If you’ve been reading my “week in woke posts you’ll know that a number of American right-wingers rooted against American athletes at the Olympics — because the athletes representing the US were supposedly too “woke” for their own good, more concerned with political correctness than with patriotism.

Some of these right-wingers took it another step, going on to argue that all this “wokeness” was actually *causing *individual athletes and teams to fail. Donald Trump endorsed this bit of magical thinking in a statement he put out after the American women’s soccer team picked up an uninspiring bronze medal instead of the gold one that had generally been expected.

“Woke means you lose,” Trump declared,

everything that is woke goes bad, and our soccer team certainly has. …

They should replace the wokesters with Patriots and start winning again.

But there are a couple of little problem with this, er, hypothesis: first, it’s utterly illogical, in that “wokeness” has no effect on performance, and second, it’s not true, at least when it comes to the performance of American athletes in the Tokyo Olympics.

True, the “woke” American women’s soccer team did a bit worse than expected, but, as Aaron Blake notes in the Washington Post, most of America’s supposedly too-woke-to-perform athletes actually did fine.

Sure, he points out, early losses by America’s Women’s soccer team and men’s basketball team seemed to provide evidence for the “get woke, go broke” narrative.

The culprit was quickly identified: The athletes were too focused on being “woke” and not focused enough on winning. Maybe if they would just “shut up and dribble,” the United States would win more medals. For most of the Olympics, the United States trailed in gold medals behind China, of all places.

Well, guess what: some of the most-criticized “wokesters” ended up at the top of the podium.

[D]espite their early stumble against France, the men’s basketball team wound up winning gold. Ditto the women’s basketball team, whose players and professional league have been more socially progressive than in any other major American sport.

And even the Women’s soccer team contributed a medal to the Americans’ collection.

If you look at the big picture, Blake points out, America’s team didn’t do too poorly at all. For one thing, they won the medal count.

With the Olympics over, the final results are in. And the argument, to the extent it should have been taken seriously in the first place, isn’t really that compelling.

The U.S. team has won the most medals at every Summer Olympics since 1992, and it did so again in this one, taking home 113. …

It wound up eventually edging out China on gold medals, too, 39 to 38.

As for women’s soccer, the irony is that the team that *did *win the gold — Canada — was, well, basically more “woke” then the team with the bronze. As Blake notes, the Canadian team

also knelt in support of racial-justice protests, and it was a focal point because one player was the first openly transgender athlete to medal at an Olympics. The team also … wore pro-transgender-rights armbands in scrimmages.

Wokesters 1, “Patriots” 0.

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@ surplus

Very few stone circles are actually circular.

Now obviously people in the Neolithic were capable making true circles; it’s not exactly hard so long as your culture has invented string.

Most though are various forms of ellipsoid. And we keep seeing recurring designs; which suggests it’s purposeful.

One theory is that Neolithic people were aware of the irrationality of Pi; and they didn’t approve (I’m the same) so they were trying to get circumferences that are integer ratios of the axes.

Or it may be they just liked ovals.

All pretty fascinating though.

Pretty rare to see someone using the term “sophont”¹. Also, a few species of wild pigs have been seen using chunks of bark to dig (as a learned behavior, not an instinctive one), and bottlenose dolphins have occasionally been seen using various objects as tools.

¹From how I’ve generally seen it used, “Sophont” means able to understand and engage in the duties and responsibilities of living in a complex society.

As for math, I occasionally wonder if there’s a subtle but fundamental flaw in the way we symbolically manipulate numbers, in which case math as we know it may not be as fundamental as we think. Though I suspect that if anyone was ever able to prove it, the chance of adopting something better would be about the chance of switching from base 10 to the superior base 12, i.e. due to inertia we’re stuck with it.

(For example, some of the arguments why you can’t divide by zero sound like special pleading. For example, it’s supposedly not infinity because if you project what happens when you approach 0 on the complex plane, it converges at both infinity and negative infinity and “obviously” it can’t be both. Except when you use that same proof the square root of 4 converges at both 2 and -2. That’s just one example of many things about math which seem questionable to a lot of people; things like this hint that, even if there’s no usable system where you can do the equivalent of dividing by 0, or make some of the other unintuitive quirks or apparent holes in the system go away, some of our working definitions might be arbitrary and less than optimal.)

@Snowberry

This is because we’re the only known* example. The term was made up by sci-fi writers/fans as a shorthand way of distinguishing between fictional nonhuman people and fictional nonhuman animals/monsters.

*Some corvids are iffy.

@Alan

It was too long to go around.

@Snowberry:

Well, with the value of the tangent of an angle (basically the height at which a line projected out in both directions from the centre of a circle intersects a vertical line tangent to the circle on one side) it whips around from positive to negative infinity when the angle hits 90 degrees (at which point the line projected out is vertical). In a lot of cases in math, positive and negative infinity are the same thing, and that’s a lot more obvious if you look at situations like the value of the tangent function.

Interestingly, there are systems where it’s easier to ‘wrap around’ the far side between infinity and negative infinity than it is to go between a really small positive number and a really small negative number. (I think this was in an old usenet sci.physics FAQ about negative temperatures, somebody defined the temperature of a magnetic spin system based on entropy so that it acted just like how we normally think of temperature as far as the math was concerned, and it turned out that under that definition ‘negative’ temperatures were higher than ‘positive’ ones, and you still couldn’t actually reach absolute zero from either direction, but you could go through and past infinity easily.)

@Insurgency

You mean it’s a game community intended to appeal to white supremacists, fascists, anti-women Misogynists and any other such ilk who think any women advocating to not be treated like an inferior doormat and sex doll for men is a “radical feminist” that deserves to be assaulted or worse? Or who operating under the myopic and defunct logic of “Arab=Muslim=Terrorist” and who think people of color and LGBT people having rights and equality is part of a “Jewish Conspiracy to enact white genocide”.

Your assertions that Insurgency is “a game designed for grown people with commonsense” strikes as a hollow falsehood given that nonse of those canards come from people I would call anything save childish and estranged from any form of rationality or commonsense. Your just a bunch of immature, deluded, co-morbidly bigoted troll man-baby’s with more hate than brains.

It’s a good thing David yeeted you out of here so actual functional human beings with any measure of critical thinking, objectivity, consideration and basic ethics and decency can actually talk shop without your nonsense waffling.

Speaking of rock climbing, seems like it’s just about even men/women these days at the crag. That’s a big change from when I started roughly 20 years ago.

@ numerobis

There was an interview with a particular free climber. She was asked why she took up such a risky sport. Her explanation was that she liked climbing but she didn’t want to pay for all the expensive equipment.

That’s the most Yorkshire thing I’ve ever heard.

@Alan Robertshaw:

Well, Alex Honnold always says in interviews that he got into solo climbing because he was too nervous, when he started out, to ask anyone if he could climb with them.

@Snowberry:

As for math, I occasionally wonder if there’s a subtle but fundamental flaw in the way we symbolically manipulate numbers, in which case math as we know it may not be as fundamental as we think. Though I suspect that if anyone was ever able to prove it, the chance of adopting something better would be about the chance of switching from base 10 to the superior base 12, i.e. due to inertia we’re stuck with it.I presume 12 is superior as an abundant number, allowing partitions by 2, 3, 4, and 6? (Somebody’s idea that the Gallifreyans had a

septenarymathematical system just slammed my shenanigans button: aprime?Did they even remotely think out how that was supposed to work, or was this something they tossed in just to be whimsically different? Any Mammotheers with an actual mathematical education are not only welcome but invited to put me in my place.)@ full metal ox

I think we’ve mentioned before about the

Yan Tan TetheraBase 20 system for counting sheep.That seems pretty old, and suggests that Base 20 was used generally in t’olden days.

Kernewek (Cornish) has a Base 20 number system

ETA: Ah, it seems that’s a Brythonic Celtic thing…

ETAA: I’v heard the old “Eeeny Meeny Miny Mo…” thing may be the remnants of an old counting system.

@Alan Robertshaw:

The fact that ‘score’ as a counting method still exists in English, even if it’s considered a bit archaic, and even the fact that all the numbers from 11-20 have their own names, certainly suggests that counting by 20s was a common thing. Honestly, the fact that ‘eleven’ and ‘twelve’ have explicit names while every other number between there and 20 is x-teen where ‘x’ is a derivation of the original number makes you wonder as well, especially since that shift at 12 seems to apply to many of the Indo-European languages.

It’s even more interesting in French, where counting up from fifty goes fifty, fifty-one, … , fifty-nine, sixty, sixty-one, … , sixty-nine, sixty-ten, sixty-eleven, … , sixty-nineteen, four-score, four-score-one, … , four-score-nine, four-score-ten, four-score-eleven, … , four-score-nineteen, one hundred. There’s remnants of both a base 20 and a base 60 system in there, and that’s on top of the base sixty stuff we still have in terms of time units where hours get divided into ‘pars

minutaprima’ (first small part) and then ‘pars minutasecunda‘ (second small part).Bases 12, 20, and 60 have all been widely used in the past, and all still have historical artifacts left today. It’s just that, eventually, people realize that using different bases for different things just causes way too many problems when you have to deal with converting units.

(I think that Babylonian systems used a base 60 system that was effectively alternating between base 10 and base 6 in the digits, rather than having 60 different possible digits, though I may be thinking of something else.)

@ jenora

I’d never spotted that before! Although it’s so obvious now (“The hat goes on the head!”). But that does very much suggest a Base 12 background.

And thank you for the etymology on

minutesandseconds. I didn’t know that either.This seems apposite.

@Jenora : also, french have individual name for figure from 1 to 16. THere’s also words for 10ish, 12ish and 15ish, but not for any other amount (not even 16ish even tho it’s the last irregular number !)

It’s basically a mess I guess. But without the officers.

@Alan Robertshaw:

The derivation of ‘minute’ and ‘second’ (as time units) and the fact that both of them being the same as other words (‘small’ and ‘ordinal number of two’) is not a coincidence, is one of those things that almost nobody knows but is so blindingly obvious when you do notice it, yes.

(There was a snarky comment in the web comic Schlock Mercenary where somebody who’s very close to dying but who has nanobots in his bloodstream says ‘Carpe Diem’, and the sort of collective intelligence of the nanobots responds ‘You don’t have a Diem, you have thirty Pars Minuta Secundae, and you’ll have to Carpe them all very carefully.’)

@Ohlmann:

You’re right, that was my mistake. French does go for special names out to ‘quinze’, and I think Spanish does as well (though my knowledge of Spanish counting is vaguely remembered old Sesame Street), but German is like English in that it shifts over after twelve.

Some more fun number facts, for those who find it fun:

Once units of time significantly smaller than a second were needed, there was an attempt to standardize it as 1/60th of a second for the “third” unit, 1/60th of that for a “fourth”, and so on, but that never caught on. Instead they ended up using hundredths of a second until even smaller units were needed. What did catch on in a very limited way was a unit of time called a “jiffy” (1/64th of a second) which was used by some early computers for their internal clocks.

Aside from counting things in 10s, 12s, 20s, and 60s, there have also been cultures which have counted things in 4s, 5s, 6s, 8s, 9s, 15s, 16s, 27s, 32s, and 64s (the latter only by ancient Egyptians in one of their fractional systems, of which they had three). Of these, only 5s and 8s were anything close to common, though. I suppose you could include “Alphanumeric” which uses 0-9 and A-Z for base 36, but does anyone actually use that?

Sumerians were all over the place; they counted things in 6s, 8s, 9s, and 10s (and as far as I’m aware, they’re the only culture which used base 9 for anything). Towards the end of their civilization, they developed an alternating base 10/6 system for complex math, which the Babylonians copied, and became the basis for doing things in 60s.

Number systems with alternating bases are called “dual radix”. Aside from 10/6, there’s also 5/2 (Roman Numerals), 5/4 (Mayan, though only in their writing system and not with spoken numbers) and 8/4 (a few North American cultures used this; it’s why there’s a 32 on the list). And no, base 27 isn’t 9/3, the Oksapin system literally used 27 digits.

The reason why we have 24 hours in a day was due to the Sumerians using sun clocks and measuring 6 hours from noon to sunrise and 6 hours from noon to sunset. And while there were theoretically 6 more hours each way measured from midnight, sun clocks don’t work in the dark. So it was originally more like 6/4 than 12/2. Or possibly 6/2 with time before noon or midnight effectively expressed as a negative number.

Romans used decimals in base 12 (6/2) rather than base 10. They indicated decimals by writing the fractional portion of the number backwards, which did have the awkwardness of sometimes being ambiguous out of context. It’s also why troy ounces are in 12s rather than 16s.

The benefits of using base 12 is that, aside from the partitioning thing Jenora mentioned earlier, multiplication and division are actually a bit easier despite the larger multiplication table (not that this matters much anymore as everyone these days uses a calculator app) and has a side benefit that really big numbers are usually slightly more comprehensible (on an abstract level; most people don’t find really big numbers to be fully comprehensible regardless of number system) due to having fewer digits. While the fewer digits thing is even more of an advantage with higher bases, go much higher than 12 and the multiplication and addition tables get too big to easily memorize and people generally had to consult charts to do math, more than negating that particular advantage.

There is an actual reason to use base 7; it plays weirdly nice with some irrational numbers. For example, π≈3.1 and √2≈1.3, and those are really close. You’d have to be really dedicated to that particular minor convenience to reasonably want to use it, though.

It’s possible to use an irrational base, a fractional base, or even a negative base – though the latter is pretty strange in that it erases any meaningful distinction between positive and negative numbers while still being able to fully represent both, and more digits doesn’t always make for larger numbers. I’m not sure what that does to imaginary numbers.

TL;DR Much math history and nerdery.

@ snowberry

That was all really interesting; thank you!

I saw a great little video about cultures that use clocks not based on 12/24 hours.

Some use different divisions but all of the same length; but others have different length hours, like that compressing nighttime thing you mentioned.

One thing I especially liked was places that had sort of ‘rollover’ hours. Like if you stay up late after midnight it becomes 13 o’clock, 14 o’clock etc. That really appeals to me as that’s sort of my innate feeling. To me it’s not ‘tomorrow’ until I’ve been to bed; even if I’ve stayed up all night and it’s now daylight again.

When I started reading historical novels in English, it took me a while to figure that score means twenty. IDK if there is/was an equivalent in Swedish, but otherwise Swedish numbers seem very much cognate with English.

In Finnish (a Uralic language), there’s nothing like special names for numbers above 10. Twenty is “two tens” and numbers 11-19 are called “x of second”, apparently referring to counting rounds in ten-base system. Historically, numbers 21-29, 31-39 and so on were often called “x of third/fourth/etc” but the modern formula is “two-tens-x” and so on.