Yesterday I took a hike in the Alps. This was my favorite Alp. It's not so tall as Alps go, but it's quite steep and remarkably green.
Lisa was attending a conference near Bern. It was called The Art of Feeling. That sounds strange, but it was about classical Greek and Chinese philosophy, and how they understood the role of the emotions in the good life. Since Lisa knows both classical Greek and classical Chinese, and not too many people do, I've gotten to know most of the people who do, and I wind up hanging out with them in unusual places. This particular conference was held in the countryside, near the town of Rubigen, in a place that's a kind of graduate school for farmers. It had cows and pigs and gardens but also classrooms and dorm rooms, and for some reason they let a bunch of philosophers pay to stay there for a few days.
One important feature of academic conferences is the 'excursion'. If you're not an academic you may not know what this is, but if you are you surely do. About halfway through the conference, when people are getting sick of spending 8 hours a day cooped up in a room listening to talks, the organizers take people out to one of the beautiful nearby places where everyone would rather have been all along. Then people have fun, stay up too late talking and drinking, and come in bleary-eyed and grumpy to the next day's talks.
This particular excursion was especially fun: a hike through the low Alps near Gurnigel Pass, about 35 kilometers south of Bern. It was a beautiful day, and we had a nice view of the more serious Alps further south: Eiger, Mönch and Jungfrau. They were distant, snowy, forbidding yet alluring. We didn't even get anywhere near this smaller, greener mountain! But it was fun to see. It may be called Nünenenfluh.
Far above a thunderstorm in the English Channel, red sprites are dancing in the upper atmosphere.
You can't usually see them from the ground — they happen 50 to 90 kilometers up. People usually photograph them from satellites or high-flying planes. But this particular bunch was videotaped from a distant mountain range in France by Stephane Vetter, on May 28th.
Sprites are quite different from lightning. They're not electric discharges moving through hot plasma. They involve cold plasma — more like a fluorescent light.
They're quite mysterious. People with high speed cameras have found that a sprite consists of balls of cold plasma, 10 to 100 meters across, shooting downward at speeds up to 10% the speed of light... followed a few milliseconds later by a separate set of upward moving balls!
Sprites usually happen shortly after a lightning bolt. And about 1 millisecond before a sprite, people often see a 'sprite halo': a faint pancake-shaped burst of light approximately 50 kilometres across 10 kilometres thick.
Don't mix up sprites and ELVES — those are something else, for another day:
You also shouldn't confuse sprites with terrestrial gamma-ray flashes. Those are also associated to thunderstorms, but they actually involve antimatter::
A lot of weird stuff is happening up there!
The photo is from here:
There's a website called Math StackExchange where people ask and answer questions. When hard integrals come up, Cleo often does them — with no explanation! She has a lot of fans now.
The integral here is a good example. When you replace \(\ln^3(1+x)\) by \(\ln^2(1+x)\) or just \(\ln(1+x)\), the answers were known. The answers involve the third Riemann zeta value: $$ \zeta(3) = \frac{1}{1^3} + \frac{1}{2^3} + \frac{1}{3^3} + \frac{1}{4^3} + \cdots $$
They also involve the fourth polylogarithm function: $$ \mathrm{Li}_4(x) = \frac{x}{1^4} + \frac{x^2}{2^4} + \frac{x^3}{3^4} + \cdots $$
Cleo found that the integral including \(\ln^3(1+x)\) can be done in a similar way — but it's much more complicated. She didn't explain her answer... but someone checked it with a computer and showed it was right to 1000 decimal places. Then someone gave a proof.
The number $$ \zeta(3) = 1.202056903159594285399738161511449990764986292... $$
is famous because it was proved to be irrational only after a lot of struggle. Apéry found a proof in 1979. Even now, nobody is sure that the similar numbers \(\zeta(5), \zeta(7), \zeta(9),\dots\) are irrational, though most of us believe it. The numbers \(\zeta(2), \zeta(4), \zeta(6), \dots\) are much easier to handle. Euler figured out formulas for them involving powers of \(\pi\), and they're all irrational.
But here's a wonderful bit of progress: in 2001, Wadim Zudilin proved that at least one of the numbers \(\zeta(5), \zeta(7), \zeta(9),\) and \(\zeta(11)\) must be irrational. Sometimes we can only snatch tiny crumbs of knowledge from the math gods, but they're still precious.
For Cleo's posts, go here:
For more on \(\zeta(3)\), go here:
This number shows up in some physics problems, like computing the magnetic field produced by an electron! And that's just the tip of the iceberg: there are deep connections between Feynman diagrams, the numbers \(\zeta(n)\), and mysterious mathematical entities glimpsed by Grothendieck, called 'motives'. Very roughly, a motive is what's left of a space if all you care about are the results of integrals over surfaces in this space.
The world record for computing digits of \(\zeta(3)\) is currently held by Dipanjan Nag: in 2015 he computed 400,000,000,000 digits. But here's something cooler: David Broadhurst, who works on Feynman diagrams and numbers like \(\zeta(n)\), has shown that there's a linear-time algorithm to compute the \(n\)th binary digit of \(\zeta(3)\):
He exploits how Riemann zeta values \(\zeta(n)\) are connected to polylogarithms... it's easy to see that $$ \mathrm{Li}_n(1) = \zeta(n) $$ but at a deeper level this connection involves motives. For more on polylogarithms, go here:
Thanks to David Roberts for pointing out Cleo's posts on Math StackExchange!
June 27, 2017
How did the publisher Elsevier get profit margins of 37% last year -
higher than almost any other business? Simple: get people to work for
free, then sell their product at high prices!
But how do you do that? Over on Google+, Richard Poynder pointed out this great article which explains the history:
Maxwell's success was built on an insight into the nature of scientific journals that would take others years to understand and replicate. While his competitors groused about him diluting the market, Maxwell knew that there was, in fact, no limit to the market. Creating The Journal of Nuclear Energy didn't take business away from rival publisher North Holland's journal Nuclear Physics. Scientific articles are about unique discoveries: one article cannot substitute for another. If a serious new journal appeared, scientists would simply request that their university library subscribe to that one as well. If Maxwell was creating three times as many journals as his competition, he would make three times more money.Later, publishers got more systematic about making their journals "prestigious"... so scientists would want to publish in them... and get their universities to subscribe to these journals:
"At the start of my career, nobody took much notice of where you published, and then everything changed in 1974 with Cell," Randy Schekman, the Berkeley molecular biologist and Nobel prize winner, told me. Cell (now owned by Elsevier) was a journal started by Massachusetts Institute of Technology (MIT) to showcase the newly ascendant field of molecular biology. It was edited a young biologist named Ben Lewin, who approached his work with an intense, almost literary bent. Lewin prized long, rigorous papers that answered big questions — often representing years of research that would have yielded multiple papers in other venues — and, breaking with the idea that journals were passive instruments to communicate science, he rejected far more papers than he published.What he created was a venue for scientific blockbusters, and scientists began shaping their work on his terms. "Lewin was clever. He realised scientists are very vain, and wanted to be part of this selective members club; Cell was 'it', and you had to get your paper in there," Schekman said. "I was subject to this kind of pressure, too." He ended up publishing some of his Nobel-cited work in Cell.
Suddenly, where you published became immensely important.
Read the whole story! It's depressing, but we need to understand why we're in this mess to get out of it.
Also, read Richard
Poynder's posts on Google+, to keep track of the scholarly
publishing world and attempts to fix it.
June 30, 2017
Today Sabine Hossenfelder wrote a nice attack on 'naturalness' in
physics:
Many particle physicists prefer theories where these constants are not incredibly huge and not incredibly tiny. They call such theories 'natural'. Naturalness sounds good — just like whole wheat bread. But there's no solid evidence that this particular kind of naturalness is really a good thing. Why should the universe prefer numbers that aren't huge and aren't tiny? Nobody knows.
For example, many particle physicists get upset that the density of the vacuum is about
0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
Planck masses per Planck volume. They find it 'unnatural' that this number is so tiny. They think it requires 'fine-tuning', which is supposed to be bad.
I agree that it would be nice to explain this number. But it would also be nice to explain the mass of the muon. Is it really more urgent to explain a tiny number than a number like 206.768, which is neither tiny nor huge?
Sabine Hossenfelder say no, and I tend to agree. More precisely: I see no a priori reason why naturalness should be a feature of fundamental physics. If for some mysterious reason the quest for naturalness always, or often, led to good discoveries, I would support it. In science, it makes sense to do things because they tend to work, even if we're not sure why. But in fact, the quest for naturalness has not always been fruitful. Sometimes it seems to lead us into dead ends.
Besides the cosmological constant, another thing physicists worry about is the Higgs mass. Avoiding the 'unnaturalness' of this mass is a popular argument for supersymmetry... but so far that's not working so well. Hossenfelder writes:
Here is a different example for this idiocy. High energy physicists think it's a problem that the mass of the Higgs is 15 orders of magnitude smaller than the Planck mass because that means you'd need two constants to cancel each other for 15 digits. That's supposedly unlikely, but please don't ask anyone according to which probability distribution it's unlikely. Because they can't answer that question. Indeed, depending on character, they'll either walk off or talk down to you. Guess how I know.Now consider for a moment that the mass of the Higgs was actually about as large as the Planck mass. To be precise, let's say it's 1.1370982612166126 times the Planck mass. Now you'd again have to explain how you get exactly those 16 digits. But that is, according to current lore, not a finetuning problem. So, erm, what was the problem again?
She explains things in such down-to-earth terms, with so few of the esoteric technicalities that usually grace discussions of naturalness, that it may be worth reading a more typical discussion of naturalness just to imbibe some of the lore.
This one is quite good, because it includes a lot of lore but doesn't try too hard to intimidate you into believing in the virtue of naturalness: