dmm, 4 days ago to random

Epic #onthisday in blues/music history:

Robert Johnson was born on this day in 1911 in Hazlehurst, Mississippi. His landmark recordings in 1936 and 1937 display a combination of singing, guitar skills, and songwriting talent that has influenced later generations of musicians. Although his recording career spanned only seven months, he is recognized as a master of the blues, particularly the Delta blues style, and as one of the most influential musicians of the 20th century.

If you are not familiar with Johnson's music, there is a nice playlist here: https://www.youtube.com/playlist?list=PLYPx-lRv1uyB8Rrw1GNrluTznSqO5-FBN

The Wikipedia also has a nice piece on Johnson: https://en.wikipedia.org/wiki/Robert_Johnson.

And of course, there's this: https://www.youtube.com/watch?v=ycNtYoxNuW8.

[Image credit: https://en.wikipedia.org/wiki/Robert_Johnson#/media/File:Robert_Johnson.png]

#robertjohnson #blues #deltablues

dmm, 16 days ago to math

Just started writing up a few of my notes on introductory Category Theory. Not much here yet (it took me awhile to get Figure 1 to look right, and it's still not perfect).

In any event, the pdf, such as it is, is here: https://davidmeyer.github.io/qc/category_theory.pdf. The LaTeX source is here: https://www.overleaf.com/read/wnptmrwwfjgv#a36a79. As always, questions/comments/corrections/* greatly appreciated.

#categorytheory #math #maths

dmm, 18 days ago to random

Squirrels taking it easy in Eugene, Oregon...

[Image credit: Susie Meyer]

#squirrels

dmm, 18 days ago to space

M104 (aka Messier 104, NGC 4594, and the Sombrero Galaxy) is a fantastic spiral galaxy which is famous for its nearly edge-on profile featuring a broad ring of obscuring dust lanes. Seen here in silhouette against an extensive central bulge of stars, the swath of cosmic dust lends a broad brimmed hat-like appearance to the galaxy suggesting its more popular moniker, the Sombrero Galaxy.

This sharp view of the well-known galaxy was made from over 10 hours of Hubble Space Telescope image data, processed to bring out faint details often lost in the overwhelming glare of M104's bright central bulge. The Sombrero galaxy can be seen across the spectrum, and is host to a central supermassive black hole. About 50,000 light-years across and 28 million light-years away, M104 is one of the largest galaxies at the southern edge of the Virgo Galaxy Cluster. Still, the spiky foreground stars in this field of view lie well within our own Milky Way.

APOD: Messier 104 (2022 Apr 23)
Image Credit: NASA, ESA, Hubble Legacy Archive;
Processing & Copyright: Ignacio Diaz Bobillo
https://apod.nasa.gov/apod/ap220423.html

#m104 #sombrerogalaxy. #nasa #astronomy

dmm, 19 days ago to ChatGPT

"No, A → B is not equivalent to - B → - A in logic."

Except that the truth table that ChatGPT [1] generated says the opposite. Also, see the law of contraposition [2].

Claude [3] makes the same mistake.

I've had pretty good luck with the chatbots. This is the first thing that I have asked that all of them seem to get wrong.

Interesting.

References

[1] "ChatGPT", https://chat.openai.com

[2] "Contraposition", https://en.wikipedia.org/wiki/Contraposition

[3] "Claude", https://claude.ai

#chatgpt #claude3 #firstorderpredicatelogic #math #maths #logic

dmm, 1 month ago to math

When I made the figure below I used LaTeX, powerpoint and then LaTeX again. Having learned some TikZ I now think I could draw it using TikZ, but apparently I'm too lazy...

A few of my notes on the subject of this figure (and other stuff) are here: https://davidmeyer.github.io/qc/dual_beam_experiment.pdf. As always, questions/comments/corrections/* greatly appreciated.

#math #maths #physics #quantumphysics #texlatex #tikz

dmm, 1 month ago to physics

RIP Peter Higgs

https://www.bbc.com/news/science-environment-68774195?utm_source=press.coop

#peterhiggs #higgsboson #physics

dmm, 1 month ago to internet

Happy birthday RFC 1!

RFC 1 was published on #onthisday in 1969. Impressive work and insight by Steve and by the IETF community over the last 55 years/9K+ RFCs.

Well done!

#IETF #RFC #internet

johncarlosbaez, 1 month ago (edited 1 month ago) to random

Some wasps are called 'parasitoids' because they lay their eggs in still-living caterpillars. The eggs develop into larvae that eat the caterpillar from the inside.

But turnabout is fair play. Sometimes, other wasps called 'hyperparasitoids' lay their eggs in the larvae of these parasitoids!

The caterpillars also fight back. Their immune system detects the wasp's eggs, and they will do things like surround the eggs in a layer of tissue that chokes them.

But many parasitoid wasps have a trick to stop this. They deploy viruses that infect the caterpillar and affect its behavior in various ways - for example, slowing its immune response to the implanted eggs.

These viruses can become so deeply symbiotic with the wasps that their genetic code becomes part of the wasp's DNA. So every wasp comes born with the ability to produce these viruses. They're called 'polydnaviruses'.

In fact some wasps are symbiotic with two kinds of virus. One kind, on its own, would quickly kill the caterpillar - not good for the wasp. The other kind keeps the first kind under control.

And I'm immensely simplifying things here. There are over 25,000 species of parasitoid wasps, so there's a huge variety of things that happen, which scientists are just starting to understand! I had fun reading this:

• Marcel Dicke, Antonino Cusumano and Erik H. Poelman, Microbial symbionts of parasitoids, Annual Review of Entomology, https://doi.org/10.1146/annurev-ento-011019-024939

Why such diversity? I think it's just that there are so many plants! So insect larvae like caterpillars naturally tend to feed on them... in turn providing a big food source for parasitoids, and so on.

dmm, 1 month ago to math

"So here is the crux of my argument. If you believe in an external reality independent of humans, then you must also believe in what I call the mathematical universe hypothesis: that our physical reality is a mathematical structure. In other words, we all live in a gigantic mathematical object — one that is more elaborate than a dodecahedron, and probably also more complex than objects with intimidating names like Calabi-Yau manifolds, tensor bundles and Hilbert spaces, which appear in today’s most advanced theories. Everything in our world is purely mathematical — including you." -- Max Tegmark, "The Mathematical Universe", https://arxiv.org/abs/0704.0646.

Something to think about...

See also "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", https://www.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf.

#math #maths #physics #erf #muh

dmm, 1 month ago to physics

The accomplishments of the Victorian physicists were (and are) amazing.

Among the great Victorian era scientists, I've been studying the work of James Clerk Maxwell, specifically Maxwell's equations [1] (along with the history of Victorian mathematics and physics [2]). In his short life, Maxwell made important contributions in many areas of physics. Unfortunately Maxwell died at age 48 from abdominal cancer in November of 1879 [3].

Among Maxwell's contributions are Maxwell's equations, which completed the unification of electricity and magnetism, thereby forming the concepts of electromagnetism and the electro-magnetic force. One of the really amazing aspects of Maxwell's equations is their generality. In particular, they apply to all charge and current densities, whether static or time-dependent and together they completely describe the dynamical behavior of the electromagnetic field.

Here's the best I could do with unicode to describe the differential form of Maxwell's equations (there are also integral forms of Maxwell's equations, see below):

(i). ∇·E = ρ/ε0 # Gauss's Law

(ii). ∇·B = 0 # Gauss's law for magnetism

(iii). ∇ × E = ∂B/∂t # Maxwell–Faraday equation (Faraday's law of induction)

(iv). ∇ × B = μ0 (J + ε0 ∂E/∂t)

Ampère's circuit law (with Maxwell's addition)

Maxwell's equations are important not only because they unified electricity and magnetism and completely characterized the electromagnetic field, but also because they paved the way for special relativity and quantum mechanics.

#maxwell #physics #math #maths #victorianphysics #electromagnetism

(1/2)

Propagation of electromagnetic waves...

dmm, 1 month ago to math

Born #onthisday 428 years ago, René Descartes was a French mathematician and philosopher. He developed the “cartesian” coordinate system, which is named after him. Among many other things, his work also provided the foundations for discovering calculus a few decades later.

Read more about Descartes' life and times here: https://plato.stanford.edu/entries/descartes/

[Image credit: https://mathigon.org/timeline/descartes]

#descartes #cartesiancoordinates #cogitoergosum #math #maths #philosophy

dmm, 1 month ago to random

I've been reading "Introductory Category Theory Notes", by Daniel Epelbaum and Ashwin Trisal.

Is there a better introductory Category Theory text (that I can find online)? Thx!

dmm, 1 month ago to math

Here's an interesting series:[S=\sum\limits_{n=1}^{\infty} {\left (\frac{a}{b}\right)}^{n}
]Does it converge, and if so, to what?

A few of my notes on all of this are here:
https://davidmeyer.github.io/qc/infinite_sum_a_over_b.pdf, and as always, questions/comments/corrections/* greatly appreciated.

#convergentseries #math #maths

dmm, 1 month ago to math

Born #onthisday in 1835, Josef Stefan was an ethnic Carinthian Slovene physicist, mathematician, and poet of the Austrian Empire [1].

During his lifetime Stefan published nearly 80 scientific articles, most appearing in the Bulletins of the Vienna Academy of Sciences.

Stefan is perhaps best known for his study of blackbody radiation [2] and for discovering what we now call Stefan's law, a physical power law which states that the total radiation from a blackbody is proportional to the fourth power of its (thermodynamic) temperature. Stefan's law was later extended to grey bodies by one of Stefan's students, Ludwig Boltzmann [3], and is now known as the Stefan–Boltzmann law [4].

I wrote a bit about blackbody radiation and the famous Stefan–Boltzmann law here: https://davidmeyer.github.io/qc/oscillators.pdf, but it looks like I got distracted (again) and never finished. The LaTeX source is here: https://www.overleaf.com/read/xjmyvksvtztb. In any event, as always questions/comments/corrections/* greatly appreciated.

References

[1] "Josef Stefan", https://en.wikipedia.org/wiki/Josef_Stefan

[2] "Josef Stefan’s – Black Bodies and Thermodynamic Temperature", http://scihi.org/josef-stefans-thermodynamics/

[3] "Ludwig Boltzmann", https://mathshistory.st-andrews.ac.uk/Biographies/Boltzmann/

[4] "Stefan–Boltzmann law", https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law

#josefstefan #stefanboltzmannlaw #blackbodyradiation #math #maths #physics