Pseudoscience in four glorious colors

This is an update of sorts to an earlier post. You may recall that back in August, philosopher Li Ming issued a challenge to skeptic Fang Zhouzi, a high-stakes bet that his solution to the Four Color Conjecture was correct. Though the deadly wager was not taken up, Li followed through with his promise to reveal his proof before the end of 2006.

In a series of posts on his blog, Li took readers from his initial "gift from 'God'" one morning in 2000 when he had a striking revelation, all the way through his application of his proof to a map of China.

Li has invented what he calls Neighboring Geometry, consists of groups of regions that all border each other. He provides two axioms for this geometry: (1) on a plane, the maximum number of regions that all border each other is 4; and (2) every region on a spherical surface is completely surrounded by its neighbors. He then goes on to introduce the "Li Ming Axiom Triangle":¹

The "Li Ming Triangle" is an axiomatic triangle in the complete neighboring geometry discovered and invented by the writer. It is a triangle of geometry and a triangle of physics, but most importantly it is a triangle of logical thought, since it first came forth out of my reflections on thought processes and logical principles. Specifically, it forms a triangle out of an arrangement of the complete neighboring numbers for areas such as points, dipoles, lines (chords), areas (planar and spherical), and areas (toroidal), as follows:

Point (supreme ultimate)	1
Dipole (Yin-Yang)	1 2
Supreme chord (line segment)	1 2 3
(spherical, planar surface)	1 2 3 4
(toroidal surface)	1 2 3 4 5
Spherical volume	1 2 3 4 5 6
toroidal volume	1 2 3 4 5 6 7
toroidal sphere volume	1 2 3 4 5 6 7 8

In later posts, Li discusses the application of his triangle to gravity (point), electromagnetism and the weak force (dipole), the strong force (chord), lower forms of life (planar surface), higher forms of life (toroidal surfaces), and intelligence (volumes).

Li attempts to prove the Four Color Theorem for any map by demonstrating certain things about various smaller regions. Essentially, he demonstrates that a system comprising one region completely surrounded by all the regions that directly neighbor it can be colored by at most four colors. No problem there, at least for planar and spherical surfaces. However, he does not provide any discussion of the relationship between these regions - a neighboring region in one system is the center region of another, and while the two systems each follow Li's Four Color Rule individually, there is no guarantee that their color schemes will be compatible when considered as part of a larger map.²

Moreover, Li makes a number of basic errors. Line 5 of his Triangle, for example, suggests that a torus should require at most five colors to fill in a map. The image at right shows a torus with seven regions that are all neighbors, so it requires seven colors. When this was pointed out in the comments, Li responded with a post titled, "Why do so many people get swallowed up in their books?"

One gentleman who "studied physics" asserted categorically that since there is a "seven color theorem" for a torus that a complete neighbor index of 7 exists for the torus. I can tell this gentleman that not only the "seven color theorem" but the "five color theorem" for a sphere are not rigorous mathematical "proofs" at all; otherwise, would this gentleman try to draw for me on a torus seven regions that are all neighboring? I'm waiting.

· Li Ming attacks his critics

In the comments to his blog posts laying out his proof, a number of people objected to Li's establishment of two new geometric axioms. Who gets to decide what counts as an axiom - must it follow from authority? On 1 January, Li Ming replied to his critics by appealing once again to the notion that outsider science was being stifled by the establishment:

Mathematicians of the past were led astray on solving the "Four Color Conjecture" by the authority of the great Euler Theorem; they were stymied for a good half-century, and until today, people still happily fill the heads of young students with the "five-color theorem" for spherical maps and the "seven-color theorem" for toroids, holding these up as the standard. In truth, the proofs of these theorems have subtle errors; authority blinds people to what is important, and travelling down that road until it turned dark, they had no recourse but to rely on a computer to cover for humanity's stubborness and stupidity. Here, I should recall Aristotle's famous words, "I love my teacher greatly, but I love the truth more." I should say, "I love Euler, but I love the freedom of mathematical thought even more."

Was proving the Four Color Conjecture by computer truly successful? We have been deceived, but we still shout: this is a great victory for human science! What a perfect irony.

Why can't the fact that on a spherical surface, "complete neighboring indices can only be 2, 3, or 4" be an axiom? This is a new, intuitive discovery for the perpetual truth. People say that this is equivalent to the Four Color Conjecture, but in fact this is entirely not the case. In my view, my second axiom must still be added. And yes, these two axioms together imply the Four Color Theorem, and it is for this reason that I can deduce the Four Color Theorem from them. In this respect, yes, they are "equivalent", but this "equivalence" only demonstrates that the "first axiom" is worthy of being an "axiom."

What is an axiom? An axiom is an intuitive, perpetual truth, absolute fact.

What is a proof? Proof is the deduction of theorems starting from axioms.

I ask you, what part of my "Solution to the Four Color Conjecture" does not follow this procedure?

It is very likely that during the deductive process I may have omitted a point or two, but I never expected that some commenters would even fail to understand what a "linear association" is, or a "plus sign". Even more shocking is that some people set their teeth against allowing a new axiom. It seems that axioms can only be issued from the mathematical authorities.

I want to tell those commenters that truly great mathematicians are not only skilled at mathematical tricks - they should be skilled mathematical thinkers. Freedom of thought within mathematics is most important. Mathematicians who only know mathematical skills should really not be called mathematicians, but at the most mathematics craftsmen, mathematics laborers. And mathematics craftsmen will never discover their own new axioms.

· Song Zhenghai on banning 'pseudoscience'

Protecting amateur scientists against accusations that what they are practicing is pseudoscience is one of the motivations behind a petition circulated late last year to ban the word from Chinese legal language. Song Zhenghai, a science historian at the Chinese Academy of Sciences, organized the petition, whose main argument is that the label "pseudoscience" is being used to denigrate traditional Chinese culture. Excerpted from an interview with The Beijing News:

XJB: Looking at thing now, academia is in constant debate over the definition of science and pseudo-science. Against this background, it seems that there won't be a verdict for the time being, and neither side can convince the other. Why is there this argument?
Song: Key here is that Fang Zhouzi et al are no longer attacking some particular group. They have leveled their attacks at parts of traditional Chinese culture like Chinese medicine, calling them pseudo-science. The effect, for many amateur scientists, has been pressure, and a denial of all amateur science that has its roots in traditional Chinese culture.

In particular, a short while ago when Zhongnan University professor Zhang Gongyao issued his 10,000-name petition against Chinese medicine, I started considering a joint measure in opposition, and wrote "Do not let the word 'pseudoscience' become an excuse to exterminate traditional culture." I urged that this word be deleted from law relating to science to protect traditional Chinese culture. Through email I received 150 signatures; these people came from research institutions like CASS, CAS, and CAMS, and the majority of them were high-ranking professors or administrators.

TBN: You believe that the word 'pseudoscience' should no longer be used?
Song: In reality, pseudoscience does exist, and there is a need to prevent fakery in academia, but the word should not be over-generalized. Internet screeds should not be used at the drop of a hat to slap a label of pseudoscience on anything that does not fit the definition of science. Internationally, the usage is "improper academic conduct", and fraud committed in the name of science can be dealt with via civil or criminal law. The word "pseudoscience" is a bit unnecessary.

TBN: Isn't there quite a bit of debate over whether The Book of Changes is science or not?
Song: The Book of Changes is traditional Chinese science. Of course it is different from modern western physical science. In the development of a discipline, some results are not widely accepted; they present a challenge, and require further verification by putting them into practice. Simple explorations in engineering physics, for example, or mathematics, can always be managed using the west's reduction and demonstration, but not everything can be proven through practical application.

Our science is holistic science. Many major inventions in China were made on the basis of holistic thought. In the 21st century, humankind is facing rapidly multiplying problems of ecology and the environment, and it is difficult to do repeated tests or to separate out different elements. A holistic approach is needed to get a grasp on things.

TBN: In this debate, you have always claimed to stand on the side of "folk scientists". Is there such a thing as "official scientists"?
Song: Yes. In general, official scientists are those that do their research using the government's money. Folk scientists have no sponsorship, and their circumstances are poor - they often given the label of pseudoscience. Last year we sent a joint letter to the central authorities urging them to respect folk scientists and researchers.

· Liu Zihua's Eight Trigrams Cosmology

Song mentions The Book of Changes in reference to the case of Liu Zihua, a Chinese astronomer who used the Eight Trigrams to predict the existence of a tenth planet in the Solar System. Liu received renewed interest in recent years with the discovery of an actual tenth planet (though it was defined out of existence last year together with Pluto). In 2005, Fang Zhouzi picked him as one of China's top 10 science frauds and was sued for libel by Liu's heirs (see this China Daily story for a mostly-accurate overview).

Fang was found to have libeled Liu in his essay by calling him a swindler. The court said:

In regards to Li Zihua's Eight Trigrams Cosmology, different people may have different scholarly perspectives, and engaging in debate over this is normal. However, attacking one's reputation cannot be done. In this case, there is nothing wrong with Fang Shimin writing an article raising doubts about the scientific nature of Liu Zihua's Eight Trigrams Cosmology, but in his writing, Fang raised his refutation of Liu Zihua's theories to a criticisms of Liu Zihua's character, using baseless, obviously defamatory smears like "actions of a swindler", "swindler" and "charlatan magician from China" that did indeed disparage Liu Zihua's character, causing harm to his reputation.

Liu's paper, actually his doctoral thesis written in French in the 1930s shortly after data on Pluto was confirmed, was published in China in 1989³ following Robert G. Harrington's calculations predicting a Planet X. Liu uses ratios of speed and density for the eleven heavenly bodies (Liu includes the Sun and Moon) in combination with pairing concepts from the Book of Changes to arrive at several proofs of an undiscovered counterpart to Pluto. No gravitational theory is involved.

Li Ming based his mathematics on Laozi's philosophy, Liu Zihua's astronomy draws its inspiration from Fuxi's methods of divination. Are these classic examples of pseudoscience? Or are they legitimate applications of traditional Chinese learning to modern science?

Liu's approach is particularly seductive because it offers up the potential for traditional Chinese learning working together with modern western science. From his summation:

The above conclusions were demonstrated through the use of the penetrating ideas of Fuxi and several other philosophers in our country's ancient history together with the fruits of devoted research from several modern European scientists; neither of the two could be omitted. Hence, I must express my gratitude to them. Eight Trigrams Cosmology achieved a perfect proof through science, but science needs the Trigrams Theory to achieve a more complete understanding of the universe, particularly the Solar System. Science can prove Trigrams Theory, and Trigrams Theory can supplement science, while at the same time it can demonstrate the correctness of astronomical data. So Eight Trigrams Cosmology and Modern Astronomy are factual, mutually explanatory, mutually clarifying, and mutually confirmative.

The uses of Eight Trigrams Theory are broad; in this book I have only applied it to celestial bodies as a starting point. I am limited in both education and capabilities, so I truly hope that the wise, both Chinese and foreign, can make corrections or extensions; I would be truly grateful.

Such a wonderful harmony of two different approaches to scientific research that it would be a shame to ruin it with actual observations, though that is precisely what the astronomer Zhang Yuzhe, Liu's first major critic, based his arguments on in 1945. From his essay, "Do you know how planets are discovered?":

If you wish to prove that you have discovered a planet, the technique is quite simple. There's no need for commendations from western professors, or an introduction from some famous countryman. All you do is take the coordinates of each time you have predicted that planet and publish them altogether. Calculating according to this data, you can learn the its orbit, its distance from the sun, and its future path and position. Now, whether what you have discovered is a planet, or comet, or minor planet can be determined through further evaluation. What has any of this to do with the Book of Changes and the Eight Trigrams?

· Harmonious purification of language

I asked Fang Zhouzi whether he thought that the judgment against him was related to the emphasis on "social harmony" under the current administration. He didn't think so, arguing instead that it was a matter of scientific ignorance on the part of the lower courts. But it's not hard imagine a link between the two. Here's one effort, from "Patriot2000":

Suggestions on the purification of language to establish harmonious public opinion

Respected, wise, almighty leaders, beloved by the people:

There have been a number of lawsuits concerning defamation and freedom of speech recently that have had a large influence both in the courts and online. The existence of conflicts in which some people have said things or written things that have made others uncomfortable has ultimately required our fair, wise, truth-speaking, stern judges to take the trouble to make a judgment. And afterward, there have been appeals, and additional judgments. This is very unhelpful to our grand plan to establish and build a harmonious society. Looking to the root of the problem, there exist in our language many terms that make people uncomfortable! When people use these words, they inevitably cause harm to others and create conflict. So, to resolve this massive complication to a harmonious society, to insure the welfare of our posterity, and to completely reject unharmonious factors, I offer up four suggestions:

1. The great authoritative governmental departments of our country will take the lead in establishing a language purification development center, which will first eliminate all non-commendatory or non-neutral words from dictionaries and glossaries. It will then work in the area of the grand educational plan, completely cleaning out all textbooks; any essays that are not laudatory, celebratory, acclamatory, or reverent will be deleted en masse so that children will be edified and educated by beautiful language from their youth.

2. The smart, clever Internet administration departments will take the lead, and the country's outstanding, high-level, innovative, high-tech companies and leading, original, breakthrough-oriented, rising universities, tertiary institutions, and research laboratories will cooperate in developing an Internet language purification system. Using new, clean, beautiful character sets, it will cause all non-laudatory, non-celebratory, non-acclamatory, non-reverent, and non-harmonious words to automatically change into laudatory, celebratory, acclamatory, reverent, and harmonious words. This will essentially solve the problem of online harmony.

3. In the long-term, the kindly, cure-all Chinese medical practitioners with their miraculous remedies will develop a kind of Chinese medicine that once taken will cause a person to speak only standard, harmonious language. The country will provide this to everyone free of charge, making the dream of a harmonious society a reality once and for all.

Imagine the grand sight that lies before us once our plan comes to fruition: everyone well-mannered with warmth in their hearts. No more discomfort. True politeness. Such a society is truly ideal!

I hope that great, glorious, correct organization can put these vital, historic, brilliant suggestions into practice as soon as possible to create a trailblazing model for the harmony of the whole world!

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Note 1: Li Ming's proof is divided among several articles, all of which can be found in the among his blog posts for the second half of December.
Note 2: The currently-accepted best proof of the Four Color Theorem uses 633 configurations (down from 1476 in the original 1976 proof) and requires a computer to demonstrate two theorems. See here.
Note 3: A 3 meg PDF made of scanned pages from this book is available via eMule, or interested readers may contact me via email.