Professor Yaroslav Sergeyev recently visited Novosibirsk and talked at two seminars about his “grossone theory” and “Infinity Computer.”

Look at the following excerpt from numerous publications by Sergeyev:

Sergeyev speaks about the change of paradigms in mathematics and some revolution in computations. Moreover, he counterpoises his approach to nonstandard analysis which is called “the analysis of the future” by Kurt Gödel. This is very attractive to a layman: he has no need to learn any intricate rigmarole like nonstandard set theory while enjoying a revolutionary new computer readily at hand. There is no wonder that few impressible persons are enchanted by the yawning heights of the new paradigm.

The mirage disappears, and the cosmic promises fade when the reader gets acquaintance with the definition of grossone, the mysterious radix of Sergeyev's positional system. It turns out that the grossone is not big and not small but simply “the biggest natural number” that is defined by Sergeyev as “the number of elements of the set of natural numbers.” Pupils know that there is neither the biggest natural number nor the natural number that expresses the number of elements of the set of all natural numbers.

Sergeyev who became a professor for his works in global optimization has published quite a few practically identical articles of a petty-philosophical nature. The articles were printed in various journals outside Russia, and the editorial boards of these journals include no specialists in foundations or nonstandard analysis. Unfortunately, science is not an ideal system. It is an occupation of hundreds of thousands of persons who fill thousands of journals with their writings of various qualities. There is no need to conceal that we can encounter not only weak and false papers but also occasional pieces of plagiarism. The only barrier is the reputation of a journal and the competence of its editorial board. Reputation and competence are volatile qualities, and so even the articles by pseudoscientists and charlatans are published sometimes.

The informational noise by Sergeyev and his challenge to nonstandard analysis are far from innocent matters that deserve no reaction. It was explained in an article in Siberian Mathematical Journal No. 5 of 2008 that the factorial N! of any arbitrary infinite N possesses all properties of a grossone that were desired by Sergeyev. Besides there is a profusion of infinites in nonstandard analysis. Moreover, the article demonstrated that there are unsurpassable obstacles to using even such a “genuine” grossone as a radix in serious symbolic calculations. The grossone by Sergeyev is one of the uncountably many typical and commonplace objects of nonstandard analysis neither generating any new paradigm in mathematics. In other words, the awkward blunders of Sergeyev can produce nothing essential even in a scientific framework, which is no wonder since the correct exposition needs only the easiest basics of nonstandard analysis.

Those enchanted by the utopia of the grossone should pay attention to nonstandard analysis. If need be, learn nonstandard analysis and use the factorial of any actually infinite natural number. Do not dump the noble paradigms of long standing for the mirage of a revolution in mathematics which is based on the concept of biggest natural number. Do not dream in vain about the Infinity Computer. What is possible of Sergeyev's promises has been already implemented and belongs to the public domain. This is the calculator Inf by Ben Crowell and Mustafa Khafateh.

These days I received a letter from a young scientist from Nizny Novgorod. He asked me why I was absent from the seminars with Sergeyev's talk in Novosibirsk, since the proponents of Sergeyev said that this proves the lack of any serious arguments against Sergeyev. I answered that I missed the talks because there had been no reasons to listen them. Sergeyev's grossone does gross one out. This would be enough if had the matter been about some delusion or even perservelance in some delusion. Unfortunately, the situation is worse than that.

We may hear that Sergeyev is a talented person who did nothing wrong but who believes in the importance of his ideas and their usefulness. Of course, Sergeev is talented. In my opinion, all humans are exceptionally talented. The problem is what one does with one's talent. There are many options and not all of them are enjoyable. The presumption of decency is unquestionable in science, but it acts only up to the first infringement. There are no foul points to be collected. It is forbidden to lie or embellish someting just a wee bit. Science is done by humans with all their subjective passions, but it preserves itself in absolutely impersonal and objective form. “Science does not tolerate subjectivism,” as Nikolay Semyonov taught us. Lies, pretentions, and shallowness are intolerable in academic circles. Sergeyev has ignored criticism in scientific publications. He has continued his advertising activities. This behavior contradicts the academic ethics and drives a scientist beyond the realm of science. Such a person becomes a pseudoscientist who is disinterested in scientific arguments and the opinion of specialists since he knows everything by himself alone.

There is no biggest natural number, but Sergeyev's articles asserting its existence are not revoked by him. This violates the ethics of science. Science knows the Levi-Civita fields which underlie the calculator Inf of the “revolutionary type” of the Infinity Computer. This is ignored by Sergeyev either. Following an impulse from Nizhy Novgorog two years after the above-mentioned mild critical paper, most Russian TV channels and mass media trumpeted about the “most prestigious Pythagoras award” to Sergeyev, the one who had “counted infinity.” I have to comment on this in the independent newspaper Troitsk Variant—Science. The noise was dampened in three days. The information about Sergeyev was withdrawn from the site of the Russian Academy of Sciences, and Newsletter of the European Mathematical Society published a letter about this scandalous award. This was insufficient either. Well, worse things happen sometimes.

The border between science and pseudoscience is rather thin and seemingly one-sided. The academics and lookers-on still have many ambiguities in these matters. So I'll try to formulate my understanding of pseudoscience and the manner of dealing with pseudoscientists.

Ignorance in an unfamiliar area of science reveals itself in the comical distortion of the area, which is the phenomenon of pseudoscience. Pretensions and neglect of criticism are the totemic features of pseudoscience. The errors within science are repaired, but the achievements of pseudoscience are just laughed at. A person who systematically makes mistakes in his science is considered to be a feeble or poor scientist. He is usually despised by his fellow colleguages. Even an ignorant mathematician practicing mathematics is called a dummy rather than a pseudoscientist. Physicists, chemists, and specialists in humanities proceed likewise. A person who makes mistakes in an alien area is considered as an intruder into others' domain. If his mistakes are comical, the specialists declare him a crank, and he is derided by his next of kin and the others. A pseudoscientist is an ignoramus and pretender who systematically makes comical mistakes in scientific matters. A pseudoscientist living on the money of science is a junk scientist. A paradox is a truth disguised as a lie. Pseudoscience collects lies in the truth's clothing. It's as simple as that. All the rest are trifles, foams, and hiding eyes.

All normal scientists never try to change the mind of pseudoscientists, since this will be a vain waste of time. Science retaliates against pseudoscience once in a while, which is enough for the well-being of science. Discussion is an internal scientific tool unfit for pseudoscience. Explaining misconceptions is not a discussion. Science owes nothing to dummies and jerks. Wiles has no discussion with anyone of the horde of fermatists. Geometers discuss nothing with the adeps of trisection. Physicists never discuss anything with the inventors of a perpetual motion machine. Geneticists avoid discussions with creationists. Science only forewarns the public about the mistakes and misdeeds of crooks and junk scientists. Science points to pseudoscience, draws a border line, and continues its travel. Science is intolerant to pseudoscience.

I never listen the talks of pseudoscientists and advise everyone to do the same.

S. Kutateladze

October 14, 2012

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© Kutateladze S. S. 2012