Omicron (the symbol) in Mathematics - Numberphile

Professor Tony Padilla discusses the Greek letter Omicron.
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[thargy]

This was fascinating! I’ve been using big-O notation for decades, and no one ever called it Omicron. The other two notations are much rarer in computer science, we tend to focus most on upper bounds.

[TheHippieRat]

“Hey did you hear about the new variant?” “The nu variant?” “No it’s called omicron.” “The nu variant is called omicron?” “No the new variant is called omicron, there is no nu variant.” “There is no new variant?” “No there is one it’s called omicron.” “Why’d the skip the nu variant?” “This is the new variant, they didn’t skip it”

[dougpowers]

Wow. If omicron really is the symbol for upper-bound growth, then I cannot stand the term Big-O notation. Omicron _literally_ means "little o" (o mikron). As opposed to omega, "big o", (o mega).

[helloitsme]

It's probably not used as much because it resembles either a zero or an O very much

[WestExplainsBest]

Thank you for clearing up that Omicron is, in fact, NOT a transformer.

[jagatiello]

I learned the Greek alphabet as a kid by playing a shoot'em up arcade called Star Force. I was amazed at the time by the fact that after the omega level one ended up in an endless level properly denoted with the infinity symbol.

[LuxiBelle]

Omicron actually means "Small O", Omega means "Large O".
But Omicron notation is called Big O notation, but there is also Little O notation and Little omega notation.
So there is Little small O, Big small O, Little large O, Big Large O. Each of these describe a different thing.

[jimskea]

omicron and iota are the standard symbols for the basis vectors in the 2-dimensional complex space SL(2, C). Elements of this spare are usually called spinors and are important in particle theory and gravitation.

[lubbertdas]

I took Greek at the University and one of the first things we learnt was that there were long vowels and short vowels, omicron is typically short and omega is long if I remember correctly (there are many exceptions to every rule like with any other language). It only took me four years to suddenly realize that it's o-micron and o-mega, literally little o and big o, so there's a little bit of contradiction in that "big omicron" expression.
The macron (that line over the letters) is (contemporarily) used in Latin to mark the long vowels, I don't know or not remember if it's also used in Greek by other students, it would be interesting to know how probable or improbable is to accidentally write an actual word when trying to write a number using these alphabetical methods...

[r..k..]

The story is different if you look in Wikipedia at Omicron:

Quote : “The big-O symbol introduced by Paul Bachmann in 1894 and popularized by Edmund Landau in 1909, originally standing for "order of" ("Ordnung") and being thus a Latin letter, was apparently viewed by Donald Knuth in 1976 as a capital Omicron, probably in reference to his definition of the symbol (capital) Omega. Neither Bachmann nor Landau ever call it "Omicron", and the word "Omicron" appears just once in Knuth’s paper, in the title.”

[dgarrard]

ζ (zeta) is the sixth letter of the Greek alphabet, but it isn't the number 6; the archaic letter ϝ (digamma/wau) was originally used for that. When Greek no longer needed that letter, it was replaced by ϛ (stigma), which is shorthand for στ (sigma-tau). In modern times, I think στ is used.

[PaulPaulPaulson]

3:12 "80 is Pi" - Numberphile
Can I cite this in my next paper? 😉

At least the word Pi is said exactly at 3:14

[thelego]

This was insane timing, I just learned about Big O notation in my CS class, and then I happened upon this video a week later by pure chance. Really cool correlation to mathematics

[ffggddss]

Among astronomers, mentioning that Greek letter will likely bring up Omicron Ceti (aka, Mira), a pulsating variable star that became the prototype for such stars.
"Ceti" is the genitive form of the name of the constellation it's in – Cetus, the whale.
The Greek letter is from Johannes Bayer's system of naming stars according to their brightness rank within their respective constellations.
He did this by assigning alpha to the brightest, beta to the 2nd brightest, etc.

Fred

PS: Bayer didn't always adhere to that scheme – the 7 stars of the Big Dipper (which is a part of the constellation Ursa Major = the Big Bear), are simply lettered in order from alpha to eta, despite the 4th one being discernibly dimmer than the other 6.

[Domihork]

Wait till you realize that the reason why Greek has two letters "O" is because one is short (Omicron - O micro) and one is long (Omega - O mega)...

Honestly, it's so obvious but as someone who doesn't speak the language and for notation has mostly only used alpha to epsilon and omega, it just never crossed my mind.

[xiinija]

The letters seem very logical to me;
- omicron = "little o" which stands for the functions somehow "smaller" than what's noted;
- omega = "big o" which stands for the functions somehow "larger" than what's noted;
- theta is a line in a circle, basically "something bound around"

[samburgess]

Glad you accurately explained why they skipped.

[ErwinSchrodinger]

Well, when I took differential equations was the first time I saw the Omicron symbol, and I buckled at my knees. I thought it was some operator representing a level of mathematics my feeble mind could not comprehend. I already affixed in my mind it represented the gateway to the limitations of my thinking. I was beaten and defeated, I raised my hand stuttering to ask the professor what the symbol meant. His reply, "It's just a variable like x, y, or z." My heart bursted in glee. It happened again, in quantum mechanics, where it represented the Eigenvalue(s) for the steady state Schrodinger equation.

Occasionally, the Omicron symbol shows in my dreams where it still represents an impossible mathematical principle, while everyone around points and laughs at me for not understanding the concept.

Omicron: the hidden horror of the Greek symbols in mathematics. Don't get me started with the wedge products (the upside down V) or tensor product or the integral... oh the integral symbol.

[macronencer]

I've worked in software for 34 years, and I never knew that O was an omicron – neither did I know about the omega and theta notations. This is enlightening!

[JustLilGecko]

I can't believe big-O notation has been Omicron all this time. Never heard it referred to that way and I'm a comp sci major - little bit of a mindblowing moment here!