# 137 (number)

 ← 136 137 138 →
Cardinal one hundred thirty-seven
Ordinal 137th
(one hundred thirty-seventh)
Factorization prime
Prime 33rd
Divisors 1, 137
Greek numeral ΡΛΖ´
Roman numeral CXXXVII
Binary 100010012
Ternary 120023
Quaternary 20214
Quinary 10225
Senary 3456
Octal 2118
Duodecimal B512
Vigesimal 6H20
Base 36 3T36

137 (one hundred [and] thirty-seven) is the natural number following 136 and preceding 138.

## In mathematics

137 is:

Using two radii to divide a circle according to the golden ratio yields sectors of approximately 137° (the golden angle) and 222°.
1/137 = 0.00729927007299270072992700..., its period value is palindromic and has only a period length of 8.

## In physics

• Since the early 1900s, physicists have postulated that the number could lay at the heart of a grand unified theory, relating theories of electromagnetism, quantum mechanics and, especially, gravity.[5][6]
• The fine structure constant, a dimensionless physical constant, 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".[7] This conjecture was not widely adopted, and by the 1940s, the experimental values for the constant were clearly inconsistent with it (i.e. closer to 137.036).[8]
• Physicist Leon M. Lederman numbered his home near Fermilab 137 based on the significance of the number to those in his profession. Lederman expounded on the significance of the number in his 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.[n 1] He added that it also "contains the crux of electromagnetism (the electron), relativity (the velocity of light), and quantum theory (Planck's constant). 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 Planck’s constant may be, will all come up with 137, because it is a pure number. Lederman recalled that Richard Feynman 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.[9]
• In the Bohr model, the innermost electron of an atom with Z = 137 would be orbiting (just below) the speed of light, and the next element (Z = 138) would be "impossible". Since the Bohr model does not include either quantum mechanics or special relativity, the fact that it breaks down in this regime is not unexpected. However, such large atoms (if their nuclei were stable) could be expected to behave rather differently from a naive extrapolation of trends in the periodic table.
• Wolfgang Pauli, a pioneer of quantum physics, died in a hospital room numbered 137, a coincidence that disturbed him.[10]

## In esoterism

• The fine structure constant of physics continues to convince esotericists that the universe has numerological fine tuning:[11] for example the age of the universe could be considered as roughly 13.7 times 1 billion years, though newer estimates put this value at 13.8.[12][13]
• The Hebrew word קבלה (Kabbalah) has a Gematria (numerical value) of 137. In Modern Hebrew, the root of Kabbalah (ק-ב-ל) can mean either "receiving" or "parallel." Kabbalah is generally taken to mean "the received tradition," which conveys the continuity of a tradition that has been passed down from generation to generation.[14] Nevertheless, the earlier nuance of meaning is seen in the first appearances of its root in the Torah (Exodus 26:5 and 36:12), where it means “parallel” or “corresponding” rather than “receiving.” It is used to describe the “corresponding loops” which, when clasped together, enjoined the two sections of the Tabernacle’s ceiling. These loops were suspended directly over the veil that divided the Holy Place and the Holy of Holies. Symbolically, this is the threshold between the physical dimension and the utterly spiritual dimension. In other words, at the boundary line of the physical world, the number 137 emerges. The wisdom of Kabbalah is to find correspondences between the mundane and spiritual levels of reality.[15]

## In religion

• The Bible says that Ishmael,[16] Levi[17] and Amram[18] all lived to be 137 years old. The three appearances make it the most common lifespan of individuals in the Bible.
• According to the verse in Genesis (17:17) there was a ten-year age gap between Abraham and Sarah. Sarah died at the age of 127 (Genesis 23:1), thus Abraham was 137 years old at her death. According to Rashi's commentary on Genesis 23:2, Sarah died when she heard that Isaac had almost been sacrificed, thus Abraham was 137 years old at the Binding of Isaac.

## In other fields

• 137: Jung, Pauli, and the Pursuit of a Scientific Obsession by Arthur I. Miller, ISBN 978-0-393-33864-5, describes the friendship of Carl Jung and Wolfgang Pauli and their search for the meaning of 137 in science, medieval alchemy, dream interpretation, and the I Ching.
• The year AD 137 or 137 BC
• 137 AH is a year in the Islamic calendar that corresponds to 754755 CE
• 137 Meliboea is a large and dark main belt asteroid discovered in 1874
• The atomic number of an element not yet observed called Untriseptium
• California Penal Code for "Offer bribe to influence testimony"
• The Samson 137 Indian reserve in Alberta, Canada
• Sonnet 137 by William Shakespeare
• Psalm 137
• The atomic number of the highest allowed element on the periodic table allowed by the Bohr Model and the Dirac equation.
• Caesium-137 is a radioactive isotope of Caesium formed by nuclear fission
• The number of atoms in a chlorophyll molecule, for which the chemical formula is C55H72MgN4O5.
• Rick Sanchez, a fictional character from the Adult Swim animated television series Rick and Morty, has an alias C-137.

## Notes

1. ^ There is a most profound and beautiful question associated with the observed coupling constant, e, the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to -0.08542455. (My physicist friends won’t recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to p or perhaps to the base of natural logarithms? Nobody knows. It’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the “hand of God” wrote that number, and “we don’t know how He pushed his pencil.” We know what kind of a dance to do experimentally to measure this number very accurately, but we don’t know what kind of dance to do on the computer to make this number come out, without putting it in secretly!—R. P. Feynman, QED: The Strange Theory of Light and Matter

## References

1. ^ "Sloane's A042978 : Stern primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
2. ^ "Sloane's A002144 : Pythagorean primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
3. ^ "Sloane's A016038 : Strictly non-palindromic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
4. ^ "Sloane's A072857 : Primeval numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
5. ^ Rutland, G., Awesome Sovereign (Bloomington: AuthorHouse, 2016), p. 33.
6. ^ Richard Feynman website, "The Mysterious 137".
7. ^ Eddington, A.S., The Constants of Nature in "The World of Mathematics", Vol. 2 (1956) Ed. Newman, J.R., Simon and Schuster, pp. 1074-1093.
8. ^ Helge Kragh, "Magic Number: A Partial History of the Fine-Structure Constant", Archive for History of Exact Sciences 57:5:395 (July, 2003) doi:10.1007/s00407-002-0065-7
9. ^ Lederman, Leon, The God Particle: If the Universe is the Answer, What is the Question? (1993), Houghton Mifflin Harcourt, pp. 28-29.
10. ^ Gratzer W, The Pauli Principle in "Eurekas and Euphorias", (2002) Oxford University Press, pp. 49-52.
11. ^ The mystery of 137, www.integralworld.net
12. ^ Planck Collaboration (2015). "Planck 2015 results. XIII. Cosmological parameters (See PDF, page 32, Table 4, Age/Gyr, last column)". Astronomy & Astrophysics. 594: A13. arXiv:1502.01589. Bibcode:2016A&A...594A..13P. doi:10.1051/0004-6361/201525830.
13. ^ Lawrence, C. R. (18 March 2015). "Planck 2015 Results" (PDF). Retrieved 27 April 2017.
14. ^ Ginsburgh, Rabbi Yitzchak (2006). What You Need to Know About Kabbalah (first ed.). Jerusalem: Gal Einai Publications. p. 3. ISBN 965-7146-119.
15. ^ Ginsburgh, Rabbi Yitzchak (2006). What You Need to Know About Kabbalah (first ed.). Jerusalem: Gal Einai Publications. p. 3. ISBN 965-7146-119.
16. ^ Genesis 25:17
17. ^ Exodus 6:16
18. ^ Exodus 6:20