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by Miles Mathis
I have used the word “heuristics” many times in my papers without defining it. Heuristic, without the “s”, is a method of problem-solving that uses math to achieve solutions without understanding why or even how the math works. I prefer the term “heuristics” for two reasons: 1) it differentiates the noun from the adjective, 2) with the “s”, the word better mirrors other branches of other studies, such as semantics or semiotics. Heuristics therefore becomes like a branch of mathematics.
In fact, heuristics is pseudo-math, a huge branch of contemporary math and science—one still growing fast. Heuristics borrows the form of math without having its logical underpinning. Mathematics is intended to be the formal expression of logic, using numbers and other symbols. But it is more than that. Mathematics must also follow a logical progression. Logic is more than just symbolism. It is also the strict adherence to procedural rules. The first step of this procedure is to work from axioms or postulates. Heuristics has no axioms or postulates, since it proceeds from basic procedural nescience. Heuristics shows no concern for making assumptions; even less for justifying those assumptions. It skips all initial steps and chooses symbols and procedures willy-nilly, based sometimes on intuition, more often on serendipity.
Now, I am a big fan of intuition and serendipity, even in mathematics. However, the best mathematicians and scientists of the past always found it necessary to justify their results after the fact. That is, they felt the problem was not really solved until they understood precisely why they had been right. They therefore worked backward, letting the solution show them what the initial steps must be. Only then could they claim to be in control of a repeatable performance.
This is no longer the case in mathematics or science. Both fields have been taken over by heuristics. Richard Feynman was probably the most influential physicist in the second half of the 20th century, and his career is the ultimate example of the rise of heuristics. This is no slur on my part, since Feynman would have cheerfully agreed with me. He said many times what I have just said, though he put an entirely different spin on it. His only interest was in creating equations that agreed with experiment. He said, “Because physics is an experimental science and the framework agrees with experiment, it is good enough for us.” Beyond that, math and logic were of no use to him. The procedures I defended above he dismissed as metaphysics. All parts of math and logic except the equations and the answer were without interest to him. The equations and the answer were the toys—the rest was not worth fooling with. “Understanding” was for him a fool’s road, one that led nowhere. In his field, QED, he and all who had come before him had made no progress on that road, and so they had abandoned it altogether. To put as good a face on this failure as possible, they had gone on to mock anyone who attempted to travel that road, or any similar road. Hence Feynman’s frequent asides to the philosophers and mathematicians who pursued understanding.
Physics became so powerful in the late 20th century that it had no need for such asides. Feynman and his colleagues could easily have ignored the dying philosophy and humanities departments without rubbing salt in the wounds. The petty comments must be read not as a bombs lobbed in a real battle, but as psychological clues to the insecurities of the physicists themselves. No matter how unassailable Feynman was, he knew the fragility of his own position. He knew, like no one else could know, how shallow the science of QED really was. This is why his book QED reads like the diary of a schizophrenic. On one page he is saying that QED is the “jewel of physics—our proudest possession.” On the next he is saying that, “theoretical physics has given up on explaining how phenomena work.” On one page he is bragging to his audience that, “we got a Nobel Prize for that.” On the next he is admitting that what they got a Nobel Prize for was “hocus pocus” and a “dippy process” that was “not mathematically legitimate.”
Twentieth century math and science always claim to be revolutionary—in the best sense. What they really are is an all-out war on the history of science itself. What Modern Art has been to the history of art is precisely what Modern Science has been to the history of science. The avant garde set out to destroy art history, to dismantle it and finish it off for good. It did this with explicit intent, vocally desiring “the death of art”. In only slightly less strident terms has physics called for the death of physics. In both fields, “classicism” became a term of abuse. Newton was joyfully forgotten, buried by both Hamilton and Einstein. He was buried not because his final equations had become useless, but because his scientific method had become limiting. Newton had jettisoned much of the rigor of the Greeks in order to proceed, and in the same way the modern physicists jettisoned the rigor of Newton. The difference is that Newton had continued to define science mainly by understanding. His calculus was in large part heuristic, but nonetheless he felt it necessary to build as many foundations beneath it as possible, even if many of them were admittedly after-the-fact. Beyond that, his physics was heavy with axioms and lemmae and proofs. He was ultimately interested in logic and in principles, which is why he named his greatest book the Principia.
Conversely, the principia of QED have not been enumerated as of yet. That would be a very short book. Feynman’s book is absent of principia. It is concerned only with “little arrows.” Even these little arrows are never assigned to anything. The fundamental variable of QED is the amplitude, but we are never told what has this amplitude. It is like a religion based on “blue.”
“What god do you worship?”
“Blue what? Do you mean blueness?”
“No. Just blue. We bless what is and must be blue.”
“Your god is blue, then?”
“Oh no, we have no conception of a god. We are sure of nothing but blue.”
“That is not a great deal of information, is it?”
“It is more than enough, my friend. We take our religion as we find it—blue. It would be a terrible sacrilege to ask for more. We seek a blue thing and a blue thing is given us. Are we not rich beyond imagining? Are we not in possession of the great sapphire of the universe? Who are we to pry more information from the unknown? If the unknown wanted to be known, it would arrive in a box.”
All very absurd, I am sure, like a meeting with some silly tribesman in a movie. Unfortunately we are not dealing with movies or tribesmen. We are dealing with a man many called the smartest man in the world. In one of Feynman’s most famous lectures, he talks of “cargo cult science”: the science of ignorant tribal people following a method that has some measure of internal consistency but that is nonetheless completely unfounded. He doesn’t say so, but this method he is describing is sympathetic magic and it was catalogued most extensively by James Frazier in his very famous book The Golden Bough. Feynman finds this sort of science at work all over the modern world—in the psychology departments, in new age studies, and so on. And his lecture is mostly correct except for one very obvious omission. Feynman does not realize that his own field is open to the very same criticism. He does not realize that his own field has long since been invaded by sympathetic magic, and that he himself is one of the primary invaders. Feynman has so much to say (most of it shallow and exclamatory) concerning the shortcomings of other fields, but is absolutely blind to the shortcomings of his own field.
Feynman says in QED, “I am going to have fun telling you about this absurdity, because I find it delightful.” At least an ignorant tribesman would have the decency to be abashed when he learned that his method was founded upon an absurdity. Not Feynman. He thinks the difference between himself and the tribesman is one of pure elevation or truth. He knows some technological tricks, so he feels unbearably superior. But this is not the important difference. History is long and the future may be even longer. The intellectual or technological distance between a tribesman and Feynman may be quite small, judged from any real distance. But the moral difference (or difference in attitude) is stark and may seem even more stark to very distant generations. The tribesman believes in his sympathetic magic because it is all he knows. It has appeared to work better than chance in the past, and this is all he has. He believes in it not because it appears absurd to him, but because he hopes it is not absurd. In contrast, Feynman is delighted by the foundational inconsistencies in his own theory, or pretends to be (I don’t know which is worse). Feynman’s only gods are science, math and rationality, but he has such a low opinion even of these gods that he can blaspheme upon them with only a chuckle and a grin.
In fact, he has a very strange view of math and logic. If we make his math and logic into a house, he appears to have a scrupulous concern for the integrity of the upper walls and the ceiling, but no concern at all for the integrity of the floor and supporting columns. Throughout his life, Feynman lived on the roof of a rubber house and only enjoyed the jiggling and sinkage. He claimed to find it delightful. I can only answer him, “Yes, I am sure you did. But tell me this: If someone should come along tomorrow and make sense of QED, would you still be delighted with your absurdity? And who do you think would be more delighted, you now in your absurdity or him with his sensible answer? More to the point, who do you think future physicists will be more delighted with, you or him? Even more to the point, who do you think Nature herself will be more delighted with?”
At least the tribesman can plead ignorance. If he embraces absurdity it is because he mistakes it for wisdom. Feynman makes no such plea to his gods, and does not need to. They are rational only on special days—the rest of the time they are delightfully absurd and tricksy. It is convenient for Feynman that his gods seem to be strictly rational just when he feels like browbeating the philosophy department and delightfully absurd just when he feels like beating the bongos or working on QED.
Feynman is like the man who went to the restaurant hoping the special of the day would be fish and chips, his favorite. Instead the special happened to be tacos. But this man liked his friends to think that everything always went his way, so he said very loudly, “Ah, tacos, delightful! Nothing better.” And when one of his friends complained that they hadn’t had fish and chips in a while, the man said to him, “Hah, I doubt they will serve that stuff again. Only a nostalgic old fool would talk of fish and chips on a day like today.”
Of course, such a man comes across immediately as a great optimist, putting smiles on the faces of all. But who are the real fools? The cook will hear of the conversation and none will ever have fish and chips again.
To return to the art analogy, the contemporary scientist and mathematician is a Futurist. Futurism was born just before the First World War. The Futurists, to put it simply, could not paint or sculpt. They had no talent for creating artifacts. But they were ambitious and politically savvy, meaning they had very few scruples—or none. Their artistic ignorance and disability notwithstanding, they desired to be known as artists and thinkers, and the realpolitik of time allowed this to be a realizable goal. They redefined art to suit their own careers and abilities and agendas. The entire history of art was dismissed with a wave of the hand. No, more than that, it was vilified. It wasn’t just useless, it was harmful. The Futurists desired to close the museums and ignore, if not destroy, the works of art. This would free future generations to concentrate on more important matters. What matters? Not coincidentally, the Futurists wanted people to concentrate on revolutionary politics—the Futurists’ revolutionary politics.
Modern science was also born just before the First World War. The coincidence of dates is almost frightening. Futurism arrived in 1909. Three years earlier, in 1906, Picasso had painted Demoiselles d’Avignon, possibly the first Modern picture. Around 1909 the first abstract picture was also painted, probably by Kandinsky. In 1905, Einstein published his paper on Special Relativity. Planck introduced the energy quantum in 1900 and Einstein confirmed it with the light quantum soon after. Bohr used the quantum to build his model of the atom in 1913.
What is so remarkable in the current context is not the theories, but the attitudes of the theorists. Despite their theories, Planck and Einstein were fairly conservative. Meaning they accepted the definition of science as a quest for truth and understanding, not just a quest for equations. That is why they were soon overcome by Bohr and Heisenberg. Neither Bohr nor Heisenberg could make any sense of quantum mechanics. Experiment gave them certain outcomes that they could partially predict by equations, but no mechanical or logical solution could be found. In response to this, they redefined physics. From then on, physics would not be about understanding phenomena. Physics would be about successful equations. This redefinition is not hard to understand: Bohr and Heisenberg were good at equations and not so good at understanding. They redefined the field in the direction of their particular talents.
In this way Bohr and Heisenberg were like the Futurists. Let me be clear: Bohr and Heisenberg were very talented physicists in some ways. They weren’t just ambitious admen or shallow revolutionaries. But they were fundamentally incapable of understanding what physics was, as a field. Planck said of James Jeans, “He is an example of [the sort of] theoretician that should not be existing,” and he might equally have said it of Bohr and Heisenberg. In fact, Planck was always violently opposed to the Copenhagen interpretation. He called Heisenberg’s matrix mechanics “disgusting” and much preferred Schrodinger’s equations.
It has been claimed that Planck was a political conservative—this despite the fact that Einstein (a revolutionary Jew) would probably never have become known without the championship of Planck, and despite the fact that Planck opposed the Nazi party from the beginning. But Planck was conservative, by my meaning, only in that he, like Einstein, held fast to the classical view of physics as an explanation of phenomenon, not just a search for equations. For him the most painful part of the Copenhagen interpretation was its claim that quantum mechanics was categorically irrational: a mechanical interpretation had not been discovered, therefore a mechanical interpretation was impossible. It is this belief that put Bohr and Heisenberg on the same intellectual and psychological level as the Futurists. For the idea boiled down to this: “We cannot do it, therefore it cannot and must not be done.”
In this way, quantum mechanics became the final solution. Complementarity became dogma, and Heisenberg and Bohr were guaranteed (as long as the fiat was obeyed) everlasting fame and adulation. They had succeeded where the Futurists had failed. The Futurists had temporarily succeeded in diminishing much of the shine of art history, but they had failed to enshrine themselves in its place. Those that didn’t die in the trenches of the first World War died the even quicker death of tabloid turnover. But Bohr and Heisenberg had just as thoroughly redefined physics, and they had made the definition stick. And they had found a way to include themselves in the definition.
They had created a small, exclusive, very powerful religion: a religion quite capable of continuance. Like other religions, this religion was based on faith, fiat, and irrationality. The irrationality was not hidden or esoteric, it was publicly embraced. As I have shown, Feynman was still joyously embracing “the absurdity” in 1985. The Copenhagen interpretiation was the fiat, a fiat that is to this day accepted by most physicists. It is accepted not because it makes sense: it does not attempt to make sense. It is accepted due to the prestige of Heisenberg and Bohr. And it is accepted because it is the stated permission, by the masters, that the disciples need not trouble themselves to think about the foundations or the mechanics of quantum mechanics. The leaders say, “We have looked into the question and have found it to be an insoluble mystery. Therefore we absolve you of any need to address it. You may continue in your search for equations unsullied by the need for explanations.” I think you can see where the faith comes in.
Duchamp, the most famous child of Futurism, admitted that art as high achievement meant nothing to him. The ghosts of Michelangelo and Leonardo were only stones in his road. He mocked them and painted mustaches on them and did all he could to replace them with his own very paltry creations. In the same way did Feynman mock those whose place he had taken in history, though he did it with a much greater finessse. His cuts at Einstein and Newton and the rest are subtle but penetrating, invisible except to the quickest eye. Like all the greatest sophists, he surrounds his hits with many a flattering remark, delivered with a wink. He would have made a clever courtier, ridiculing the pompous princes to their faces without their least suspicion.
But despite his undeniable PR skills, he will not, in the long run, be remembered as either a great scientist or a great mathematician. Like Bohr and Heisenberg, he will be remembered as one of the great salesmen of QED. Very soon, though, QED will yield to a mechanical explanation, and when it does the scales will fall from the eyes of the world, and all will see the lie for it was. When the amplitude is at last assigned clearly and unambiguously to some real motion of the electron and photon, the Copenhagen interpretation and all the variations on it, including Feynman’s embracing of an irrational cosmos, will be seen for what they are: obfuscation and misdirection and transparent careerism, all driven by ego.
How can I state this with such certainty, you may ask? Let us return to Feynman’s book QED for an answer. His method, taught to his audience in the book, is not just an overview of the math taught to graduate students. It is the method itself, simplified by addressing only the most basic examples. Graduate students really are taught a method of little arrows and turning clocks, the shrink and turn method. Feynman states that with his method, the Heisenberg Uncertainty Principle can be dispensed with: it becomes unnecessary. This is true, and it is part of what makes the method so useful as a heuristic device. Not that the students aren’t still taught the HUP as well: it remains a useful piece of mystification, one that prevents most students from asking foundational questions. But Feynman’s method is superior to both Heisenberg’s and Schrodinger’s in that it at least gives the student some pseudo-mechanics to hold onto. Vectors and turning clocks are after all physical objects. They can be diagrammed and looked at and imagined in the mind’s eye. The shrink and turn method therefore becomes a sort of virtual physics, a mechanical chew toy that fills the place of real physics for most students.
However, any analysis shows that Feyman’s method must beg many questions. Anyone the least bit clever should notice that a clock turning acts like a wave. Just assign numbers to the dial and you get a periodic recurrence of the number 12, for instance, at the top of the dial. Write out the numbers in a line, instead of in a circle, and you get a periodic wave. Amazingly, Feynman never addresses this in his book. You will say he is speaking to an audience of laymen: he may not have much of an opinion about their cleverness. But the fact is that Feynman and QED treat its graduate students with as little respect as they treat the laymen in the audience. Graduate students are dissuaded with every possible trick from asking this sort of question. And they repay their teachers by failing to ask them, confirming the low opinion of them. The master says, “Do not ask these questions!” and the disciple says only, “Yes, master!”
Feynman’s first postulate in the book is that light is a particle, not a wave. He wants to get beyond the duality and the complementarity and all the quibbling and cavilling. I agree that we must get beyond the 20th century’s sloppy conception of duality, but Feynman gets beyond it only by ignoring it. It is somewhat like ignoring a hyena in the bathtub. That little clock he draws on every page is screaming, “I’m a wave, I’m a wave, I’m a wave!” but Feynman sails on with wax in his ears.
Likewise, every time he cancels two vectors pointing at eachother, the hyena in the bathtub is howling, “Probabilities don’t cancel! Only physical objects cancel. For physical reasons!” Adding and multiplying vectors means that some events are taking place at the quantum level, but Feynman refuses to acknowledge this fact. Because he can’t tell you what those events are, he pretends they do not exist. He blithely floats his rubber duckies between the paws of the very wet and furry hyena, and makes believe that the noise is only the water heater.
The funny thing is that Feynman’s method is the most transparent of any of the methods of QED. Schrodinger’s equations are all math, without the least hint of a diagram or a visualization or a pseudo-mechanics. Heisenberg’s method is a much denser math—which acts as a protective fog—and this fog in adumbrated with the shade of many pseudo-philosophical principles, interpretations, and rules. A theory that wanted to remain unanalyzed could not have hoped for a more perfectly inpenetrable form. But Feynman’s method is a thousand times more suggestive. It not only sets the begged questions out on the front lawn like a bunch of elephants, it even points you in the direction of solving those questions. I must take it as sheer accident that it does this, since Feynman wastes half his ink telling you not to ask those questions. But the entire interest of the book QED is in its ability to partially visualize what we are not supposed to be visualizing. Feynman all but shows how the waves in Schrodinger’s equations interact with eachother mechanically. [Go here to see my full explanation of Feynman's shrink and turn method, and the mechanics it is hiding.]
Another funny thing is that it is precisely this fact that has caused some physics departments to retreat from Feynman’s method. His colleagues didn’t like Feynman publicly joking about renormalization, and in the same way they didn’t like the dangerous clarity that turning clocks gave to the problem. Heisenberg’s method remains the safest method to teach graduate students, since there is no likelihood they will penetrate it. They will memorize the math only, and this is what the teachers desire. In this way it is precisely like the tensor calculus: the math is so formidable and takes so long to master, that no one who comes out at the far end wants to give it up. Such a long and arduous mental investment is a cathexis not easily dislodged. The human brain is protective of its achievements, no matter what they are, and modern math and science make full use of this fact. In this way young scientists most naturally become self-censoring, and old scientists are only young scientists who are no longer young.
Feynman admits that contemporary applied maths are almost absurdly complex, numerous, and time-consuming. He peppers his lectures and books with brags about the number of years it takes to learn the methods. But to him it is only a good thing, since it weeds out all those who won’t “shut up and calculate.” Those who have “shut up” don’t have time to ask questions or analyze any of the foundations of the methods they are using, and this is just as Feynman and the other masters want it. “Openness” is one of those gods that everyone quotes and tithes but that no one believes in. “Truth” is another. It is carved on the capitals of all our universities: “Seek the truth and the truth shall set you free.” But no one appears to believe it. In the modern world, truth is just a prejudice or a shibboleth of power. Even science has retreated to the idea of knowledge as a human creation, one which is infinitely malleable.
Of what use is openness in such a world? Most questions are frowned upon in graduate physics courses, especially in QED or Relativity, where you are memorizing formulae and dogma. And this is true after graduation as well. Academia is heavily policed. Peer review is the same as peer pressure, transported from junior high into the “highest” levels of “scholarship”. It is the tyranny of the majority codified and solidified and candy-coated with the patina of respect. It is those who have not discovered anything in a given field sitting in judgment upon those who have. How can this be expected to yield results, given human nature?
The major mathematical and physical journals want us to believe that they are the qualified gatekeepers, that they are completely objective—opposed to the vanity publishers where anything goes. But a closer look shows that the journals are all vanity publishers themselves, since they do not pay authors. In fact, they request payment from the authors’ universities and require that the authors gift them the copyright to the work. By the standards of the free press this is extraordinary. In fact, by the standards of any real market, this must be extraordinary. A man creates something and he has to pay someone to take it from him? But the thing is considered to be so entirely worthless, in the present, that the man must also promise to give the “buyer” all future rights to profits. A system that works by such rules must be topsy-turvy. How could it yield truth or quality, openness or profit, to anyone? It must encourage mediocrity, since no man of worth would be part of such a system, or consent to have his work taken from him in such a thoroughly emasculating way.
No, like most other modern systems, this one is in place mainly to prevent what it professes to encourage. Professional scientists must publish, and this is the system that allows most to do so. As long as they don’t really say anything or ask any questions, they are allowed so many pages per year. As long as the institution is willing to underwrite it, the journal must publish its major players. The peer review is there to be sure that nothing of substance actually makes it into print. Nothing that threatens the career of anyone important or threatens the funding of any major project.
In such a system it is perhaps not surprising the sort of professional physicists that we get. We get the ambitious little phonies that flocked to string theory like geese. And they end up treating Feynman like he treated Einstein. Out of one corner of their mouths they praise him to the heavens, since he was famous and they want to be famous. Out of the other corner they curse him as a has-been. There is nothing a climber hates more than a has-been. A person who lives only for now can hardly have any use for the past.
But the phonies should never stop praising Feynman for a moment. They should make burnt offerings to him, with incense and wild dancing. He was the latest god of heuristics and their field is now heuristics. They only have to fill their papers with equations and the peers will funnel them through. There is no need to explain anything or make sense of anything or address the understanding or talk of truth or existence or any of the old bugbears of science. The string theorists in particular owe Feynman their first child. The ungrounded mathematics of string theory takes heuristics boldly where no math has gone before—into a realm where logic and understanding are of so little matter that anything goes. Here Feynman’s love of adsurdity is richly rewarded: theory is pasted over heuristics as a joke. Here theory has become so debased it can be paraded openly through town as a trollop, dressed in meretricious rags and rolled by every sailor.
Yes, Feynman is owed a great debt by string theorists. But I would mention one last irony. The book QED ends with two very strange and very short addenda. In the first addendum, Feynman says that since the book was typeset, something big may have happened in the field of physics. The second addendum, dated five months later, says, basically, “Nevermind.” This thing was of course the birth of string theory. Nevermind indeed.
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