2011-05 Skeptical Inquirer: The Numerology of 23

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Source: Skeptical Inquirer, May/June 2011, Vol. 35, No. 3, pages 49 - 53

The Numerology of 23

A Berlin biologist/physician and a psychology professor from Vienna found an increasingly inscrutable connection between the numbers twenty-three and twenty-eight. They applied their system to explanations of nearly all events in life and nature-but it doesn't quite add up

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The number twenty-three may be well known to readers of the SKEPTICAL INQUIRER for its supposed significance, which originated with the term "23 skidoo" pop ularized in the early 1920s. Many uses of"23 skidoo" can be found in newspapers as early as 1906, mostly as slang meaning "it's time to leave while the getting is good." In the Illuminatus! Trilogy, written by Robert Shea and Robert Anton Wilson, twenty-three is the number of misfortune and destruction, as weil as - of course - the alleged key to the Illuminati. Wilson describes how he came by his interest in the number from author William Burroughs, who wrote a short story in 1967 called "23 Skidoo":

According to Burroughs, he had known a certain Captain Clark, around 1960 in Tangier, who anee bragged that he had been sailing nventy-three years withour an accident. That very day, Clark's ship had an accident that killed hirn and everybody else aboard. Furthermore, while Burroughs was thinking about this erode example of the irony of the gods that evening, a bulletin on the radio announced the crash of an akliner in Florida. The pilot was another captain Clark, and the flight was Flight 23. Burroughs began collecting odd 235 after chis gruesome synchronicity, and after 1965 I also began collecting them. (Wilson 1977)

In the course of the following decades, Shea and Wilson's beautiful fairytale about the secret-and yet so openly recognizable-number lastingly embedded itself in popular culture, not only in connection with conspiracies. Among other examples,

  • In the western comedy Support Your Local Gunfighter (1971), the hero repeatedly bets all his money on the number twentythree. He loses until at last he actually breaks the bank, winning everything.
  • In 1980, industriallavant-garde band Throbbing Gristle recorded the song "The Old Man Smiled,"which explicitly references Burroughs's "Captain Clark,""twenty-three days and twenty-three hours of the day", "Flight 23", and so forth (Throbbing Gristle 1993).
  • The German movie 23 (1998) revolves around the conspiracy theories ofHagbard Celine (i.e., computer hacker Karl Koch [1965-1989]), who believed in the existence of the Illuminati in today's society, hacked for the KGB (among others), and (as the official story goes) died by burning himself to death.
  • The German minimalist electronic band Welle:Erdball, which supposedly composes its music with the help of a Commodore-64 computer, devoted one of their best-known songs, "C = 64123," to the conspiracy theory connected with the number twenty-three:

"Commodore 64, is that correct?"
"If,one divides this by two?"
"lt's ... thwenty-two."
"And if one turns that around!?"
"Then it's twenty-three!"
(Welle, Erdball 2000)

The significance of twenty-three can be found in all kinds of imaginative number games, but the possibilities greatly increase if one combines it with another number. I would like to introduce another dalliance with the number twenty-three, because it is an impressive example of how easy it is to become obsessed with a supposition one is fond of, in light of perplexing yet only ostensible evidence.

Older skeptics will notice immediately that the two numbers discussed below are also the basis for the pseudoscientific concept of the biorhythmth - idea that favorable, critical, and negative days in an individual's life can be predicted through calculation (Gardner 1981). The calculation of biorhythm (widespread in the 1970s but currently less prominent) employs three numbers (seen here as measured "number of days"): twenty-three for the physical rhythm, twenty-eight for the emotional rhythm, and thirty-three for the intellectual rhythm. Each rythm is said to set out on its sinusoidal course starting at birth. This assumption, however, has never been confirmed.

Rhythms of Life

The underlying idea of biorhythm is not completely fallacious. The constant repetition of the seasons, as weil as many processes observed in the course of a lifetime, gives the impression that there are basic rhythms of nature in which all cycles repeat. Blossoms open and dose; animals migrate and come back. Is there a master dock that conducts the life cyde? Are the smalllife rhythms subordinated to a greater one? Does this all-encompassing rhythm explain growth and decay?

These questions were asked at the beginning of the twentieth century by the Berlin biologist and physician Wilhelm Fliess, based on his observations of nature. Fliess then became lost in the increasingly inscrutable connections between cause and effect of his mathematically correct but wrongly applied observations (Benecke 2002; Fliess 1906). Herman Swoboda (1873-1963), a psychology professor at the University of Vienna, also claimed to have (independently) found a natural biorhythm at the same time, quite similar to Fliess's (e.g., a spontaneous repetition of thoughts after twenty-three hours and again after twenty-three days) (Swoboda 1904).

According to his own report, Fliess found initial traces of the temporal order of life in the biological fact that women usually ovulate every twentyeight days. He noticed this during the examination of a re1ated issue: the "typical changes in sharply defined areas of the nose, the 'genital parts of the nose,' which are located at the nasal concha and the septum," of women during menstruation (Fliess 1906).

Fliess then asked his female patients to record the exact dates of their menstrual bleeding. It became evident that the assumed standard interval of twentyeight days almost never occurred. Because Fliess was convinced that "a pulse courses through all of life," he did not give up but was rather even more intrigued. He calculated until he found that the deviations of the twenty-eightday standard are related to another number, which renders them explainable: twenty-three.

Now Fliess scoured medical journals and personal accounts of friends and acquaintances for temporal recurrences and rhythms, which he found could always be mathematically described in conjunction with the numbers twentythree and twenty-eight. He claimed that each and every repetitive growth or decay process in human, animal, and plant life was deconstructable and understandable by means of the two numbers. These events ranged from intervals between the births of one particular mother's children to the firnes of death of family members. Fliess connected everything with his mathematical discovery: the time when plants budded or discarded their blossoms, the occurrence of hermaphroditic humans, the time at which children teethe, and even the personal histories of many generations of a family.

Abrief example illustrates his method:

On four days of the year 1815, namely on August 19th and 25th as well as on October 15th and 19th, Schubert composed an astonishing amount and his best songs. The intervals between the days result in the following:

19 August to 19 October = 61 days = 2 times 28 plus (28 minus 23)
as well as
25 August to 15 Oetober = 51 days = 2 times 28 minus (28 minus 23).
(Fliess 1906)

Only basic arithmetic operations and two numbers are necessary to correlate days of exceptional creativity. Truly astonishing!

Fliess documented the life cycles of two amaryllis plants, which he observed for eight years, in much more detail. One of the two plants was an offshoot of the other, so the plants were genetically identical. Fliess noted the times when the plants budded, blossomed, and discarded their flowers. At first glance, there was no correlation among the numbers. Quite elegantly, Fliess then established a link with the help of an auxiliary number, as he spelled out the foilowing equation: "The formation of buds from one year to the next is equal to the period betvveen blossoming in the first year and blossoming in the second year plus four times 28 minus four times 23" (Fliess 1906).

According to Fliess, even illness and death are subject to the numbers twentythree and twenty-eight: "Of two times (23 plus 28) people who fall ill with St. Vitus' dance, 28 are men. Little Wolfgang learned how to walk after twenty-four times 28 plus (28 squared) minus two times 28 times 23 days. He lived twentyfour times 23 plus (28 squared) minus (two times 23 squared) days" (Fliess 1906).

Fliess also correct1y calculated the ages of death of Goethe, Bismarck, Kaiser Wilhelm, and Alexander von Humboldt, as weil as those of many other celebrities of the time by combining the nurnbers tvventy-three and tvventy-eight. How is this possible?


The first indication of an error in Fliess's arduous work appears if one tries to calculate, in advance, the age at which a person will die. This calculation does not work with biorhythms and number combinations. A known death can only later be described by the tvvo basic numbers; this is contrary to the scientitlc principle that one can predict future events (within the realms of the calculable) based on a "naturallaw. "Thus, biorhythms as such cannot be a naturallaw, because they do not allow for predictions to be drawn from them.

Another source of error in Fliess's work is the fact that the numbers, which Fliess had found in works of other authors, were not always correct. Contrary to the above example, three times more women than men do not fall ill with St. Vitus's dance (Huntington's disease). If Fliess was able to squeeze such false data inta his system, it is very likely that all data can easily be incorporated into the biorhythm scheme.

How about calculations based on correct data, such as the budding times of flowering plants? Are these number links also calculated artificially, or do they reflect an intrinsic property of nature? The answer is that even in the "real" cases, Fliess unwittingly succumbed to his basic assumption, which he took for granted and therefore did not properly examine again (for exampIe, by using other numbers or methods). If one exarmines any group of numbers, whether taken from nature or "randomly" generated according to arbitrary rules (for example, by a computer program), many of these numbers will be divisible by either twenty-three or twenty-eight and can be matched with a natural rhythm. As early as 1928, medical doctor Jakob Aebly (1885-1934) from Zürich calculated that approximately every twelfth random number is a suitable "candidate" for division by either twenty-three or twenty-eight (Aebly 1928).

Because Fliess arbitrarily considers certain numbers as belonging together (see the earlier example of Sehubert's songs), he artificially !ncreases the probability of finding numbers that fit his rhythms. It is perfect circular reasoning: Numbers belong together "because they simply belong together," so they are grouped together. The result is a rhythm that is assumed from the outset. Without it, the numbers would not have been combined and could not create a rhythm.

Armadillo and Spaee Year

So the rhythms derived from Fliess's numbers are artificial. No one has ever taken the trouble to reealculate the many hundreds of pages of Fliessian examples in a different manner or without using twenty-three and twenty-eight. In 1928, however, Aebly showed that many biorhythmic number games also work with a different set of numbers, for example with three and five. lt nevertheless remains surprising that Fliess, with dogged determination, succeeded in creating a view of the world that appeared correet down to the last detail.

Hans Schlieper, a follower of the Fliessian periodicity theory, went even further than its creator. In 1929 he invented another value, the "space year," to manipulate along with the numbers twenty-three and twenty-eight. This value not only enabled him to mathematically recreate personal histories but also to mathematically represent the "regular" occurrenee of certain dreams and the composition ofliving bodies:

I frequently dream of a wa1k through the streets of Paris to the green of the Bois de Boulogne, and the recurrence of the image made me want to write down the dates. The first two intervals already represent half the space year with interconnection of the quadraric complex. The interval of 44 days denotes a frequently occurring circular bond ("Bindungsring"); the intem of 139 days therefore is the value of half a year, for which its form is correct. (Schlieper 1929)

While examining the mosaic on the armor of an armadillo, Schlieper noticed "structures, which immediately meet the eye of the expert as infallibly true: Truly! There they were again, the intervals between the births of my own siblings, only transferred into space, represented physically!" (Schlieper 1929).

Schlieper did not conceal that the wish was father to the thought in this case. From his point of view, however, bis conclusions seemed to merely reflect bis scientific curiosity, not bis possible blindness to a false assumption:

I never had doubts that, someday, one would be able to make visible the period values, and especially the space year, using living beings. In some cases, this rather unscientific wishful thinking bore rich fruit, for example in the event of Louis Pasteur's first experiments regarding a rabies vaccination. He held tenaciously to his theory and asserted himself against the enrire world. The periodicity theory, however, failed due to its circular thought. (Schlieper 1929)

Rows, Roundels, and Rhythms

Unintentionally, natural science magazines like the German Bild der Wissenschaft - which annually honors the best mathematical approaches to "calculating" the current year solely with the help of the four numbers of which the year is made-provide elegant proof against the periodicity theory. Readers connect the four numbers of the year through simple mathematical methods and calculate the respective year by playing surprising games with numbers. If you look for it long enough, there will always be a meaning. But no one embraces the idea that the four digits of the year in question must have magical or rhythmic properties, just because you can manipulate them mathematically to arrive at that respective year.

In short, a mathematically inclined (and knowledgeable) person can connect almost all numerical values to a rhythmic sequence, using similarly simple calculations with some constant basic numbers; or, they can simply transform and invent the sequence if necessary. Whether the figures are "true" or "false" (i.e., whether they are obtained randomly or through observation) is not important. Connections can always be made, although with some combinations of numbers this is easier than with others. This strategy is even simpler given the right amount of creativity for explaining exceptions to the rule by means of "circular bonds" and "excessive units," which Schlieper invented to allow his calculations to work properly.


The obituary that Hans Schlieper wrote for his teacher Wilhelm Fliess reads as follows:

Wilhelm Fliess, born 24 Oetober 1858, died shortly before his 70th birthday. For him too the year drew the line, the leap year, which had become a scientifie experience for him through the births of his children:

His son Robert, born 29 Decernber 1895 1
1461 = 4 J

His son Conrad, born 29 Decernber 1899
8 10515 = 32 J -51 x 23

Wilhelm Fliess, died 13 Oetober 1928

The values 1173 = 51 x 23 = 28 x 23 + 232 and 1428 = 51 x 28 = 23 x 28 + 282 are typical connection values. (Schlieper 1929)

Reflecting on the dogged determination with which Fliess and Schlieper approached their subjcct, we might smile at this tragicomic swan song. But Fliess would have probably considered this epitaph appropriate.

lnterest in the Fliessian doctrine of biorhythms, which at first glance appears to be built on a solid mathematical and empirical foundation, vanished mainly because it worked only in retrospect: Everything can be linked together, but only after the fact; these connections are not predictable.

Nevertheless, these deliberations, which only much later became known as biorhythms, contain a grain of truth: obviously there are other biological regularities, such as circadian rhythms (e.g., Smith 1970; Hastings et a1. 2003). Yet no one should prematurely laugh about the works of Fliess and Schlieper, even if they are inaccurate. Even today it is often tricky - and unfortunately also tempting - for natural scientists and psychologists to draw strict conclusions about life and death from mathematical relationships. This is particularly true if the data sample-intentionally or unintentionally - is small or has been preselected based on erroneous presuppositions.


  • Aebly, Jakob. 1928. Die Fliesssche Periodenlehre im Lichte der Biologischen und Mathematischen Kritik. Ein Beitrag zur Geschichte der Zahlenmystik im 20. Jahrhundert (The Science of Periodicity Cheeked against Mathematical and Biological Criticism on Number Mythology in the 20th Century). Stuttgart, Leipzig and Zürich: Hippokrates-Verlag.
  • Benecke, Mark. 2002. The Dream of Eternal Life: Biomedicine, Aging, and Immortality. New York: Columbia University Press.
  • Fliess, Wilhe1m. 1906. Der Ablauf des Lebens: Grundlegung zur exakten Biologie (The Course of Life: Basic Principles in Exact Biology). Leipzig & Vienna: Deuticke.
  • Gardner, Martin. 1981. Fliess, Freud, and biorhythm. In Science: Good, Bad and Bogus. Amherst, NY: Prometheus Books, 131-40.
  • Hastings, Michael, Akhilesh Reddy, and E.S. Maywood. 2003. A clockwork web: Circadian timing in brain and periphery, in health and disease. Nature Reviews Neuroreiente 4(8) (August) 649-61.
  • Schlieper, Hans. 1929. Das Raumjahr: Die Ordnung des lebendigen Stoffes! (The Spau Year: Order of All Living Materia/) Jena, Germany: Diederichs.
  • Smith, Anthony. 1970. The Seasons: Rhythms of Life, Cycles of Change. London: Weidenfeld and Nicolson.
  • Swoboda, Hermann. 1904. Die Perioden des Menschlichen Organismus in Ihrer Psychologischen und Biologischen Bedeutung. (The Periods of the Human Organism in Their Psychological and Biological Meaning). Leipzig and Vienna: Deuticke.
  • Throbbing Gristle. 1993. "The Old Man Smiled" (recorded November 1980). TGBox 1. London: The Grey ArealMute Records Ltd.
  • Welle:Erdball. 2000. "C = 64/23." Starfighter Fl04G. Hannover, Germany: SPV/Synthetic Symphony.
  • Wilson, Robert A. 1977. The 23 phenomenon. Fortean Times 23. Available online at www.forteantimes.com/features/commentary/396/ the_23_phenomenon.html.

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