dmm, 1 month 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, 2 months 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, 2 months 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, 2 months 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

dmm, 2 months ago to random

@christianp Is there a bug in 4.2.7 in which the Notifications bell turns on with a whole bunch of notifications, many of which are old, and can't be cleared?

In any event I've been observing that. Please let me know if there is additional information I can provide.

--dmm

dmm, 2 months ago to physics

English polymath Isaac Newton, who was a mathematician, physicist, astronomer, alchemist, and theologian, died #onthisday in 1727.

His pioneering book Philosophiæ Naturalis Principia Mathematica (1687) consolidated many previous results and established classical mechanics [1]. He also made seminal contributions to optics (among many other things), and shares credit with Gottfried Wilhelm Leibniz for developing calculus.

Books by Newton at Project Gutenberg: https://www.gutenberg.org/ebooks/author/6288

[Image credits: https://en.wikipedia.org/wiki/Isaac_Newton and https://www.westminster-abbey.org/abbey-commemorations/commemorations/sir-isaac-newton]

References

[1] "Newton’s Philosophiae Naturalis Principia Mathematica", https://plato.stanford.edu/entries/newton-principia/

#newton #calculus #physics #optics #math #maths

dmm, 2 months ago to space

This piece [1] is a bit older but still interesting on the origin of the famous Drake equation, which estimates the number of advanced civilizations likely to exist in the Milky Way galaxy.

References

[1] "The Origin of the Drake Equation", https://astrosociety.org/file_download/inline/58ee6041-5f61-4f88-8b15-d2d3d22ab83d

[2] "Drake equation", https://en.wikipedia.org/wiki/Drake_equation

#drakeequation #seti #extraterrestriallife #nasa

johncarlosbaez, 2 months ago (edited 2 months ago) to random

There's a bunch of bigshots on YouTube who pontificate about string theory, the mysteries of quantum mechanics, and other profound issues in physics. But you can't really learn much physics from most of them. It's just chat.

Angela Collier here is so much better! So much more humble - and so much more fun if you really care about physics. I actually learned something: how to estimate the distance of a pulsar!

When pulses of radio waves from a pulsar move through space, they get smeared out as they go, and you can use this to guess how far away the pulsar is. Why? Because waves of lower frequency move a bit slower. Why? Because they interact more with the ionized gas in the Milky Way.

But how much slower, and why? That's what she explains - and actually this part, how radio waves interact with ionized gas, is what will stick with me.

This is the first episode of a series she calls Coffee and The Problem:

"We have coffee and I solve a problem, and the idea is that it's like a cozy weekend morning and you pull out your notebook and you solve the problem right along with me. I will give you time to pause and solve it yourself if you want and compare your answer with mine if you want. That's the game! That's the fun."

This time she's solving a problem about estimating the distance of pulsar. The problem just hands you a formula. But she's good. She doesn't just use the formula, she shows how to derive it from more fundamental principles! And also, at the end, she raises the question I was worrying about all along: how reliable is this method in practice? So she's not blindly solving a problem: she's thinking about physics.

https://www.youtube.com/watch?v=iox8Z-NGGS8

dmm, 2 months ago to random

Why do I have cognitive dissonance with the idea of judges and judicial systems in general?

Here's one example: #onthisday in 1857, Chief Justice Roger B. Taney read the majority opinion of the Court in Dred Scott v. Sandford. The ruling deprived every inhabitant of African descent - slave or not- of the right to citizenship. The ruling also stripped Congress of the authority to prohibit slavery in the country's federal territories, moving the nation closer to civil war.

Yes, it's true. Taney and #SCOTUS ruled that slaves were not citizens of the United States.

References

[1] "Dred Scott v. Sandford", https://en.wikipedia.org/wiki/Dred_Scott_v._Sandford

[2] "Roger B. Taney", https://en.wikipedia.org/wiki/Roger_B._Taney

[3] "Dred Scott v. Sandford (1857)", https://www.archives.gov/milestone-documents/dred-scott-v-sandford