The Great Math Mystery Episode of the PBS popular science series NOVA asks the question: Is math a human invention or the discovery of the language of the universe? It seems to this writer that there is actually no question here at all. The correct answer is that mathematics is a human invention. So one has to contemplate, why is the question being asked at all? Obviously, the answer is because there is an attempt by the mainstream science establishment to promote the idea that mathematics is what the universe consists of. That is mathematics is the new version of GOD. So they want us to worship mathematics and the elite people who can manipulate and control how we interpret nature through their control over the mathematical machinery by which establishment science tells us what is true about the world that we live in.
It is entirely disappointing that the thesis being presented is basically a fallacy of human reasoning. It has its roots in the distant past where the cult of Pythagoras worshiped numbers as the ultimate mystery. This cult has been resurrected by modern science in the guise of a new intellectual fashion. The new fashion being modern theoretical physics, which pretends to know the laws of the universe as mathematical relations and presents the resulting imaginative speculations as a way to unravel the hidden secrets of the universe. This is the uncritical philosophy of mathematical worship that is being promoted in the NOVA episode. We need to examine the fallacy to see why it is popular and needs to be revealed for the hoax that is behind it.
The main reason for the modern revival of the math worship can be traced back to Einstein and his relativity theories. That initiated a revolution in physics that dispensed with the experimental philosophy that had guided the pursuit of scientific knowledge during the previous 300 years. Simply put, the relativity theories have very little experimental support, but were accepted primarily because of their so called mathematical beauty. Towards the close of the 20th century, Eugene Wigner wrote a paper in which he introduced the idea that it was a mystery why mathematics was so unreasonably effective in unraveling the secrets of the universe. This has led to the modern fallacy. The main point is that all discussions of the claim, are based upon inductive reasoning. That is the proponents of the thesis look at the world and then proceed to enumerate all of the wonderful ways in which mathematics turns out to be a useful tool in making predictions about how nature works. However, this method of reasoning by enumeration can not prove the thesis that mathematical laws are what define the nature of our universe. All that is needed is one counter example, there are many such counter examples, but we never hear about them in the NOVA film.
The issues discussed in the NOVA film can be seen as a modern version of an ancient Greek controversy between Plato and Aristotle. Plato believed that mathematics reflected real laws of nature that govern the world, while for Aristotle, mathematics reflected abstract entities called numbers which reflected the measurement of physical quantity. Modern theoretical physics has adopted the Platonist philosophy to the extent that science teaches us that physical laws govern or control reality and that it is the job of physics to discover these laws. This approach suffers from the fallacy that we humans have to invent these laws out of some kind of scientific method. In conducting the scientific method, the illusion is created by scientists that we humans are discovering laws of the universe that exist independently of our minds. This process is basically a reflection of the Platonic philosophy. Unfortunately for adherents of the Platonist philosophy, there is no justification in the method of scientific discovery that assures us that the method actually discovers true laws and not erroneous laws that appear to be valid. Unless and until such a method is actually discovered, one simply has to adhere to the philosophical view that what we discover as physical laws are merely technical constructions. That is rules for making things that are used by engineers and artisans. These rules don’t reflect any deep philosophical meaning, they just are useful guides to understand how to build the house or bridge that is desired.
Hence, until and unless, the so called scientific method can demonstrate that mathematical laws discovered through the operation of the method upon nature actually produce the deep underlying mathematical laws that govern nature, we as humans ought not to invest our belief in mathematical systems with any Godlike powers or possessing ultimate secrets of the nature of the universe. Unfortunately, modern theoretical physics is enamored with its apparent ability to discover the hidden laws of nature as mathematical and so we have presented to us in explanations of modern science such as the NOVA program, a rather mystical view of mathematics and physical science as it is practiced by the academic elites. This is a fallacy that leads us into a realm of dangers. Hence it is better to view mathematics as merely a useful human invention and all of theoretical physics as just a useful tool that aids our interpretation of reality and nothing more.
Lets take a look at the so called science that is presented in the NOVA program and see how well it is verified. Early on we are told that Fibonacci numbers show up in flower petal counts. The screen displays flowers which have petals counted in accordance with the Fibonacci sequence. That sequence goes 1,1, 2,3,5,8,13,21,34, 55… However, when I go outside my house I discover a lot of flowers with petal count of four and four is not a Fibonacci number. That is a disturbing fact. Next an expert tells us that “Statistically the Fibonacci numbers show up a lot”. So now the statement is modified to take account that not all flowers follow the mathematical law of the Fibonacci numbers. In fact what appears to be a mathematical law governing nature turns out to be only a statistical likelihood which is not overwhelmingly convincing as a rule for governing nature, because mathematics is the language of the universe. The fact that math is said to be the language of the universe follows from a simple definition. Since in nature we humans want to measure things and measurement is counting, then it follows by definition that any conclusions that we humans desire to make regarding the universe resulting from a measurement are necessarily going to involve numbers and thereby be mathematical. It doesn’t imply that nature is mathematical simply because we humans have invented numbers in order to measure or count things.
What is counting and measurement is addressed by a fashionable scientific approach. After showing the viewer that math ability is a facet of brain development, we are told that the ability to count numbers is not a human skill but can be found among many species of animals. But we are never appraised of a critical issue, how is it that quantity becomes number as we humans conceive it? The experiments indicate that animals and infant humans can recognize different quantities but they do not employ this knowledge in an abstract way as we do in mathematics, which allows numbers to be manipulated through the rules of arithmetic. Are these rules human inventions or are they discovered by humans? It seems pretty obvious that the notion that arithmetic is somehow a property of the universe that exists prior to human discovery is a human metaphysical conception and not an actual deeply hidden property of the universe.
One of the deceptive arguments presented in the film, is the claim that mathematics is responsible for the great technological achievements of our age. That has just enough truth in it to perpetuate the deception that the universe is mathematics. However, we also know that the Egyptian pyramids and many wonders of the ancient world were not accomplished using the scientific method or its accompanying mathematical techniques. So technological achievement is not dependent upon either of these two things. It seems that they have merely enhanced what humans were doing before those techniques were developed. Modern science likes to present the concept that modern science as we know it it is a purely intellectual achievement arising out of the application of mathematics to the study of nature.
If we examine the examples cited in support of the thesis that mathematics has produced the great scientific advances of our present human culture, we find some glaring misstatements of truth. Probably the most obvious is the claim regarding electromagnetism. Contrary to what most people might think, the development of radio and television did not arise from mathematics or a correct understanding of the physics involved. This is one of the prevalent myths of modern science. The truth is the laws of electromagnetism are not very well understood and the theory as described in the film is entirely false. In the film they say that according to Maxwell’s equations light waves travel by a reciprocal effect where electricity creates magnetism and magnetism creates electricity. Now this is entire false and erroneous. In other words it is factually incorrect according to the equations of electromagnetic waves. In these equations, the electric and magnetic fields are in phase, however, for electricity to create magnetism and magnetism to create electricity the fields must be related so that they are out of phase by ninety degrees. But the equations of electromagnetic waves do not agree with this prediction. Hence what the film says in this regard is totally incorrect.
The actual history of how radio was invented is a lot more complicated than the deceptive presentation in the film. It is not true that Maxwell made a prediction of electromagnetic waves, what he did was make a claim that light was an electromagnetic wave and tried to give a theory that explained it in mathematical form. Later, Heinrich Hertz made experiments that verified the existence of these waves. But now we encounter the deceptive part of the story. It was really Hertz who invented radio. The invention was inspired by the mathematical theory of Maxwell, which we know is false, because of the flaw discussed previously. Contrary to what the film asserts, it was the process of human invention that made radio, and mathematics was not used to actually invent it. The invention process involved technology and use of technical inventions, which were not understood in terms of mathematics at all. That is because they were using the incorrect theory discussed above. This is illustrated by Marconi, who did not develop radio in terms of mathematics, but used experiments and technology to create radio. Later the mathematicians and physicists came along and fit the mathematics into the technology of radio. But in the process they never really got the correct understanding of how electromagnetic waves actually work physically. So we have the confused explanation that we find today in the physics books.
Here we see that in the process of invention, mathematics did not play a decisive role, but only made a crude suggestion that electromagnetic waves could actually exist. It was through the process of human invention based upon trial and error that radio came into being. What we have here is not a case of humankind discovering a law of mathematics, that is because the law as currently understood is false. It is simply not true that in electromagnetic waves electricity creates magnetism and vice versa. That is an incorrect erroneous myth. But it is a useful myth, and it does deceptively support the viewpoint of modern physics as long as we ignore the actual history and real facts of the claim.
This example regarding the theory of electromagnetism is an example of the fallacy of the claim being made in the film regarding the metaphysical justification of physics as discovering the mathematical laws that govern the universe. That fallacy is how do we know that what we think are the mathematical laws of the universe, actually are true mathematical laws governing the universe. In the case of electromagnetism, we find that the mathematics doesn’t actually produce the physics that scientists believe it does. The question then must be asked, how do we really know that the mathematical laws that we humans invent are actually real true laws of the universe? How do we know that physical laws are not just an illusion and not real truth?
The answer to this question, is that we don’t actually know the real and true laws of the universe completely. What we know is only how to use certain mathematical laws in what are called idealizations to solve certain types of problems with constrained boundaries through idealization. The film gives us an example of how idealizations work and how they can be used to produce deceptions regarding conclusions of fact. The particular example is the example of Galileo’s law of falling bodies. The film and physics textbooks tell us in no uncertain terms that what Aristotle said regarding the law of falling bodies was false. The film then proves that Aristotle was false by using an idealization that does not exist in the real world. We are supposed to believe that air resistance does not exist, and if we do experiments in which there is no air, we will find that different bodies all fall at the same rate. But this idealization is not true in the real world, where air resistance actually does exist. If we drop a feather and a hammer, as they do in the film, the feather falls slowly because of air resistance. In the film, we are told to simply ignore this fact as being wrong. That is we are supposed to say the fact is irrelevant and agree that the idealization of no air resistance is the correct law of physics. This is an example of deception, because we are told that Aristotle was wrong. He is only wrong if we don’t want the mathematical law for a falling feather. In the case of a falling feather Aristotle gives us a better answer than Galileo does. This is an example of how idealizations can be deceptive, and unfortunately all of the laws of physics are idealizations and so they can not be real and true laws. They are only true in abstraction as idealizations. But since the world as we know it is not an idealization, then it must be the case that mathematical laws are not true in the real world, they are only true in an abstract idealized world of the human imagination.
The claim of modern physics which is based upon the Plationist metaphysical philosophy, is that the universe is governed by mathematical laws to the extent that the ultimate reality of the universe is mathematics. It is claimed that the objective of physics is to discover these laws. However, we see from the previous example that what is discovered by physics are idealizations that apply only to an abstract human imagined world that is highly simplified in the form of mathematical abstractions called laws of physics. However, modern physics has moved to a high degree of technological and mathematical sophistication such that they claim to have proved the existence of something called the Higg’s Boson or God particle. This is claimed to be the most important breakthrough of modern physics and an example of how mathematics is discovering the laws of the universe.
Unfortunately, the celebrated discovery of the Higg’s Boson as discussed in the film seems to be another example of faulty scientific method. Here we have the crux of the problem. Does physics really have a method whereby they can discover such abstract idealizations as Higg’s Bosons in the real world. In other words, do abstract mathematical idealizations actually exist in reality? Physicists think they do. Unfortunately, there are a lot of reasons to suspect that their claims to this effect are entirely fabricated and false. In the celebrated Higg’s discovery it looks like we have a repeat of the Hafele-Keating type of experiment where it is claimed that they proved Einstein’s special relativity time dilation prediction. In hindsight looking back, this celebrated experiment looks to be a false verification. That is the experiment did not prove the time dilation effect as claimed.
Unfortunately, it is not the only example of this type of deceptive science discovery regarding special relativity. While there are many experiments that do appear to be consistent with special relativity, there are many that are not. What is of concern is why we don’t hear about the ones that don’t confirm special relativity, and in addition why we don’t hear that the Hafele-Keating seems to refute relativity rather than confirming it. What this indicates is a problem in the scientific method. That problem relates to deliberate misinterpretation or outright fraud. In the case of Hafele-Keating there are two possibilities. One is the the experiment is a fraud in that the data was selected or as the term is normally used fudged. That is the data was selected to fit the desired proof. In other words data that did not agree with the special relativity prediction was deleted and only data that proved the theory was deemed as good data. Then it followed that the theory was verified by the experiment, because only data that agreed that the theory was right was deemed as good data. This is deceptive and fraudulent. But there is another problem. That is that the data that they used did not agree with the actual theory of relativity, It agreed with a version of the theory that is not actually what special relativity says. This is confusing, and resembles the electromagnetic wave theory deception discussed above. That is the Hafele-Keating data does not agree with special relativity but agrees with a similar mathematical theory which is mathematically different but similar.
The conclusion that is drawn from these examples of experiments that don’t really confirm the predictions illustrate a difficulty in scientific method. That is theories become so compelling to the people who believe them that no evidence can be produced that will change their firmly rooted belief that they are correct. That is much of physics could be wrong and false because the people who do physics are convinced that their mathematical theories are correct laws of nature because they believe firmly in the idea that nature is mathematics and that a mathematically beautiful theory must be true, because nature is beautiful, and so the mathematics, which is beautiful, must also be the underlying laws of nature. This is basically fallacious thinking, but physics is full of this kind of thing.
In the case of the Higg’s particle, the experiment produced a result, but the result did not match the predictions of the theory. The discovery of the Higg’s particle was announced as proven anyway despite the discrepancy. So we probably have another example of a false theory being promoted as truth, because the mathematics is beautiful and physicists are persuaded that it must be true, despite the real facts of nature. We see other examples of this in cosmology, where fictitious entities such as dark matter and dark energy are invented to explain away discrepancies in the theories. It never occurs to scientists that the mathematics they are using is wrong, because they are persuaded that nature uses their mathematics and so they must be right in their theories. Humans being what they are, are trapped in this human fallacy. If the world doesn’t conform the the way humans conceive it in terms of mathematics then it must be that the world is wrong and not the mathematics. Hence there is a problem with the very first premise of science. That is that the scientific method actually discovers truth. What is more likely is that the method only discovers truth as fallible humans invent it to be.
To conclude. The film, The Great Math Mystery, pretends to be asking the question: Is mathematics a human invention or a deeply mysterious facet of the universe. The obvious conclusion is that mathematics is a human invention and that invention persists as a mystery, because we humans have invested a kind of godlike property in the idea of mathematics as the fundamental reality of the universe. The film leaves the question unanswered, but strongly implies that nature is mathematical. That idea is supported by the effectiveness of the method of modern science, which appears to prove the unreasonable efficacy of mathematics in making predictions about nature. Unfortunately, we find that upon examining, the scientific method we discover that so called scientific laws of nature are abstract idealizations that seldom exist in the real world. Finally, it is shown that the scientific method itself is flawed, because the human illusion that nature is mathematical is a self fulfilling type of illusion. That is because humans want to believe that nature is deeply mathematical we search for and find evidence that purports to prove that this is true. But such discoveries are just illusions created by the desire of the human mind to find mathematical order in the morass of confusing sense impressions that we experience in the real world. So it must be concluded that mathematics and the idea that nature is governed by mathematical laws is a human invention based upon the creation of an idealized abstract world that exists only our minds as human imagination and not actual physical reality.