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.
Same here but the big-O notation for software seems a bit different to me. When we say an algorithm has an O(n²) time complexity, we don't mean it could be anything under that, we actually mean that it scales roughly with n². It's closer to the theta definition in the video.
Big-O can be used to determine the estimated duration time for an algorithm/program to run. I have a program on my TI-84 CE calculator that calculates the digits of pi and stores it to a list. The calculation time grows nonlinear. 10 digits of pi: 7 sec 50 digits: 1 min 45 sec 100 digits: 6 min 50 sec 500 digits: 3 hr 10 min 1000 digits: 13 hr 27 min 1440 digits: 28 hr 51 min (calculator runs out of memory after this number)
I’ve always understood Big-O as “worst case”, many algorithms only hit worst case in certain situations. It is true that we should probably use Theta more than we do though, to indicate a more consistent measure - but you almost never see it mentioned.
“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”
- But why did they skip Xi? - Because it sounds like the name of the Chinese leader. - Who? - No, not Hu, the new guy. - But I thought they didn't want to call it new...
Ahh I wonder how many kids will get to stumble across Abbott and Costello. Like, even as a kid watching them in the 1990s, it was already super old and I only saw their films because my parents controlled the TV and there was a limited number of things to do otherwise. It was like the one old thing I watched with them that I actually enjoyed. I suppose its possible that their sketches could go viral on Tik Tok or something.
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).
I think that Knuth and others use Greek terminology in this annoying way, but I do not think that it is so universal that yet others do not simply mean the Latin letter. That having been said, keeping it all Greek is kinda pleasing. The English adjective is just a shorter way of saying "uppercase" (big) or "lowercase" (small). So, there is a twofold distinction. The Greek adjectives, which have been incorporated into the names themselves, indicate the symbol and its sound; the English adjectices specify casing and thus what kind of bound is being used.
Does it make you feel better if rather than thinking of it as an upper bound, you think of it as a set which are lower than it? Ie O(n^2) is the set of functions that are lower bounds of (a multiple of) n^2?
Literally this. Have you ever seen a capital alpha in physics and maths? No? And what about a capital beta? Neither? Well, that's because they look like this: A & B. Maths is information-*dense*, and its many hives of definitions need clear, known, easily-identifiable and easily-implementable symbols. Greek alphabet is a no-brainer, since it's the second most known alphabet in America&Europe. But of course only the letters that don't straightup look like a latin letter are "interesting" (better said, useful) for a mathematician.
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.
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.
Glad to see another Star Force fan. I wonder who many people learned the Greek alphabet that way? I actually played Star Force at a Labor Day party just this year.
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.
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.”
@@llllllllllllllllllllllllIIIIl1 Big O notation is based on the latin letter and not the Omicron. It is a latin Big O derived from the German term for "Order of" called "Ordnung". The German work starts with a big O latin letter and therefore Bachmann/Landau uses the Latin O. It's called Landau Notation - and not Omicron. Knuth was re-defining it - decades later - as Omicron - and all in all the greek letter as symbol for it is not academic consensus.
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...
@@adarshmohapatra5058 I'm reasonably certain these exact vowel sounds don't exist in English. English does vowels very weirdly compared to lots of other languages. If you know the IPA, omicron is /o/ and omega is /ɔː/. If you look these up on wikipedia, it has recordings (the pages are called "mid back rounded vowel" and "open-mid back rounded vowel" respectively). Also, this is Ancient Greek. Modern Greek has a different phonology but I'm fairly certain it still has at least some distinction between ο and ω (that's lowercase omega, btw). And I know for sure there are no exceptions on ο being short and ω being long in Ancient Greek. Unless you count stuff like ου, that is.
@@fghsgh Completely bilingual English/Modern Greek, schooled in both languages. There's no difference in sound between omicron (ο) and omega (ω). They are used however in different contexts within a word. First person present verbs that end in an -o sound (θέλω [I want], ζιτάω [I ask]) all end in omega. Phonetically however, there's no difference. Please keep in mind that this is with respect to Modern Greek, and this may not hold for some of the older Hellenic languages.
I often see the macron used when transliterating japanese sounds,for example the word for "today" is "今日" which is pronounced as kyo but with a long o,so you'd see it written as kyō in romaji (japanese words transliterated in latin alphabet)
@@gabor6259 They didn't do it just to be nice, but that's also not the reason. It's more because rule one international diplomacy is don't insult China.
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
Not just non-Greeks. Even ancient Greeks didn't pronounce Greek letters the way you contemporary Greeks do! You call π "pea" πῖ, [pi], but your distant ancestors called it "pay" πεῖ, [peː]. I'm not Greek, but as an amateur linguist and phonetician, I study sound shifts-across time as well as across languages. Things like why [peː] in ancient Greek ended up becoming [pi] in modern Greek and "pie" /pʰaɪ/ in English.
I usually pronounce Greek letters in Greek fashion, but make an exception for π, which would be confused with p when speaking English. In Spanish, θ and ζ could be confused. Leftpondian Spanish substitutes /s/ for /θ/, there is no phonemic distinction between [z] and [s], and is pronounced /θ/ in Spain (except the south) and /s/ over here.
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"
"Little o" is actually commonly used to mean "Big O" excepting functions in "Theta". So Θ(f(n)) = O(f(n)) \ o(f(n)) There are also big and small omega notations with a similar distinction. Of course the whole point of Knuth's paper mentioned in the video was that the mathematical community has always been notoriously inconsistent with this notation, so there are a bunch of competing definitions floating around
"Little" and "big o" notation either are derived from or still are (depending on whom you ask) the Greek capital and minuscule omicrons, not the Latin O. But in most fonts, the two characters are either identical or virtually identical, so it makes no difference. Look: with Greek letters: Ο( *·* ) and ο( *·* ), or with Latin letters: O( *·* ) and o( *·* ). The big and little omegas are clearly distinct, written Ω( *·* ) and ω( *·* ), respectively. And big theta Ө( *·* ) means both big Ο and big Ω. The logic is that the "little" letters represent strictly weak bounds, while the "big" letters represent bounds that may be weak or strong, and the big theta represents the exact growth rate. So ω(f(n)) < Ө(f(n)) < o(f(n)), while Ω(f(n)) ≤ Ө(f(n)) ≤ O(f(n)) (asymptotically, up to a constant factor).
Actually, "little o" and "big O" both are Omicron symbols -> for upper bounds.... For "little o" -> For *every* choice of a constant k > 0, you can find a constant a such that the inequality 0 a For "big O" -> For *at least one* choice of a constant k > 0, you can find a constant a such that the inequality 0
@@sangramkapre That's a different thing though. "Little O" and "Big O" are the literal translation of the Greek words "O-micron" and "O-mega" (micron=little, mega=big). So Omicron means "little O" and Omega means "big O". Which makes their use as an upper/lower bound quite logical. A capital Theta Θ is literally a line that's bounded above and below by a curve.
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.
Maths has an innate beauty on its own. And I say that as a career physicist, not a mathematician. The better analogy is science is literature, and maths is grammar/linguistics. You need language for literature, but language has its own worth even without literature.
@@QuantumHistorian ew, that romanticizes science so much. Science is experimental. Most beauty you attain is trickled down from the abstract world of math.
If you like thinking about limits: Omicron(f(n)) is all the functions g(n) where lim_(n -> infinity) (g(n)/f(n)) < infinity Omega(f(n)) is all the functions g(n) where 0 < lim (g(n)/f(n)) Theta(f(n)) is all the functions g(n) where 0 < lim (g(n)/f(n)) < infinity
Well that makes sense. In my programming classes, big O notation is absolutely used as the biggest possible course of action and reducing the n term makes the code more efficient. Idk, I think we've been using it right in my field at least
I definitely hear things like "bubble sort is bad, it's O(n^2); quicksort is good, it's O(nlogn)", and everyone knows what that means, but TECHNICALLY it should be "bubble sort is Omega(n^2) and quicksort is O(n^2), but the average case is nlogn". Usually it's totally clear what people mean, but people definitely play it fast and loose with the term "big-O"
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.
Languages are so strange. I'm so used to just repeating the letter when it's pronounced twice. Well, english does not follow this rule (to - too, yes, but _not_ later - latter).
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!
When I heard the word Omicron it had to look it up. It sounded like a foreign word, I never thought it would be of greek origin but just knowing it's greek origin I figured mathematics would be involved
Given the fact that it is indistinguishable from Latin O, which itself is difficult to distinguish from 0, it is uncommon for it to be used in Mathematics. I do see O as the name for a point such as the origin, but it is a general recommendation to avoid this letter for this reason.
Working with algorithms, I've encountered another version of that. One "big Oh" symbol indicates the execution time or memory requirements with respect to the value of n, which is the normal use. But another "fancy" O is used to indicate the resources needed with respect to the _length_ of the input; that is, the number of digits in n rather than the value of n itself.
@@SimonBuchanNz Or O(n) and O(log n), depending on what you think is natural. If you're talking about sorting a list, n is obviously going to be the length of the list, not the list itself. If you're searching a string, n is the length of the string. If you're factoring a number, is n the number, or the length of the number? It gets more vague because factoring cares about all the numbers that are less than the number, not just about the bits that are in the number, and sometimes you need to think about some operations that depend on both in the same paper.
Omicron seems to be one of the few Greek letters where no one seems to make a special version to distinguish it from its Latin counterpart, not even in lowercase. Every other lowercase letter that looks similar to a Latin letter gets some modification.
Capital letters that are quite interchangeable, in both Greek and Latin alphabet are: A, B, E, H, I, K, M, N, O, P, T, X, Y, Z. Lowercase, depending on handwriting: α/a, (sometimes I use the α for either of them, or draw something like a small fish instead. The latter is faster.) ι/i (sometimes the ι has an accent, like so: ί), o/ο (as you mentioned), p/ρ (totally different letters though), u/υ (if there's a following letter, υ might seem like u if you don't pick up the pen at all), x/χ (can use x for the Greek one too), y/ψ (ψ can be written almost like y. Again, though, totally different letters). Source: I speak both languages, mother tongue is Greek, and the way I sometimes write the aforementioned letters is indistinguishable, while preserving text clarity.
Well, after all the latin alphabet comes from the greek one, so it makes sense that some symbols are literally the same. I don't see a reason to try to distinguish the symbol for omicron from the symbol for latin o.
@@jackozeehakkjuz no, but in physics you are sometimes expected to know the diference between rho and p. If your teacher has sufficiently bad handwriting they are almost indistinguishable.
My 2c's worth... I've never thought of that as a 'omicron' anything. It has always been (at least in my head) 'Order of'. So if something is O(n^2) then the complexity increases with the square of n, and O(n*log(n)), is proportional to the log of n. The symbol is kind of irrelevant, but happens to imply the word 'Order'. Hey ho, thank we're all different!
@@SimonBuchanNz Yes. Whenever I see a talk by a Greek computer scientist, it takes me a while to get used to the way they mispronounce the names of all the Greek letters.
0:40 "That's the theory" Is it just a theory? The other day I heard an explanation that stated the WHO has banned the use of 'Nu' and 'Xi' as variant designations for the stated reasons *years* ago.
Yes iirc they came out and explicitly said “nu is like new and xi is a common last name” but I doubt it was years ago, given that the Greek naming system was only brought in in may of this year
@numberphile, for info, in contrary to popular English speakers belief, the corect pronunciation of Greek letters μ and ν is closer to "mee" and "nee" not miu amd niu... (in the same 'ee' sound as in "lee") and if written they should be written mi, ni like pi which also has a pee pronunciation but whatever...
Another use of omicron is in physics, in relativity when you're describing different observers you use the "O" symbol for each observer. Again I thought this was an O, but I think it's actually meant to be an omicron.
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!
😁 Well, they've simply replaced the English (Latin) letters in 'Numberphile' with the nearest Greek equivalents. If you want to approximate the English _pronunciation_ of 'Numberphile' using Greek letters, then this is closer: ναμβαφαιλ. (In British English, the 'r' isn't pronounced, but feel free to add a 'ρ' if you like.)
1:36 since he went down that path (even though he actually wrote down the number 667 instead of 666), "ΟΜΙΚΡΟΝ" => 70+40+10+20+100+70+50 = 360. The degrees of a circle, "ο"
Nevermind mind skipping Nu and Xi. Are you saying there was Mu variant? I know this is a math channel but did I miss something? Last I i heard of was Delta. Why say skipped 2? What happened to Epsilon, Zeta, Eta, Theta, Iota, Kappa, and Lambda?
Relax, no need to panic. Yes, all those variants exist, including Mu. They are all VBMs-Variants Being Monitored. But they are not VOCs-Variants of Concern. The only VOC are the Delta and Omicron variants. And that's why-outside of specialists-most people have heard of only those two.
If Ptolemy wrote his omicron like you did as ō, that may suggest that it was an abbreviation. Writing a line above was how some Greek scribes would abbreviate well-known words, particularly in the New Testament.
Ζ is 7. The Greek numeral for 6 is a letter called wau or digamma; the capital looks like F. There are three letters (wau, qoppa, sampi) which are obsolete for writing words but still used for writing numbers. Wau was used for /w/, which dropped out early from Greek (e.g. wanax -> anax άναξ, a kind of king). Sampi was used for a sound that evolved into /s/ in some dialects and /t/ in others. And qoppa was used for /k/ before /u/ or /o/, then discarded as superfluous. All three, when used as numerals, evolved into shapes that look different than when used as letters.
@@opterios Numberphile is a hybrid word, like television. The number part of it has Latin roots. It would probably be something like Numberamor, if it were a Latin-only word.
Greeks still use letters to represent numbers. Phillip the Second, is written Φίλιππος Β, but called "Φίλιππος Δεύτερος". 4th Grade is written Τάξη Δ but called "Τέταρτη Τάξη". In my modern Greek language textbook the lists are numbered α, β, γ, δ, ε, στ, ζ, η, θ, ι, ια, ιβ, ιγ, ιδ, ιε, ιστ etc. So "ι" becomes 10 and works as numbers would from there.
3:35 "What if you didn't have any minutes? What if you have zero minutes?" Sometimes I use Stellarium to calculate lunar and planetary conjunctions and occassionally I land on something weird like 1 degree, 0 arc minutes, and 5 arc seconds.
The big O notation is only related to the omicron notation, it's not the same. The big O - notation was established by a German mathematicians in 1894 and the letter O stands for the German word "Ordnung" ("order" in English, which works equally fine). But the difference between O-notation and omicron-notation is actually only exactly this, notation: It's written slightly diffently but in the end means the same.
4:33, the (ancient) greek word for 'nothing' is οὐδέν (ouden); but interestingly, the greek word for zero is μηδέν (meden). In its original use, it did not of course refer to the number (or the numeral) zero, which were unknown to ancient greeks, but simply meant "nothing" in another grammatical context, e.g. in the adage μηδέν ἄγαν (nothing in excess). Both words stem from the negative prefix for "no" (οὐ) and "don't" (μή), the difference being the grammatical case (οὐ is nominative, μή is imperative). For example, in the Odyssey, Odysseus tells the cyclops Polyphemus his name is "Οὖτις" (no-one), making a play with words, as "μῆτις" (metis) was one of his epithets, meaning cunning, wisdom.
can you write a short greek sentence using only letters used in mathematics and have it make sense while the number assosiated with the letters arranged in a formula also make sense? just a stoned thought.... anythere there?
Awesome, you just rediscovered the secret of isopsephy, numerology, mysticism (such as 'the number of the Beast' and Kabbalah), coded messages, and-more practically-mnemonic aids.
Just to clarify, Omicron doesn't have a line above it as a letter on its own - 2:06 - I noticed at 3:10 they clarify the addition of the line for the numbering (which is new info to me). Cool. - P.S - Happy to be corrected. It's just that I've started learning Greek so was thinking critically of the symbol.
My pedantic self cannot resist correcting the pronunciation of Knuth: it's kuh-NOOTH, with a hard 'K'. I once took a discrete math class from him. The man is extremely droll and *extremely* intelligent!
Can you do video about all the common uses of the greek/Latin alphabet? I have not seen a comprehensive video or article on all the non-standard symbols on the internet.
In fact, the Landau symbols are all Greek letters. Apart from upper case Theta, it's omicron (lower case and upper case) and omega (both cases). It makes much more sense than O, because, well, _micro_ and _mega_ aren't in the names by accident. Therefore, it makes no sense to use script O for the Landau symbol.
Need to clarify that the ancient Greek word for nothing is: uden with the u spelled as in put. Two syllables: [1] u [2] den. Accent on e . Great video!
What is the possibility that the Indians (typically credited with inventing a symbol for 0) had copies of Ptolemy's work and got the symbol for 0 from there? I know that earlier Greek work spread east (such as trigonometry), but I don't know of any other examples from this deep in the Roman era.
Fun fact. And it's something I didn't realize until I looked it up in an online dictionary recently, at which point I did a mental head-slap. "Omicron" actually means, "little o;" while "omega" means, "big o" - notice the "micron" and "mega" in those names. Which is kind of funny, since it makes "big omicron" and "little omega" oxymoronic. And "little omicron" and "big omega" redundant. ;-) Fred
The little o actually says that the quotient must go to zero. For instance, the function (x/2)^2 is always in the region between the x-axis and the function x^2 (except at zero, when all coincide), and yet (x/2)^2 / x^2 = 1/4 won't go to zero as x goes to zero. Fortunately, Donald Knuth is too old to punch you for it. (Apart from that, he doesn't always have an easy time accepting suggestions himself.) The o notation is originally due to Edmund Landau, a number theorist.
As someone that studied Comp Sci, I'm obviously familiar with big-O notation, but I had no idea that it was actually an omicron, I've always heard it referred to "big-O" or "of order".
Problem-reaction-solution. Create a solution (That which the ruler desires). Contrive the problem (That which causes suffering and death in the lowest members in the dominance hierarchy) that will cause the reaction where the willfully blind masses will demand the solution (The great reset).
In my experience the O(n) notation has never been portrayed graphically, it's just the worst case scaling. So with a sequential search, an algorithm where you check each element in a list to find the one you want, we'd say that that algorithm is O(n). This is because the worst case scenario, that the one you want is the last element, increasing in time at the same rate as the input. If you double the size of the list then it takes twice as much time to find that last element. Conversely we described big omega as the "best case scenario". It's rarely useful since that pretty much always 1. Big Theta is the average case. It's often the same as Big O but not always. That's how I learned it anyways.
That's not quite an accurate use of the terms though. If you say "in the best case, this algorithm is Ω(n)" then what you're saying is "this algorithm is never faster than linear". But you're *not* saying that the best case *is* linear; you would still need to use O or theta to express that.
@@TylerMcHenry Typically we would say that Omega(n)=1. It almost always does in that framework. It's rarely used as it's generally useless. O(n) is the standard for quickly summarizing the efficiency of an algorithm.
I'm a physicist and the only context I can recall ever having seen the letter Omicron is in the name of the planet "Omicron Persei 8" in Futurama. [Yes, there's complexity and error bounds, but they were only ever referred to as little and big O ("Oh") and spoken as "of the order of".]
4:09 I feel like there's an obvious followup question that isn't asked here: Since Ptolemy couldn't use omicron for the degrees, how would he have written "0° 41 min 3 sec"? Wouldn't the answer to that tell us something useful about how he used the symbol?
Objectivity video about The Almagest: ruclips.net/video/QW29uaD78OU/видео.html
I have missed Tony videos! More Tony!
Bring back Grimey
The most important : see how the shape of O like Omicron represents physically a picture of the CORONA virus...
OMICRON DELTA
An anagram of
MEDIA CONTROL
Everybody gangsta till pi variant comes (it's after omicron in the alphabet)
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.
Omega is used sometimes putting tight bounds on recursive algorithms.
Same here but the big-O notation for software seems a bit different to me. When we say an algorithm has an O(n²) time complexity, we don't mean it could be anything under that, we actually mean that it scales roughly with n². It's closer to the theta definition in the video.
Big-O can be used to determine the estimated duration time for an algorithm/program to run. I have a program on my TI-84 CE calculator that calculates the digits of pi and stores it to a list. The calculation time grows nonlinear.
10 digits of pi: 7 sec
50 digits: 1 min 45 sec
100 digits: 6 min 50 sec
500 digits: 3 hr 10 min
1000 digits: 13 hr 27 min
1440 digits: 28 hr 51 min (calculator runs out of memory after this number)
Sure but there are many deterministic algorithms like quicksort in O(n.log(n)) where it's actually fairly precise.
I’ve always understood Big-O as “worst case”, many algorithms only hit worst case in certain situations. It is true that we should probably use Theta more than we do though, to indicate a more consistent measure - but you almost never see it mentioned.
“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”
I see you’re directly quoting from Abbott and Costello’s, “Nu’s on first?”
"but, *who* named it like that?" - "yes, exactly, WHO gave it that name."
Third base!
- But why did they skip Xi?
- Because it sounds like the name of the Chinese leader.
- Who?
- No, not Hu, the new guy.
- But I thought they didn't want to call it new...
Ahh I wonder how many kids will get to stumble across Abbott and Costello. Like, even as a kid watching them in the 1990s, it was already super old and I only saw their films because my parents controlled the TV and there was a limited number of things to do otherwise. It was like the one old thing I watched with them that I actually enjoyed.
I suppose its possible that their sketches could go viral on Tik Tok or something.
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).
WOW this really upsets me now. Going to try and forget I ever learned this.
I think that Knuth and others use Greek terminology in this annoying way, but I do not think that it is so universal that yet others do not simply mean the Latin letter.
That having been said, keeping it all Greek is kinda pleasing. The English adjective is just a shorter way of saying "uppercase" (big) or "lowercase" (small). So, there is a twofold distinction. The Greek adjectives, which have been incorporated into the names themselves, indicate the symbol and its sound; the English adjectices specify casing and thus what kind of bound is being used.
Big little o notation would’ve been even beter
Just call it Landau notation
Does it make you feel better if rather than thinking of it as an upper bound, you think of it as a set which are lower than it? Ie O(n^2) is the set of functions that are lower bounds of (a multiple of) n^2?
Thank you for clearing up that Omicron is, in fact, NOT a transformer.
No, those are omnicrons.
And that it's a real thing. Not just another fake China virus control tactic.
It's actually a planet where Lrrr rules in his attempt to destroy the universe.
Did they force antivirus installs on Cybertron?? If so, is that what destroyed the Planet?? Hmmmmm...
@@jamesmonroe3043 dude cybertron got destroyed by the transformers war, not an antivirus
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
Wow, that timestamp! When citing pi being 80, don’t forget to put the bar above it though ;-)
It's probably not used as much because it resembles either a zero or an O very much
Well to be fair we did adopt it from there
I was gonna say the same thing. Lol...
Well, it is an O, not zero.
Exactly. That’s why I avoid it.
Literally this. Have you ever seen a capital alpha in physics and maths? No? And what about a capital beta? Neither? Well, that's because they look like this: A & B.
Maths is information-*dense*, and its many hives of definitions need clear, known, easily-identifiable and easily-implementable symbols. Greek alphabet is a no-brainer, since it's the second most known alphabet in America&Europe. But of course only the letters that don't straightup look like a latin letter are "interesting" (better said, useful) for a mathematician.
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.
Yeah I've seen this notation in Wald's general relativity book.
Elements are not spinors, but matrices that act on those spinors (to rotate them) no?
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.
Glad to see another Star Force fan. I wonder who many people learned the Greek alphabet that way? I actually played Star Force at a Labor Day party just this year.
I played that same game on NES, learned some of the letters there.
@@mittarimato8994 I've got some sad news for you then - the creator of the NES just died. :/
man that game is hard. I can only memorize the greek alphabet up to zeta because of it
@@wiseSYW αβγδεζ
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.
Exactly
Yes, these older Phoenician letters also appear as 90 and 900 (koppa and sampi, respectively) in the Ionian number system.
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.”
How is this a different story ?
@@llllllllllllllllllllllllIIIIl1 Big O notation is based on the latin letter and not the Omicron. It is a latin Big O derived from the German term for "Order of" called "Ordnung". The German work starts with a big O latin letter and therefore Bachmann/Landau uses the Latin O. It's called Landau Notation - and not Omicron. Knuth was re-defining it - decades later - as Omicron - and all in all the greek letter as symbol for it is not academic consensus.
Despite of it, I like the channel and thinking about Landau notation is a great topic.
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...
Wait so how do you actually pronouce these letters? How do you pronounce Omicron and Omega if one is little o and one is big o?
Is one pronounced like "oh" and the other like "oooo" ?
@@adarshmohapatra5058 I'm reasonably certain these exact vowel sounds don't exist in English. English does vowels very weirdly compared to lots of other languages.
If you know the IPA, omicron is /o/ and omega is /ɔː/. If you look these up on wikipedia, it has recordings (the pages are called "mid back rounded vowel" and "open-mid back rounded vowel" respectively).
Also, this is Ancient Greek. Modern Greek has a different phonology but I'm fairly certain it still has at least some distinction between ο and ω (that's lowercase omega, btw).
And I know for sure there are no exceptions on ο being short and ω being long in Ancient Greek. Unless you count stuff like ου, that is.
@@fghsgh Completely bilingual English/Modern Greek, schooled in both languages. There's no difference in sound between omicron (ο) and omega (ω). They are used however in different contexts within a word. First person present verbs that end in an -o sound (θέλω [I want], ζιτάω [I ask]) all end in omega. Phonetically however, there's no difference. Please keep in mind that this is with respect to Modern Greek, and this may not hold for some of the older Hellenic languages.
I often see the macron used when transliterating japanese sounds,for example the word for "today" is "今日" which is pronounced as kyo but with a long o,so you'd see it written as kyō in romaji (japanese words transliterated in latin alphabet)
So it was the Greeks that started covid ?
Glad you accurately explained why they skipped.
It would have been accurate, if they had mentioned that the WHO is controlled by China. They didn't skip ksi out of sheer goodwill.
@@gabor6259 They didn't do it just to be nice, but that's also not the reason. It's more because rule one international diplomacy is don't insult China.
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
Being a Greek, I always find funny how non-Greeks pronounce Greek letters! :D
A great and interesting video, though!
Aw-mi-kron
Being English I always find it embarrassing how little effort we make to learn pronunciations like these.
@@ChrisLee-yr7tz potayto potahto
Not just non-Greeks. Even ancient Greeks didn't pronounce Greek letters the way you contemporary Greeks do!
You call π "pea" πῖ, [pi], but your distant ancestors called it "pay" πεῖ, [peː].
I'm not Greek, but as an amateur linguist and phonetician, I study sound shifts-across time as well as across languages. Things like why [peː] in ancient Greek ended up becoming [pi] in modern Greek and "pie" /pʰaɪ/ in English.
I usually pronounce Greek letters in Greek fashion, but make an exception for π, which would be confused with p when speaking English. In Spanish, θ and ζ could be confused. Leftpondian Spanish substitutes /s/ for /θ/, there is no phonemic distinction between [z] and [s], and is pronounced /θ/ in Spain (except the south) and /s/ over here.
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"
"Little o" is actually commonly used to mean "Big O" excepting functions in "Theta". So Θ(f(n)) = O(f(n)) \ o(f(n))
There are also big and small omega notations with a similar distinction.
Of course the whole point of Knuth's paper mentioned in the video was that the mathematical community has always been notoriously inconsistent with this notation, so there are a bunch of competing definitions floating around
"Little" and "big o" notation either are derived from or still are (depending on whom you ask) the Greek capital and minuscule omicrons, not the Latin O. But in most fonts, the two characters are either identical or virtually identical, so it makes no difference. Look: with Greek letters: Ο( *·* ) and ο( *·* ), or with Latin letters: O( *·* ) and o( *·* ). The big and little omegas are clearly distinct, written Ω( *·* ) and ω( *·* ), respectively. And big theta Ө( *·* ) means both big Ο and big Ω.
The logic is that the "little" letters represent strictly weak bounds, while the "big" letters represent bounds that may be weak or strong, and the big theta represents the exact growth rate. So ω(f(n)) < Ө(f(n)) < o(f(n)), while Ω(f(n)) ≤ Ө(f(n)) ≤ O(f(n)) (asymptotically, up to a constant factor).
Actually, "little o" and "big O" both are Omicron symbols -> for upper bounds....
For "little o" -> For *every* choice of a constant k > 0, you can find a constant a such that the inequality 0 a
For "big O" -> For *at least one* choice of a constant k > 0, you can find a constant a such that the inequality 0
@@EebstertheGreat Exactly this. I was just lazy with the Unicode on my phone keyboard
@@sangramkapre That's a different thing though. "Little O" and "Big O" are the literal translation of the Greek words "O-micron" and "O-mega" (micron=little, mega=big). So Omicron means "little O" and Omega means "big O". Which makes their use as an upper/lower bound quite logical. A capital Theta Θ is literally a line that's bounded above and below by a curve.
Love your vids! I am following for a few years and each time I get thrilled again from completely different topics.
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.
_"Without perturbation theory, physicists are useless."_ Never have I been so insulted by something so true.
Nonperturbative qcd has left the chat
@@obaidbalkhair7647 not true. I need math to know how much 25 watermelons will cost
Maths has an innate beauty on its own. And I say that as a career physicist, not a mathematician. The better analogy is science is literature, and maths is grammar/linguistics. You need language for literature, but language has its own worth even without literature.
@@QuantumHistorian ew, that romanticizes science so much. Science is experimental. Most beauty you attain is trickled down from the abstract world of math.
??
If you like thinking about limits:
Omicron(f(n)) is all the functions g(n) where lim_(n -> infinity) (g(n)/f(n)) < infinity
Omega(f(n)) is all the functions g(n) where 0 < lim (g(n)/f(n))
Theta(f(n)) is all the functions g(n) where 0 < lim (g(n)/f(n)) < infinity
Well that makes sense. In my programming classes, big O notation is absolutely used as the biggest possible course of action and reducing the n term makes the code more efficient. Idk, I think we've been using it right in my field at least
I definitely hear things like "bubble sort is bad, it's O(n^2); quicksort is good, it's O(nlogn)", and everyone knows what that means, but TECHNICALLY it should be "bubble sort is Omega(n^2) and quicksort is O(n^2), but the average case is nlogn". Usually it's totally clear what people mean, but people definitely play it fast and loose with the term "big-O"
Look up P vs NP if you don't know it already. Super interesting stuff for computer scientists
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.
🤯
This is positively mindblowing. Its the sort of thing you can't unsee!
I learned the greek alphabet like 8 years ago and you still just blew my mind
Languages are so strange. I'm so used to just repeating the letter when it's pronounced twice. Well, english does not follow this rule (to - too, yes, but _not_ later - latter).
but we use o micro for big O notation aparently
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!
When I heard the word Omicron it had to look it up. It sounded like a foreign word, I never thought it would be of greek origin but just knowing it's greek origin I figured mathematics would be involved
Given the fact that it is indistinguishable from Latin O, which itself is difficult to distinguish from 0, it is uncommon for it to be used in Mathematics. I do see O as the name for a point such as the origin, but it is a general recommendation to avoid this letter for this reason.
Working with algorithms, I've encountered another version of that. One "big Oh" symbol indicates the execution time or memory requirements with respect to the value of n, which is the normal use. But another "fancy" O is used to indicate the resources needed with respect to the _length_ of the input; that is, the number of digits in n rather than the value of n itself.
That sounds like the difference between O(n) and O(k^n).
@@SimonBuchanNz Or O(n) and O(log n), depending on what you think is natural. If you're talking about sorting a list, n is obviously going to be the length of the list, not the list itself. If you're searching a string, n is the length of the string. If you're factoring a number, is n the number, or the length of the number? It gets more vague because factoring cares about all the numbers that are less than the number, not just about the bits that are in the number, and sometimes you need to think about some operations that depend on both in the same paper.
@@iabervon yeah, in fact as worded just "n" is the big one, so log n should be the other. I just have passwords on the brain, I guess.
Omicron seems to be one of the few Greek letters where no one seems to make a special version to distinguish it from its Latin counterpart, not even in lowercase. Every other lowercase letter that looks similar to a Latin letter gets some modification.
I don't know about that rho is barely any different in appearance than a p.
Capital letters that are quite interchangeable, in both Greek and Latin alphabet are:
A, B, E, H, I, K, M, N, O, P, T, X, Y, Z.
Lowercase, depending on handwriting:
α/a, (sometimes I use the α for either of them, or draw something like a small fish instead. The latter is faster.)
ι/i (sometimes the ι has an accent, like so: ί),
o/ο (as you mentioned),
p/ρ (totally different letters though),
u/υ (if there's a following letter, υ might seem like u if you don't pick up the pen at all),
x/χ (can use x for the Greek one too),
y/ψ (ψ can be written almost like y. Again, though, totally different letters).
Source: I speak both languages, mother tongue is Greek, and the way I sometimes write the aforementioned letters is indistinguishable, while preserving text clarity.
@@alexandertownsend3291 the Greek ρ can't be written as p, but the reverse stands true.
Well, after all the latin alphabet comes from the greek one, so it makes sense that some symbols are literally the same. I don't see a reason to try to distinguish the symbol for omicron from the symbol for latin o.
@@jackozeehakkjuz no, but in physics you are sometimes expected to know the diference between rho and p. If your teacher has sufficiently bad handwriting they are almost indistinguishable.
My 2c's worth... I've never thought of that as a 'omicron' anything. It has always been (at least in my head) 'Order of'. So if something is O(n^2) then the complexity increases with the square of n, and O(n*log(n)), is proportional to the log of n. The symbol is kind of irrelevant, but happens to imply the word 'Order'. Hey ho, thank we're all different!
me as a Greek: They used omicron because that is one of the only letters they can pronounce correctly
Hypothesis : there are more mathematicians, scientists, and programmers using these letters than Greeks. Therefore it is the Greeks that are wrong!
@@SimonBuchanNz Yes. Whenever I see a talk by a Greek computer scientist, it takes me a while to get used to the way they mispronounce the names of all the Greek letters.
How funny you just have used half of the sentence Greek words to prove that the Greeks are wrong
0:40 "That's the theory"
Is it just a theory? The other day I heard an explanation that stated the WHO has banned the use of 'Nu' and 'Xi' as variant designations for the stated reasons *years* ago.
Yes iirc they came out and explicitly said “nu is like new and xi is a common last name” but I doubt it was years ago, given that the Greek naming system was only brought in in may of this year
0:36 i love how the pause bars fit right over the pi symbol
@numberphile, for info, in contrary to popular English speakers belief, the corect pronunciation of Greek letters μ and ν is closer to "mee" and "nee" not miu amd niu... (in the same 'ee' sound as in "lee") and if written they should be written mi, ni like pi which also has a pee pronunciation but whatever...
Another use of omicron is in physics, in relativity when you're describing different observers you use the "O" symbol for each observer. Again I thought this was an O, but I think it's actually meant to be an omicron.
Or 'origo'.
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!
Great video! Minor question tho, at the beginning shouldn't the Greek spelling of Numberphile be νυμβερφιλε instead of νυμβερπηιλε?
😁 Well, they've simply replaced the English (Latin) letters in 'Numberphile' with the nearest Greek equivalents.
If you want to approximate the English _pronunciation_ of 'Numberphile' using Greek letters, then this is closer: ναμβαφαιλ. (In British English, the 'r' isn't pronounced, but feel free to add a 'ρ' if you like.)
Omicron? More like “Oh, more of my time is gone.” Thanks for another captivating video!
I pulled this exact information thru the night before they named it. This is so validating thank you!
My teacher uses your videos to teach math and we always have fun and everyone is always interested. Keep making your amazing content!
1:36 since he went down that path (even though he actually wrote down the number 667 instead of 666), "ΟΜΙΚΡΟΝ" => 70+40+10+20+100+70+50 = 360. The degrees of a circle, "ο"
Coincidence?
Do all math people in the UK use large pieces of brown paper, or does Brady supply it? In one meter rolls? Brady?
Great video
Just disapointed that you used "pi" and "eta" instead of "phi" to write the letters "ph"...
o: Who are you?
ο: I'm you but... actually never mind, I might as well literally just be you.
If I had no familiarity with computer science, I would've been completely lost during his explanation of algorithmic complexity
Nevermind mind skipping Nu and Xi. Are you saying there was Mu variant? I know this is a math channel but did I miss something? Last I i heard of was Delta. Why say skipped 2? What happened to Epsilon, Zeta, Eta, Theta, Iota, Kappa, and Lambda?
Relax, no need to panic. Yes, all those variants exist, including Mu. They are all VBMs-Variants Being Monitored. But they are not VOCs-Variants of Concern. The only VOC are the Delta and Omicron variants. And that's why-outside of specialists-most people have heard of only those two.
'Xi' was the perfect name. Very fitting.
If Ptolemy wrote his omicron like you did as ō, that may suggest that it was an abbreviation. Writing a line above was how some Greek scribes would abbreviate well-known words, particularly in the New Testament.
Ζ is 7. The Greek numeral for 6 is a letter called wau or digamma; the capital looks like F. There are three letters (wau, qoppa, sampi) which are obsolete for writing words but still used for writing numbers. Wau was used for /w/, which dropped out early from Greek (e.g. wanax -> anax άναξ, a kind of king). Sampi was used for a sound that evolved into /s/ in some dialects and /t/ in others. And qoppa was used for /k/ before /u/ or /o/, then discarded as superfluous. All three, when used as numerals, evolved into shapes that look different than when used as letters.
ζ (zeta) represents 7 not 6, 6 is represented by the archaic letter stigma (ϛ).
the real letters of the Greek alphabet are 27 = 3^3 and not 24
Stigma male
Thanks for that. That explains the στ in α, β, γ, δ, ε, στ, ζ, η, θ, ι...
Correction: Xi is not pronounced “sigh”, it’s pronounced “zie”. The way he said it is similar to Psi which is the penultimate letter of the alphabet.
Numberphile in greek would be Αριθμόφιλος (Arithmophilos), which means "numbers lover".
And it has two omicrons, one accented and one unaccented!
@@viljami.haakana.laulut Correct. In greek, every word that is longer than one syllabe, always has one (and only one) accented vowel.
@@opterios Numberphile is a hybrid word, like television. The number part of it has Latin roots. It would probably be something like Numberamor, if it were a Latin-only word.
Greeks still use letters to represent numbers. Phillip the Second, is written Φίλιππος Β, but called "Φίλιππος Δεύτερος". 4th Grade is written Τάξη Δ but called "Τέταρτη Τάξη". In my modern Greek language textbook the lists are numbered α, β, γ, δ, ε, στ, ζ, η, θ, ι, ια, ιβ, ιγ, ιδ, ιε, ιστ etc. So "ι" becomes 10 and works as numbers would from there.
this is giving me early Numberphile vibes nice
Yo let’s go!! A new numberphile video is always awesome!
3:35 "What if you didn't have any minutes? What if you have zero minutes?" Sometimes I use Stellarium to calculate lunar and planetary conjunctions and occassionally I land on something weird like 1 degree, 0 arc minutes, and 5 arc seconds.
Please in another video explain the Cantor set or maybe nowhere dense sets.- also the Sorgenfrey line ("the arrow") and the associated plane?
Welcome back, Dr. Padilla. 👍
The big O notation is only related to the omicron notation, it's not the same. The big O - notation was established by a German mathematicians in 1894 and the letter O stands for the German word "Ordnung" ("order" in English, which works equally fine). But the difference between O-notation and omicron-notation is actually only exactly this, notation: It's written slightly diffently but in the end means the same.
4:33, the (ancient) greek word for 'nothing' is οὐδέν (ouden); but interestingly, the greek word for zero is μηδέν (meden). In its original use, it did not of course refer to the number (or the numeral) zero, which were unknown to ancient greeks, but simply meant "nothing" in another grammatical context, e.g. in the adage μηδέν ἄγαν (nothing in excess).
Both words stem from the negative prefix for "no" (οὐ) and "don't" (μή), the difference being the grammatical case (οὐ is nominative, μή is imperative). For example, in the Odyssey, Odysseus tells the cyclops Polyphemus his name is "Οὖτις" (no-one), making a play with words, as "μῆτις" (metis) was one of his epithets, meaning cunning, wisdom.
Yes! We finally covered order-of approximations! Now for some juicy physics videos!
The ancients believed that pi was equal to 80. Our approximation methods have come a long way since then!
Perfect time to release a video on Omicron.
can you write a short greek sentence using only letters used in mathematics and have it make sense while the number assosiated with the letters arranged in a formula also make sense?
just a stoned thought.... anythere there?
Awesome, you just rediscovered the secret of isopsephy, numerology, mysticism (such as 'the number of the Beast' and Kabbalah), coded messages, and-more practically-mnemonic aids.
VERY NICELY EXPLAINED, THANKS.
thanks for specifying numberphile
Just to clarify, Omicron doesn't have a line above it as a letter on its own - 2:06 - I noticed at 3:10 they clarify the addition of the line for the numbering (which is new info to me). Cool.
- P.S - Happy to be corrected. It's just that I've started learning Greek so was thinking critically of the symbol.
My pedantic self cannot resist correcting the pronunciation of Knuth: it's kuh-NOOTH, with a hard 'K'. I once took a discrete math class from him. The man is extremely droll and *extremely* intelligent!
I always thought the O in big O notation stood for Order (as in function of order x^2)
Should do a video talking about all letter for maths / engineering applications (each subject had different) but examples maybe
2:35 Turn on automatic captions. It's worth the effort!
I understand the use of Greek letters, but Omicron sounds like the villain of a Transformers movie
Because it rhymes with Megatron/Galvatron
Can you do video about all the common uses of the greek/Latin alphabet? I have not seen a comprehensive video or article on all the non-standard symbols on the internet.
In fact, the Landau symbols are all Greek letters. Apart from upper case Theta, it's omicron (lower case and upper case) and omega (both cases). It makes much more sense than O, because, well, _micro_ and _mega_ aren't in the names by accident. Therefore, it makes no sense to use script O for the Landau symbol.
Please make a video on why there is no quintic formula
I’d like to have some tea and just listen to Prof Padilla talk whilst sitting at his table…lol.
I guess one could represent 2'0'' as 1'60'' without needing to have a zero or a special symbol.
bijective sexagesimal?
I love the Greek alphabet. It's so simple yet complex at the same time
0:37
Was really hoping he'd say "Not even the disease wants to be associated with him"
Oh my Cron is a Unix oath when a daily process fails to run
I like how Tony can draw the Greek characters beautifully. Some mathematicians ans physicists manage to disfigure even pi...
Need to clarify that the ancient Greek word for nothing is: uden with the u spelled as in put. Two syllables: [1] u [2] den. Accent on e . Great video!
...which is written as ουδέν, so it does start with an omicron.
@@gekylafas Well... Typically the first letter *is* omicron ! [ Yes I know the two vowels together as one... ]
What is the possibility that the Indians (typically credited with inventing a symbol for 0) had copies of Ptolemy's work and got the symbol for 0 from there? I know that earlier Greek work spread east (such as trigonometry), but I don't know of any other examples from this deep in the Roman era.
None, because they used a dot originally. It evolved into a circle later.
@@JohnDlugosz ah, thanks. Seems like a massive coincidence, but I guess those do happen sometimes.
I never knew the O in big-O notation was an omicron. I thought it was an O.
same
Learned a new word today - I'm adding cantankerous to my everyday language. Lovely.
Fun fact. And it's something I didn't realize until I looked it up in an online dictionary recently, at which point I did a mental head-slap.
"Omicron" actually means, "little o;" while "omega" means, "big o" - notice the "micron" and "mega" in those names.
Which is kind of funny, since it makes "big omicron" and "little omega" oxymoronic.
And "little omicron" and "big omega" redundant. ;-)
Fred
What are you on about omicron not being used in maths...? It denotes the 0 element of fields, groups, etc.
Convergent evolution of mathematical symbols!! Pretty neat stuff 😄
The little o actually says that the quotient must go to zero. For instance, the function (x/2)^2 is always in the region between the x-axis and the function x^2 (except at zero, when all coincide), and yet (x/2)^2 / x^2 = 1/4 won't go to zero as x goes to zero.
Fortunately, Donald Knuth is too old to punch you for it. (Apart from that, he doesn't always have an easy time accepting suggestions himself.)
The o notation is originally due to Edmund Landau, a number theorist.
As someone that studied Comp Sci, I'm obviously familiar with big-O notation, but I had no idea that it was actually an omicron, I've always heard it referred to "big-O" or "of order".
A bit off topic, but what is the percentage of the worlds brown paper that's consumed in the making of Brady Haran videos?
Omicron (ο) is a :
Greek Alphabet (✔️)
COVID-19 Variant (❌)
Next, COVID-19 Coronavirus Pi (π) Variant.
Problem-reaction-solution. Create a solution (That which the ruler desires). Contrive the problem (That which causes suffering and death in the lowest members in the dominance hierarchy) that will cause the reaction where the willfully blind masses will demand the solution (The great reset).
In my experience the O(n) notation has never been portrayed graphically, it's just the worst case scaling. So with a sequential search, an algorithm where you check each element in a list to find the one you want, we'd say that that algorithm is O(n). This is because the worst case scenario, that the one you want is the last element, increasing in time at the same rate as the input. If you double the size of the list then it takes twice as much time to find that last element. Conversely we described big omega as the "best case scenario". It's rarely useful since that pretty much always 1. Big Theta is the average case. It's often the same as Big O but not always. That's how I learned it anyways.
That's not quite an accurate use of the terms though. If you say "in the best case, this algorithm is Ω(n)" then what you're saying is "this algorithm is never faster than linear". But you're *not* saying that the best case *is* linear; you would still need to use O or theta to express that.
@@TylerMcHenry Typically we would say that Omega(n)=1. It almost always does in that framework. It's rarely used as it's generally useless. O(n) is the standard for quickly summarizing the efficiency of an algorithm.
They didn't name it Xi because they didn't want it to be associated with a person. Tell that to my friend, Omic Ronvar Iant
Numberphile being cheeky with the RUclips algorithm, i see
I'm a physicist and the only context I can recall ever having seen the letter Omicron is in the name of the planet "Omicron Persei 8" in Futurama. [Yes, there's complexity and error bounds, but they were only ever referred to as little and big O ("Oh") and spoken as "of the order of".]
"I'm going to call you T."
4:09 I feel like there's an obvious followup question that isn't asked here: Since Ptolemy couldn't use omicron for the degrees, how would he have written "0° 41 min 3 sec"? Wouldn't the answer to that tell us something useful about how he used the symbol?
Numberphile Coverage of Omicron > News media coverage of Omicron
You should talk about Brazilian tally marks. They are the best!
Mathematician: pi = 3,141592...
Scientist: pi = 3,14
Engineer: pi = 3
Old mathematician: no, pi = EIGHTY
Dietician: No Pie.
Mr. Incredible: PIE IS PIE!
Now i want to see a video about numbers which, written in greek notation, make up words.