“This brings up an interesting question: Why is it that particles with half-integral spin are Fermi particles whose amplitudes add with the minus sign, whereas particles with integral spin are Bose particles whose amplitudes add with the positive sign?” — Richard Feynman, Lectures in Physics
Comparative Science and Relational Complexity
We would debate for hours.
When I was young, my father would introduce and discuss, around the dinner table, the ideas of philosophers, scientists, and historians: like Adam Smith, Charles Darwin, Herbert Spencer, John Stuart Mill, Georg Hegel, William James, Arthur Schopenhauer, Bertrand Russell, Oswald Spengler, Will Durant, and Ayn Rand, to name a few.
I had a question early on “How and Why does the World Work?” He had a more difficult question: “What are the long-term patterns of an ‘Individual’s Human Action?” He was clinical school psychologist, who was identifying deviant habits of children, parents, and teachers. He was developing techniques aimed at enabling them to abandon such habits. His methods of research and reasoning enabled him to evolve his ideas into a coherent system. His model of Human Temperament has helped many people to better understand themselves and others.
He was good at qualitative reasoning, wholistic thought: the Gestalt (despite [and because] of having lots of training in statistics). I became good at quantitative reasoning: conventional science and mathematics. Between the two of us, as we debated, I realized that there was a middle way, much more powerful than ad hoc wholistic reasoning or ad hoc atomistic reasoning, when they are used separately. The new middle way, The Slow Idea, is using Comparative Science and Relational Complexity in conjunction as fields of scientific endeavor using systematic qualitative and quantitative reasoning together. To some extent: (hard and soft) science, mathematics, and computer science are towers of Babel, not able to understand each other’s argot and considered irrelevant to other.
The idea of: Slow Ideas <=> Fast Ideas
FAST IDEAS WORK
eventually, SLOW IDEAS WORK BETTER, and longer
Atul Gawande introduced the idea of slow and fast ideas with an example from the 19th century. The fast idea was anesthesia and the slow idea was antiseptics. To quote him:
“Why do some innovations [ideas] spread so swiftly and others so slowly? Consider the very different trajectories of surgical anesthesia and antiseptics, both of which were discovered in the nineteenth century.”
“The first public demonstration of anesthesia was in 1846…”
“The idea [anesthesia] spread like a contagion, travelling through letters, meetings, and periodicals. By mid-December, surgeons were administering ether to patients in Paris and London. By February, anesthesia had been used in almost all the capitals of Europe, and by June in most regions of the world.”
Antiseptics, on the other hand, was a slow idea. It took decades for antiseptics to accepted by doctors, who had no incentives to change their practices that didn’t help them immediately. Blood stained clothes was a sign of a experienced surgeon; and washing hands, sterilizing instruments, and keeping hospitals clean seemed unnecessary. Germ theory was dismissed by doctors because the “germs” were not readily observed. Miasma Theory still was used as an excuse to not change.
Hey buddy, can you spare a Para-digm?
“Science advances one funeral at a time.” — Max Planck
“The trouble with specialists is that they tend to think in grooves” — Elaine Morgan
Establishment science needs to protect themselves from quacks, but it also resists slow ideas that are not easily incorporated into the current fashionable (often fast) ideas. This is natural, this is the way evolution works. However, Kuhnian revolutions (as in Margulian-Darwinian evolution) are necessary in science to progress and leap across the Quantum Gap.
“I think the world of theoretical physics is in a very strange place.” — George Ellis — in Hossenfelder, Sabine. Lost in Math: How Beauty Leads Physics Astray (p. 221). Basic Books. Kindle Edition.
“What are you worried about?” I begin. “There are physicists now saying we don’t have to test their ideas because they are such good ideas,” George says. He leans forward across the table and stares at me. “They’re saying — explicitly or implicitly — that they want to weaken the requirement that theories have to be tested.” — Hossenfelder, Sabine. Lost in Math: How Beauty Leads Physics Astray (p. 213). Basic Books. Kindle Edition.
Quantum Mechanics and General Relativity have been relatively fast ideas. They took over Physics in the 1920's-1930’s.
Early quantum theory was profoundly re-conceived in the mid-1920s by Erwin Schrödinger, Werner Heisenberg, Max Born, Paul Dirac, and others. The modern theory is formulated in various specially developed mathematical formalisms, relying on infinity and statistical probability. In one of them, a mathematical function, the wave function (a recursive equation), provides “information” about the probability amplitude of “position”, “momentum”, and other physical properties of a “particle.”
What is “in-form-ation?”
“It seems clear that the present quantum mechanics is not in its final form” — Paul Dirac
“This brings up an interesting question: Why is it that particles with half-integral spin are Fermi particles whose amplitudes add with the minus sign, whereas particles with integral spin are Bose particles whose amplitudes add with the positive sign? We apologize for the fact that we cannot give you an elementary explanation. An explanation has been worked out by Pauli from complicated arguments of quantum field theory and relativity. He has shown that the two must necessarily go together, but we have not been able to find a way of reproducing his arguments on an elementary level. It appears to be one of the few places in physics where there is a rule which can be stated very simply, but for which no one has found a simple and easy explanation. The explanation is deep down in relativistic quantum mechanics. This probably means that we do not have a complete understanding of the fundamental principle involved. For the moment, you will just have to take it as one of the rules of the world.…The principle seems so simple… I cannot help you, we understand it more mathematically than physically… Richard Feynman [Lectures in Physics]
Particle physicists have a simple notion (ala Susskind, d’Hooft, and Hawking) of Information; that is, Shannon information.
“If you don’t understand something said, don’t assume you are at fault.”
— David West Keirsey
In the Lost and Found of Mathematics and “Information” Theory
There has been a lot of progress in Information and Computer Science that can now be used to further understanding in relating discoveries in cosmology and particle physics. Adding some Discrete Mathematics (in the form of Group Theory and Number Theory, for example) that has been developed in the later part of the 20th century, a relational complexity approach can be effective in making a meaningful correspondence between physical concepts and information [and mathematical] concepts.
However, the entrenched paradigm of using differential, integral, and tensor calculus to approximating or/and correlating to particle physics concepts needs to step aside, so Formatics can try to pass them by. Abandon the Shannon. Embrace the Hamming and Golay.
“We can’t solve problems by using the same kind of thinking we used when we created them.” — Albert Einstein
Physics has gradually come to a kind of impasse. General Relativity (Einstein’s field equations) and Quantum Mechanics (The Standard Model) have “parameters” that are arbitrary (they are experimental physical measures in the form of “real numbers” [which imply the notion of infinity], that are plugged into the mathematical models)— like Newton’s gravitational constant, the possible “cosmological constant”, the electron charge (e.g., the fine structure constant), the Higgs mass, and numerous coupling constants and mixing angles. Theoretical models like SUSY (Super Symmetry), WIMPS (Weakly Interacting Massive Particles), CDM (Cold Dark Matter) and etcetera, etcetera, etcetera … are trying to extend the these statistical models in higher energies, but so far the experimentalists are coming up empty, quantum foam wise. The problem with GR and QM is that the physics community is trying to escape easily with Tarski’s monster (real numbers), avoiding the Diophantine (whole number polynomials) nightmare.
Implicit in all the current models of both cosmology and high energy physics is the assumption of notion of infinity and some kind of continuity. These are limiting kinds of assumptions; it excludes an important form of entailment.
Moreover, Quantum Mechanics, using the crutch of Born-Schrödinger probabilities in the guise of Fermi-Dirac and Bose-Einstein statistics, is a very very very precise, but incomplete. Although probabilistic unitary quadratic forms (a “real” scalar product or action of a linear functional on a vector in a complex vector space) can help in calculating measures, there is no “definite qualities”. At the quantum levels, one does not have separable “qualities” — just postulated mixed measures denoted by “quantum numbers” and “probabilistic measures” in the form of “real” and/or “complex numbers”.
Adding the two statistical conceptions: GR and QM has not been accomplished and will not work. A non-statistical methodology is needed to relate phenomena at the scales of large (GR) and the phenomena at the scales of small (QM). That methodology needs Relational Forms Frameworks.
The world is discrete and finite, but patterns recur.
The Nine Levels of Major Complexity.
To be continued….