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A biorhythm (from Greek βίος - bios, "life" and ῥυθμός - rhuthmos, "any regular recurring motion, rhythm") is an attempt to predict various aspects of a person's life through simple mathematical cycles. Most scientists believe that the idea has no more predictive power than chance and consider the concept an example of pseudoscience.
According to the theory of biorhythms, a person's life is influenced by rhythmic biological cycles that affect his or her ability in various domains, such as mental, physical and emotional activity. These cycles begin at birth and oscillate in a steady (sine wave) fashion throughout life, and by modeling them mathematically, it is suggested that a person's level of ability in each of these domains can be predicted from day to day. The theory is built on the idea that the biofeedback chemical and hormonal secretion functions within the body could show a sinusoidal behavior over time.
Most biorhythm models use three cycles: a 23-day physical cycle, a 28-day emotional cycle, and a 33-day intellectual cycle.  Although the 28-day cycle is the same length as the average woman's menstrual cycle and was originally described as a "female" cycle (see below), the two are not necessarily in any particular synchronization. Each of these cycles varies between high and low extremes sinusoidally, with days where the cycle crosses the zero line described as "critical days" of greater risk or uncertainty.
The equations for the cycles are:
where indicates the number of days since birth.
Basic arithmetic shows that the simpler 23- and 28-day cycles repeats every 644 days (or 1-3/4 years), while the triple 23-, 28-, and 33-day cycles repeats every 21,252 days (or 58.2+ years).
The notion of periodic cycles in human fortunes is ancient; for instance, it is found in natal astrology and in folk beliefs about "lucky days". The 23- and 28-day rhythms used by biorhythmists, however, were first devised in the late 19th century by Wilhelm Fliess, a Berlin physician and patient of Sigmund Freud. Fliess believed that he observed regularities at 23- and 28-day intervals in a number of phenomena, including births and deaths. He labeled the 23-day rhythm "male" and the 28-day rhythm "female", matching the menstrual cycle.
In 1904, psychology professor Hermann Swoboda claimed to have independently discovered the same cycles. Later, Alfred Teltscher, professor of engineering at the University of Innsbruck, came to the conclusion that his students' good and bad days followed a rhythmic pattern of 33 days. Teltscher believed that the brain's ability to absorb, mental ability, and alertness ran in 33-day cycles. One of the first academic researchers of biorhythms was also Estonian-born Nikolai Pärna, who published a book in German called Rhythm, Life and Creation in 1923.
The practice of consulting biorhythms was popularized in the 1970s by a series of books by Bernard Gittelson, including Biorhythm — A Personal Science, Biorhythm Charts of the Famous and Infamous, and Biorhythm Sports Forecasting. Gittelson's company, Biorhythm Computers, Inc., made a business selling personal biorhythm charts and calculators, but his ability to predict sporting events was not substantiated.
Charting biorhythms for personal use was popular in the United States during the 1970s; many places (especially video arcades and amusement areas) had a biorhythm machine that provided charts upon entry of date of birth. Biorhythm charts were common in newspapers, usually found with horoscopes, at the time as well. Biorhythm programs were a common application on personal computers; and in the late 1970s, there were also handheld biorhythm calculators on the market, the Kosmos 1 and the Casio Biolator. Though biorhythms have declined in popularity, there are numerous websites on the Internet that offer free biorhythm readings. In addition, there exist free and proprietary software programs that offer more advanced charting and analysis capabilities.
Proponents of biorhythmics call it an established interdisciplinary area of scientific endeavor which is still speculative—a protoscience. Critics state that biorhythms are based only upon numerological associations. The plausibility of biorhythmics is contested by mathematicians, biologists and other scientists. The most basic assertion is that even if it is assumed that physiological rhythms do exist, it is not clear why they should necessarily begin on the day of one's birth. One potential reason is that before detachment from the placenta, the infant is responding to its mother's body chemistry.
In some ways, biorhythmics resembles chronobiology, the study of biological rhythms. Through medical research, doctors have found that there are periodic biological cycles in a person's lifespan, such as the circadian rhythm (from Latin circa diem; literally, "about a day"), but few doctors believe they correspond to those described as biorhythms. To proponents, these discoveries (among others) demonstrate that people are affected by physiological, emotional and intellectual rhythms, though the exact relationships to the biorhythm cycles are not precisely understood. Studies regarding the effects of biorhythms on the human condition are still conducted.
The biorhythm theory is often presented as having scientific validity. Biorhythm critics' responses range from opposing it as harmful, to ignoring it, to treating it as entertainment. Some of the criticisms of the various theories in the category of biorhythmics are:
Some biorhythm critics say that biorhythms can be thrown off by such occurrences in the calendar as the beginning of the new year, holidays, or something as simple as the start of the week.[clarification needed]
There have been some three dozen studies supporting biorhythm theory, but all of them have suffered from methodological and statistical errors. An examination of some 134 biorhythm studies found that the theory is not valid.
Supporters continued defending the theory after Hines's review of 134 studies, causing other scientists to consider the field as pseudoscience:
An examination of some 134 biorhythm studies found that the theory is not valid (Hines, 1998). It is empirically testable and has been shown to be false. Terence Hines believes that this fact implies that biorhythm theory 'can not be properly termed a pseudoscientific theory'. However, when the advocates of an empirically testable theory refuse to give up the theory in the face of overwhelming evidence against it, it seems reasonable to call the theory pseudoscientific. For, in fact, the adherents to such a theory have declared by their behaviour that there is nothing that could falsify it, yet they continue to claim the theory is scientific. (from Carroll's "The Skeptic's Dictionary"):175
They'll cheerfully empty their pockets to anyone with a twinkle in their eye and a pseudoscience in their pocket. Astrology, biorhythms, ESP, numerology, astral projection, scientology, UFOlogy, pyramid power, psychic surgeons, Atlantis real state (...). (...) your pseudoscience will have better sales potential if it makes use of a mysterious device, or a lot of calculations (but simple calculations) (...) The great models [of this sales potential] are astrology and biorhythms (...).
If we take such pseudosciences as astrology, the theory of biorhythms, suitable parts of parapsychology, homeopathy and faith healing (...) Such examples of pseudoscience as the theory of biorhythms, astrology, dianetics, creationism, [and] faith healing may seem too obvious examples of pseudoscience for academic readers.
the following quote about the pseudoscientific biorhythm theory [p. 174–175] (...) we can eliminate ad hoc hypotheses (i.e. arbitrariness) that are the hallmark of all pseudosciences (astrology, biorhythm theory, (...) [p. 176] Unfortunately, in the case of the most socially successful [not scientific] theories, just as in the case of astrology and biorhythm "theory", we are dealing with something that resembles quackery closely. [p.186] (...) what matters is that falsifying data is systematically discounted in this pseudotheory. [p. 199].