Posts Tagged ‘Buridan’

How Fake Anglo-Saxon Mental Supremacy Was Established: Gross Lies. The Case Of Newton Turned Into God

September 20, 2020

Authorities want to make us believe that the spiritual ancestors of today’s rulers invented everything. Often they are even the genetic ancestors, but that is besides the point: by extolling imaginary predecessors, Anglo-Saxon supremacists have installed an aura of supremacy… for the systems of thought they installed and rule with, enabling them to reign effortlessly.

Now this is deep and systematic. Even Anglo-Saxon intellectuals who pretend to be against the system are part of the plot. An easy hint is who feeds and powers them: if it is the establishment, and the establishment likes them, that’s a warning sign.

Most of the world’s top historical minds who contributed to most of humanity’s mental progress got serious difficulties with the establishment, because new ideas threaten old oligarchies always: if what was always known is suddenly found to be wrong… what about the ruling establishment? Could possibly be the ruling establishment wrong too? This is why the genuine geniuses of creative thinking always smell of Lucifer, Lux-ferre, light carrying… As far as public opinion is concerned.

Socrates’ execution is famous, but just earlier Aspasia’s son had been executed (Aspasia was the philosopher telling Pericles what to say), so would be Demosthenes (fleeing Macedonian henchmen), Archimedes assassinated by a Roman soldier (for doing geometry in the sand), Hypatia (raped, flayed and dragged alive until dead, courtesy of the local Christians), or Boetius… And so were executed or terrified most Muslim intellectuals… Not to mention countless French intellectuals in the early Sixteenth Century, Bruno (burned alive in 1600 CE for suggesting exoplanets and solar systems around stars), Kepler (his mom was tried for witchcraft), Galileo and Descartes fleeing France (just for reasoning in public, after inventing algebraic geometry), and so on. Yes, the examples extend all the way to the Twentieth Century.

Most of these top thinkers had this in common: they had unusual careers, typically outside of the mainstream, and they lived dangerously. Because of this, they are often belittled to this day: little thinkers paid by the establishment tend to have resentment towards the great minds who had the courage to discover the bulk of human knowledge, because great minds are not small employees.

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Kepler’s work was necessary for Newton to contribute to human understanding. But Kepler’s work, on the face of it, was much harder than Newton’s. By the way, Kepler thought gravitation went as the inverse of the distance. The true law is the square of that. That was found by Bullaldius. All astronomers had an intuitive understanding, originating with Buridan’s explicit texts, that the gravitational force, in combination with the laws of motion, gave planetary orbits. The idea was published by 1350 CE. Newton proved most of the detailed mathematical reasoning (but arguably not all, he missed what came to be known as “Gauss theorem”… Although he tried to prove it). Great, but not the end all be all, as White Anglo-Saxon Supremacists pretend…

Richard Dawkins FRS (Fellow Royal Society), FRSL is a British ethologist, evolutionary biologist, and author. He is an emeritus fellow of New College, Oxford, and was the University of Oxford’s Professor for Public Understanding of Science from 1995 until 2008. Dawkins first came to prominence with his 1976 book The Selfish Gene, which popularised the gene-centred view of evolution and introduced the term meme. He just penned the following opinion, typical of white Anglo-Saxon supremacists:

Richard Dawkins, @RichardDawkins

“In 1665 Cambridge University closed because of plague. Isaac Newton retreated to rural Lincolnshire. During his 2 years in lockdown he worked out calculus, the true meaning of colour, gravitation, planetary orbits & the 3 Laws of Motion. Will 2020 be someone’s Annus Mirabilis?”

That statement of Dawkins sounds innocent enough: everybody agrees Newton invented everything he is famous for, and that’s a lot, as described by Dawkins. Yeah, except that most of what is attributed to Newton was actually not discovered by Newton. It is propaganda, to make us believe a WASP (White Anglo-Saxon Protestant) was this unfathomable genius. That is done by attributing to him centuries of discoveries, and turning the history of humanity into systemic racism.

Indeed, Newton didn’t invent calculus: Fermat did. (at most Newton invented a geometric way to solve some problems of calculus pertaining to orbits; using geometry to solve calculus problems was inaugurated by Buridan’s students… in the 1300s…).

And Newton didn’t find the second law of motion (which implies the first): Buridan did, three centuries before Newton (nowadays some Anglo-Saxons recognize that the law was known before Newton). The gravitation law was from French astronomer Bullaldius/Boulliau, Newton said it himself. And planetary orbits were Kepler’s great work, with his three law of planetary orbits!

So what did Newton do? Mostly he tried to prove that the law of motions plus the gravitation force as the inverse square of the distance implied Kepler’s laws. That’s great, but not of the order of Descartes’ Algebraic Geometry, or Fermat’s Calculus. To add insult to injury the notation of Leibnitz for calculus is used to this day… while Newton’s geometric calculus is ignored (that may be a mistake…) Newton and Leibnitz had a quarrel about this…

To establish their model of civilization, the English  propaganda has know no bounds: Sir Francis Drake, a great explorer, savior of England when confronting the Great Armada, was also a corsair mandated by the Queen, and a slave trader operating slave ships for profit. Not just that, but that plutocrat was one of the original “West Country men” who devastated Ireland. That mood and methods were then exported to America, where they established systemic racism as jurisprudence.

And central to propaganda was to establish English mental supremacy, for the entire planet to be awed by. As the great rival was France, the other Western superpower of the Middle Ages, many French discoveries were attributed to Englishmen. An example is Emilie Du Chatelet, who discovered and demonstrated energy… thus rising above Newton, who confused energy and momentum (discovered circa 1340 CE by Buridan; momentum is mv, energy is 1/2 mvv). This is a case of sexism hobbling civilization.

Another case is Denis Papin. Papin, who was a French physicist who trained with the best minds of his day, was a university professor of engineering. Papin fabricated the first powerful steam engine, and one capable of propelling a boat. After Papin’s death, Watt was born, and Watt, an inventor out of many, perfected the steam engine. So the unit of power is called a Watt because many people in England spent a lot of time trying (and succeeding) to steal Papin’s invention: the efforts of thieves should not go to waste. In the latest twist, British propaganda now calls Papin a British scientist… in truth Papin’s boat was built in Germany where he was professor, and, after steaming a hundred miles was destroyed by monks, who are professionals in fighting Lucifer…

An even more spectacular case is Lamarck, who published his establishment of the theory of evolution (from studying mollusk fossils with a microscope, for decades), before Darwin was born. Napoleon, and the Christian churches hated Lamarck, who was outlawed in english universities (Lyell and Darwin had to go to Scotland to be taught Lamarck’s discoveries). To this day, the disdain for Lamarck is a duty shared by those who want to teach in Anglo-Saxon universities, otherwise one would be called a charlatan.

Those who want to fight systemic racism have learned recently that they are made to revere false idols. Yes, and it did not happen by accident, but by intelligent design.

Simplicius: OK, as usual, you evoked some of the great minds and things we Anglo-Saxons tend to have never heard of: Buridan, Fermat, Papin, Du Châtelet, Lamarck… All French. And then Algebraic Geometry, Energy…

PA: Descartes invented how to describe geometry algebraically. Then Fermat developed Calculus, all the way to showing differentiation and integration were inverse to each other… As far as so many of the deepest thinkers being French, that comes from two things: First, France, or more exactly the Francia of the Franks was the creator of Europe (named by the Franks). Both Germany (by 800 CE) and Britain (1066) were Frankish creations. In either case, slavery was made unlawful. Second, France had three times the population of England. 

The case of Du Châtelet should be famous: here is a woman and she establishes what is perhaps the most important concept in physics. Buridan: momentum. Du Châtelet: energy. Sorry, but Newton’s discoveries pale in comparison (by the way, she died young, from childbirth; had she lived longer her contributions may have been even more amazing; she was an excellent philosopher of science).

Simplicius: Why would we, simple folks, care about who established the great scientific advances? Somebody did. So what?

PA: Which societies advance human understanding is crucial. Most do not, most of the time. We want to save humanity, going forward, and that means discovering what makes us more intelligent. Moreover in the case of England versus France, I detailed the fact that their colonization models in America were different. The French approach was governmental, and determined not to force the Natives. The English model was that of the “West Country Men”, as refined in England: exterminate, maximize profits.

Simplicius: What does who invented what have to do with how colonization was performed?

PA: The “West Country Men” model weaponized systemic racism. Racism is the idea that some human beings are biologically superior to others. By attributing all the discoveries to Englishmen, the Englishman is established as a higher species, or at least one which invents everything. In particular, the British plutocracy invented the most superior system of thought pertaining to civilization. So the “West Country Men” mentality, keen to line alleyways with Irish skulls, came to rule America. A practical consequence was the eradication of the Indians. 

Simplicius: Is not that all so yesterday? 

PA: Far from it. The mentality that greed and higher profits should rule is itself ruling, because it has ruled for four centuries, and penetrated the institutions. Trump came along and said: ‘Down with profits in China, bring back the jobs!’ The establishment, which uses the maximization of profits as its most superior moral principle, hated him for it. They hated him for it to the point they started to degrade the political process. An example is Biden calling Trump an “arsonist”, while it is the Obama-Biden administration which developed fracking, and was very loud about it. 

Claiming England had a superior model of civilization in its civilization relative to France (let alone Spain or Portugal) is claiming that the world should go on with that system of civilization… which is the dominant system of civilization, worldwide. The real situation is of course very complex. For example at this point the Brexiter Boris Johnson is applying old French like methods… While the European Union is officially led by greed is right, that is the “West Country Men” way… with the caveat that the COVID pandemic has proven that old fashion governmentalism, the French way, as practiced successfully by China… saves lives. So maybe then, Trump was right all along, and both France and Germany have decided to operate the same U turn towards more industrialization, planning and self sufficiency. 

Simplicius: OK, please, I have a headache! Let’s stop here! So then your point is that, by extolling Englishmen as great geniuses, when in fact they are not as great as that, one extolls English plutocracy and its systems of thought, moods and mentality, and that this is bad for civilization and the planet, promoting systemic racism, among other things. Got it.   

PA: It also distorts the refined history of systems of thought. And that’s not neglectable, because it teaches us how humanity learned to think better.  

Simplicius: Once again I don’t understand why correct attribution of the origins of systems of thought are relevant to the common person.

PA: It works this way: thinkers such as Dawkins go to school and are conditioned to believe the greatest minds are Anglo-Saxon. So they are naturally inclined to believe anything Anglo-Saxon is mentally superior, and this is what they teach in turn to the intellectual class of reporters, lawyers, doctors, engineers, CEOs, boards of directors, etc.

Those who want to fight systemic racism have learned recently that they are made to revere false idols. Yes, and it did not happen by accident, but by intelligent design. And yes it starts with the apparently innocent divinization of  Sir Francis Drake, Isaac Newton, or James Watt…

There is no innocence in the world of logic, contrarily to repute…

Patrice Ayme

 

Perverse Logic: Saving the Multiverse with Unhinged Cosmic Inflation!

February 1, 2018

When The Unobservable Universe Is Used To Justify Various Follies, Such As The Multiverse, Civilization Is In A Bad Way:

Physics is the laboratory of reason. This where the most advanced, most subtle logics are forged (even more so than in pure mathematics, where the navel’s importance is too great). So what physicists ponder, matters to the entire civilization which nurtures them. When physics goes to the dogs, so does civilization. The follies of state of the art theoretical physics, reflect an ambient madness which pervades civilization. (If you don’t believe this, may I sell you some imaginary bitcoins for millions of dollars?)

Astrophysicist Ethan Siegel, a continual source of excellent articles in physics, wrote an interesting essay which I disagree with. His reasons are interesting, and have the merit of honesty. My answers are even more striking, and I bring the full weight of 24 centuries of history as meta-evidence for crushing the feeble, pathetic, short-sighted considerations of my fellow physicists. Ethan’s essay is entitled: “Yes, The Multiverse Is Real, But It Won’t Fix Physics
Surprisingly, the evidence points towards the existence of the unobservable multiverse. But it isn’t the answer you’re looking for.

Ethan proposes to use cosmic inflation to provide for the proliferation of Schrödinger cats and Wigner’s friends. One folly would thus provide for the other, and they would thus stay up, like two drunks falling into each other’s arms. I will instead humbly suggest to do away with madness altogether. But first a little recap.

The universe is expanding. This experimental evidence was established around 1920, by a number of astronomers in Europe and the USA, the most famous of whom was lawyer turned astronomer, Edwin Hubble. Hubble had the biggest telescope. The expansion is presumed to be looking everywhere the same, and this is what seems to be observed. That also means that, if one looks far away, galaxies will seem to be receding from us at speed ever closer to the speed of light. As the apparent speed of these galaxies approach c, their light gets shifted to lower and lower frequencies, until they become invisible (same reason as why Black Holes are blacker than black).

Where the transition to invisibility occurs is called the “event horizon”. Beyond the event horizon is the unobservable universe (we can’t detect it gravitationally, as gravity goes at the speed of light, a theoretical prediction now experimentally verified).

The observed universe is “flat” (namely there is no detected distortion in the distribution of clouds, filaments and superclusters of galaxies). That sounds unlikely, and indicates that the observed universe is a tiny portion of a much larger whole.

This unobservable universe has nothing to do with the “Multiverse” brandished recently by many theoretical physicists who have apparently run out of imagination for something more plausible. Eighty years ago, Schrödinger pointed out that Quantum Mechanics, as formalized then (and now!) was observer dependent, and filled up the universe with waves of dead and live cats (when applied to macroscopic objects). That’s called the Schrödinger Cat Paradox. Instead of calling for a re-thinking of Quantum Mechanics (as I do!), Ethan Siegel (and many other physicists and astrophysicists) embrace the dead and alive cats, settling them in “parallel universes”. So basically they reenact Solomon Judgment: instead of cutting the baby in two, they cut the universe in two. Zillions of time per second, in zillions of smaller places than you can possibly imagine… Here is a picture of Schrödinger cat: as the branches separate in that movie, two universes are created. This is what Ethan Siegel wants to justify, thanks to cosmic inflation…

Ethan’s revealing comment: “The idea of parallel Universes, as applied to Schrödinger’s cat. As fun and compelling as this idea is, without an infinitely large region of space to hold these possibilities in, even inflation won’t create enough Universes to contain all the possibilities that 13.8 billion years of cosmic evolution have brought us. Image credit: Christian Schirm.”
To explain crazy, we will go more crazy, thus making the previous crazy sound more rational, relatively speaking…

The Multiverse”, with baby universes all over the universe, has more to do with the “Many Worlds Interpretation” of Quantum Mechanics, a theory so absurd that the great popes of physics ruling around 1960 rejected it outright. Wheeler was ashamed of himself for having had a PhD student, Everett, who suggested this folly(Everett couldn’t get an academic job, at a time when academic employment in physics was booming!)

Ethan wrote: “In the region that became our Universe, which may encompass a large region that goes far beyond what we can observe, inflation ended all-at-once. But beyond that region, there are even more regions where it didn’t end.”

This sort of statement, and I say this with all due respect to the divine, is equivalent to saying:”Me, Ethan, having checked all that exists, observable by simple humans, or not, thereby informs you that I am either God, or that She is an interlocutor of mine. We checked that cosmic inflation thing, and saw it all over all the possible universes. Don’t talk, just learn.”

There is no way for us humans to know, for sure, or not, what is going on beyond the observable universe (aside from having no gravitational field distortions when approaching the event horizon, as I said above when considering “flatness”).

Ethan notices that Many Worlds fanatics have tried to use cosmic inflation to save their (ridiculous) theory. (“Many Worlds” is ridiculous, as Schrödinger tried to show, long ago, because there would be as many ways to cut the universes into “Many Worlds” as there are observers. So, so to speak, the “Many World Interpretation”, call it MWI, is actually MWI ^ {Observers} (MWI to the power of the set of all possible Observers, the latter set being itself something of an uncountably infinite function of MWI.)

Ethan says: “But just because variants of the Multiverse are falsifiable, and just because the consequences of its existence are unobservable, doesn’t mean that the Multiverse isn’t real. If cosmic inflation, General Relativity, and quantum field theory are all correct, the Multiverse likely is real, and we’re living in it.

What Ethan is saying is that if a number of crazy (cosmic inflation), or incomplete (Quantum Field Theory), ideas are “all correct”, then something as useful as angels on pin heads is real.Yes, indeed, if one believes that Muhammad flew to Jerusalem on a winged horse (!), one may as well believe all the rest of the Qur’an. That is a proof by crystal balls. After Ptolemy and company had established their (half correctly) predicting “epicycles” theory, one could have used it in turn to “prove” Aristotle ridiculous theory of motion.

23 centuries ago a much saner theory existed, that of Aristarchus. It was rejected at the time, precisely because it was not insane, and even though it was used to make a nearly correct prediction of the distance of the Moon. Aristarchus underestimated the distance of the Sun, but a telescope could have changed this (by showing more precisely the angle of the terminus on the Moon). If astronomers had the time had accepted heliocentrism as a possibility, it would have led them to invent the telescope. Similarly, right now, rejecting Many Worlds and Multiverse will lead to develop instruments which don’t exist yet (I have proposed at least one).

Astrophysicist Ethan Siegel suggests that: “The Multiverse is real, but provides the answer to absolutely nothing.” My opinion is that the Multiverse is worse than useless: the unhinged mood it provides prevents to develop more fruitful avenues of research, both theoretically and experimentally.

Insanity is the rule in crowds (Nietzsche). Thus follies are the truths crowds love, at first sight, before being corrected by higher minds. Why? Follies bind, because they are so special.

https://patriceayme.wordpress.com/2015/02/20/commonly-accepted-delusions-follies-that-bind/

In Aristarchus’ times, heliocentrism, the fact Earth and its Moon rotate around the Sun, should have been obvious. Indeed, people, let’s think for a moment: where was the Sun supposed to be, considering the phases of the Moon? If the Sun turned around Earth, the Moon’s illumination should have changed all day long! It didn’t require much geometrical analysis to discover that this source of light could only be where Aristarchus computed it to be, far away from the Earth-Moon system.

It took 19 centuries to correct that (obvious!) mistake. Interestingly, Jean Buridan, circa 1350 CE, did it in the most theoretical fashion.

https://patriceayme.wordpress.com/2016/03/20/momentum-force-inertia-middle-ages-buridan/

Buridan first showed that Aristotle’s ridiculous theory of motion made no sense, and had to be replaced by inertia and momentum (what Buridan called “impetus”). Having done this, the motion of the planets in a heliocentric system could be explained by “circular impetus”, Buridan pointed out (then he observed sardonically that we couldn’t observe the difference between epicycles and heliocentrism, so may as well go for “Scripture”).

Similarly, nowadays, instead of arguing with the “angels on a multiverse pinhead” authorities, we better point out to the glaring inconsistencies of Quantum Mechanics.

Civilization without reason is like a chicken without a head: it can run, but not forever.

Patrice Aymé

Nature Of The Physical Law & Reaction Law

December 5, 2016

Human laws are modelled, in spirit, after physical laws. So it is socially important to realize how physical laws are established, and that they are not immutable. Physical laws are established by observation (some direct, some axiomatic; yes, a paradox). However, if you read the magazine “Wired”, you may feel that physical laws are established, like the Bible or the Qur’an, by the sheer power of a personality cult:

“LAST MONTH, NASA researchers dropped news with potentially huge consequences for space travel and science as a whole: They ran an experiment whose results seem to defy the very laws of physics, and could change how we travel through outer space. Problem is, experts say that it’s incredibly unlikely that Isaac Newton is wrong. Instead, the most likely explanation is the team simply made a mistake somewhere along the way

The team was testing a theory that there’s a new way to propel satellites, instead of using rockets powered by a limited supply of fuel. So they put a radio antenna in a specially designed, sealed container. Turned on, the antenna bounced 935MHz radio waves (similar to those used by some cell phones) around, and the container apparently moved a tiny, tiny bit. This violates Newton’s third law of motion, one of the basic tenets of physics.

Loosely put, Newton taught us that no action can occur without an equal and opposite reaction.”

[WIRED from August 2014: https://www.wired.com/2014/08/why-nasas-physics-defying-space-engine-is-probably-bogus/]

Reaction = Action Is An Experimental Fact. Or Was, Until Recently. Does not have to stay that way

Reaction = Action Is An Experimental Fact. Or Was, Until Recently. Does not have to stay that way

Right, the article is from 2014. However, the riddle got more interesting in 2016, when the same tests were conducted in hard vacuum… with the same results (it was initially thought that radiation heated air, which expanded, creating a push; without air, that counter-idea failed).

Who are these “experts”? People who gave the Nobel Prize to each other? Newton did not “teach” us that action = reaction inasmuch as he demonstrated it (thanks to arcane mathematics). Before I explain what I mean, let me mention that Richard Feynman wrote a famous book “The Character of the Physical Law” (which I read). Feynman observes that there is a hierarchy of laws. Here I will observe something even more subtle: there is a hierarchy of how fundamental laws are viewed as fundamental.

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Newton ASSUMED this “Third Law”, he made an hypothesis of it (and the law was probably known to cannoneers for centuries). Using in part this action = reaction hypothesis, Newton was able to deduct, from a large axiomatic system, with lots of arcane mathematics, theorems. And some of these theorems had practical consequences which were found, or known, to be true (Kepler laws). So it was reasonably assumed that Newton’s Third Law was correct: it is an axiom the use of which bring the correct theorems. The same sort of reasonings established the First and Second Laws of motion, which were discovered by the stupendous genius Buridan, three centuries BEFORE Newton.  

To my knowledge, the Third Law was first stated by Newton. However, that law was certainly well-known by Roman artillery engineers, who were used to catapult large masses at enormous distances: they knew of the recoil all too well. Roman and European Middle Age artillery enabled to seize cities (armies which were less competent in artillery found seizing cities difficult to do; the Turks used Hungarians engineers to breach the walls of Constantinople with giant guns).

Thus we see there are two sorts of physical laws: those we assume as axioms, and then we certify them, because the mathematical logic they give rise to bring apparently correct results. Other natural laws are observed directly.

For example, the so-called “Standard Model” can be viewed as a sort of giant law. It uses, in its axioms, the so-called Higgs boson, and that was indeed found (sort of).

Thus direct observations can suggest a law (say action = reaction; or gravitation) which then is established through the axiomatic method (heavily used in modern physics). Actually the case of gravitation is even more interesting: observations suggested an attractive force. Then Ismaël Bullialdus, a French priest-astronomer-mathematician found a reasoning why it should be an inverse square law (Bullialdus has a crated named after him on the Moon). Armed with Bullialdus inverse-square law, Isaac Newton used the inverse square law as an axiom to “deduce” Kepler’s laws  (I wrote “deduce”, because, centuries later, it was called into question whether Newton had properly demonstrated Gauss’ law, which reduce, gravitationally speaking, planets to massive points)

Examples of laws observed directly are numerous: they include the classical laws of optics, of forces (depicted by vectors; but one cannot use vector theory to prove how force behave… because vectors are abstracted forces), much of electrical behavior, etc.

Some laws were deduced from axiomatics before being demonstrated experimentally. Newton’s crowning achievement was more or less) demonstrating the equivalence of Kepler Laws with the 1/dd inverse square universal attraction law… given the laws of “Newtonian” Mechanics.

As I said, the laws of mechanics were greatly deduced by Buridan and various engineers, generations before Newton.

Could the same be going on now? Who knows?

It is a question of observation. Ultimately physics, nature, is what is observed, nothing less. It gets to be more than what is observed, because of our imagination, and the fact it needs to use the logics and maths it knows.

Meta-lesson? Politics degenerated in the West, in the last 50 years, because what was really going on was observed only in a fragmentary way. This is in particular the drama of so-called “left”, or progress. We have to stick to what is observed.

In the case of democrats, what was observed is that “Democrats” selected a candidate who was the object of 4 Congressional inquiries (Sanders had none, never had any).

Now they insult us.

Patrice Ayme’

BURIDAN: MOMENTUM, FORCE, INERTIA, MIDDLE AGES…

March 20, 2016

Buridan was the real author of the so-called Copernican Revolution… Nearly Two Centuries Prior…

When did mechanics and calculus of the Seventeenth Century start? Well, around 1350 CE, in Paris, thanks to the genius Buridan, and his students.

WHAT’S MASS? It is not an easy question. An answer for inertial mass was given seven centuries ago. Astoundingly, it’s still the foundation of our most modern physics. Let me explain. (And the thinker who suggested this, Buridan, used this new mechanics to suggest that the Earth turned around the Sun, and generally planets went into circular orbits; thanks to Catholic terror, most physicists, let alone the Plebs, have any inkling of this: religious terror works!)

Momentum, force, and inertial mass were defined from trajectory deviation, first. This, I will show below, is incredibly modern (the idea is found in Riemann ~ 1860 CE, as I explained within the text of “Quantum Trumps Spacetime”). This was all in Buridan’s work, in the Fourteenth Century (14C).  Jean Buridan postulated the notion of motive force, inventing a notion he named impetus… which is exactly momentum (= mv). Consider this, from Buridan’s Quaestiones super libros De generatione et corruptione Aristotelis:

When a mover sets a body in motion he implants into it a certain impetus, that is, a certain force enabling a body to move in the direction in which the mover starts it, be it upwards, downwards, sidewards, or in a circle. The implanted impetus increases in the same ratio as the velocity. It is because of this impetus that a stone moves on after the thrower has ceased moving it. But because of the resistance of the air (and also because of the gravity of the stone) which strives to move it in the opposite direction to the motion caused by the impetus, the latter will weaken all the time. Therefore the motion of the stone will be gradually slower, and finally the impetus is so diminished or destroyed that the gravity of the stone prevails and moves the stone towards its natural place. In my opinion one can accept this explanation because the other explanations prove to be false whereas all phenomena agree with this one

 In 14 C, In The Late Middle Ages, Buridan Defined Momentum And Force By Considering Deviation Of Particle Trajectory

In 14 C, In The Late Middle Ages, Buridan Defined Momentum And Force By Considering Deviation Of Particle Trajectory

Buridan writes an explicit formula:  impetus = weight x velocity. Just a word of the modernity of it all: the idea translates directly into defining force(s) with changes of distance between geodesics (in differential manifold theory). Also Buridan launches the vector theory of force (the impetus goes in the direction of the force imparted)… and the force of gravity. (Buridan identifies implicitly gravitational and inertial mass, another correct assumption.)

Buridan states that impetus = weight x velocity (modern momentum). All the predecessors of Buridan thought one needed a force to keep on moving, but Buridan did not. Famous predecessors such as Hibat Allah Abu’l-Barakat al-Baghdaadi, who modified Avicenna’s theory, which followed John Philoponus believed in inertia NOT. They all followed Aristotle, who believed all and any motion died away, if no force was applied. (Not to say no Muslim ever invented anything scientific: the Uzbek ibn-Musa al-Khowarizmi crucially put the finishing touch on the zero, which he partly got from India, in the Ninth Century.)

Buridan’s pupil Dominicus de Clavasio in his 1357 De Caelo, pointed out that this extended to gravity:

“When something moves a stone by violence, in addition to imposing on it an actual force, it impresses in it a certain impetus. In the same way gravity not only gives motion itself to a moving body, but also gives it a motive power and an impetus, …”.

Buridan knew celestial bodies were moving from inertia: “God, when He created the world, moved each of the celestial orbs as He pleased, and in moving them he impressed in them impetuses which moved them without his having to move them any more…And those impetuses which he impressed in the celestial bodies were not decreased or corrupted afterwards, because there was no inclination of the celestial bodies for other movements. Nor was there resistance which would be corruptive or repressive of that impetus.”

By definition, inertial mass is what resists an applied force. The greater the resistance to a force, the greater the inertial mass of what it is applied to.

Buridan invented the tunnel thought experiment (and thus, the idea of thought experiments). If a tunnel were bored through the center of the Earth and a heavy body dropped into it, what would happen to it? Well, Buridan gave the correct answer, repeated as a good parrot by Galileo… nearly three centuries later:

Galileo Galilei expressed this fundamental principle of his dynamics in his 1632 Dialogo:

The heavy falling body acquires sufficient impetus [in falling from a given height] to carry it back to an equal height.

Buridan had many students: Buridan’s thought was pursued up by his pupil Albert of Saxony (1316–1390), by Poles such as John Cantius, and the Oxford Calculators Nicole Oresme pioneered the practice of demonstrating laws of motion in the form of graphs (equations weren’t available yet); some of these are now known as central and basic theorems of calculus (like the theorem of the mean, guessed in Oxford, proven by Oresme)

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Buridan’s Revolution:

Buridan introduced p = mv, called it “impetus” and stated that it did not change if no force was applied. Thus Buridan buried the complete idiocy known as Aristotle’s physics. (That Aristotle could be a complete idiot at the mental retard level is philosophically, and historically capital, as Aristotle set in place the leadership system through celebrities, which we enjoy to this day).

Buridan’s Inertia Law is known as Newton’s First Law (because Buridan was from Paris, while Newton demonstrates the superiority of the English born three centuries later by attributing to him what Isaac did not discover).

More generally Newton asserted clearly his Second Law: dp/dt = F (where  F is the Force, by definition). It’s an axiom. (Weirdly the Second Law implies the First…)

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Force = Deviation From Trajectory:

This is Buridan’s idea. It was taken over again by Bernhard Riemann, in the early 1860s (five centuries after Buridan’s death). In modern mathematical parlance, force is depicted by geodesic deviation. It’s this idea which is at the triple core of Einstein’s theory (with the idea that gravitation/spacetime is a field, and that it’s Newton’s theory, in first order).

So this is ultramodern: the idea got carried over in “Gauge Theories”, and, because there are several forces, there are many dimensions.

***

Thought Experiment Often Precedes Experiment: 

Yesterday I bought a (2015) book by a (British academic) historian of science. In it, the honorably paid professional asserted modern science started with Tycho in 1572. Tycho, a Count set his student Kepler onto the refined study of the orbit of Mars. Both Tycho and Kepler were 5 star scientists (differently from, say Copernicus or Einstein, both of whom too little inclined to quote their sources). So they were, because, differently from, say, Obama, they had strong personalities. Great ideas come from great emotions. Tycho believed the Ancients had lied. And he was right, they had lied about the orbits of the planets: observations with the same instruments gave different results from the ones the Ancients had claimed.

The preceding shows that this trite notion is profoundly false; the scientific revolution was launched by Buridan and his students (among them Oresme, Albert of Saxony), contemporaries and predecessors (including Gerard de Bruxelles and the Oxford Calculators). Some of their work on basic kinematics, the exponential and the mean theorem of calculus was erroneously attributed to Galileo or Newton, centuries later.

To believe everything got invented around the seventeenth century is not to understand how the human mind works. Experience has to be preceded by thought-experiment (even Einstein understood that). Buridan and his contemporaries did the preliminary thinking (while others were making clocks and hydraulic presses). All of this would become immensely easier after the invention of algebra and Descartes’ analytic geometry, true.

So let’s have a loving and admirative thought for Buridan, the main author of the scientific revolution, whose reputation, and WISDOM was destroyed by the (TERRORIST) CATHOLIC STATE: Buridan’s astronomical reputation was destroyed by the Catho-fascists, more than a century after his death. That’s why the heliocentric system is attributed to an abbot from a rich family (Copernicus), instead of the master physicist said abbot was forced to read as a student.

Studying the history of science, and mathematics uncovers the fundamental axioms, in the natural order given by their obviousness.

Determining which ideas came first, and why is not about determining who is the brightest child, or most impressive bully in the courtyard. In 1907, Einstein made a big deal that he, Albert, was the discoverer of Energy = Mass (“E = mcc”). A careful inspection shows that this either reflects dishonesty, or misunderstanding on his part. Or both. I will address this soon, as I keep on studying mass and momentum.

Buridan put momentum at the core of physics, and thought-measured if dynamically. Momentum is still at the core: photons have momentum, but not mass.

It’s important to realize that many of the latest ideas in physics (all of “Gauge Theories”)  rest on an idea invented in Paris seven centuries ago. Not to slight it, or to heap contempt on all the noble Nobels. But, surely, the time has come for really new ideas!

Patrice Ayme’  

MATH AS NEUROLOGY, NEUROLOGY AS PHYSICS

April 22, 2015

 

After demolishing erroneous ideas some 25 centuries old, some brand new, I explain why Mathematics Can Be Made To Correspond To A Subset Of Neurology. And Why Probably Neurology Is A Consequence Of Not-Yet Imagined Physics.

Distribution of Prime Numbers Reworked Through Fourier Analysis: It Nearly Looks Like Brain Tissue

Distribution of Prime Numbers Reworked Through Fourier Analysis: It Nearly Looks Like Brain Tissue

SOCRATISM, PLATONISM ARE WRONG:

Einstein famously declared that: “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”

Well, either it is an unfathomable miracle, or something in the premises has to give. Einstein was not at all original here, he was behaving rather like a very old parrot.

That the brain is independent of experience is a very old idea. It is Socrates’ style “knowledge”, a “knowledge” given a priori. From there, naturally enough aroses what one should call the “Platonist Delusion”, the belief that mathematics can only be independent of experience.

Einstein had no proof whatsoever that”thought is independent of experience”. All what a brain does is to experience and deduct. It starts in the womb. It happens even in an isolated brain. Even a mini brain growing in a vat, experiences (some) aspects of the world (gravity, vibrations). Even a network of three neurons experiences a sort of inner world unpredictable to an observer: https://patriceayme.wordpress.com/2015/03/15/three-neurons-free-will/

Latest Silliness: Smolin’s Triumph of the Will:

The physicist Lee Smolin has ideas about the nature of mathematics:

Smolin:

“the main effectiveness of mathematics in physics consists of these kinds of correspondences between records of past observations or, more precisely, patterns inherent in such records, and properties of mathematical objects that are constructed as representations of models of the evolution of such systems … Both the records and the mathematical objects are human constructions which are brought into existence by exercises of human will; neither has any transcendental existence. Both are static, not in the sense of existing outside of time, but in the weak sense that, once they come to exist, they don’t change”

Patrice Ayme: Smolin implies that “records and mathematical objects are human constructions which are brought into existence by exercises of HUMAN WILL; neither has any transcendental existence”. That’s trivially true: anything human has to do with human will.

However, the real question of “Platonism” is: why are mathematical theorems true?

Or am I underestimating Smolin, and Smolin is saying that right and wrong in mathematics is just a matter of WILL? (That’s reminiscent of Nietzsche, and Hitler’s subsequent obsession with the “will”.)

As I have known Smolin, let me not laugh out loud. (“Triumph of the Will” was a famous Nazi flick.)

I have a completely different perspective. “Human will” cannot possibly determine mathematical right and wrong, as many students who are poor at mathematics find out, to their dismay!

So what determines right and wrong in mathematics? How come enormously complex and subtle mathematical objects, which are very far from arbitrary, exist out there?

I sketched an answer in “Why Mathematics Is Natural”. It does not have to do with transcendence of the will.

***

AXONAL LOGIC IS MATHEMATICAL LOGIC, NEUROLOGY IS MORE:

Neurology, the logic of neurons, contains what one ought to call axonal logic, a sub-category.

Axonal logic is made of the simplest causal units: neuron (or another subset of the brain) A acts on neuron (or brain subset) B, through an axon. This axonal category, a sub-category, corresponds through a functor, from neurology to mathematical logic. To A, and B are associated a and b, which are propositions in mathematical logic, and to the axon, corresponds a logical implication.

Thus one sees that mathematics corresponds to a part of neurology (it’s a subcategory).

Yet, neurology is vastly more complicated than mathematical logic. We know this in many ways. The very latest research proposes experimental evidence that memories are stored in neurons (rather than synapses). Thus a neuron A is not a simple proposition.

Neurons also respond to at least 50 hormones, neurohormones, dendrites, glial cells. Thus neurons need to be described, they live, into a “phase space” (Quantum concept) a universe with a vast number of dimensions, the calculus of which we cannot even guess. As some of this logic is topological (the logic of place), it is well beyond the logic used in mathematics (because the latter is relatively simplistic, being digital, a logic written in numbers).

The conclusion, an informed guess, is that axons, thus the implications of mathematical logic, are not disposed haphazardly, but according to the laws of a physics which we cannot imagine, let alone describe.

And out of that axonal calculus springs human mathematics.

***

HOW TO PROVE THAT MATHEMATICS IS NEURONAL PHYSICS?

If my hypothesis is true, mathematics reduces to physics, albeit a neuronal physics we cannot even imagine. Could we test the hypothesis?

It is natural to search for guidance in the way the discovery, and invention, of Celestial Mechanics proceeded.

The Ancient Greeks had made a gigantic scientific mistake, by preferring Plato’s geocentric hypothesis, to the more natural hypothesis of heliocentrism proposed later by Aristarchus of Samos.

The discovery of impetus and the heliocentric system by Buridan and his followers provides guidance. Buridan admitted that, experimentally heliocentrism and “scripture” could not be distinguished.

However, Buridan pointed out that the heliocentric theory was simpler, and more natural (the “tiny” Earth rotated around the huge Sun).

So the reason to choose heliocentrism was theoretical: heliocentrism’s axiomatic was leaner, meaner, natural.

In the end, the enormous mathematical arsenal to embody the impetus theory provided Kepler with enough mathematics to compute the orbit of Mars, which three century later, definitively proved heliocentrism (and buried epicycles).

Here we have a similar situation: it is simpler to consider that mathematics arises from physics we cannot yet guess, rather than the Platonic alternative of supposing that mathematics belong to its own universe out there.

My axiomatic system is simpler: there is just physics out there. Much of it we call by another name, mathematics, because we are so ignorant about the ways our mind thinks.

Another proof? One can make a little experiment. It requires a willing dog, a beach, and a stick. First tell the dog to sit. Then grab the stick, and throw it in the water, at 40 degree angle relative to the beach. Then tell the dog to go fetch the stick. Dogs who have practiced this activity a bit will not throw themselves in the water immediately. Instead they will run on the beach a bit, and then go into the water at an angle that is less than 90 degrees.

A computer analysis reveals that dogs follow exactly the curve of least time given by calculus. Dogs know calculus, but they did not study it culturally! Dogs arrived at correct calculus solutions by something their neurology did. They did not consult with Plato, they did not create calculus with their will as Smolin does.

It’s neurology which invents, constructs the mathematics. It is not in a world out there life forms consult with.

Patrice Ayme’

Flat Universe Flattens Twisted Logic

April 11, 2015

The observed universe is flat. I will explain what it means in practice, before going into a bit of theory. Including a sickle move through the lamentable precedent of the heliocentric system.

Basically, when we look at a galaxy which is very very very far away, it appears to have the same size as it should have considering its distance. Ah, yes, because we can determine the distance of a very very remote galaxy, or so we think, by looking at its red shift (how much redder it looks than what it would be if it were next door).

This apparently innocuous set-up creates lots of problems for the ruling cosmological theory, the Big Noise Bang. The barnacles attached to the Big Noise, thousands of professional cosmologists, would not be happy to see their ship sink, so they insist it’s doing all right. Yet I am dancing all around with the facts, and, should they read me carefully, they would be less sanguine about the respect they will enjoy, in the fullness of time.

Gravitational Lensing. Lensing Without Gravitation Would Signal Curvature. So Would Apparent Size Variations. Neither Is Observed, However far We Look.

Gravitational Lensing. Lensing Without Gravitation Would Signal Curvature. So Would Apparent Size Variations. Neither Is Observed, However far We Look.

The Big Noise cosmologists may well be wrong, because they suppose plenty of things for their model. All too many things, some of them, pretty weird. I get to the same observations, while being much more parsimonious with my hypotheses.

We have seen it all before, this conflict between common sense , and complicated absurdities by great priests, themselves at the service of higher authorities. Remember the Ptolemaic system? That claimed the Sun rotated around Earth. That absurdity ruled for around 15 centuries

***

Cosmology is serious business:

The Ptolemaic System Was An Obese Lie, Thus Contradicting It, A Capital Crime:

The bigger the lie, the greater the authority. So great authority loves big lies: it is a training ground for the feeble minds which make authority so great.

The greatest philosopher of the Fourteenth Century, and the greatest physicist of the Middle Ages, the Parisian Johannes Buridanus, sent the Ptolemaic system to the bottom of the sea (1320s CE).

However Jean Buridan, adviser to 4 kings, and head of the University of Paris, did not want to be burned alive. So Buridan presented all his new physics and cosmology as something “supporters” of the point of view that “authority does not demonstrate” were talking about (he named no names).

Buridan believed that the Earth turned on itself each day, and around the sun in a year, that the arrow would fall at the same point, because of his own theory of impetus. Etc. It’s all very clear, and some of it can even be read. (In this extract Buridan supports geocentrism; in later extracts, he concludes he cannot be distinguished from heliocentrism observationally; a full study of Buridan is not extant. Some of the later arguments of Buridan are found in Oresme.)

Even the ship example used by Galileo, 300 years later, to demonstrate the undetectability of uniform motion is Buridan’s invention, for the same purpose (Buridan’s student, bishop Oresme wrote about it too).

The Catholic Church, supported by King Plutocrat Louis XI, made reading Buridan a capital crime in 1473 CE. Buridan’s cosmology was posthumously re-amplified by his student and (self) publicist, the dying Abbot Copernicus.

That fancy, the heliocentric system, was, on the face of it, quite ridiculous: Buridan said the Earth was “tiny” so it was only understandable that the tiny thing would rotate on itself, while enormous thing would stay put.

***

Authorities Love Systems Which Lie And Make No Sense:

Why the heliocentric system, was entertained so long explains much of the enthusiasm for the Big Bang. The psychology is similar: an obscure set of ideas was made more hermetic by computations nobody understands. Actually, it’s Plato who launched the Big Ptolemaic Noise, six centuries prior to Ptolemy’s efforts.

Believing in the heliocentric system was good training for submitting to stupid authority, and learning to become non-critical.

But let’s go back to flatness.

Basic Math Of Flatness:

Our universe of stars, clouds, and galaxies, is three dimensional (as I often talk of high dimensions, see note: the “3” maybe an average of the “many”).

Geometries can be flat (a plane) or spherical (aka “elliptic”; as on a round planet), or “hyperbolic” (a saddle).

A mighty theorem (Perelman-Thurston; see technical note on mathematical background) implies that astronomically plausible non-flat geometries contain flat, spherical or hyperbolic elements.

I will simplify further.

Geometries are determined by their geodesics (the shortest paths). At least locally.

A non-flat universe means that that some perspective can be found so that two neighboring geodesics will either converge or diverge.

For a proof, just look at a sphere, or a saddle; the geodesics can be determined by pulling a string between two points, making the shortest paths. They are the greatest circles in the case of a sphere. Notice that the distances between two nearby strings, once pulled to make geodesics, vary. The big math proof, with equations, does not say anything more.

No Empty Space Lensing, No Curvature:

In space, geodesics are paths followed by light. If the universe is not flat, light will either diverge, or converge, as if space itself was a lens. This means that a galaxy, or a galactic cluster, will appear bigger, or smaller, than it should.

Some may object that lensing in space is well known, and is even used to look at the furthest galaxies. However that lensing is due to gravity slowing down, and bending light, as happens with light grazing the sun. That’s called gravitational lensing. Entire galactic clusters are known to operate as giant lenses.

If one saw lensing, with nothing in between, the lensing would not be gravitational and the universe would not be flat.

But so far, this has not been observed.

A perfectly flat universe means global curvature zero. However the basic idea of the Einstein Field Equation (EFE) is:

CURVATURE = MASS-ENERGY-MOMENTUM

Actually, this equation is the basic idea, thus the ultimate simplification. As it is, it cannot work without further complications, because the object on the left has much higher dimension than the 10 dimensional tensor on the right; so one has to simplify the curvature first). The real equation is more like:

Function of Curvature = Mass-Energy-Momentum

There are a lot of mathematical details to figure out, to make that basic idea fit in. It took many stupendous mathematicians and physicists many years working together frantically to figure them out. In particular, Einstein and Hilbert cooperated intensely, helped by many collaborators… And the initial idea comes from the mathematician/physicist/philosopher Riemann (1866). So it took 60 years to make the idea work, and one should not expect casual readers to get the ideas in 60 lines, let alone 60 seconds.

An obvious (sort of) prediction was that, as the Mass-Energy of the universe is not zero (it’s full of galaxies, which have mass, and energy), then the curvature could not be zero. But then, if curvature (of the space-time of the universe) is not zero, then the universe has got to be moving.

Revolted by a moving universe, Einstein then added another curvature term, Lg. Lg counterbalanced Mass-Energy-Momentum, and gave a static (but unstable) universe.

Thus Einstein did not predict what the astronomers were starting to observe, namely the expansion of the universe. Einstein abandoned L (“Lambda”), calling it the “biggest blunder [he] ever made”.

(According to me, he made a much graver error in 1905.)

***

Dark Energy Flattens Cosmological Logic:

Ninety years later, the most basic supernovas were studied. They arise in binary systems: a star transfers part of itself to its companion, a super hot white dwarf. It is a bit like transferring gasoline on an amber: when enough mass has been transferred to Dwarf, the pressure and heat in the depth is just right for thermonuclear fusion to re-ignite explosively. It happens in exactly the same way always (although some argue about this). So these Type 1a supernovae are viewed as candles always of the same luminosity.

Large surveys (rejecting some explosion viewed as outliers) concluded that far-away Type 1a explosions were weaker than the Hubble law of expansion predicted. And the further one looked, the more the 1a explosions faded.

The conclusion was drawn that the universe expanded faster than the old model of Hubble and Einstein’s Gravitation theory predicted.

Greater expansion meant greater energy, and its source was not clear, so it was named DARK ENERGY.

Ironically to describe the simplest way to describe it was just to re-introduce the Lg term Einstein had introduced and then rejected, while he blundered about clumsily.

***

Your Humble Servant Flattens All:

It remains that the original theory of Einstein requires a very fine tuning of parameters to make our universe explode into its present very flat state in a bit less than 14 billion years. It also requires a supplementary explosion, called “Cosmological Inflation”.

I don’t have this problem.

I just wipe Einstein and his cohorts clean. I am master of my own soul. They have two Cosmological Inflations. I have just one, the one that is observed.

And my version of the universe can be 100 billion years old, or more.

I don’t confuse gravitation and revolution, inflation and what not. The Einstein Field Equations are correct, I just don’t apply them to the universe.

Simple does it.

Making something complicated simply because it allows to “shut and calculate” (the philosophical doctrine of contemporary physics) has been seen before. This was the trap into which Ancient Greek astronomy fell, making ever more sophisticated versions of the Ptolemaic system.

We should avoid duplicating our forebears’ mistakes.

Patrice Ayme’

Mathematical Note:

That I consider the universe three dimensional may sound as a strange admission, as I always advocate all sorts of dimensions, from the brain to fundamental physics. But not so: just view the three dimensional aspect as an… average.

(Here I am going to talk as a common physicist or mathematician, and elide the tweaking of fundamental axioms of topology and logic that I am wont to engage in, because I want to present the simplest picture.)

More precisely, this is what happens in two dimensions. In one dimension, the line or circle, there is just one geometry.

The USA mathematician Thurston launched a theorem, proven by the Russian Perelman, which showed there were just eight fundamental geometries in three dimensions.

(Disgusted by the dog eat dog attitude of famous mathematicians, some of whom I personally know, Perelman refused prizes, and abandoned math; I do share Perelman’s indignation, and then, more. Austerity, as imposed by plutocrats, has made even mathematicians like rats, prone to devour the innocent. The problem is not just in physics.)

META

October 8, 2013

I pursue my (energy motivated) program of turning all mathematics and logic, FINITE. I define the appropriate notion of META. Not just that, but I use the notion to make any logic into a chrono-logy. (A Chronology/Semantic Hierarchy evades the logical paradoxes.)

This is extremely advanced material, well beyond the edge of what’s commonly understood, using implicitly the implicated order from my sub-Quantum theory. Still most of the notions used below are easy to understand!

***

The notion of “META” is fundamental for the analysis of any system of thoughts or emotions. What’s going meta? I claim: Any theory has meta-theories associated to itself.

If one looks at the literature of meta, it’s a big mess. Recently it was encumbered by a sensation author obsessed by “strange loops” (Douglas Hofstadter, in books starting in 1979 with Gödel, Escher, Bach…)

Studying meta with “strange loops” is older than Aristotle (see the Cretan paradox below).

However the notion of meta I introduce here is much more general (although it contains the “strange loops” thingy, it also evades it, see below!)

To understand the essence of meta, one has to go back to bare-bone logic.

Given a language L, one can talk within that language L. However, what’s L made of? L = (LOG, TRUTH, U). “LOG” is the logic, U the Universe of objects the logic applies to. The logic consists in a set of assemblies that can be applied again and again to objects of U and make constructions. “TRUE” is a label applied to some Well Formed Formulas (WFF) within LOG. (Not all WFF are TRUE.)

Example: suppose LOG is the usual logic, and U consists only of the set made of 3 elements: eat, banana, good. Then ((eat, banana) –> good), a Well Formed Formula from LOG and U, could be the (one and only) TRUE formula (all WFFs are true in some purely formal sense).     

Metalogic and metamathematics, as usually understood, arose when Cantor showed that the Real Numbers were uncountable. Cantor was the metamathematician per excellence (he invented cardinal and ordinal theories). Cynics would say that’s why Cantor became crazy: he went a few “meta” too far.

Relatively simple modifications of (one of) Cantor’s proof(s), his diagonalization trick, led to the revelation that any logical system that contains the usual arithmetic is incomplete: statements can be made that are neither true nor false (which statements, that’s not clear; although Cantor’s Continuum Hypothesis is one of them…).

From my point of view, the problem with the most honorable, and usual, metalogic is that it uses infinity to go from logic to metalogic. I believe only in finite stuff. (Still the Cretan/Liar paradox, that started the field, 26 centuries ago, looks finite, although it truly is not really…)

However one can define meta easily in a finite (or not!) setting:

TRUE, (by definition the set of all true WFFs) is a subset of WFF, the set of all WFFs. (LOG2, TRUTH2, U2) is meta relative to (LOG1, TRUTH1, U1) if and only if each of three sets of the latter is a subset of the corresponding set of the former, one of them strictly (say TRUTH 2 includes TRUTH1, or U2 includes U1).

So meta carries as a useful concept in the finite realm, and has nothing to do with confusing causal loops.

How is the 26 centuries old Liar paradox solved in this scheme? That’s the paradox presented by the statement:

“This statement is false.”

Well, that deserves its own essay. Let’s just say I was chuckling all the way about how clever I was, until I discovered that my first solution was exactly the one found by Buridan seven centuries ago, and the second one, using my theory of meta above, resulting in a semantic hierarchy, was somewhat similar in spirit to that of Alfred Tarski.

Buridan’s solution is excellent (he notices that “This statement is false” is equivalent to A and non A, so is obviously false). However this is too ad hoc. One needs to handle contradictions where the implication chain is longer (A –> B –> Non A). Thus:

My hierarchy idea is to build the Language L by layers, like an onion, starting with a core (L, TRUE, U). One assumes that the initial TRUE of WFFs is non contradictory. Call that SEMANTIC (0). And then one grows TRUE by using L and U, one implication (or operation) of L at a time. Operating L once on TRUE, one gets TRUE (1). Either TRUE (1) has a self contradiction, or not. If it does, stop: (L, TRUE, U) admits no META. If it does not, call it SEMANTIC (1), and proceed to (L, TRUE(2), U). And so on. The iteration operation gives a notion of time (like a clock in a computer). L(n + 1) is richer than L(n), etc.

Thus META allows to build a hierarchy of logics, and semantics. To say that a theory is “meta” relative to another can be rigorously defined.

Progress in understanding is always achieved by climbing up the Semantic Hierarchy of meta.

***

Patrice Ayme


Artificial Turf At French Bilingual School Berkeley

Artificial Turf At French Bilingual School Berkeley

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in truth, only atoms and the void

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because all (Western) philosophy consists of a series of footnotes to Plato

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Dogs are animals of integrity. We have much to learn from them.

ianmillerblog

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an evolving guide to practical Stoicism for the 21st century

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Artificial Turf At French Bilingual School Berkeley

Artificial Turf At French Bilingual School Berkeley

Patterns of Meaning

Exploring the patterns of meaning that shape our world

Sean Carroll

in truth, only atoms and the void

West Hunter

Omnes vulnerant, ultima necat

GrrrGraphics on WordPress

www.grrrgraphics.com

Skulls in the Stars

The intersection of physics, optics, history and pulp fiction

Footnotes to Plato

because all (Western) philosophy consists of a series of footnotes to Plato

Patrice Ayme's Thoughts

Striving For The Best Thinking Possible. Morality Needs Intelligence As Will Needs Mind. Intelligence Is Humanism.

Learning from Dogs

Dogs are animals of integrity. We have much to learn from them.

ianmillerblog

Smile! You’re at the best WordPress.com site ever

Defense Issues

Military and general security

RobertLovesPi.net

Polyhedra, tessellations, and more.

How to Be a Stoic

an evolving guide to practical Stoicism for the 21st century

Donna Swarthout

Writer, Editor, Berliner

coelsblog

Defending Scientism

EugenR Lowy עוגן רודן

Thoughts about Global Economy and Existence

Artificial Turf At French Bilingual School Berkeley

Artificial Turf At French Bilingual School Berkeley

Patterns of Meaning

Exploring the patterns of meaning that shape our world

Sean Carroll

in truth, only atoms and the void

West Hunter

Omnes vulnerant, ultima necat

GrrrGraphics on WordPress

www.grrrgraphics.com

Skulls in the Stars

The intersection of physics, optics, history and pulp fiction

Footnotes to Plato

because all (Western) philosophy consists of a series of footnotes to Plato

Patrice Ayme's Thoughts

Striving For The Best Thinking Possible. Morality Needs Intelligence As Will Needs Mind. Intelligence Is Humanism.

Learning from Dogs

Dogs are animals of integrity. We have much to learn from them.

ianmillerblog

Smile! You’re at the best WordPress.com site ever

Defense Issues

Military and general security

RobertLovesPi.net

Polyhedra, tessellations, and more.

How to Be a Stoic

an evolving guide to practical Stoicism for the 21st century

Donna Swarthout

Writer, Editor, Berliner

coelsblog

Defending Scientism

EugenR Lowy עוגן רודן

Thoughts about Global Economy and Existence