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“Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.”*…

No scripture is as old as mathematics is. All the other sciences are younger, most by thousands of years. More than history, mathematics is the record that humanity is keeping of itself. History can be revised or manipulated or erased or lost. Mathematics is permanent. A² + B² = C² was true before Pythagoras had his name attached to it, and will be true when the sun goes out and no one is left to think of it. It is true for any alien life that might think of it, and true whether they think of it or not. It cannot be changed. So long as there is a world with a horizontal and a vertical axis, a sky and a horizon, it is inviolable and as true as anything that can be thought.

As precise as mathematics is, it is also the most explicit language we have for the description of mysteries. Being the language of physics, it describes actual mysteries—things we can’t see clearly in the natural world but suspect are true and later confirm—and imaginary mysteries, things that exist only in the minds of mathematicians. A question is where these abstract mysteries exist, what their home range is. Some people would say that they reside in the human mind, that only the human mind has the capacity to conceive of what are called mathematical objects, meaning numbers and equations and formulas and so on—the whole glossary and apparatus of mathematics—and to bring these into being, and that such things arrive as they do because of the way our minds are structured. We are led to examine the world in a way that agrees with the tools that we have for examining it. (We see colors as we do, for example, because of how our brains are structured to receive the reflection of light from surfaces.) This is a minority view, held mainly by neuroscientists and a certain number of mathematicians disinclined toward speculation. The more widely held view is that no one knows where math resides. There is no mathematician/naturalist who can point somewhere and say, “That is where math comes from” or “Mathematics lives over there,” say, while maybe gesturing toward magnetic north and the Arctic, which I think would suit such a contrary and coldly specifying discipline.

The belief that mathematics exists somewhere else than within us, that it is discovered more than created, is called Platonism, after Plato’s belief in a non-spatiotemporal realm that is the region of the perfect forms of which the objects on earth are imperfect reproductions. By definition, the non-spatiotemporal realm is outside time and space. It is not the creation of any deity; it simply is. To say that it is eternal or that it has always existed is to make a temporal remark, which does not apply. It is the timeless nowhere that never has and never will exist anywhere but that nevertheless is. The physical world is temporal and declines; the non-spatiotemporal one is ideal and doesn’t.

A third point of view, historically and presently, for a small but not inconsequential number of mathematicians, is that the home of mathematics is in the mind of a higher being and that mathematicians are somehow engaged with Their thoughts. Georg Cantor, the creator of set theory—which in my childhood was taught as a part of the “new math”—said, “The highest perfection of God lies in the ability to create an infinite set, and its immense goodness leads Him to create it.” And the wildly inventive and self-taught mathematician Srinivasa Ramanujan, about whom the movie “The Man Who Knew Infinity” was made, in 2015, said, “An equation for me has no meaning unless it expresses a thought of God.”

In Book 7 of the Republic, Plato has Socrates say that mathematicians are people who dream that they are awake. I partly understand this, and I partly don’t.

Mathematics has been variously described as an ideal reality, a formal game, and the poetry of logical ideas… an excerpt from “What is Mathematics?” from Alec Wilkinson— eminently worthy of reading in full.

* Albert Einstein


As we sum it up, we might send carefull-calcuated birthday greetings to Georgiy Antonovich Gamov; he was born on this date in 1904. Better known by the name he adopted on immigrating to the U.S., George Gamow, he was a physicist and cosmologist whose early work was instrumental in developing the Big Bang theory of the universe; he also developed the first mathematical model of the atomic nucleus.

But mid-career Gamow began to shift his energy to teaching and to writing popular books on science… one of which, One Two Three… Infinity, inspired legions of young scientists-to-be and kindled a life-long interest in science in an even larger number of other youngsters (like your correspondent).


“A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it”*…

A curious thing happened at the end of the 19th century and the dawning of the 20th. As European and American industries became increasingly confident in their methods of invention and production, scientists made discovery after discovery that shook their understanding of the physical world to the core. “Researchers in the 19th century had thought they would soon describe all known physical processes using the equations of Isaac Newton and James Clerk Maxwell,” Adam Mann writes at Wired. But “the new and unexpected observations were destroying this rosy outlook.

These observations included X-rays, the photoelectric effect, nuclear radiation and electrons; “leading physicists, such as Max Planck and Walter Nernst believed circumstances were dire enough to warrant an international symposium that could attempt to resolve the situation.” Those scientists could not have known that over a century later, we would still be staring at what physicist Dominic Walliman calls the “Chasm of Ignorance” at the edge of quantum theory. But they did initiate “the quantum revolution” in the first Solvay Council, in Brussels, named for wealthy chemist and organizer Ernest Solvay.

“Reverberations from this meeting are still felt to this day… though physics may still sometimes seem to be in crisis” writes Mann (in a 2011 article just months before the discovery of the Higgs boson). The inaugural meeting kicked off a series of conferences on physics and chemistry that have continued into the 21st century. Included in the proceedings were Planck, “often called the father of quantum mechanics,” Ernest Rutherford, who discovered the proton, and Heike Kamerlingh-Onnes, who discovered superconductivity.

Also present were mathematician Henri Poincaré, chemist Marie Curie, and a 32-year-old Albert Einstein, the second youngest member of the group. Einstein described the first Solvay conference (1911) in a letter to a friend as “the lamentations on the ruins of Jerusalem. Nothing positive came out of it.” The ruined “temple,” in this case, were the theories of classical physics, “which had dominated scientific thinking in the previous century.” Einstein understood the dismay, but found his colleagues to be irrationally stubborn and conservative…

For more– and a complete list of attendees in the photo above: ““The Most Intelligent Photo Ever Taken”: The 1927 Solvay Council Conference, Featuring Einstein, Bohr, Curie, Heisenberg, Schrödinger & More.”

* Max Planck (second from the left in the first row of the photo above)


As we ponder paradigms, we might send insightful birthday greetings to Edward Williams Morley; he was born on this date in 1838. A chemist who was first to precisely determine the atomic weight of oxygen, he is probably best remembered for his collaboration with the physicist Albert A. Michelson. In what we call the Michelson–Morley experiment (actually a number of experiments conducted between April and July in 1887), they attempted to detect the luminiferous aether, a supposed medium permeating space that was thought to be the carrier of light waves; their method was the very precise measurement of the speed of light (in various directions, and at different times of the year, as the Earth revolved in its orbit around the Sun). Michelson and Morley always found that the speed of light did not vary at all depending on the direction of measurement, or the position of the Earth in its orbit– the so-called “null result.”

Neither Morley nor Michelson ever considered that these null results disproved the hypothesis of the existence of “luminiferous aether.” But other scientists began to suspect that they did. Almost two decades later the results of the Michelson–Morley experiments supported Albert Einstein’s strong postulate (in 1905) that the speed of light is a constant in all inertial frames of reference as part of his Special Theory of Relativity.


“The ‘paradox’ is only a conflict between reality and your feeling of what reality ‘ought to be’”*…

One of the most bizarre aspects of quantum physics is that the fundamental entities that make up the Universe, what we know as the indivisible quanta of reality, behave as both a wave and a particle. We can do certain experiments, like firing photons at a sheet of metal, where they act like particles, interacting with the electrons and kicking them off only if they individually have enough energy. Other experiments, like firing photons at small thin objects — whether slits, hairs, holes, spheres, or even DVDs — give patterned results that show exclusively wave-like behavior. What we observe appears to depend on which observations we make, which is frustrating, to say the least. Is there some way to tell, fundamentally, what the nature of a quanta is, and whether it’s wave-like or particle-like at its core?

That’s what Sandra Marin wants to know, asking:

“I wonder if you could help me to understand John Wheeler – the delayed choice experiment and write an article about this.”

John Wheeler was one of the most brilliant minds in physics in the 20th century, responsible for enormous advances in quantum field theory, General Relativity, black holes, and even quantum computing. Yet the idea about the delayed choice experiment hearkens all the way back to perhaps our first experience with the wave-particle duality of quantum physics: the double-slit experiment…

Although Einstein definitively wanted us to have a completely comprehensible reality, where everything that occurred obeyed our notions of cause-and-effect without any retrocausality, it was his great rival Bohr who turned out to be correct on this point. In Bohr’s own words:

“…it…can make no difference, as regards observable effects obtainable by a definite experimental arrangement, whether our plans for constructing or handling the instruments are fixed beforehand or whether we prefer to postpone the completion of our planning until a later moment when the particle is already on its way from one instrument to another.”

As far as we can tell, there is no one true objective, deterministic reality that exists independently of observers or interactions. In this Universe, you really to have to observe in order to find out what you get.

The history and the results of John Wheeler‘s famous “delayed choice” experiments: “Is Light Fundamentally A Wave Or A Particle?

* Richard Feynman


As we reconsider categories, we might recall that it was on this date in 1404 that King Henry IV signed the “Act Against Multipliers,” stipulating that “None from hereafter shall use to multiply gold or silver, or use the craft of multiplication; and if any the same do, they incur the pain of felony.” Great alarm was felt at that time lest any alchemist should succeed in “transmutation” (the conversion of a base metal into gold or silver), thus undermining the sanctity of the Royal currency and/or possibly financing rebellious uprisings. Alchemy, which had flourished since the time of Bacon, effectively became illegal.

The Act was repealed in 1689, when Robert Boyle, the father of modern chemistry, and other members of the vanguard of the scientific revolution lobbied for its repeal.


“Sometimes the only way to move forward is to revisit the things in your past that were holding you back”*…

Adobe Flash was the language of choice for a generation of game developers, helping kickstart an indie revolution on the still-young web of the 1990s and 2000s. But it withered on the proprietary and insecure vine, and both web browsers and Adobe have now canned it, threatening countless games and interactive presentations with the memory hole. The Internet Archive comes to the rescue, not only archiving the flash files but emulating the player itself, allowing history to live on.

“The Internet Archive has begun emulating Flash Animations, Games and Toys in a new collection,” wrote archivist Jason Scott on Twitter. “It’s at https://archive.org/details/softwarelibrary_flash and it’s going to be past 1,000 items in 24 hours. You can add your own and get them running, and the animations have never ran smoother or better.”…

From our friends at Boing Boing: “Internet Archive turns on Flash emulation, already has 1000 items to check out.”

* “Barry Allen” (The Flash)


As we celebrate that what’s old is new again, we might recall that it was on this date in 1915 that Albert Einstein presented the Einstein Field Equation to the Prussian Academy of Sciences.  Einstein soon after elaborated it into the set of 10 equations that account for gravitation in the curved spacetime that he described in his General Theory of Relativity; they are used to determine spacetime geometry.

(German mathematician David Hilbert reached the same conclusion, and actually published the equation before Einstein– though Hilbert, who was a correspondent of Einstein’s, never suggested that Einstein’s credit was inappropriate.)

On the right side of the equal sign, the distribution of matter and energy in space; on the left, the geometry of the space, the so-called metric, a prescription for how to compute the distance between two points.


“Once we introduce the possibility of applying the quantum principle to the universe, we are forced to consider parallel universes”*…




In the Antarctic, things happen at a glacial pace. Just ask Peter Gorham. For a month at a time, he and his colleagues would watch a giant balloon carrying a collection of antennas float high above the ice, scanning over a million square kilometres of the frozen landscape for evidence of high-energy particles arriving from space.

When the experiment returned to the ground after its first flight, it had nothing to show for itself, bar the odd flash of background noise. It was the same story after the second flight more than a year later.

While the balloon was in the sky for the third time, the researchers decided to go over the past data again, particularly those signals dismissed as noise. It was lucky they did. Examined more carefully, one signal seemed to be the signature of a high-energy particle. But it wasn’t what they were looking for. Moreover, it seemed impossible. Rather than bearing down from above, this particle was exploding out of the ground.

That strange finding was made in 2016. Since then, all sorts of suggestions rooted in known physics have been put forward to account for the perplexing signal, and all have been ruled out. What’s left is shocking in its implications. Explaining this signal requires the existence of a topsy-turvy universe created in the same big bang as our own and existing in parallel with it. In this mirror world, positive is negative, left is right and time runs backwards. It is perhaps the most mind-melting idea ever to have emerged from the Antarctic ice ­­– but it might just be true…

Strange particles observed by an experiment in Antarctica could be evidence of an alternative reality where everything is upside down: “We may have spotted a parallel universe going backwards in time.”

* Michio Kaku


As we consider our alternatives, we might recall that it was on this date in 1912, in his “Manuscript on the Special Theory of Relativity,” that Einstein first identified the fourth dimension as time… or so it is widely accepted.  Some physicists believe that Einstein was making a subtler– and much more complicated– suggestion, “x4 = ict”: that the fourth dimension, not “physical” like the other three, but emergent (in a way “understandable” as time) as the fourth dimension expands from the other three at the rate of “c.”

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Written by LW

April 15, 2020 at 1:01 am

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