the contest would come down to a question of millimetres. The reality turned out to be nothing of the sort. Less than 40 of the 3,864 contestants were average size on just five of the nine dimensions and none of the contestants — not even Martha Skidmore — came close on all nine dimensions. Just as Daniels’ study revealed there was no such thing as an average-size pilot, the Norma Look-Alike contest demonstrated that average-size women did not exist either.”

https://www.thestar.com/news/insight/2016/01/16/when-us-air-...

On the other hand, maybe the editor of Scientific American being unaware of this is why there’s room for a not so new book, “The End of Average”:

”Yet, as Rose, Ed.M.’01, Ed.D.’07, a lecturer at the Ed School and director of the Mind, Brain, and Education Program, writes in his forthcoming book, The End of Average, from the moment we’re born to the moment we die, we are measured against a mythical yardstick — the average human — and it’s hurting everyone. That’s why with this book and through his nonprofit, the Center for Individual Opportunity, Rose is on a mission to dismantle this myth of the average and instead help the public understand the importance of the individual.”

https://www.gse.harvard.edu/news/ed/15/08/beyond-average

http://www.toddrose.com/endofaverage

Note the difference here is that your examples use multiple dimensions at once. Assuming Gaussian distributions are a good fit, most of the population will look relatively normal on a single variable measurement. It’s only on multivariate measurements where this stops being true. Though this is exactly what the mode expects. Plot a 2D cross section of a 9 dimensional Gaussian curve and you’ll see the center lose its density very quickly.

I'll add a fast guess from some earlier, solid experiences: Let R be the set of real numbers and n a positive integer. Consider R^n, the common n-dimensional space. Assume this Rn is Euclidean, that is, has the usual inner product, norm, metric, topology, and measure (area, volume, e.g., in the sense of classic Lebesgue measure* theory). With this overly detailed description of context (WHEW!), we move on to the main point:

In the R^n, consider a sphere. To be more clear, for some positive real number r, consider the set of all points in R^n with distance <= r from the the origin, that is, the point in R^n with zeros in all its coordinates.

Now for the big point: Consider the volume of that sphere and let n grow. Will discover that very soon nearly all the volume of the sphere is in a thin shell just inside the surface of the sphere. Or to be more explicit, for positive real number s a little less than r, nearly all the volume is in the set of points x where the distance from the origin d(x) is

s <= d(x) <= r

I encountered this in some analysis, I have forgotten, maybe generation of random points in the sphere independent and uniformly distributed in the sphere.

So, for the 10 or so body measurements of the pilots and the women, it's going to be tough (small probability for nearly any reasonable, non-pathological probability distribution on the sphere) to expect all 10 measurements to be close to the expectations, i.e., the center of the sphere (for people, the center will not be at the origin, that is, all n coordinates zero).

There is a counterexample: The girl I dated in high school, the most beautiful female I ever saw, in person or otherwise, was essentially perfect on all dimensions!

I agree. More details that may be helpful for the GP.

One trick to compare dimensions is to assume each one is somewhat a normal distribution, but each one has a different mean and variance. It makes no sense to add the difference from the average height in inches and the difference from the average weight in pounds.

It's better to divide each difference by the variance, to remove the problems with choosing the scale. Also, it's better to sum the squares of them, for technical reasons. Pulling numbers out of the air, it's something like

Points = ((height-60inches)/8inches)^2 + ((weigh-120pounds)/7pounds)^2 + ...

[I just invented some numbers. I'm too lazy to lookup some realistic numbers. I live in a metric country, so I may even had a bad conversion.]

And in the contest, they had 9 variables, so it's a long ...

What is the expected distribution of something like this?

If you have only one variable, then you expect that most people will get near 0 points. But each variable you add, the distribution changes, and most people will be further away from 0. There are some graphics of this in https://en.wikipedia.org/wiki/Chi-squared_distribution and get even more technical details. With 3 variables, most people will be close to 1 point, but with 9 variables most people will be close to 7 points.

With real data is more complicated, because the distributions are not normal. Also, there is correlation, and this model assumes no correlation. (For example tall people use to weight more.) So it's a very simplified model, but it's useful in some cases.

This is a standard part of any statistic course, perhaps the first or second course, but it's not cutting edge math.

>>> Before the competition, the judges assumed most entrants’ measurements would be pretty close to the average, and that the contest would come down to a question of millimetres. The reality turned out to be nothing of the sort.

Going from ideal mathematical models to real cases it's always difficult. In the contest the variables have correlation, and it's not a random sampling because the selection process have strong bias. But with 9 variables anyone that took a statistics course will expect a result like this, where nobody is too close to the average in all measurements.

> Which was, frankly, shocking to see coming from Scientific American, something I had assumed was a respectable scholarly publication

TBF SciAm has been popsci since the 50s (before that it was mostly about new patents apparently, the original styling was "The Advocate of Industry and Enterprise" and the "Journal of Mechanical and other Improvements").

It's never been a scholarly publication per se, though it used to be pretty respectable in the sense that reading sciam is what you'd do if you were well-read middle-class and weren't going to read the papers and reports straight but wanted to keep abreast of the major stuff. The "level of depth" so to speak has varied a lot since it switched to popsci. But the recent years are some pretty damn shallow levels.

The problem with the cult of The Science is that like all religions it needs outs when the actual data and science contradicts the faith. This is where the "math is racist" type of craziness comes from.

I think most of the problem with the statement is that it is ambiguous. If she is saying that the Gaussian distribution is used because it assumes there exists people who are the mean average representatives of humanity; then she is just failing to understand what the law of large numbers implies about the distribution of sample mean(X) regardless of the distribution of X.

If on the other hand she is saying that a problem in healthcare is that significantly different sub-populations are lumped together resulting in inappropriate benchmarks for some sub-populations, that is more palatable. Even if this latter interpretation is not true, at least it isn't false by definition.

it's like reading something from Derrida.. you have to abandon all assumption that technical terms mean what they're supposed to

When you sample a population you infer the type of distribution and try to sample it in a way that respects the distribution properties, because that can have a great impact on the results.

I'm afraid most people here criticizing her normal distribution remarks are oversimplifying it much more than her.

Very funny how you are doing more of that Derrida thing yourself.

The problem with the claim lies in the attempt to associate a strictly technical concept (the normal distribution) to $GENERIC_BAD_STUFF with nothing more than vague wordplay.

Also, just FYI, you have it the other way around. When you sample from a population, you (usually) assume a certain distribution (at most you infer parameters). For example, if you're sampling for opinion polls, you would actually want to oversample minorities and then correct back.

Sorry, I meant assume instead of infer. *not english native.

I think most of the problem with the statement is that it is ambiguous. If she is saying that the Gaussian distribution is used because it assumes there exists people who are the mean average representatives of humanity; then she is just failing to understand what the law of large numbers implies about the distribution of sample mean(X) regardless of the distribution of X.

If on the other hand she is saying that a problem in healthcare is that significantly different sub-populations are lumped together resulting in inappropriate benchmarks for some sub-populations, that is more palatable. Even if this latter interpretation is not true, at least it isn't false by definition.

The author’s word salad honestly doesn’t qualify as ‘remarks about the normal distribution.’ The author is wildly flinging random technical terms around. Try substituting ‘normal distribution’ with ‘exponential distribution’ or simply with ‘collecting data’. You can draw two possible conclusions from that sentence: either the author believes that observing data or —- horror —- drawing it is racist, a violently anti-knowledge stance, or the author is stringing words together like GPT-3 in hopes of sounding woke. This kind of discourse is an insult to science and an embarrassment to the journal.