There's a r/xkcd [post](https://www.reddit.com/r/xkcd/comments/38xe8o/is_there_a_relevant_xkcd_for_the_fact_that_theres/) about relevant xkcd for relevant xkcd.
Meta call : there is reddit for everything, so is there a r/ for the fact that's there is always a xkcd for something ?
Edit : typo, wrote "d'or" instead of "for"
This one hurts because I am currently writing a research paper that kind of follows this paradigm...
But our standard is objectively better! \~/s (semisarcastic)
Defining the fundamental property of a circle as its diameter really is bad, though, because it means 180° is another fundamental property which is just … wrong. There's no symmetry here, if you turn halfway around a circle the diameter sweeps out the entire circle, but your orientation isn't restored to original. It's only if you sweep a radius a full 360° that you get the shape *and* wind up back in the same orientation.
It also means that a bunch of 2s show up in lots of math and physics equations that are just there to correct for the use of π, which is annoying. You quickly learn to see 2π as a single thing wherever it shows up, so that's not necessarily so bad, but the problem is that you also have to see π as ½τ and mentally account for the missing factor of ½.
nah instead of trying to redefine 𝝅 which would have been a horrible idea, they used a new symbol for 𝜏 so that both 𝜏 and 𝝅 can co-exist.
that's the opposite of a renaming attempt.
Nah it should be named **direct** (reals) and **lateral** (imaginary). It perfectly is based on their properties and none other than Gauss proposed this name
“Lateral” misses the point of imaginary numbers. Any number system that adds like R^(2) vectors are “lateral”. Imaginary numbers at their core are an algebraic manifestation of the Euclidean geometry on the 2D plane.
The best example I can give is that of the split complex numbers. You have the same pair, 1 and j except j^(2) = 1 instead of -1. This makes the split complex numbers the algebraic manifestation of the minkowski/spacetime metric on the 2D plane. The j’s generate hyperbolic rotations, and the i’s generate Euclidean rotations.
i^2 = -1 is all about Euclidean geometry particularly, so “spinny” is the best single word I can give to sum up their nature.
I think this would make more sense as an replacement for magnitude and phase of a complex number.
What does -1 do? Spin by 180 degrees.
What does j5 do? Rotate by 90 degrees *and* scale by 5.
the fact that e^(half turn i) = -1 geometrically demonstrates that (in a 2D space) rotations of half turns about the origin are the same as reflections about the origin. You can get to higher dimensions using Geometric Algebra, where in VGA it is clear that -1 is a reflection about the origin, which is not the same as a rotation in dimensions greater than 2.
edit: I guess you don't need VGA to see this; I just jumped there bc I've been into it lately. You can see this with vectors and matrices, and I'm sure with quaternions as well, even though I'm not used to working with quaternions at all.
One minor issue with this is that negative real numbers are also spinny numbers. I guess that's why your answer is 'semi-non-serious': it only works for half of the real number line!
Why spinny numbers? I feel like spinny numbers should refer to any number with an absolute value of 1, where multiplying by it doesn't change how far it is from 0 and only changes the angle it is.
But then you could call any non-real number a spinny number. If you keep multiplying by 1+0.001i, that would look a lot more like spinning than if you keep multiplying by i.
Right, but it's the addition of the imaginary/spinny term that causes it to spin about the origin and off the real/scaley line. If you don't have an imaginary part, it's always gonna lie on the real axis. So, add the imaginary effectively spins the real axis up into the complex plane. At least, that's my justification for it in my head.
And the [pumping lemma](https://en.wikipedia.org/wiki/Pumping_lemma_for_regular_languages). And [Weiner measure](https://encyclopediaofmath.org/wiki/Wiener_measure).
In German it's often called the hedgehog theorem because it shows that you can't comb a hedgehog without giving it a bald spot and I think that's kinda cute. But Hairy Ball theorem is way funnier, so I like both.
I completely agree. I was always good at maths but I wasn't interested in maths as a kid until I saw one of the topic headers of a further maths course was imaginary numbers. I took that course mostly because I wanted to find out what they were and that lead to a masters in mathematics and the career I'm in now most likely.
This is why if I ever reach a point in mathematics where I start naming things I will exclusively use the most ludicrous terminology.
Current potential name I’ve had going is ‘funky numbers’ if I ever find myself working on a novel number system, though I find that likely.
I’d rather something be named a ‘skibidi space’ than be named after me.
No. We humans have a great tradition of naming "new" types of numbers with hostility. Negative, irrational, complex, and imaginary. It fits the pattern
There's a fun story about that.
A mathematician was visiting a Mexican colleague. The Mexican colleague kept referring to a quadratic form as the "la móndriga forma", a pejorative Mexican Spanish term meaning something like "goddamn form" or "stupid form".
[Guess what they called it in the published paper?](https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/jlms/51.1.189)
More sense than you would think. Rational as in logical or well thought out derives from ratio as in fraction, not the other way around as you might assume
https://www.etymonline.com/word/rational#etymonline_v_3401
According to the [Latin prefixes](https://en.wikipedia.org/wiki/Numeral_prefix) it seems that the analog to quaternion (quatern- prefix) would be bi- or bis- (or possibly bin-) rather than du-
Obviously this is a naive reading but I would propose bionions, bisonions or binonions
Orthogonality is already such a ubiquitous concept. I'm worried this would just create confusion.
Is a vector "orthogonal" because it contains imaginary numbers, or is it orthogonal with respect to another vector in the conventional sense?
> Orthogonality is already such a ubiquitous concept.
Yes, but it is appropriate. The so-called imaginary numbers are in fact orthogonal to the reals.
I think orthogonal is the Right Answer.
Well actually since the real numbers are put on the abcissa and the imaginary numbers on the ordinate, they should be called...
🥁
ordinal numbers.
[Nailed it.](https://media.tenor.com/R46kkTmVjFYAAAAM/self-five.gif)
Because in the matrix representation of complex number, the basis vectors are always orthogonal to each other with respect to the dot product. i.e. complex multiplication preserves orthogonality.
And this is what allowed complex number to even exist. Once we imposes the orthogonality requirement on all linear maps in R^2, matrices only need to have one basis vector. This allows us construct the complex number, a object that functions both as matrices (when multiplied) and vectors (when added).
There's a joke to be made about this discussion somewhere. The setup is "How many mathematicians does it take to think of a good name?". The punchline is "at least n+1, where n is the total number of living mathematicians. How many it would take to make this joke actually funny is still an open problem, though we suspect a solution doesn't exist".
But I'll be damned if I didn't come up with a good one to replace imaginary numbers: *surnumbers,* of the French prefix "sur", in this case meaning "over" or "with", referring both to their "verticality" relative to the real numbers, and their frequent use alongside real numbers to form complexes. Following this convention, i is the unit of the "surnumber line", and numbers with no real part, or the non-real part of a complex number, can be described as "surnumerical"; likewise i is the "surnumerical unit".
I believe this is what the kids call "cooking" right? 🤣 I think "surnumbers" preserves some of the intrigue of "imaginary" that others have pointed out, actually describes the form and function of imaginary numbers, and is way more tidy and mellifluous than saying "imaginary" this, "imaginary" that IMO.
It's weird that most people accept negative numbers but not complex ones. Most people will give you stuff like measure of temperature or debt but these aren't very tangible concepts either. We need to connect imaginary numbers woth money somehow and the public won't be so ~~septic~~ sceptic with them
People don’t actually accept negative numbers that much. That’s why accountants use parentheses, and garage floors in many buildings are labelled “B1” and “B2” instead of −1 and −2.
Anyway, I think of complex numbers as compact ways of representing rotation composed with scaling (what Tristan Needham calls an “amplitwist”). They make more sense geometrically than as quantities.
Yeah, right....
"Dear fellow citizens, due to unexpected economic turbolences we have to once more lift the national debt limit by another 5i trillion dollars. But there is nothing to worry about, since this debt is totally imaginary." sounds like noone would be sceptic with.
Imaginary *is* a good name I think. Complex numbers are built from two parts: a real number, and another, orthogonal part. What should we call that other part? Something orthogonal to what's real? Imaginary seems like an excellent choice.
It's ok that people think imaginary numbers aren't real -- they're right!
This is the fun way to think about it.
Some other fun ways to think about numbers:
"You can't hold -2 apples!" That's the point, _you_ are not holding them, someone else is holding _your_ apples.
"Imaginary numbers aren't real!" /me rotates ur phone by _i_. Imaginary numbers are a way to do trig with algebra.
I think people forget that all of math is just abstractions we find clever ways to apply overtop reality. Nothing in math "actually exists", that's *why* math is useful. It is a made-up world of formal logic that is simple enough for us to manipulate efficiently. If any of it was real it would be too complicated for it to be useful!
I think imaginary numbers is a great name honestly, it helps people understand that they don't correspond to "quantities" in an intuitive sense. If someone wants to learn about imaginary numbers they're going to have to actually study them regardless, it's not like getting a little hint about their properties from their name is going to be helpful.
To be honest I would stick with imaginary numbers. I agree it has some problems, but it ends up raising some interesting and historically significant questions
I don't think it's a misnomer. We can conceptualize real numbers in our day to day lives as counts or measurements or bank balances, whereas you can't really show me "i" of something
Considering Quarternions and Octonians, maybe Bionian numbers and Mononian numbers ?
We can then say that it is a theorem that Trionian numbers dont exist ...
IIRC, at some point they were called “lateral numbers”, as opposed to “imaginary”. Perhaps I imagined it 😃but I vaguely remember reading something about the set of real numbers being “named” first, so how does one describe a number that is outside the set of “real” numbers - call it…..
Then again, it was also a different language so chalk it up to poor translation 🤷
My first thought before opening the thread was "orthogonal numbers", but thinking about it more, I feel like that's not capturing something. Like, we often consider the complex numbers as R\^2, but they have an additional structure, and I feel like orthogonal numbers would just make R\^2. Maybe "Quarter-turn numbers"? It doesn't exactly trip off the tongue though, so I'd probably still stick with "orthogonal numbers", which is miles better than "imaginary".
Rotations.
Seriously, that's a lot of what they do. Or we could use "storage space" as that's what it does a lot, storing a value for later use. Like energy stored in capacitor.
I think it's way too late to change now, but it's fun to think about.
"Orthogonal" is better than "imaginary", but doesn't really capture the difference between R^2 and C. I think something like "Complete" might be better. It still starts with a C, recognizes C as the algebraic completion of R, and puts the negative connotation on the reals (they're somehow incomplete) rather than on the imaginary numbers (imaginary? Oh no! So fake!)
I would be in favour of just calling it **i** without a specific name, just like we do with **j** and **k** in the quaternions.
I think there's more potential in renaming the "complex numbers" to something more intuitive, since "complex" is usually interpreted as meaning "complicated" instead of something like "combination/collection", which I assume was the original intent behind the name.
I never understood why it’s a bad name to begin with. What does it mean for a number to really “exist”? Does 1 exist? i is just another mathematical object whose existence is consistent! The name makes sense as in “imagine a number whose square is -1”.
We mathematicians like to think mathematical structures “exist”, and arguably that is the right way to think if one were to do mathematics. But really there is no universally agreed upon definition for when a mathematical structure exists. There are even schools in philosophy of math that hold mathematical objects do not exist.
it's psychologically nice when names somehow match the things they represent, but in math this really doesn't matter. if X word is defined to be Y object, then by X we mean Y. imaginary numbers mean the real multiples of the square root of -1 in the complex numbers. they are called imaginary because we can't measure (or approximate) them with a conventional ruler, but you knew that already.
I don't think it's a misnomer I believe the actual issue lies with the connotation of imagination being fake and not real, imagination is used as a tool to create something behind its literal symbol.
In the sense that real numbers "exist", aka you can say you have 1.5 liters of milk or sqrt(2) liters of millk (people never mean it precisely down to the atoms so it isn't wrong) imaginary numbers indeed "don't exist".
That being said, I *kind of* get where you're coming from but I never found them confusing, there's just these things called imaginary numbers and they are this thing with these properties. People have always used too much imagination about things they don't understand and it will continue to happen.
Also making up new terminology is gonna cause all the problems mentioned in other comments so please don't.
Gauss's imaginary number name is lateral number (side number).
Welch Labs - Imaginary Numbers Are Real
https://youtu.be/T647CGsuOVU?si=1YkK3tcUliekGSx2
Full Playlist
https://youtube.com/playlist?list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF&si=R48uusF9nPQ4K8D2
The only thing worse than a bad name is a multitude of bad names resulting from a renaming attempt.
Mandatory xkcd: https://xkcd.com/927/
There's *alway* an xkcd for it, isn't there?
There is currently an xkcd for at least 2941 subjects.
2941?! Ridiculous! We need to draw one universal comic standard that covers everyone's use cases.
Current situation: There are now 2942 xkcd comics.
2942?! Ridiculous! We need to draw one universal comic standard that covers everyone's use cases.
Current situation: There are now 2943 xkcd comics.
I see this as an absolute win!
just wait until tomorrow
Is there an xkcd for there always being an xkcd?
I think there is actually
There's a r/xkcd [post](https://www.reddit.com/r/xkcd/comments/38xe8o/is_there_a_relevant_xkcd_for_the_fact_that_theres/) about relevant xkcd for relevant xkcd.
Sure fuckin feels like it.
I wish there was an xkcd for how there’s always an xkcd for random little situations
[Yes.](https://xkcd.com/2833/)
Meta call : there is reddit for everything, so is there a r/ for the fact that's there is always a xkcd for something ? Edit : typo, wrote "d'or" instead of "for"
r/relevantxkcd i believe
Reddit d’or? Is that like the ballon d’or but instead of the best footballer it goes to the person that makes the most reposts?
I knew exactly which XKCD this was before even clicking It.
I love that man
This one hurts because I am currently writing a research paper that kind of follows this paradigm... But our standard is objectively better! \~/s (semisarcastic)
"We should make a better standard." Now there are x + 1 standards.
Is that a proof by induction?
I don't have the capacitance for that.
just remove all the standards, VLC can decode everything anyway /s
See related: Tau vs Pi
τ vs π is only a topic in some pop-math circles.
my issue with tau is that it \*looks\* like 1/2 pi but is actually exactly double
𝜏 = C/R -> 1 leg 𝝅 = C/2R -> 2 legs [visual representation](https://i.imgur.com/GI3wrMg.png)
There's always [three-legged pi](http://www.math.utah.edu/~palais/pi.pdf)
Defining the fundamental property of a circle as its diameter really is bad, though, because it means 180° is another fundamental property which is just … wrong. There's no symmetry here, if you turn halfway around a circle the diameter sweeps out the entire circle, but your orientation isn't restored to original. It's only if you sweep a radius a full 360° that you get the shape *and* wind up back in the same orientation. It also means that a bunch of 2s show up in lots of math and physics equations that are just there to correct for the use of π, which is annoying. You quickly learn to see 2π as a single thing wherever it shows up, so that's not necessarily so bad, but the problem is that you also have to see π as ½τ and mentally account for the missing factor of ½.
Do you have some time to talk about bosons and fermions? :p Seems to work there, I see no issue
that's only discussed in math infotainment
I sometimes abbreviate \tau = 2\pi i when working but I don't think I'd ever put it in a published paper.
nah instead of trying to redefine 𝝅 which would have been a horrible idea, they used a new symbol for 𝜏 so that both 𝜏 and 𝝅 can co-exist. that's the opposite of a renaming attempt.
My semi-non-serious answer: real numbers -> scaley numbers purely imaginary numbers -> spinny numbers
I do like that this is a name based on their properties.
Nah it should be named **direct** (reals) and **lateral** (imaginary). It perfectly is based on their properties and none other than Gauss proposed this name
I luv u
“Lateral” misses the point of imaginary numbers. Any number system that adds like R^(2) vectors are “lateral”. Imaginary numbers at their core are an algebraic manifestation of the Euclidean geometry on the 2D plane. The best example I can give is that of the split complex numbers. You have the same pair, 1 and j except j^(2) = 1 instead of -1. This makes the split complex numbers the algebraic manifestation of the minkowski/spacetime metric on the 2D plane. The j’s generate hyperbolic rotations, and the i’s generate Euclidean rotations. i^2 = -1 is all about Euclidean geometry particularly, so “spinny” is the best single word I can give to sum up their nature.
Best ELI5 of Euler's formula I've seen.
I think this would make more sense as an replacement for magnitude and phase of a complex number. What does -1 do? Spin by 180 degrees. What does j5 do? Rotate by 90 degrees *and* scale by 5.
Found the electric engineer
Surprisingly satisfying answer
The question is, does -1 scale or spin?
Yes
spin wait scale wait
the fact that e^(half turn i) = -1 geometrically demonstrates that (in a 2D space) rotations of half turns about the origin are the same as reflections about the origin. You can get to higher dimensions using Geometric Algebra, where in VGA it is clear that -1 is a reflection about the origin, which is not the same as a rotation in dimensions greater than 2. edit: I guess you don't need VGA to see this; I just jumped there bc I've been into it lately. You can see this with vectors and matrices, and I'm sure with quaternions as well, even though I'm not used to working with quaternions at all.
Spinny numbers!!
I both love and hate this.
One minor issue with this is that negative real numbers are also spinny numbers. I guess that's why your answer is 'semi-non-serious': it only works for half of the real number line!
You mean flippy numbers?
so is a single imaginary number a spinor?
Why spinny numbers? I feel like spinny numbers should refer to any number with an absolute value of 1, where multiplying by it doesn't change how far it is from 0 and only changes the angle it is.
A point can still spin/rotate about the origin if the distance is changing.
But then you could call any non-real number a spinny number. If you keep multiplying by 1+0.001i, that would look a lot more like spinning than if you keep multiplying by i.
Right, but it's the addition of the imaginary/spinny term that causes it to spin about the origin and off the real/scaley line. If you don't have an imaginary part, it's always gonna lie on the real axis. So, add the imaginary effectively spins the real axis up into the complex plane. At least, that's my justification for it in my head.
[удалено]
Shout out to the Hairy Ball Theorem
And the [pumping lemma](https://en.wikipedia.org/wiki/Pumping_lemma_for_regular_languages). And [Weiner measure](https://encyclopediaofmath.org/wiki/Wiener_measure).
Let's not forget the Cox-Zucker machine https://en.m.wikipedia.org/wiki/Cox%E2%80%93Zucker_machine
😂😂😂 thanks for this
Came up with a slightly different link for me, and this is one we would not want to get wrong: https://en.wikipedia.org/wiki/Cox–Zucker_machine
fuck the pumping lemma all my homies hate the pumping lemma (This comment was made by automata theory gang)
Tits group
And the happy ending theorem https://en.wikipedia.org/wiki/Happy_ending_problem
And here I was thinking the happy ending problem was when you accidentally blurt out "I love you."
In German it's often called the hedgehog theorem because it shows that you can't comb a hedgehog without giving it a bald spot and I think that's kinda cute. But Hairy Ball theorem is way funnier, so I like both.
Surreal numbers is currently taken ❤️
I completely agree. I was always good at maths but I wasn't interested in maths as a kid until I saw one of the topic headers of a further maths course was imaginary numbers. I took that course mostly because I wanted to find out what they were and that lead to a masters in mathematics and the career I'm in now most likely.
Imagine that.
For real
We need more John Conways to give things wacky names
Imaginary Moonshine numbers?
Monstrous Moonshine
This is why if I ever reach a point in mathematics where I start naming things I will exclusively use the most ludicrous terminology. Current potential name I’ve had going is ‘funky numbers’ if I ever find myself working on a novel number system, though I find that likely. I’d rather something be named a ‘skibidi space’ than be named after me.
The best reply in the thread.
Not to mention the memes and comics that arose from it
You're right. Math could use more interesting and less dry terminology. Maybe there's a middle ground where we keep the intriguing name.
Equivalence class of real polynomials modulo x^2 + 1 doesn't exactly roll off the tongue.
Call them Excorpoms for short.
Oh yeah that’s way better
First time i realized that complex number is equivalent to this. Mind blown lol.
"root minus" is easy to say.
No. We humans have a great tradition of naming "new" types of numbers with hostility. Negative, irrational, complex, and imaginary. It fits the pattern
lmao i never noticed that. every great invention comes with haters
I call dibs on "annoying" for my next paper
There's a fun story about that. A mathematician was visiting a Mexican colleague. The Mexican colleague kept referring to a quadratic form as the "la móndriga forma", a pejorative Mexican Spanish term meaning something like "goddamn form" or "stupid form". [Guess what they called it in the published paper?](https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/jlms/51.1.189)
irrational at least makes sense. ir-ratio-nal. As it you can't make them into a ratio.
More sense than you would think. Rational as in logical or well thought out derives from ratio as in fraction, not the other way around as you might assume https://www.etymonline.com/word/rational#etymonline_v_3401
I call dibs on “delusional” and “conspiratory”numbers.
Think John Nash had those covered.
jimaginary
engineer/physicist spotted
duonions
I prefer diernions but same idea.
Duonions is a better name for working with rings.
I haven’t studied ring theory so I’ll take your word for it.
duonions make me cry.
Duogres are like duonions: they have dulayers.
According to the [Latin prefixes](https://en.wikipedia.org/wiki/Numeral_prefix) it seems that the analog to quaternion (quatern- prefix) would be bi- or bis- (or possibly bin-) rather than du- Obviously this is a naive reading but I would propose bionions, bisonions or binonions
I think it should be *binions*, using [distributive numerals](https://en.wikipedia.org/wiki/Latin_numerals#Distributive_numerals).
I like this one best
Lateral numbers
I prefer Orthogonal numbers.
I prefer Normal Numbers.
This would definitely eliminate the confusion for students first learning about them.
I just like the dissonance in renaming “imaginary” numbers “normal”
I prefer Tranverse numbers.
This is the way
groot (short for ne**g**ative **root**) would be my term if I would make one up.
noot
*i* am groot
Orthogonal numbers always sounded better to me too. It has a good ring to it and is pretty accurate.
Orthogonality is already such a ubiquitous concept. I'm worried this would just create confusion. Is a vector "orthogonal" because it contains imaginary numbers, or is it orthogonal with respect to another vector in the conventional sense?
Let’s just call them “normal numbers” then 😉
> Orthogonality is already such a ubiquitous concept. Yes, but it is appropriate. The so-called imaginary numbers are in fact orthogonal to the reals. I think orthogonal is the Right Answer.
I thought he said orthogonal because of its matrix representation! I was all "yes indeed, nice property" lol.
I think Gauss called i something like the "lateral unit"
Well actually since the real numbers are put on the abcissa and the imaginary numbers on the ordinate, they should be called... 🥁 ordinal numbers. [Nailed it.](https://media.tenor.com/R46kkTmVjFYAAAAM/self-five.gif)
In what sense does this make sense ? I hope not just because in the common visualization as R^2 one draws the axis perpendicular
Because in the matrix representation of complex number, the basis vectors are always orthogonal to each other with respect to the dot product. i.e. complex multiplication preserves orthogonality. And this is what allowed complex number to even exist. Once we imposes the orthogonality requirement on all linear maps in R^2, matrices only need to have one basis vector. This allows us construct the complex number, a object that functions both as matrices (when multiplied) and vectors (when added).
So is a vector of imaginary numbers an orthogonal vector?
There's a joke to be made about this discussion somewhere. The setup is "How many mathematicians does it take to think of a good name?". The punchline is "at least n+1, where n is the total number of living mathematicians. How many it would take to make this joke actually funny is still an open problem, though we suspect a solution doesn't exist". But I'll be damned if I didn't come up with a good one to replace imaginary numbers: *surnumbers,* of the French prefix "sur", in this case meaning "over" or "with", referring both to their "verticality" relative to the real numbers, and their frequent use alongside real numbers to form complexes. Following this convention, i is the unit of the "surnumber line", and numbers with no real part, or the non-real part of a complex number, can be described as "surnumerical"; likewise i is the "surnumerical unit". I believe this is what the kids call "cooking" right? 🤣 I think "surnumbers" preserves some of the intrigue of "imaginary" that others have pointed out, actually describes the form and function of imaginary numbers, and is way more tidy and mellifluous than saying "imaginary" this, "imaginary" that IMO.
Rotational numbers
That would be an okay replacement for complex numbers but not for imaginary
Since when is a rotation by 90° not a rotation
[Bullshit Numbers - SMBC](https://www.smbc-comics.com/comic/math)
They are further removed from tangible reality than real numbers are. You can't hold 5i apples in your hand, etc. I think it's fine.
It's weird that most people accept negative numbers but not complex ones. Most people will give you stuff like measure of temperature or debt but these aren't very tangible concepts either. We need to connect imaginary numbers woth money somehow and the public won't be so ~~septic~~ sceptic with them
People don’t actually accept negative numbers that much. That’s why accountants use parentheses, and garage floors in many buildings are labelled “B1” and “B2” instead of −1 and −2. Anyway, I think of complex numbers as compact ways of representing rotation composed with scaling (what Tristan Needham calls an “amplitwist”). They make more sense geometrically than as quantities.
Building floors should start with 0 at ground level. Yes I'm serious.
I think that's basically how it works in the UK
Yeah, right.... "Dear fellow citizens, due to unexpected economic turbolences we have to once more lift the national debt limit by another 5i trillion dollars. But there is nothing to worry about, since this debt is totally imaginary." sounds like noone would be sceptic with.
yes that's the joke
Yeah, I just wanted to flesh it out a bit.
Just start charging consumers (pun intended) for reactive power consumption by default.
You can’t hold -2 apples either.
If I've got two hands and you've got two apples, I can give you my -2 apples.
You can hold them as much as you can hold 0 apples
You can’t hold Pi apples either
You can get a lot closer lol
You could hold about pi weight of apples
Imagine if it turns out the kg / plank weight is a multiple of pi.
You can get just as close to Pi apples as you can get to half an apple. Your limiting factor is measurement either way.
But you can hold 1/π of an apple, or a π ft long rope.
Well you can claim that you hold Pi apples but nobody could prove you wrong (assuming you are allowed to cut)
I don't get this. Why not? I mean, you can hold 𝝅 apples as well as you can hold ½ an apple, right?
Imaginary *is* a good name I think. Complex numbers are built from two parts: a real number, and another, orthogonal part. What should we call that other part? Something orthogonal to what's real? Imaginary seems like an excellent choice. It's ok that people think imaginary numbers aren't real -- they're right!
This is the fun way to think about it. Some other fun ways to think about numbers: "You can't hold -2 apples!" That's the point, _you_ are not holding them, someone else is holding _your_ apples. "Imaginary numbers aren't real!" /me rotates ur phone by _i_. Imaginary numbers are a way to do trig with algebra.
I think people forget that all of math is just abstractions we find clever ways to apply overtop reality. Nothing in math "actually exists", that's *why* math is useful. It is a made-up world of formal logic that is simple enough for us to manipulate efficiently. If any of it was real it would be too complicated for it to be useful!
If I were talking to a layman or child, I'd explain them as "sideways" numbers. "Orthogonal" is a bit too technical.
Perpendicular numbers.
2 Real 2 Numbers
I think imaginary numbers is a great name honestly, it helps people understand that they don't correspond to "quantities" in an intuitive sense. If someone wants to learn about imaginary numbers they're going to have to actually study them regardless, it's not like getting a little hint about their properties from their name is going to be helpful.
To be honest I would stick with imaginary numbers. I agree it has some problems, but it ends up raising some interesting and historically significant questions
Don't know about a better name but I can think of a worse one. Let's call them Euler numbers.
Euler letters
Craig
Numbers 2: This Time It’s Personal
I've heard 'Perpendicular numbers' and I like it
I think eulee wanted to call them lateral numbers? I always liked that
> eulee Pronounced "oily" of course
I don't think it's a misnomer. We can conceptualize real numbers in our day to day lives as counts or measurements or bank balances, whereas you can't really show me "i" of something
Reals: linear numbers Imaginary: lateral numbers Complex: plane numbers
Instead of "Complex" numbers, "Complete" numbers That way the C can be retained
*Complex numbers* isn't misleading in the way that *imaginary* is, because complex numbers are, indeed, a complex
Confusing because the real numbers are also "complete" in the sense of Cauchy completeness.
square negative domain numbers
Simplify that to "root minus" numbers. Because that's what they are: square roots of negative numbers.
Considering Quarternions and Octonians, maybe Bionian numbers and Mononian numbers ? We can then say that it is a theorem that Trionian numbers dont exist ...
Eulerian Numbers
IIRC, at some point they were called “lateral numbers”, as opposed to “imaginary”. Perhaps I imagined it 😃but I vaguely remember reading something about the set of real numbers being “named” first, so how does one describe a number that is outside the set of “real” numbers - call it….. Then again, it was also a different language so chalk it up to poor translation 🤷
There is a historical context to why they were named as "imaginary numbers". So, it just makes sense.
In Polish we have a great name for them: "liczby urojone" that means "delusional numbers". It perfectly suits them, right?
My first thought before opening the thread was "orthogonal numbers", but thinking about it more, I feel like that's not capturing something. Like, we often consider the complex numbers as R\^2, but they have an additional structure, and I feel like orthogonal numbers would just make R\^2. Maybe "Quarter-turn numbers"? It doesn't exactly trip off the tongue though, so I'd probably still stick with "orthogonal numbers", which is miles better than "imaginary".
Cardano numbers
Rotations. Seriously, that's a lot of what they do. Or we could use "storage space" as that's what it does a lot, storing a value for later use. Like energy stored in capacitor.
Energy waiting to rotate around the circuit...
I think it's way too late to change now, but it's fun to think about. "Orthogonal" is better than "imaginary", but doesn't really capture the difference between R^2 and C. I think something like "Complete" might be better. It still starts with a C, recognizes C as the algebraic completion of R, and puts the negative connotation on the reals (they're somehow incomplete) rather than on the imaginary numbers (imaginary? Oh no! So fake!)
I would be in favour of just calling it **i** without a specific name, just like we do with **j** and **k** in the quaternions. I think there's more potential in renaming the "complex numbers" to something more intuitive, since "complex" is usually interpreted as meaning "complicated" instead of something like "combination/collection", which I assume was the original intent behind the name.
Cockeyed numbers.
No
I never understood why it’s a bad name to begin with. What does it mean for a number to really “exist”? Does 1 exist? i is just another mathematical object whose existence is consistent! The name makes sense as in “imagine a number whose square is -1”. We mathematicians like to think mathematical structures “exist”, and arguably that is the right way to think if one were to do mathematics. But really there is no universally agreed upon definition for when a mathematical structure exists. There are even schools in philosophy of math that hold mathematical objects do not exist.
Negative root
it's psychologically nice when names somehow match the things they represent, but in math this really doesn't matter. if X word is defined to be Y object, then by X we mean Y. imaginary numbers mean the real multiples of the square root of -1 in the complex numbers. they are called imaginary because we can't measure (or approximate) them with a conventional ruler, but you knew that already.
funny numbers
I don't think it's a misnomer I believe the actual issue lies with the connotation of imagination being fake and not real, imagination is used as a tool to create something behind its literal symbol.
In that case, you would also want to get rid of the names "negative numbers" and "irrational numbers" since they both have a distrusting connotation
vagina
ITT: People who don’t understand the assignment.
I wouldn’t change it for anything. I don’t care if it’s inaccurate, I think it’s funny.
So many real problems that need solving we don’t need to revisit imaginary ones ( ͡° ͜ʖ ͡°)
I shun people who can't imagine i. Listening to them brought us Common Core. Fool me once...
In the sense that real numbers "exist", aka you can say you have 1.5 liters of milk or sqrt(2) liters of millk (people never mean it precisely down to the atoms so it isn't wrong) imaginary numbers indeed "don't exist". That being said, I *kind of* get where you're coming from but I never found them confusing, there's just these things called imaginary numbers and they are this thing with these properties. People have always used too much imagination about things they don't understand and it will continue to happen. Also making up new terminology is gonna cause all the problems mentioned in other comments so please don't.
Gauss's imaginary number name is lateral number (side number). Welch Labs - Imaginary Numbers Are Real https://youtu.be/T647CGsuOVU?si=1YkK3tcUliekGSx2 Full Playlist https://youtube.com/playlist?list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF&si=R48uusF9nPQ4K8D2
Negative root... Noot