From Galileo to Einstein

In mid‑2026 a post circulated on social media claiming that without understanding the mathematics: the equations, one could not understand the physics. Einstein and Infeld’s superbly written Evolution of Physics, which traces the development of physical thought from classical mechanics to relativity, stands as a decisive counterpoint to this numerical hubris. The truth is almost the opposite. When one can explain first principles without resorting to complicated equations, then one really does understand the physics.

Einstein and Infeld manage to educate the curious lay reader, including high‑school students, without using a single equation, however simple. Their narrative is so lucid that even the most elusive quantum concepts settle cleanly in the reader’s mind. It is a pedagogical feat achieved only a handful of times in modern scientific writing.

Two other books, that I’m aware of, belong to this rare category where understanding comes first and formalism second. The 1910 classic Calculus Made Easy by Thompson and Gardner remains the book every serious student should read before confronting the thousand‑page, three‑semester tomes that pass for calculus instruction in colleges today. The other is the 2011 first edition of Plate Tectonics by Frisch, Meschede, and Blakey; a pleasure to read and a model of how to teach geology from first principles.

The Evolution of Physics begins where physics itself begins: with experiment guiding theory, and by their reckoning that story starts with Galileo. In a sense, Galileo was Einstein’s intellectual ancestor: his three‑hundred‑year‑younger self pondering many of the same questions that Einstein would later expand and refine. Galileo studied velocity, gravity, and the principle of relativity: the idea that the laws of physics remain the same no matter where one stands. He also invented early military compasses, close cousins to the magnetic instrument that fascinated Einstein as a boy.

Einstein and Infeld emphasize that physics, and science in general, is not static. Discoveries are followed by more discoveries; old theories are supplanted by new ones. “Science arises from a crisis in the old theory,” they write. Crises force attempts to resolve the difficulties, and in doing so physics evolves.

One example of this evolution, not revolution, is the comparison between Newtonian gravity and gravity as articulated in General Relativity. In weak gravitational fields, Newton’s concepts are adequate. But Einstein’s theory removes the ghosts of absolute time and absolute space, replacing them with spacetime geometry. In GR, inertial mass and gravitational mass become identical, light bends in the presence of gravity, Mercury’s orbit is correctly accounted for, and a clock on the Sun ticks differently than one on Earth.

Returning to the theme of understanding without equations, Einstein and Infeld explain the most famous relation in physics, without ever writing it down. Instead of presenting , they simply tell the reader that matter is a vast reservoir of energy, and energy is matter in another form. In a few plain sentences they convey the physical meaning of the equation that reshaped modern science and, ultimately, ended WWII, and they do so without the reader ever needing to see a single symbol.

The book concludes its romp through scientific discovery from the Renaissance to WWII with a discussion of the then‑new science of quantum mechanics and all its strangeness. Much of it is a loving description of the photon and electron, but it also reminds us that evolution takes time.

As a parenthetical ending, it is worth noting that because The Evolution of Physics was written before WWII, it contains at least one archaic spelling that is amusing in hindsight. Einstein and Infeld repeatedly use the word clue spelled as clew. I had to read it twice before the meaning clicked.

The word goes back to Old English cliewen, meaning a ball of thread or yarn. That is why in Greek myth Ariadne gives Theseus a clew: a ball of thread to help him find his way out of the labyrinth. The metaphor later shifted: a clew became anything that helps one navigate a difficulty, and eventually the modern sense of a hint or piece of evidence.

By the 1700s and 1800s, clew and clue coexisted in literature. By the early 1900s, clew persisted mainly in British writing. By the time of WWII, clew had passed fully into the realm of archaic English. Its appearance in Einstein and Infeld’s prose is thus a small linguistic fossil; a reminder of how even scientific writing carries the imprint of its era.

Source: The Evolution of Physics: From Early Concepts to Relativity and Quanta. 1938. Cambridge University Press.

Quantum Computing

In 1977, the science-fiction writer Philip K. Dick told an audience in Metz, France, that “we are living in a computer-programmed reality.” His claim was speculative, even playful, but it anticipated a question that would eventually move well beyond science fiction: what if computation is not something that happens inside the universe, but something the universe itself does?

That distinction is at the heart of Seth Lloyd’s Programming the Universe. Lloyd is not primarily interested in the familiar science-fiction question of whether we happen to be living inside someone else’s simulation. His more fundamental question, and his thesis, is whether the physical universe can itself be understood as a computational process. If it can, then information is not merely something we use to describe physical reality. It may be one of the things from which physical reality is built.

This possibility has been explored, in different forms and with very different commitments, by figures including John Archibald Wheeler, Carlo Rovelli, Stephen Wolfram, Lee Smolin, and Nick Bostrom. Their arguments do not amount to a single theory, nor do they establish that the universe is literally a computer. But taken together, they point toward a remarkable shift in perspective: from asking what the universe is made of to asking what the universe does. And if I may be so bold: its telos.

Lloyd goes further. For him, computation is not simply a useful description of physical processes; it is fundamental to the physical processes themselves. The universe, in his formulation, computes its own evolution. And here the argument begins to turn back upon itself.

Computation requires rules. A computer does not create the rules by which it operates; the rules must in some sense be prior to the computation. Yet if the universe is both the computer and the thing being computed, where do those rules come from? If the laws of physics are the program, and the universe is the machine executing that program, what is it that establishes the laws? Lloyd’s answer seems to require the universe to supply both the machine and the instructions for its own operation.

This is more than a problem of terminology. In an ordinary computer, we can distinguish the hardware from the software, the state of the machine from the instructions acting upon that state, and the computation from the object being computed. Lloyd’s universal computer collapses these distinctions. The physical system is the hardware; its physical laws are the program; its state is the data; its evolution is the computation; and the result of the computation is the physical universe itself.

The analogy has therefore reached its limit. A computer can compute a model of the universe, but that does not by itself establish that the universe is a computer. A description of a process in computational terms is not necessarily an explanation of why that process exists or why its rules have the form they do. To say that the universe computes itself may ultimately be little more than a new vocabulary for saying that the universe evolves according to its physical laws.

The problem becomes still more complicated when Lloyd moves between the quantum and classical descriptions of reality. Quantum mechanics provides the natural language for his computational universe because quantum states can preserve and transform information in ways that classical computers cannot. But the world we actually observe is not simply a universal wavefunction evolving in an abstract computational space. It is a world of classical objects, definite records, irreversible processes, and apparent information loss. The transition from the quantum substrate to classical spacetime therefore cannot simply be ignored.

This is where the distinction between computation and physical reality becomes essential. At the level of the complete quantum state, evolution can be unitary and information-preserving. At the level of subsystems and classical observations, however, information can become inaccessible through processes such as decoherence. The computational picture therefore depends upon specifying exactly what constitutes the computer, what constitutes its state, and at what level information is being conserved.

Lloyd’s argument would have been compelling if the computer is identified with the underlying quantum state of the universe. It becomes considerably less clear when the same computational language is transferred wholesale to the emergent classical world of spacetime. If the computer is spacetime itself, then spacetime must somehow provide simultaneously the hardware, the state, the rules, and the computation. At that point the computational metaphor begins to explain the universe by presupposing the very structure it was introduced to explain.

The difficulty can be put more simply. A computer normally computes something other than itself. Lloyd’s universe computes its own evolution. But if the computer, the program, the data, the computation, and the output are all the same physical system, what explanatory work is left for the word computation to do?

It is rather like trying to lift yourself off the ground by pulling upward on your own hair.

Lloyd begins with bits generated by particle interactions, but the true primitive is spin: the representation structure of Hilbert space. If he had started from spin, he would have been forced to treat information as a property of the wavefunction itself rather than as a byproduct of spacetime events.

But he didn’t start with spin because it would collapse his entire “the universe is a quantum computer” narrative. If his thesis would have begun at the wavefunction there would have never been a “the universe computes itself.”  Starting with spin would have forced him to confront the idea that the wavefunction exists under a different symmetry than spacetime.

The deeper difficulty is that Lloyd treats quantum mechanics as if it were simply the microscopic layer of the same spacetime reality we inhabit. In his account, the universal wavefunction is a physical object evolving in physical time, and its informational content is generated by physical interactions occurring at definite locations in spacetime. But this is not how the wavefunction is understood in contemporary quantum theory. The wavefunction does not live in spacetime. It is defined on configuration space, a high‑dimensional structure whose symmetries are not the symmetries of spacetime at all. It is not a field distributed over the universe; it is the mathematical object from which the appearance of a spacetime universe is derived.

Once this distinction is acknowledged, Lloyd’s computational metaphor becomes unstable. If the wavefunction belongs to a deeper, non‑spatiotemporal domain, then the “computer” cannot be spacetime itself. The computer would have to be whatever reality the wavefunction inhabits, and spacetime would be the rendered output: the interface produced by the evolution of the underlying quantum state. In that case, computation would not be something the spacetime universe performs. It would be something performed prior to spacetime, generating spacetime as a secondary description. The universe we observe would be the display, not the machine.

Lloyd never entertains this possibility because it would force him to abandon the idea that the universe computes itself. A system cannot compute its own interface. If the wavefunction is ontologically deeper than spacetime, then spacetime cannot be both the hardware and the output of the computation. The rules governing the wavefunction would have to be prior to spacetime, and therefore prior to the physical universe Lloyd wants to identify with the computer. His model requires a single domain in which the wavefunction, the laws of physics, the computational rules, and spacetime all coexist. But quantum theory does not support that unity. The wavefunction and spacetime obey different symmetries, inhabit different mathematical spaces, and participate in different kinds of evolution.

This is why Lloyd begins with bits generated by particle interactions rather than with spin, the true primitive of Hilbert space. Starting with spin would force him to acknowledge that information is a property of the wavefunction itself, not a byproduct of spacetime events. And once the wavefunction is treated as primary, spacetime becomes emergent: a rendered interface rather than a computational substrate. At that point, the universe cannot compute itself, because the computation would occur in a domain spacetime does not contain.

Lloyd’s argument depends on treating spacetime as the single, all‑encompassing domain in which information exists and computation occurs. For him, spacetime is not an emergent interface or a rendered classical description of a deeper quantum reality. It is the entire physical substrate: the hardware, the memory, the processor, the operating system, and the program. Every quantum interaction is a spacetime event; every bit is generated by a spacetime process; every computational step is performed by the spacetime universe itself. Lloyd never confronts the fact that the wavefunction does not inhabit spacetime and does not evolve within it. If he had, his model would have collapsed into a very different picture: spacetime as information only, a classical simulation produced by the decohered configuration of the underlying quantum state. Lloyd’s model requires spacetime to process all information in the wavefunction, but spacetime is informationally impoverished. Decoherence prevents spacetime from accessing the global relational structure that his computation metaphor requires.

But acknowledging that distinction would destroy the central claim of Programming the Universe. A universe that emerges from the wavefunction cannot compute itself, because the computation would occur in a domain spacetime does not contain.

Lloyd makes an intriguing aside that he never develops. He notes that a quantum computer the size of the universe, running a simulation of the universe, would be indistinguishable from the real thing. The remark is meant to be clever, but it quietly undermines his entire framework. If a simulation of the universe is indistinguishable from the universe itself, then the distinction between the computer and the simulation collapses. The universe would be both the machine and the model, both the substrate and the output. But this is only possible if spacetime is already a simulation: the classical, decohered configuration of the underlying wavefunction. A simulation running a model or simulation of itself.

Lloyd cannot pursue this implication because it would force him to acknowledge that the wavefunction belongs to a deeper domain than spacetime, and that spacetime is therefore informational rather than fundamental. His universal computer would dissolve into a rendered interface rather than a physical machine.

Had Lloyd begun with spin and the wavefunction, his quantum‑computational ideas might have endured. But by elevating spacetime to the status of fundamental substrate and insisting that it computes itself, he leaves the universe with no deeper domain from which its rules arise. What remains is a self‑explanatory physical reality: an ontology in which spacetime functions as its own ground of being. The metaphor of computation dissolves into metaphysics and omniscience.

Thought for the Day

T.H. Huxley, Darwin’s Bulldog, anatomist, and autodidact, reflecting upon time and matter, makes the humorous connection that, “It is very possible that atoms which once formed an integral part of the busy brain of Julius Caesar may now enter into the composition of Caesar, the housedog in an English homestead.”

Source: Elementary Physiology, T.H. Huxley, 1902. Graphic: English Sheepdog, AI generated.

GOAT Gas

Water vapor is the most abundant and the most powerful greenhouse gas in the atmosphere and is responsible for about half of the Earth’s greenhouse effect. The amount of water vapor in the lower atmosphere is largely controlled by temperature, such that warmer air holds more moisture. Water vapor returns to the Earth’s surface usually within two weeks but only if the vapor is in the troposphere, the atmospheric layer closest to the Earth.

Water vapor in the stratosphere, the layer above the troposphere, on the other hand, can stay there for a long time due to the lack of physical mechanisms to bring it back to the surface of the Earth. MIT has estimated that a water molecule, or any atmospheric molecule, can stay in the troposphere for about 1.5 years, possibly longer, before circulating back to the troposphere or Earth’s surface.

On 15 January 2022 the South Pacific volcano, Hunga Tonga-Hunga Ha’apai, erupted sending a huge jet of water vapor into Earth’s stratosphere, estimated to have been around 40 billion gallons in volume.  This is estimated to have increased the water vapor in the stratosphere by 10% in a matter of hours or days.

For reference, the greenhouse effect for selected gases by its 20-year GWP (Greenhouse Warming Potential) value:

  1. Water Vapor = A very large value but difficult to find in print.
  2. Hydrofluorocarbons (HFCs) = 460-9100 GWP
  3. Bromides = 7140 (varies)
  4. Chlorofluorocarbons (CFCs) = 4400-6200 GWP
  5. Nitrous oxide = 280 GWP
  6. Methane = 56 GWP
  7. Carbon dioxide = 1 GWP

Source: NASA. MIT. Graphic by AGeremia, 2020, Creative Commons.

It Happened Already

The Stars and The Earth or Thoughts upon Time, Space, and Eternity

By Felix Eberty

Translator: Josephine Caruana

Published by Comino-Verlag

Copyright: © 2018

A short read reflecting on the information carried by a photon as it reaches your eye from the far reaches of space.

Originally the book was published in two volumes, both together totaling less than 80 pages, in 1846 and 1847. The book sought the union of physics and religion, metaphysics; for God sees the past and the present as a single point in the space time continuum, time stopping when moving with the light, observing all in three dimensions rather than four. Eberty continues his thesis from an all-seeing God to a time when man’s technological progress allows him to see as God sees or the child of God becomes a god.

Eberty knowing that the speed of light was finite, about 300,000 km/s, contemplated that all visuals captured by any type of eye, human or otherwise, happened in the past. The past including an inconceivably, insignificantly small amount of time in the past, such as a plate of mac and cheese in front of you, is still in the past, what you see has already occurred. Jurgen Neffe, author of a biography of Albert Einstein, stated it succinctly “time travels with light”. Observing light traveling from a billion light years away exhibits events as they happened a billion years ago but if you traveled with those photons for those billion years the past occurs at the same time as your present.

Eberty’s thoughts on the meaning of time and space were recognized at the time not only as novel but metaphysical in nature, maybe not so much today.