Posts Tagged ‘Physics’
“I think the next century will be the century of complexity”*…
… and as Philip Ball reports, a team of scientists at Carnegie Science agrees…
In 1950 the Italian physicist Enrico Fermi was discussing the possibility of intelligent alien life with his colleagues. If alien civilizations exist, he said, some should surely have had enough time to expand throughout the cosmos. So where are they?
Many answers to Fermi’s “paradox” have been proposed: Maybe alien civilizations burn out or destroy themselves before they can become interstellar wanderers. But perhaps the simplest answer is that such civilizations don’t appear in the first place: Intelligent life is extremely unlikely, and we pose the question only because we are the supremely rare exception.
A new proposal by an interdisciplinary team of researchers challenges that bleak conclusion. They have proposed nothing less than a new law of nature, according to which the complexity of entities in the universe increases over time with an inexorability comparable to the second law of thermodynamics — the law that dictates an inevitable rise in entropy, a measure of disorder. If they’re right, complex and intelligent life should be widespread.
In this new view, biological evolution appears not as a unique process that gave rise to a qualitatively distinct form of matter — living organisms. Instead, evolution is a special (and perhaps inevitable) case of a more general principle that governs the universe. According to this principle, entities are selected because they are richer in a kind of information that enables them to perform some kind of function.
This hypothesis, formulated by the mineralogist Robert Hazen [here] and the astrobiologist Michael Wong [here] of the Carnegie Institution in Washington, D.C., along with a team of others, has provoked intense debate. Some researchers have welcomed the idea as part of a grand narrative about fundamental laws of nature. They argue that the basic laws of physics are not “complete” in the sense of supplying all we need to comprehend natural phenomena; rather, evolution — biological or otherwise — introduces functions and novelties that could not even in principle be predicted from physics alone. “I’m so glad they’ve done what they’ve done,” said Stuart Kauffman, an emeritus complexity theorist at the University of Pennsylvania. “They’ve made these questions legitimate.”…
[Ball explains the origin and outline of Hazen’s and Wong’s conjecture, explores the critiques– among them, that it’s not clear how to test the hypothesis– and examines the resonant work on Assembly Theory being done by Lee Cronin and Sara Walker…]
… Wong said there is more work still to be done on mineral evolution, and they hope to look at nucleosynthesis and computational “artificial life.” Hazen also sees possible applications in oncology, soil science and language evolution. For example, the evolutionary biologist Frédéric Thomas of the University of Montpellier in France and colleagues have argued that the selective principles governing the way cancer cells change over time in tumors are not like those of Darwinian evolution, in which the selection criterion is fitness, but more closely resemble the idea of selection for function from Hazen and colleagues.
Hazen’s team has been fielding queries from researchers ranging from economists to neuroscientists, who are keen to see if the approach can help. “People are approaching us because they are desperate to find a model to explain their system,” Hazen said.
But whether or not functional information turns out to be the right tool for thinking about these questions, many researchers seem to be converging on similar questions about complexity, information, evolution (both biological and cosmic), function and purpose, and the directionality of time. It’s hard not to suspect that something big is afoot. There are echoes of the early days of thermodynamics, which began with humble questions about how machines work and ended up speaking to the arrow of time, the peculiarities of living matter, and the fate of the universe…
A new suggestion that complexity increases over time, not just in living organisms but in the nonliving world, promises to rewrite notions of time and evolution: “Why Everything in the Universe Turns More Complex,” from @philipcball.bsky.social and @quantamagazine.bsky.social.
See also: Benjamin Bratton‘s explantion of the work he and his collegues are doing at a new institute at UCSD: “Antikythera.” See his recent Long Now Foundation talk on this same subject here.
* Stephen Hawking
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As we celebrate complication, we might spare a thought for G. N. Ramachandran (Gopalasamudram Narayanan Ramachandran); he died on this date in 2001. A biophysicist, he discovered the triple helical “coiled coil” structure of the collagen molecule, among other remarkable contributions to structural biology.
Ramachandran was a master of X-ray crystallography, and with his colleagues, constructed space filling models of protein molecules. He devised the Ramachandran Plot, a method to diagram the conformation of polypeptides, polysaccharides and polynucleotides– which remains the international standard to describe protein structures.
Ramachandran, inspired by the ancient Syaad Nyaaya (doctrine of “may be”), also explored artificial intelligence. He developed the Boolean Vector Matrix Formulation which has important application in writing software for AI.
“Truth is ever to be found in the simplicity, and not in the multiplicity and confusion of things”*…
From Kim (Scott) Morrison‘s and Dror Bar-Natan‘s, The Knot Atlas, “a complete user-editable knot atlas, in the wiki spirit of Wikipedia“– a marvelous example of a wide-spread urge in mathematics to find order through classification. As Joseph Howlett explains, that quest continues, even as it proves vexatious…
Biology in the 18th century was all about taxonomy. The staggering diversity of life made it hard to draw conclusions about how it came to be. Scientists first had to put things in their proper order, grouping species according to shared characteristics — no easy task. Since then, they’ve used these grand catalogs to understand the differences among organisms and to infer their evolutionary histories. Chemists built the periodic table for the same purpose — to classify the elements and understand their behaviors. And physicists made the Standard Model to explain how the fundamental particles of the universe interact.
In his book The Order of Things, the philosopher Michel Foucault describes this preoccupation with sorting as a formative step for the sciences. “A knowledge of empirical individuals,” he wrote, “can be acquired only from the continuous, ordered and universal tabulation of all possible differences.”
Mathematicians never got past this obsession. That’s because the menagerie of mathematics makes the biological catalog look like a petting zoo. Its inhabitants aren’t limited by physical reality. Any conceivable possibility, whether it lives in our universe or in some hypothetical 200-dimensional one, needs to be accounted for. There are tons of different classifications to try — groups, knots, manifolds and so on — and infinitely many objects to sort in each of those classifications. Classification is how mathematicians come to know the strange, abstract world they’re studying, and how they prove major theorems about it.Take groups, a central object of study in math. The classification of “finite simple groups” — the building blocks of all groups — was one of the grandest mathematical accomplishments of the 20th century. It took dozens of mathematicians nearly 100 years to finish. In the end, they figured out that all finite simple groups fall into three buckets, except for 26 itemized outliers. A dedicated crew of mathematicians has been working on a “condensed” proof of the classification since 1994 — it currently comprises 10 volumes and several thousand pages, and still isn’t finished. But the gargantuan undertaking continues to bear fruit, recently helping to prove a decades-old conjecture that you can infer a lot about a group by examining one small part of it.
Mathematics, unfettered by the typical constraints of reality, is all about possibility. Classification gives mathematicians a way to start exploring that limitless potential…[Howlett reviews attempts to classify numbers by “type” (postive/negative, rational/irrational), and mathematical objects by “equivalency” (shapes that can be stretched or squeezed into the other without breaking or tearing, like a doughnut and and coffee cup (see here)…]
… Similarly, classification has played an important role in knot theory. Tie a knot in a piece of string, then glue the string’s ends together — that’s a mathematical knot. Knots are equivalent if one can be tangled or untangled, without cutting the string, to match the other. This mundane-sounding task has lots of mathematical uses. In 2023, five mathematicians made progress on a key conjecture in knot theory that stated that all knots with a certain property (being “slice”) must also have another (being “ribbon”), with the proof ruling out a suspected counterexample. (As an aside, I’ve often wondered why knot theorists insist on using nouns as adjectives.)
Classifications can also get more meta. Both theoretical computer scientists and mathematicians classify problems about classification based on how “hard” they are.
All these classifications turn math’s disarrayed infinitude into accessible order. It’s a first step toward reining in the deluge that pours forth from mathematical imaginings…
“The Never-Ending Struggle to Classify All Math,” from @quantamagazine.bsky.social.
* Isaac Newton
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As we sort, we might spare a thought for the author of our title quote, Sir Isaac Newton; he died in this date in 1727. A polymath, Newton excelled in– and advanced– mathematics, physics, and astronomy; he was a theologian and a government offical (Master of the Mint)… and a dedicated alchemist. He was key to the Scientific Revolution and the Enlightenment that followed.
Newton’s book Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687, achieved the first great unification in physics and established classical mechanics (e.g., the Laws of Motion and the principle of universal gravitation). He also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for formulating infinitesimal calculus. Indeed, Newton contributed to and refined the scientific method to such an extent that his work is considered the most influential in the development of modern science.
“I love to talk about nothing. It’s the only thing I know anything about.”*…
It took centuries for people to embrace the zero. Now, as Benjy Barnett explains, it’s helping neuroscientists understand how the brain perceives absences…
When I’m birdwatching, I have a particular experience all too frequently. Fellow birders will point to the tree canopy and ask if I can see a bird hidden among the leaves. I scan the treetops with binoculars but, to everyone’s annoyance, I see only the absence of a bird.
Our mental worlds are lively with such experiences of absence, yet it’s a mystery how the mind performs the trick of seeing nothing. How can the brain perceive something when there is no something to perceive?
For a neuroscientist interested in consciousness, this is an alluring question. Studying the neural basis of ‘nothing’ does, however, pose obvious challenges. Fortunately, there are other – more tangible – kinds of absences that help us get a handle on the hazy issue of nothingness in the brain. That’s why I spent much of my PhD studying how we perceive the number zero.
Zero has played an intriguing role in the development of our societies. Throughout human history, it has floundered in civilisations fearful of nothingness, and flourished in those that embraced it. But that’s not the only reason it’s so beguiling. In striking similarity to the perception of absence, zero’s representation as a number in the brain also remains unclear. If my brain has specialised mechanisms that have evolved to count the owls perched on a branch, how does this system abstract away from what’s visible, and signal that there are no owls to count?
The mystery shared between the perception of absences and the conception of zero may not be coincidental. When your brain recognises zero, it may be recruiting fundamental sensory mechanisms that govern when you can – and cannot – see something. If this is the case, theories of consciousness that emphasise the experience of absence may find a new use for zero, as a tool with which to explore the nature of consciousness itself…
[Barnett provides a fascinating history of the zero, of its uses, and of brain scientost’s attepts to understand the (not so masterful) human ability to perceive absence…]
… All of this returns us to zero. The question is, does the same underlying neural mechanism drive experiences of both zero and perceptual absence? If it does, this would show us that, when we’re engaged in mathematics using zero, we’re also invoking a more fundamental and automatic cognitive system – one that is, for instance, responsible for detecting an absence of birds when I’m birdwatching.
The brain systems used to extract positive numbers from the environment are relatively well understood. Parts of the parietal cortex have evolved to represent the number of ‘things’ in our environment while stripping away information of what those ‘things’ are. This system would simply indicate ‘four’ if I saw four owls, for example. It is thought to be central to learning the structure of our environment. If the neural systems that govern our ability to decide if we consciously see something or not were found to rely on this same mechanism, it would help theories like HOSS and PRM get a handle on how exactly this ability arises. Perhaps, just as this system learns the structure and regularities of our environment, it also learns the structure of our brain’s sensory activity to help determine when we have seen something. This is what PRM and HOSS already predict, but grounding the theories in established ideas about how the brain works may provide them with a stronger foothold in explaining the precise mechanisms that allow us to become aware of the world.
An intriguing hypothesis inspired by the ideas above is that, if the brain basis of zero relies on the kinds of absence-related neural mechanisms that the above frameworks take to be necessary for conscious experience, then for any organism to successfully employ the concept of zero, it might first need to be perceptually conscious. This would mean that understanding zero could act as a marker for consciousness. Given that even honeybees have been shown to enjoy a rudimentary concept of zero, this may seem – at least to some – far fetched. Nonetheless, it seems attractive to suggest that the similarities between numerical and perceptual absences could help reveal the neural basis of not only experiences of absence but conscious awareness more broadly. Jean-Paul Sartre testified that nothingness was at the heart of being, after all.
The evolution of the number zero helped unlock the secrets of the cosmos. It remains to be seen whether it can help to unpick the mysteries of the mind. For now, studying it has at least led to less disappointment about my birdwatching failures. Now I know that there’s great complexity in seeing nothing and that, more importantly, nothing really matters…
Noodling on nowt: “Why nothing matters,” from @benjyb.bsky.social in @aeon.co.
Apposite: Percival Everett‘s glorious novel, Dr. No.
* Oscar Wilde
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As we analyze our apprehension of absence, we might send empty bithday greetings to a man who ruled out the use of “0” in one specific case: Georg Ohm; he was born on this date in 1789. A mathematician and physicist, he demonstrated by experiment (in 1825) that there are no “perfect” electrical conductors– that’s to say, no conductors with 0 resistance.
Working with the new electrochemical cell, invented by Italian scientist Alessandro Volta, Ohm found that there is a direct proportionality between the potential difference (voltage) applied across a conductor and the resultant electric current— a relationship since known as Ohm’s law (V=iR). The SI unit of resistance is the ohm (symbol Ω).
“Reality favors symmetry”*…
Emmy Noether showed that fundamental physical laws are themselves a consequence of simple symmetries. As Shalma Wegsman explains, a century later, her insights continue to shape physics…
In the fall of 1915, the foundations of physics began to crack. Einstein’s new theory of gravity seemed to imply that it should be possible to create and destroy energy, a result that threatened to upend two centuries of thinking in physics.
Einstein’s theory, called general relativity, radically transformed the meaning of space and time. Rather than being fixed backdrops to the events of the universe, space and time were now characters in their own right, able to curve, expand and contract in the presence of matter and energy.
One problem with this shifting space-time is that as it stretches and shrinks, the density of the energy inside it changes. As a consequence, the classical energy conservation law that previously described all of physics didn’t fit this framework. David Hilbert, one of the most prominent mathematicians at the time, quickly identified this issue and set out with his colleague Felix Klein to try to resolve this apparent failure of relativity. After they were stumped, Hilbert passed the problem on to his assistant, the 33-year-old Emmy Noether.
Noether was an assistant in name only. She was already a formidable mathematician when, in early 1915, Hilbert and Klein invited her to join them at the University of Göttingen. But other faculty members objected to hiring a woman, and Noether was blocked from joining the faculty. Regardless, she would spend the next three years prodding the fault line separating physics and mathematics, eventually setting off an earthquake that would shake the foundations of fundamental physics.
In 1918, Noether published the results of her investigations in two landmark theorems. One made sense of conservation laws in small regions of space, a mathematical feat that would later prove important for understanding the symmetries of quantum field theory. The other, now just known as Noether’s theorem, says that behind every conservation law lies a deeper symmetry.
In mathematical terms, a symmetry is something you can do to a system that leaves it unchanged. Consider the act of rotation. If you start with an equilateral triangle, you’ll find that you can rotate it by multiples of 120 degrees without changing how it looks. If you start with a circle, you can rotate it by any angle. These actions without consequences reveal the underlying symmetries of these shapes.
But symmetries go beyond shape. Imagine you do an experiment, then you move 10 meters to the left and do it again. The results of the experiment don’t change, because the laws of physics don’t change from place to place. This is called translation symmetry.
Now wait a few days and repeat your experiment again. The results don’t change, because the laws of physics don’t change as time passes. This is called time-translation symmetry.
Noether started with symmetries like these and explored their mathematical consequences. She worked with established physics using a common mathematical description of a physical system, called a Lagrangian.
This is where Noether’s insight went beyond the symbols on the page. On paper, symmetries seem to have no impact on the physics of the system, since symmetries don’t affect the Lagrangian. But Noether realized that symmetries must be mathematically important, since they constrain how a system can behave. She worked through what this constraint should be, and out of the mathematics of the Lagrangian popped a quantity that can’t change. That quantity corresponds to the physical property that’s conserved. The impact of symmetry had been hiding beneath the equations all along, just out of view.
In the case of translation symmetry, the system’s total momentum should never change. For time-translation symmetry, a system’s total energy is conserved. Noether discovered that conservation laws aren’t fundamental axioms of the universe. Instead, they emerge from deeper symmetries.
The conceptual consequences are hard to overstate. Physicists of the early 20th century were shocked to realize that a system that breaks time-translation symmetry can break energy conservation along with it. We now know that our own universe does this. The cosmos is expanding at an accelerating rate, stretching out the leftover light from the early universe. The process reduces the light’s energy as time passes…
… Noether’s theorem has shaped the quantum world too. In the 1970s, it played a big role in the construction of the Standard Model of particle physics. The symmetries of quantum fields dictate laws that restrict how fundamental particles behave. For instance, a symmetry in the electromagnetic field forces particles to conserve their charge.
The power of Noether’s theorem has inspired physicists to look toward symmetry to discover new physics. Over a century later, Noether’s insights continue to influence the way physicists think…
“How Noether’s Theorem Revolutionized Physics,” from @shalmawegs in @QuantaMagazine.
* Jorge Luis Borges
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As we contemplate cosmology, we might send insightful birthday greetings to the man who “wrote the book” on perspective, Leon Battista Alberti; he was born on this date in 1404. The archetypical Renaissance humanist polymath, Alberti was an author, artist, architect, poet, priest, linguist, philosopher, cartographer, and cryptographer. He collaborated with Toscanelli on the maps used by Columbus on his first voyage, and he published the the first book on cryptography that contained a frequency table.
But he is surely best remembered as the author of the first general treatise– Della Pictura (1434)– on the the laws of perspective, which built on and extended Brunelleschi’s work to describe the approach and technique that established the science of projective geometry… and fueled the progress of painting, sculpture, and architecture from the Greek- and Arabic-influenced formalism of the High Middle Ages to the more naturalistic (and Latinate) styles of Renaissance.
“It’s peculiar. It’s special. There’s very little of it, but it has this pivotal role in the universe.”*…
One of the oldest, scarcest elements in the universe has given us treatments for mental illness, ovenproof casserole dishes, and electric cars. Increasingly, our response to climate change seems to depend on it. But how much do we really know about lithium? Jacob Baynham explains…
The universe was born small, unimaginably dense and furiously hot. At first, it was all energy contained in a volume of space that exploded in size by a factor of 100 septillion in a fraction of a second. Imagine it as a single cell ballooning to the size of the Milky Way almost instantaneously. Elementary particles like quarks, photons and electrons were smashing into each other with such violence that no other matter could exist. The primordial cosmos was a white-hot smoothie in a blender.
One second after the Big Bang, the expanding universe was 10 billion degrees Kelvin. Quarks and gluons had congealed to make the first protons and neutrons, which collided over the course of a few minutes and stuck in different configurations, forming the nuclei of the first three elements: two gases and one light metal. For the next 100 million years or so, these would be the only elements in the vast, unblemished fabric of space before the first stars ignited like furnaces in the dark to forge all other matter.
Almost 14 billion years later, on the third rocky planet orbiting a young star in a distal arm of a spiral galaxy, intelligent lifeforms would give names to those first three elements. The two gases: hydrogen and helium. The metal: lithium.
This is the story of that metal, a powerful, promising and somehow still mysterious element on which those intelligent lifeforms — still alone in the universe, as far as they know — have pinned their hopes for survival on a planet warmed by their excesses…
[Baynham tells the story of this remarkable element, the development of it many uses (in psychopharmacology, in materials science, and of course in electronics– especially batteries), the rigors of extracting it for those purposes, and the challenges that its scarcity– and its potency– present…]
… Long before cell phones and climate anxiety and the Tesla Model Y, long before dinosaurs and the first creatures that climbed out of the ocean to walk on land, long before the Earth formed from swirling masses of cosmic matter heavy enough to coalesce, back, way back, to the infant universe, to the dawn of matter itself, there were just three types of atoms — three elements in the blank canvas of space. One of them was lithium. It was light, fragile and extremely reactive, its one outer electron tenuously held in place.
Everything we have done with lithium, all its wondrous applications in energy, industry and psychiatry, somehow hinges on this basic structure, a sort of magic around which we’re increasingly engineering our future. Lightness is usually associated with abundance on the periodic table — almost 99% of the mass of the universe is just the lightest two elements. Lithium, however, is the third lightest element and still mysteriously scarce…
That most elemental of elements: “The Secret, Magical Life of Lithium,” from @JacobBaynham in @noemamag.com.
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As we muse on materials, we might send densely-packed birthday greetings to Philip W. Anderson; he was born on this date in 1923. A theoretical physicist, he shared (with John H. Van Vleck and Sir Nevill F. Mott) the 1977 Nobel Prize for Physics for his research on semiconductors, superconductivity, and magnetism. Anderson made contributions to the theories of localization, antiferromagnetism, symmetry breaking including a paper in 1962 discussing symmetry breaking in particle physics, leading to the development of the Standard Model around 10 years later), and high-temperature superconductivity, and to the philosophy of science through his writings on emergent phenomena. He was a pioneer in the field that he named: condensed matter physics, which has found applications in semiconductor and laserr technology, magnetic storage, liquid crystals, optical fibers, nanotechnology, quantum computing, and biomedicine.
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