Damus
John Carlos Baez profile picture
John Carlos Baez
@John Carlos Baez

I'm a mathematical physicist who likes explaining stuff. I'm the Maxwell Fellow of Public Engagement at the School of Mathematics and the School of Physics and Astronomy at the University of Edinburgh.

Check out my blog Azimuth! I'm also a member of the n-Category Café, a group blog on math with an emphasis on category theory. I also have a YouTube channel, full of talks about math, physics and the future.

Relays (1)
  • wss://relay.ditto.pub – read & write

Recent Notes

John Carlos Baez profile picture
BIOMIMETIC TECHNOLOGIES

How can we learn from nature? One of the most obvious ways is to look at natural systems and design technologies based on them. These are called biomimetic technologies. A single example can illustrate some of the issues that arise.

Termites maintain nearly constant internal temperatures in their mounds through a system of channels. They don’t need fans that require power. For a time, it was believed that they used a simple convective cooling system, where hot air rises through the central chimney, drawing in cool air at the base. In 1996, a large office and retail building was built based on this idea: the Eastgate Centre in Harare, Zimbabwe, designed by the architect Mick Pearce [TS]. It has chimneys and ventilation channels that draw cool night air through the building’s thermal mass. It uses roughly 90% less energy for climate control than a conventional building of comparable size! That translates directly into far lower carbon emissions from heating and cooling.

This success inspired emulation. Pearce himself used similar termite-chimney-inspired designs in a Melbourne office building [HB]. More recently the Startup Lions Campus in Kenya, designed by Kéré Architecture on the banks of Lake Turkana, features three tall terracotta-colored ventilation towers modeled after local termite mounds.

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[TS] Turner, J.S. & Soar, R.C. (2008). Beyond biomimicry: What termites can tell us about realizing the living building, Proc. I3CON, p. 18.

[HB] Hes, D. & Bayudi, R. (2005). Council House 2 (CH2), Melbourne CBD: a green building showcase in the making. Proceedings of Conference on Sustainable Building South East Asia, pp. 231-241.

John Carlos Baez profile picture
1/1² - 1/2² + 1/4² - 1/5² + 1/7² - 1/8² + ⋯

Together with Calegari, Dimitrov and Tang proved this number is irrational... and they just won a $100,000 prize!

It's the biggest advance in irrationality since Apéry showed

ζ(3) = 1/1³ + 1/2³ + 1/3³ + ⋯

is irrational back in 1978. But I should emphasize that it's just the tip of what Dimitrov, Tang and Calegari actually did.

In this video:

https://www.ias.edu/video/arithmetic-some-dirichlet-l-values

Calegari explains that this is essentially the second "genuinely new" number called a Dirichlet L-value at an integer point to be proved irrational since the 19th century - the first being Apéry's proof that ζ(3) is irrational. Euler had shown

ζ(2n) = 1/1²ⁿ + 1/2²ⁿ + 1/3²ⁿ + ⋯

is a rational multiple of π²ⁿ, so Lindemann's 1882 proof that π is transcendental showed all the numbers ζ(2n) are irrational... but then things slowed down except for Apéry's result, and now this. Nobody knows how to prove ζ(5) is irrational.

For the actual paper, see:

https://arxiv.org/abs/2408.15403

It's a 218-page blast of abstraction, but it also proves these numbers are irrational:

1/4² + 1/7² + 1/10² + 1/13² + ⋯ (going up 3 each time)
1/2² + 1/5² + 1/8² + 1/11² + ⋯ (going up 3 each time)
1/1² + 1/7² + 1/12² + 1/19² + ⋯ (going up 6 each time)

and more!

John Carlos Baez profile picture
I've been thinking about a lot of stuff lately. Literally. Humans are currently using over 1,100 gigatonnes of stuff, which exceeds the mass of all living creatures on Earth. Also, since the dawn of agriculture we have roughly halved the mass of living creature on Earth, mainly by killing trees.

Animals count for only about 0.4% of all biomass, and mammals only about 0.0016%. Wild mammal biomass has probably declined by something like 85% since the late Pleistocene. Now over 90% of mammal biomass is livestock.

https://www.researchgate.net/publication/354866369_The_human-made_mass_-Would_you_like_a_little_more
John Carlos Baez profile picture
President Bush and Secretary Rumsfeld thought that the Iraq-Afghanistan war would cost $40 billion and it ended up costing at least $3 trillion. So they were off by a factor of 75. And that's not counting how the US owes $7.3 trillion to veterans - mainly Iraq and Afghanistan and Gulf War veterans mostly, and some Vietnam vets.

For the Iran war, the White House has just asked for a $500 billion per year increase in the defense budget. That works out at roughly $4,000 per American household. But it's almost surely just the start - and it doesn't count the economic damage.

https://www.wbur.org/onpoint/2026/04/13/the-real-cost-of-the-war-with-iran
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Have you read There Is No Antimemetics Division? Would I like it?

A review in The Guardian says:

"Memes are ideas that easily spread; antimemes are literally unthinkable, “self-keeping secrets”, impossible to record or to remember. Some feed on memories and pose an existential threat. But how is it possible to win a war when there’s no identifiable enemy, and every attack is immediately forgotten? Against these odds, the Antimemetics Division somehow exists, part of a secret organisation with bases deep underground in the English countryside, as related in this unforgettable, mind-bendingly brilliant novel."

https://en.wikipedia.org/wiki/There_Is_No_Antimemetics_Division
John Carlos Baez profile picture
In the northern hemisphere, the sun moves clockwise in the sky. This is why clocks, which were based on sundials, have hands that move clockwise.

In 2014 the Bolivians finally decided to break free of this colonial legacy. They're in the southern hemisphere, after all! So the clock on their parliament now looks like this.

I like it. But it must make a tempting target for counter-revolutionaries.

1
Bart Smit / ⲁⲗⲍⲓⲙⲟⲛ · 10w
nostr:nprofile1qy2hwumn8ghj7un9d3shjtnyd968gmewwp6kyqpqknzsux7p6lzwzdedp3m8c3c92z0swzc0xyy5glvse58txj5e9ztqt54hp5 "clocks have hands that move clockwise" sounds rather tautological. So, did the Bolivians also redefine the meaning of "clockwise"? 🤔
Skewray Research (ZF¬C) · 11w
nostr:nprofile1qy2hwumn8ghj7un9d3shjtnyd968gmewwp6kyqpqknzsux7p6lzwzdedp3m8c3c92z0swzc0xyy5glvse58txj5e9ztqt54hp5 Sounds like an asymptotic expansion, right? https://en.wikipedia.org/wiki/Asymptotic_...
John Carlos Baez profile picture
@nprofile1q... - yes, it sounds like that, and I hope it's something like that! But I haven't seen it proved, and I don't even know exactly what's the statement to prove. Since the Riemann Hypothesis is a big deal, someone might have done some of the work already.