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According to Burroughs, he hadknown a certain Captain Clark,around 1960 in Tangier, who oncebragged that he had been sailingtwenty-three years without an acci-dent. That very day, Clark’s ship hadan accident that killed him andeverybody else aboard. Furthermore,while Bur roughs was thinking aboutthis crude example of the irony of thegods that evening, a bulletin on theradio announced the crash of an air-liner in Florida. The pilot was anothercaptain Clark, and the flight wasFlight 23. Burroughs began collectingodd 23s after this gruesome syn-chronicity, and after 1965 I also begancollecting them. (Wilson 1977)In the course of the following

decades, Shea and Wilson’s beautifulfairytale about the secret—and yet soopenly recognizable—number lastinglyem bedded itself in popular culture, not

only in connection with conspiracies.Among other examples,

!In the western comedy SupportYour Local Gunfighter (1971),the hero re peatedly bets all hismoney on the number twenty-three. He loses until at last heactually breaks the bank, win-ning everything.

!In 1980, industrial/avant-gardeband Throbbing Gristlerecorded the song “The OldMan Smiled,” which explicitlyreferences Burroughs’s “CaptainClark,” “twenty-three days andtwenty-three hours of the day,”“Flight 23,” and so forth(Throbbing Gristle 1993).

!The German movie 23 (1998)revolves around the conspiracytheories of Hagbard Celine (i.e.,computer hacker Karl Koch[1965–1989]), who believed inthe existence of the Illuminatiin today’s society, hacked for theKGB (among others), and (asthe official story goes) died byburning himself to death. !The German minimalist elec-tronic band Welle:Erdball,which supposedly composes itsmusic with the help of a Com-modore-64 computer, devotedone of their best-known songs,“C=64/23,” to the conspiracytheory connected with the num-ber twenty-three:

“Commodore 64, is that cor-rect?”

“Yes, 64.”“If one divides this by two?”“It’s . . . thirty-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 imaginativenumber games, but the possibilitiesgreatly increase if one combines it withanother number. I would like to intro-duce another dalliance with the numbertwenty-three, because it is an impres-

The Numerology of A Berlin biologist/physician and a psychology professor from Viennafound an increasingly inscrutable connection between the numberstwenty-three and twenty-eight. They applied their system to explanationsof nearly all events in life and nature—but it doesn’t quite add up.

MARK BENECKE

The number twenty-three may be well known to readersof the SKEPTICAL INQUIRER for its supposed signifi-cance, which originated with the term “23 skidoo” pop-

ularized in the early 1920s. Many uses of “23 skidoo” can befound in newspapers as early as 1906, mostly as slang mean-ing “it’s time to leave while the getting is good.” In the Illu-minatus! Trilogy, written by Robert Shea and Robert AntonWilson, twenty-three is the number of misfortune and de-struction, as well as—of course—the alleged key to the Illu-minati. Wilson describes how he came by his interest in thenumber from author William Burroughs, who wrote a shortstory in 1967 called “23 Skidoo”:

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sive example of how easy it is to becomeobsessed with a supposition one is fondof, in light of perplexing yet only osten-sible evidence.

Older skeptics will notice immedi-ately that the two numbers discussedbelow are also the basis for the pseudo-scientific concept of the biorhythm—the idea that favorable, critical, and neg-ative days in an individual’s life can bepredicted through calculation (Gardner1981). The calculation of biorhythm(widespread in the 1970s but currentlyless prominent) employs three numbers(seen here as measured “number ofdays”): twenty-three for the physicalrhythm, twenty-eight for the emotionalrhythm, and thirty-three for the intel-lectual rhythm. Each rythm is said to setout on its sinusoidal course starting atbirth. This assumption, however, hasnever been confirmed. Rhythms of Life

The underlying idea of biorhythm isnot completely fallacious. The constantrepetition of the seasons, as well asmany processes observed in the courseof a lifetime, gives the impression thatthere are basic rhythms of nature inwhich all cycles repeat. Blossoms openand close; animals migrate and comeback. Is there a master clock that con-ducts the life cycle? Are the small life

rhythms subordinated to a greater one?Does this all-encompassing rhythm ex-plain growth and decay?

These questions were asked at the be-ginning of the twentieth century by theBerlin biologist and physician WilhelmFliess, based on his observations of nature. Fliess then became lost in the in-creasingly inscrutable connections be-tween cause and effect of his math -ematically correct but wrongly appliedobservations (Benecke 2002; Fliess1906). Herman Swoboda (1873–1963),a psychology professor at the Universityof Vienna, also claimed to have (indepen-dently) found a natural biorhythm at thesame time, quite similar to Fliess’s (e.g., aspontaneous repetition of thoughts aftertwenty-three hours and again aftertwenty-three days) (Swoboda 1904).

According to his own report, Fliessfound initial traces of the temporalorder of life in the biological fact thatwomen usually ovulate every twenty-eight days. He noticed this during theexamination of a related issue: the “typ-ical changes in sharply defined areas ofthe nose, the ‘genital parts of the nose,’which are located at the nasal conchaand the septum,” of women duringmenstruation (Fliess 1906).

Fliess then asked his female patientsto record the exact dates of their men-strual bleeding. It became evident that

the assumed standard interval of twenty-eight days almost never oc curred. Be-cause Fliess was convinced that “a pulsecourses through all of life,” he did notgive up but was rather even more in-trigued. He calculated until he foundthat the deviations of the twenty-eight-day standard are related to anothernumber, which renders them explain-able: twenty-three.

Now Fliess scoured medical journalsand personal accounts of friends andacquaintances for temporal recurrencesand rhythms, which he found could al-ways be mathematically described inconjunction with the numbers twenty-three and twenty-eight. He claimedthat each and every repetitive growth ordecay process in human, animal, andplant life was deconstructable and un-derstandable by means of the two num-bers. These events ranged from inter-vals between the births of one particularmother’s children to the times of deathof family members. Fliess connectedeverything with his mathematical dis-covery: the time when plants budded ordiscarded their blossoms, the occur-rence of hermaphroditic humans, thetime at which children teethe, and eventhe personal histories of many genera-tions of a family.

A brief example illustrates his method: On four days of the year 1815,namely on August 19th and 25th aswell as on October 15th and 19th,Schubert composed an astonishingamount and his best songs. The in-tervals between the days result in thefollowing: 19 August to 19 October = 61 days =

2 times 28 plus (28 minus 23) as well as

25 August to 15 October = 51 days =2 times 28 minus (28 minus 23).

(Fliess 1906) Only basic arithmetic operations andtwo numbers are necessary to correlatedays of exceptional creativity. Truly as-tonishing!

Fliess documented the life cycles oftwo amaryllis plants, which he ob servedfor eight years, in much more detail.One of the two plants was an offshootof the other, so the plants were geneti-cally identical. Fliess noted the timeswhen the plants budded, blossomed,and discarded their flowers. At first

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Figure 1. Original front covers of the books of Wilhelm Fliess and Hans Schlieper (Fliess 1906; Schlieper 1929).

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glance, there was no correlation amongthe numbers. Quite elegantly, Fliessthen established a link with the help ofan auxiliary number, as he spelled outthe following equation: “The formationof buds from one year to the next isequal to the period between blossomingin the first year and blossoming in thesecond year plus four times 28 minusfour times 23” (Fliess 1906).

According to Fliess, even illness anddeath are subject to the numbers twenty-three and twenty-eight: “Of two times(23 plus 28) people who fall ill with St.Vitus’ dance, 28 are men. Little Wolfganglearned how to walk after twenty-fourtimes 28 plus (28 squared) minus twotimes 28 times 23 days. He lived twenty-four times 23 plus (28 squared) minus(two times 23 squared) days” (Fliess1906).

Fliess also correctly calculated theages of death of Goethe, Bismarck,Kaiser Wilhelm, and Alexander vonHumboldt, as well as those of manyother celebrities of the time by combin-ing the numbers twenty-three andtwenty-eight. How is this possible? Predictions The first indication of an error in Fliess’sarduous work appears if one tries to cal-culate, in advance, the age at which aperson will die. This calculation does notwork with biorhythms and numbercombinations. A known death can onlylater be described by the two basic num-bers; this is contrary to the scientificprinciple that one can predict futureevents (within the realms of the calcula-ble) based on a “natural law.” Thus, bio-rhythms as such cannot be a natural law,because they do not allow for predictionsto be drawn from them.

Another source of error in Fliess’swork is the fact that the numbers, whichFliess had found in works of other au-thors, were not always correct. Con traryto the above example, three times morewomen than men do not fall ill with St.Vitus’s dance (Hunting ton’s disease). IfFliess was able to squeeze such false datainto his system, it is very likely that alldata can easily be incorporated into thebiorhythm scheme.

How about calculations based oncorrect data, such as the budding times

of flowering plants? Are these numberlinks also calculated artificially, or dothey reflect an intrinsic property of na-ture? The answer is that even in the“real” cases, Fliess unwittingly suc-cumbed to his basic assumption, whichhe took for granted and therefore didnot properly examine again (for exam-ple, by using other numbers or meth-ods). If one examines any group ofnumbers, whether taken from nature or

“randomly” generated according to ar-bitrary rules (for example, by a computerprogram), many of these numbers will bedivisible by either twenty-three ortwenty-eight and can be matched with anatural rhythm. As early as 1928, medicaldoctor Jakob Aebly (1885–1934) fromZürich calculated that approximatelyevery twelfth random number is a suit-able “candidate” for division by eithertwenty-three or twenty-eight (Aebly

Figure 2. Typical page from Fliess’s book: A person with diabetes suffers from an embolism and dies. All eventscan be expressed through rhythms that are composed of the numbers twenty-three and twenty-eight (Fliess1906, 142).

A known death can only later be described by the two basic

numbers; this is contrary to thescientific principle that one can

predict future events (within therealms of the calculable) based

on a “natural law.”

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1928). Because Fliess arbitrarily considers

certain numbers as belonging together(see the earlier example of Schubert’ssongs), he artificially increases theprobability of finding numbers that fithis rhythms. It is perfect circular rea-soning: Numbers belong together “be-cause they simply belong together,” sothey are grouped together. The result isa rhythm that is assumed from the out-set. Without it, the numbers would nothave been combined and could not cre-ate a rhythm.Armadillo and Space Year So the rhythms derived from Fliess’snumbers are artificial. No one has evertaken the trouble to recalculate the manyhundreds of pages of Fliessian examplesin a different manner or with out usingtwenty-three and twenty-eight. In 1928,however, Aebly showed that many bio-rhythmic number games also work witha different set of numbers, for examplewith three and five. It nevertheless re-mains surprising that Fliess, with doggeddetermination, succeeded in creating aview of the world that appeared correctdown to the last detail.

Hans Schlieper, a follower of theFliessian periodicity theory, went evenfurther than its creator. In 1929 he in -vented another value, the “space year,”to manipulate along with the numberstwenty-three and twenty-eight. Thisvalue not only enabled him to mathe-matically recreate personal histories butalso to mathematically represent the“regular” occurrence of certain dreamsand the composition of living bodies:

I frequently dream of a walk throughthe streets of Paris to the green of theBois de Boulogne, and the recurrenceof the image made me want to writedown the dates. The first two inter-vals already represent half the spaceyear with interconnection of thequadratic complex. The interval of 44days denotes a frequently occurringcircular bond (“Bindungsring”); theinterval of 139 days therefore is thevalue of half a year, for which its formis correct. (Schlieper 1929)While examining the mosaic on the

armor of an armadillo, Schlieper noticed“structures, which immediately meet theeye of the expert as infallibly true: Truly!There they were again, the intervals be-tween 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 thiscase. From his point of view, however,his conclusions seemed to merely reflecthis scientific curiosity, not his possibleblindness to a false assumption:

I never had doubts that, someday, onewould be able to make visible the pe-riod values, and especially the spaceyear, using living beings. In somecases, this rather unscientific wishfulthinking bore rich fruit, for examplein the event of Louis Pasteur’s firstexperiments regarding a rabies vacci-nation. He held tenaciously to histheory and asserted himself againstthe entire world. The periodicity the-ory, however, failed due to its circularthought. (Schlieper 1929)

Rows, Roundels, and Rhythms Unintentionally, natural science maga-zines like the German Bild der Wissen -schaft—which annually honors the bestmathematical approaches to “calculat-ing” the current year solely with the helpof the four numbers of which the yearis made—provide elegant proof againstthe periodicity theory. Readers connectthe four numbers of the year throughsimple mathematical methods and cal-culate the respective year by playing sur-prising games with numbers. If you lookfor it long enough, there will always bea meaning. But no one em braces theidea that the four digits of the year inquestion must have magical or rhythmicproperties, just because you can manip-ulate them mathematically to arrive atthat respective year.

In short, a mathematically inclined(and knowledgeable) person can connectalmost all numerical values to a rhythmicsequence, using similarly simple calcula-tions with some constant basic numbers;or, they can simply transform and inventthe sequence if necessary. Whether thefigures are “true” or “false” (i.e., whetherthey are obtained randomly or throughobservation) is not important. Connec-tions can always be made, although withsome combinations of numbers this iseasier than with others. This strategy iseven simpler given the right amount ofcreativity for explaining exceptions to

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Figure 3. While examining the mosaic on the armor of an armadillo, Schlieper noticed “structures, which imme-diately meet the eye of the expert as infallibly true: Truly! There they were again, the intervals between the birthsof my own siblings, only transferred into space, represented physically!” (Schlieper 1929, 110).

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the rule by means of “circular bonds” and“excessive units,” which Schlieper in -vented to allow his calculations to workproperly.Conclusion The obituary that Hans Schlieperwrote for his teacher Wilhelm Fliessreads as follows: Wilhelm Fliess, born 24 October 1858, diedshortly before his 70th birthday. For himtoo the year drew the line, the leap year,which had become a scientific experiencefor him through the births of his children: His son Robert, born 29 December 1895 1

1461 = 4 J His son Conrad, born 29 December 1899

8 10515 = 32J - 51×23Wilhelm Fliess, died 13 October 1928 The values 1173 = 51×23 = 28×23 + 232 and1428 = 51×28 = 23×28 + 282 are typical con-nection values. (Schlieper 1929)

Reflecting on the dogged determi-nation with which Fliess and Schlieperapproached their subject, we mightsmile at this tragicomic swan song. ButFliess would have probably consideredthis epitaph appropriate.

Interest in the Fliessian doctrine ofbiorhythms, which at first glance ap -pears to be built on a solid mathemati-cal and empirical foundation, vanishedmainly because it worked only in retro-spect: Everything can be linked to -gether, but only after the fact; theseconnections are not predictable.

Nevertheless, these deliberations,which only much later became known asbiorhythms, contain a grain of truth: ob-viously there are other biological regular-ities, such as circadian rhythms (e.g.,Smith 1970; Hastings et al. 2003). Yet noone should prematurely laugh about theworks of Fliess and Schlieper, even ifthey are inaccurate. Even today it is oftentricky—and unfortunately also tempt-ing—for natural scientists and psychol-ogists to draw strict conclusions aboutlife and death from mathematical rela-tionships. This is particularly true if thedata sample—intentionally or uninten-tionally—is small or has been preselectedbased on erroneous presuppositions. n

References Aebly, Jakob. 1928. Die Fliess’sche Periodenlehre im

Lichte der Biologischen und MathematischenKritik. Ein Beitrag zur Geschichte der Zahlen -mystik im 20 Jahrhundert (The Science of Peri-odicity Checked against Mathematical and Bio-logical Criticism on Number Mythology in the20th Century). Stuttgart, Leipzig and Zürich:Hippokrates-Verlag.

Benecke, Mark. 2002. The Dream of Eternal Life:Biomedicine, Aging, and Immortality. NewYork: Columbia University Press.

Fliess, Wilhelm. 1906. Der Ablauf des Lebens:Grundlegung zur exakten Biologie (The Courseof Life: Basic Principles in Exact Biology).Leipzig & Vienna: Deuticke.

Gardner, Martin. 1981. Fliess, Freud, and bio-rhythm. In Science: Good, Bad and Bogus.Amherst, NY: Prometheus Books, 131–40.

Hastings, Michael, Akhilesh Reddy, and E.S.Maywood. 2003. A clockwork web: Circadiantiming in brain and periphery, in health anddisease. Nature Reviews Neuroscience 4(8)(August) 649–61.

Schlieper, Hans. 1929. Das Raumjahr: Die Ord-nung des lebendigen Stoffes! (The Space Year:Order of All Living Material) Jena, Ger many:Diederichs.

Smith, Anthony. 1970. The Seasons: Rhythms ofLife, Cycles of Change. London: Weidenfeldand Nicolson.

Swoboda, Hermann. 1904. Die Perioden des Men-schlichen Organismus in Ihrer Psycholo gischenund Biologischen Bedeutung. (The Periods of theHuman Organism in Their Psychological andBiological Meaning). Leipzig and Vienna:Deuticke.

Throbbing Gristle. 1993. “The Old Man Smiled”(recorded November 1980). TG Box 1. Lon -don: The Grey Area/Mute Records Ltd.

Welle:Erdball. 2000. “C=64/23.” Starf ighter F-104G. Han nover, Germany: SPV/SyntheticSym phony.

Wilson, Robert A. 1977. The 23 phenomenon.Fortean Times 23. Available online at www.forteantimes.com/features/commentary/396/the_23_phenomenon.html.

Figure 4. Development of a Limax snail, following an “independent” observation that Schlieper took from a bookon snails. The footnote goes further, referring to Gregor Mendel’s (founder of classical genetics) original obser-vations: “Out of 15 plants, Mendel got 556 seeds. From those however only 529 [which equals] 232 did growfruits. 27 seeds did not develop fully or at all, i.e., 282 / 2 –365 which is a pure bond” (Schlieper 1929, 309).

Mark Benecke, PhD, is acertified, sworn forensic biologist in Cologne, Ger-many, and a member ofthe scientific advisoryboard of the German skep-tics organization GWUP. Heearlier wrote for SI on spon-

taneous human combustion and magneticmountains. E-mail: forensic@benecke.com.

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