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137 (one hundred ndthirty-seven) is the
natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following
136 136 may refer to: *136 (number) *AD 136 *136 BC *136 (MBTA bus), a Massachusetts Bay Transportation Authority bus route *136 Austria 136 Austria is a main-belt asteroid that was found by the prolific asteroid discoverer Johann Palisa on 18 Ma ...
and preceding 138.


Mathematics

137 is: * the 33rd
prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
; the next is 139, with which it comprises a
twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ...
, and thus 137 is a Chen prime. * an Eisenstein prime with no imaginary part and a real part of the form 3n - 1. * the fourth Stern prime. * a Pythagorean prime: a prime number of the form 4n+1, where n=34 (137=4\times 34+1) or the sum of two squares 11^+4^ = (121+16). * a combination of three terms 4^+3^-2^ = (64+81-8), cube of 4 +
Triangular number A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...
T4+T2 on each cube face (along 3 axes) - peaks (single 6th peak as free link) * a strong prime in the sense that it is more than the
arithmetic mean In mathematics and statistics, the arithmetic mean ( ), arithmetic average, or just the ''mean'' or ''average'' is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results fr ...
of its two neighboring primes. * a strictly non-palindromic number and a primeval number. * a factor of 10001 (the other being 73) and the
repdigit In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of "repeated" and "digit". Ex ...
11111111 (= 10001 × 1111). * using two radii to divide a circle according to the
golden ratio In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their summation, sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if \fr ...
yields sectors of approximately 137.51° (the golden angle) and
222 __NOTOC__ Year 222 ( CCXXII) was a common year starting on Tuesday of the Julian calendar. In the Roman Empire, it was known as the Year of the Consulship of Antoninus and Severus (or, less frequently, year 975 ''Ab urbe condita''). The denomi ...
° in degree system so 137 is the largest integer before it. * In decimal notation, 1/137 = 0., so its period value happens to be
palindromic A palindrome ( /ˈpæl.ɪn.droʊm/) is a word, number, phrase, or other sequence of symbols that reads the same backwards as forwards, such as ''madam'' or '' racecar'', the date " 02/02/2020" and the sentence: "A man, a plan, a canal – Pana ...
and has a period length of only 8. However, this is only special to decimal, as in pentadecimal it (1/92) has a period length of twenty-four (24) and the period value is not at all palindromic. * a combination of 5! + 4! - 3! - 2! + 1!


Physics

* 1/137 was once thought to be the exact value of the
fine-structure constant In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Alpha, Greek letter ''alpha''), is a Dimensionless physical constant, fundamental physical constant that quantifies the strength of the el ...
. The fine-structure constant, a
dimensionless physical constant Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that align with another sy ...
, is approximately 1/137, and the astronomer Arthur Eddington conjectured in 1929 that its reciprocal was in fact precisely the integer 137, which he claimed could be "obtained by pure deduction". This conjecture was not widely adopted, and by the 1940s, the experimental values for the constant were clearly inconsistent with the conjecture, being roughly 1/137.036. In 2021, researchers at the Kastler Brossel Laboratory in Paris reported the most precise measurement yet, determining the value to be with an accuracy of 81 parts per trillion. * Physicist
Leon M. Lederman Leon Max Lederman (July 15, 1922 – October 3, 2018) was an American experimental physicist who received the Nobel Prize in Physics in 1988, along with Melvin Schwartz and Jack Steinberger, for research on neutrinos. He also received the Wolf Pr ...
numbered his home near
Fermilab Fermi National Accelerator Laboratory (Fermilab), located in Batavia, Illinois, near Chicago, is a United States Department of Energy United States Department of Energy National Labs, national laboratory specializing in high-energy particle phys ...
137 based on the significance of the number to those in his profession. Lederman expounded on the significance of the number in his 1993 book '' The God Particle: If the Universe Is the Answer, What Is the Question?'', noting that not only was it the inverse of the fine-structure constant, but was also related to the probability that an electron will emit or absorb a photon—i.e., Feynman's conjecture. He added that it also "contains the crux of electromagnetism (the electron), relativity (the velocity of light), and quantum theory (the
Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...
). It would be less unsettling if the relationship between all these important concepts turned out to be one or three or maybe a multiple of pi. But 137?" The number 137, according to Lederman, "shows up naked all over the place", meaning that scientists on any planet in the universe using whatever units they have for charge or speed, and whatever their version of the Planck constant may be, will all come up with 137, because it is a pure number. Lederman recalled that
Richard Feynman Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist. He is best known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of t ...
had even suggested that all physicists put a sign in their offices with the number 137 to remind them of just how much they do not know.


Jungian psychology and mysticism

* 137 has been the subject of psychological speculation by Swiss psychiatrist and psychoanalyst
Carl Jung Carl Gustav Jung ( ; ; 26 July 1875 – 6 June 1961) was a Swiss psychiatrist, psychotherapist, and psychologist who founded the school of analytical psychology. A prolific author of Carl Jung publications, over 20 books, illustrator, and corr ...
concerning his theory of
synchronicity Synchronicity () is a concept introduced by Carl Jung, founder of analytical psychology, to describe events that coincide in time and appear meaningfully related, yet lack a discoverable causal connection. Jung held that this was a healthy fu ...
. Jung and physicist
Wolfgang Pauli Wolfgang Ernst Pauli ( ; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and a pioneer of quantum mechanics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics "for the ...
, according to the book ''Jung, Pauli, and the Pursuit of a Scientific Obsession'' by Arthur I. Miller, Emeritus Professor of History and Philosophy of Science at University College London, Jung and Pauli struggled in their search for a primal number that everything in the world hinges on, as well as a desire to quantify the unconscious. *
Wolfgang Pauli Wolfgang Ernst Pauli ( ; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and a pioneer of quantum mechanics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics "for the ...
had a series of significant dreams when he engaged in psychoanalysis with
Carl Jung Carl Gustav Jung ( ; ; 26 July 1875 – 6 June 1961) was a Swiss psychiatrist, psychotherapist, and psychologist who founded the school of analytical psychology. A prolific author of Carl Jung publications, over 20 books, illustrator, and corr ...
, published in the 12th volume of The Collected Works of C. G. Jung. The dreams were progressively sophisticated, and eventually described a mandalic "world clock", which might be a symbolic format describing an estimate of the inverse of fine structure constant: α^(-1) = π^1 + π^2 + 4π^3 = 137.036... . The "world-clock" was carried by a black flying bird and consist of three discs and three pulses : SMALL pulse consist of a small pointer on a blue vertical disc advancing by 1/32, representing π ; MIDDLE pulse was one completion of the vertial blue disc of 32 segments, representing π^2, which causes 1/32 advancement of a second outer horizontal disc; GREAT pulse being the complete rotation of the second horizontal disc, which contained 4 coloured sections standing 4 men holding 4 pendulums, representing 4π^3 . The completion of the second disc in the GREAT pulse will cause a full rotation of the third outer ring, which turns from black colour to golden. The function of three pulses of the World-Clock symbolically add up to 137 from π^1 + π^2 + 4π^3. * While
Carl Jung Carl Gustav Jung ( ; ; 26 July 1875 – 6 June 1961) was a Swiss psychiatrist, psychotherapist, and psychologist who founded the school of analytical psychology. A prolific author of Carl Jung publications, over 20 books, illustrator, and corr ...
and
Wolfgang Pauli Wolfgang Ernst Pauli ( ; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and a pioneer of quantum mechanics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics "for the ...
were fascinated with the number 137, their lives had been entwined with meaningful synchronicities with this number. Carl Jung was born on the 26 July 1875 (207th day of the 75th year) and died on the 6 June 1961 (157th day of the 61th year), 207days + 75years + 157days + 61years = 136 Years & 364 Days, which is one day from 137 years. Wolfgang Pauli died , as himself expected, in room 137 of the Red-Cross hospital at Zurich. Carl Jung's Magnum Opus title "Liber Novus", also bears an English
Gematria In numerology, gematria (; or , plural or ) is the practice of assigning a numerical value to a name, word, or phrase by reading it as a number, or sometimes by using an alphanumeric cipher. The letters of the alphabets involved have standar ...
value of 137. The English Gematria values of the initials of name of Carl Gustav Jung, also hinted a value of 137 with numbers 3,7,10. ** '' 137: Jung, Pauli, and the Pursuit of a Scientific Obsession'' by Arthur I. Miller, , describes the friendship of
Carl Jung Carl Gustav Jung ( ; ; 26 July 1875 – 6 June 1961) was a Swiss psychiatrist, psychotherapist, and psychologist who founded the school of analytical psychology. A prolific author of Carl Jung publications, over 20 books, illustrator, and corr ...
and
Wolfgang Pauli Wolfgang Ernst Pauli ( ; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and a pioneer of quantum mechanics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics "for the ...
and their search for the meaning of 137 in science, medieval alchemy, dream interpretation, and the ''
I Ching The ''I Ching'' or ''Yijing'' ( ), usually translated ''Book of Changes'' or ''Classic of Changes'', is an ancient Chinese divination text that is among the oldest of the Chinese classics. The ''I Ching'' was originally a divination manual in ...
''.


Other uses

* The
atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of its atomic nucleus. For ordinary nuclei composed of protons and neutrons, this is equal to the proton number (''n''p) or the number of pro ...
of an element not yet observed called untriseptium, the largest element on the
periodic table The periodic table, also known as the periodic table of the elements, is an ordered arrangement of the chemical elements into rows (" periods") and columns (" groups"). It is an icon of chemistry and is widely used in physics and other s ...
allowed for a point nucleus by the
Bohr model In atomic physics, the Bohr model or Rutherford–Bohr model was a model of the atom that incorporated some early quantum concepts. Developed from 1911 to 1918 by Niels Bohr and building on Ernest Rutherford's nuclear Rutherford model, model, i ...
and the
Dirac equation In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1/2 massive particles, called "Dirac ...
.


Notes


References


External links


137 at VirtueScience



What is the significance of the number 137 in physics?
{{DEFAULTSORT:137 (Number) Integers