Notices by David Meyer (dmm@mathstodon.xyz)

Published #onthisday 165 years ago, "On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life" by Charles Darwin created the foundations of evolutionary biology, which today is one of the organizing principles of modern biology.

[Image credit: https://commons.wikimedia.org/wiki/File:Origin_of_Species.jpg]

#biology #evolution #naturalselection #darwin

Born #onthisday in 1946, Duane Allman was the legendary Allman Brothers Band guitarist and slide guitar virtuoso. Allman (aka Skydog) was tragically killed in a motorcycle accident in Macon, Georgia on October 29, 1971. He was only 24 years old [1,2].

Allman left us a huge body of work (especially considering his short life). If you haven't checked out his music, here are a few places to start:

- Statesboro Blues (ABB): https://www.youtube.com/watch?v=UB1W98CKbjM
- Little Martha (ABB): https://www.youtube.com/watch?v=ngyk7wE0Peg
- Done Somebody Wrong (ABB): https://www.youtube.com/watch?v=EjhsLblrctI
- Mountain Jam (ABB): https://www.youtube.com/watch?v=9vLk_82PdxA
- Dreams (ABB): https://www.youtube.com/watch?v=JN1SVl0gzao
- Why Does Love Got To Be So Sad? (Derek and the Dominos): https://www.youtube.com/watch?v=wFeYVTPv0t8
- Layla (Derek and the Dominos): https://www.youtube.com/watch?v=TngViNw2pOo
- The Weight (Aretha Franklin): https://www.youtube.com/watch?v=HtR7QbfT8Tg
- Hey Jude (Wilson Pickett): https://www.youtube.com/watch?v=0y8Q2PATVyI
- Please Be With Me (Cowboy): https://www.youtube.com/watch?v=fBXZ1leNv8k
- Down in the Alley (Ronnie Hawkins): https://www.youtube.com/watch?v=2etew_D2FP0

It never ceases to amaze me how many people Skydog touched (and continues to touch) in his short life...

References
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[1] "Duane Allman, Skydog, Explained", https://lareviewofbooks.org/article/duane-allman-skydog-explained/

[2] "DUANE ALLMAN", https://duaneallman.info/

#skydog #allmanbrothers #allmanbrothersband #duaneallman #ABB

Born #onthisday in 1889, Edwin Hubble was an American astronomer who played a crucial role in establishing the fields of extragalactic astronomy and observational cosmology.

Hubble proved that many objects previously thought to be clouds of dust and gas and classified as "nebulae" were actually galaxies beyond the Milky Way. He used the strong direct relationship between a classical Cepheid variable's luminosity and pulsation period (discovered in 1908 by Henrietta Swan Leavitt [2]) for scaling galactic and extragalactic distances.

Hubble also discovered Hubble's law (aka the Hubble–Lemaître law), which is the observation that galaxies are moving away from Earth at speeds proportional to their distance. Said another way, the farther away a galaxy is, the faster it is moving away. The velocity of the galaxies has been determined by their redshift, a shift of the light they emit toward the red end of the visible spectrum [4].

Hubble's law is considered the first observational basis for the expansion of the universe, and today it serves as one of the pieces of evidence most often cited in support of the Big Bang model [5].

[Image credit: https://www.space.com/]

References
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[1] "Edwin Hubble", https://en.wikipedia.org/wiki/Edwin_Hubble

[2] "Henrietta Leavitt – Celebrating the Forgotten Astronomer", https://www.aavso.org/henrietta-leavitt-%E2%80%93-celebrating-forgotten-astronomer

[3] "Extra-galactic nebulae", https://www.gutenberg.org/ebooks/68428

[4] "Hubble's law", https://en.wikipedia.org/wiki/Hubble's_law

[5] "Hubble’s Law and the expanding universe", https://www.pnas.org/doi/10.1073/pnas.1424299112

#hubble #space #galaxies #universe #astronomy

Born #onthisday in 1902, Eugene Wigner was a Hungarian-American theoretical physicist who also contributed to mathematical physics. He received the Nobel Prize in Physics in 1963 "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles".

One of my favorite Wigner things: his essay titled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" [1].

Wigner also formulated the famous paradox in quantum mechantics known as "Wigner's friend" [4]. Wigner's friend is a thought experiment first published by Wigner in 1961 and further developed by David Deutsch in 1985. The scenario involves an indirect observation of a quantum measurement: An observer W observes another observer F who performs a quantum measurement on a physical system. The two observers then formulate a statement about the physical system's state after the measurement according to the laws of quantum theory. In the Copenhagen interpretation, the resulting statements of the two observers contradict each other. In some sense the observer F becomes entangled with the measurement so that W cannot know the outcome without another measurement (even though F knows the outcome).

#math #maths #mathematics #unreasonableeffectiveness #physics #naturalsciences #wignersfriend #measurementproblem

(1/2)

#onthisday in 2008 Satoshi Nakamoto [1] posted a paper to to gmane.comp.encryption.general with the subject "Bitcoin P2P e-cash paper" that outlined how a cryptocurrency (and Bitcoin in particular) might work [2].

Important properties of Satoshi's system included:

o Double-spending is prevented with a peer-to-peer network.
o No mint or other trusted parties.
o Participants can be anonymous.
o New coins are made from Hashcash style Proof-of-Work (PoW).
o PoW for new coin generation also enables the network to prevent double-spending.

Satoshi's original code can be found here: https://satoshi.nakamotoinstitute.org/code.

More on everything Satoshi can be found here: https://satoshi.nakamotoinstitute.org/.

References
--------------
[1] "Satoshi Nakamoto", https://en.wikipedia.org/wiki/Satoshi_Nakamoto

[2] "Bitcoin: A Peer-to-Peer Electronic Cash System", https://nakamotoinstitute.org/static/docs/bitcoin.pdf

#bitcoin #blockchain #satoshi

Archimedes discovered that if you add the volume of a cone and a sphere you get the volume of their bounding cylinder.

A truly beautiful result.

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

#math #maths #geometry #Archimedes

It's crazy how biology has these scaling laws.

For example, the number of calories a mammal needs daily ≈ m^{3/4}, where m is the mass of the mammal. This relationship apparently holds for all known mammals. Incidentally (or maybe not), the forth root turns up in almost all of these biological scaling laws.

Why should biology have these incredibly regular patterns, including the 4th root stuff? See "A General Model for the Origin of Allometric Scaling Laws in Biology" [1] for some ideas.

References
--------------
[1] "A General Model for the Origin of Allometric Scaling Laws in Biology", http://umdberg.pbworks.com/w/file/fetch/48318752/Science-1997-West.pdf

#biology #scalelaws

Born #onthisday in 1871, Ernest Rutherford discovered alpha and beta radiation, postulated the concept of the nucleus and founded the field of nuclear physics. Regarded as one of the greatest experimentalists, he was awarded the Nobel Prize in Chemistry in 1908.

References
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[1] "Ernest Rutherford", https://www.atomicheritage.org/profile/ernest-rutherford

#physics #chemistry

Doing a bit of clean up on my simple harmonic oscillator notes.

A few of my notes on simple harmonic oscillators and related topics are here: https://davidmeyer.github.io/qc/oscillators.pdf. The LaTeX source is here: https://www.overleaf.com/read/xjmyvksvtztb. As always, questions/comments/corrections/* greatly appreciated.

#simpleharmonicoscillators #hookeslaw #math #maths #physics #texlatex #tikz

#onthisday in 1687 Sir Isaac Newton published Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), one of the most significant works in the history of science.

References
---------------
[1] "Philosophiæ Naturalis Principia Mathematica", https://en.wikipedia.org/wiki/Philosophi%C3%A6_Naturalis_Principia_Mathematica

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

#newton #physics #math #maths

#onthisday in 1903, Marie Curie defended her doctoral thesis on radioactive substances at Université de la Sorbonne in Paris, becoming the first woman in France to receive a doctoral degree.

The examination committee expressed the opinion that Curie's findings, including the determination of Radium’s atomic weight, represented the greatest scientific contribution ever made in a doctoral thesis. Of the committee’s three members, were two future Nobel Laureates Gabriel Lippmann (Physics 1908) and Henri Moissan, (Chemistry 1906).

[Image credit: https://www.nobelprize.org/]

#mariecurie #physics #chemistry #nobelprize

Born #onthisday in 1918, Richard Feynman was an American theoretical physicist. He is probably best know known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, as well as his work in particle physics for which he proposed the parton model.

For his contributions to the development of quantum electrodynamics, Feynman received the Nobel Prize in Physics in 1965 jointly with Julian Schwinger and Shin'ichirō Tomonaga

[Image credit: https://en.wikipedia.org/wiki/Richard_Feynman#/media/File:Richard_Feynman_Nobel.jpg]

References
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[1] "Richard P. Feynman", https://www.nobelprize.org/prizes/physics/1965/feynman/biographical

[2] "Richard P. Feynman", http://www.richardfeynman.com

[3] "Richard P. Feynman", https://www.nsf.gov/news/special_reports/medalofscience50/feynman.jsp

#feynman #physics #quantumelectrodynamics #math #maths

I've been studying harmonic oscillators [1] and that led me to blackbody radiation which in turn led me to try to understand how heat transfer works. Here's one of the interesting things I've noticed in this process:

Apparently there are three possible mechanisms for transferring energy: conduction, convection, and thermal radiation.

In the case of conduction in a solid, energy is carried through an atomic lattice by free electrons or by phonon–phonon interactions (i.e., excitation of vibrational energy levels for interatomic bonds). In gases and liquids, energy is transferred from molecule to molecule through collisions (i.e., the faster molecule loses some of its kinetic energy to the slower one).

Heat transfer by convection is similar, except that here many of the molecules with raised kinetic energy are carried away by the flow and are replaced by colder fluid (low-kinetic-energy molecules), resulting in increased energy transfer rates.

So both conduction and convection require the presence of a medium for the transfer of energy.

Thermal radiation, on the other hand, is transferred by electromagnetic waves, or photons, which may travel over a long distance without interacting with a medium. The fact that thermal radiation does not require a medium for its transfer makes it of great importance in vacuum and space applications.

(1/2)

#blackbodyradiation #electromagneticspectrum #physics

Born #onthisday 118 years ago, Kurt Gödel was an Austrian mathematician and philosopher. Gödel discovered the “Incompleteness Theorem”, which essentially states that there will always be theorems in mathematics that are impossible to prove. Gödel''s discovery of the Incompleteness Theorems effectively drove a stake though the heart of Hilbert's Program [1] (or at least badly damaged it; see Hilbert's Second Problem [2]).

In 1949 Gödel demonstrated the existence of solutions to Einstein's field equations in General Relativity which involve "rotating universes" and featured closed timeline curves which allow for time travel to the past. Gödel's solutions are known as the Gödel metric and are an exact solution of the Einstein field equations [3].

Along with Aristotle, Alfred Tarski and Gottlob Frege, Gödel is considered to be one of the most significant logicians in history and had an immense effect upon scientific and philosophical thinking in the 20th century (and beyond).

Read more about Gödel's life and times here: https://mathshistory.st-andrews.ac.uk/Biographies/Godel.

References
--------------
[1] "Hilbert’s Program", https://plato.stanford.edu/entries/hilbert-program/

[2] "Hilbert's second problem", https://en.wikipedia.org/wiki/Hilbert%27s_second_problem

[3] "THE GODEL SOLUTION TO THE EINSTEIN FIELD EQUATIONS", http://www.math.toronto.edu/~colliand/426/Papers/A_Monin.pdf

#godel #incompletenesstheorems #math #maths #physics

A factorion is an interesting kind of natural number that equals the sum of the factorials of its decimal digits [1,3].

40585 is the largest known factorion and was discovered in 1964 by Leigh Janes [2].

#factorion #math #maths #numbertheory

References
--------------
[1] "Factorion", https://en.wikipedia.org/wiki/Factorion

[2] "Mathematician:Leigh Janes", https://proofwiki.org/wiki/Mathematician:Leigh_Janes

[3] "Factorion", https://mathworld.wolfram.com/Factorion.html