
Why j for imaginary unit? - edwintorok
http://www.johndcook.com/blog/2013/04/23/why-j-for-imaginary-unit/
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claudius
But this is only a problem if you use i, j, and k as unit vectors. I found
$\hat e_{x,y,z}$ or even $\hat{e}_{1,2,3…}$ etc. to be the usual convention in
physics, as it generalises much nicer to more dimensions.

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johndcook
I agree. I was just about to write a similar comment.

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btilly
Before vector notation became popular in the last 1800s, people used
quaternions. The three independent square roots of -1 in quaternion notation
are i, j, and k. Therefore the use of j or (in need) k as a square root of -1
seems natural to me.

My understanding is that this history is why people in physics - even today -
frequently use i, j, and k as the names of the three spatial unit vectors.
(The real numbers, of course, represented time.) However I've not personally
looked into any of this history, so you should treat my understanding more as
hearsay rather than informed comment.

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yummyfajitas
People still use quaternions. They are an excellent method of representing
spatial rotations, since they avoid Gimbal lock (and similar phenomena caused
singularities in polar coordinates).

[https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotati...](https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation#Quaternion_rotation_operations)

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hkmurakami
Addendum: frequently used in Aerospace, Navigation, and Motion Tracking
applications.

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kaoD
And computer games!

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rm999
I actually see that as an argument against using j. The _meanings_ of a unit
vector in real space and a dimensional unit in imaginary space are different
concepts even if it's common to represent both in 2-dimensions plots. It seems
to me that this would only cause confusion/ambiguity. When I look at a plot I
want to know what it's representing as soon as possible, and the way the axes
are labeled is part of what helps me.

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hkmurakami
Exactly what I thought. I studied EE in undergrad so I used this sort of
notation all the time, and my thought upon reading the article was that I'd be
rather confused upon looking at the graph and would struggle to figure out
what it was even representing.

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jonpeda
Yes, ultimately we are bound by tradition, since changing over to any system
is too expensive and confusing.

Path dependence and local optima.

See also: English vs Metric units.

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marblar
Want to know what's worse? Spherical coordinates.

[http://en.wikipedia.org/wiki/Spherical_coordinates#Conventio...](http://en.wikipedia.org/wiki/Spherical_coordinates#Conventions)

You need to remember two different sets of conversions from cartesian to
spherical coordinates and two sets of differential elements -and of course,
you need to remember which is assumed by which audience.

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sohamsankaran
Speaking as someone just graduating high school in India, this sort of
unintuitive convention discrepancy often flummoxes people at the 9th grade
level, causing them to drop out of Physics altogether. Once you drop Physics,
it's essentially impossible to get onto the Engineering or CS tracks in India,
and U.S. universities are often too expensive.

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PeterWhittaker
Perhaps my comment will be considered harsh, but my view has long been that if
you are hung up on the notation, you miss the physics, you miss the science.

There is no such as "an intuitive convention". Notation is simply that:
Convention. If someone cannot grasp this, they lack either or both of the
intellectual maturity and the doggedness necessary to understand the science.

If teachers failed to make the point that notation is simply convention,
chosen for largely historical reasons, then they have not helped the situation
- but fundamentally it is up to the student to see past, to see through the
conventions and to perceive what the notation is saying.

Why does "W" represent the "wa" sound? Convention. Do you see the individual
letters or do you read the words, the sentences?

Arguing whether you should use i or j for square root -1 is like arguing
whether you should o or u for a particular vowel sound.

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jonpeda
> If someone cannot grasp this, they lack either or both of the intellectual
> maturity

Yes, that's entirely the point! >> flummoxes people at the _9th_ grade level,

> There is no such as "an intuitive convention".

 _consistency_ is intuitive. _inconsistency_ is _un_ intuitive. That's not the
same as a hypothetical complaint that a certain convention is unintuitive.

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claudius
Even if we set out to build an entirely consistent set of notation for use in
all of physics, maths and engineering today, we would face obvious problems,
mostly that there are only about 100 different symbols (Latin + Greek + some
extras) with maybe a handful of modifiers (primes, dots, tildes…and no,
combining them is not good) and typefaces (difficult to replicate in
handwriting).

So if we wanted to name every quantity and every concept possibly encountered
by physics/maths/engineering today consistently, we already would have a hard
time fitting everything in. Add to this that you also need a ‘working space’
of free, unencumbered symbols, a space of symbols free to use in the future[0]
and the possibility that seemingly unrelated concepts today might well be
linked in a few years time, and you will come to the conclusion that there is
no way we could possibly build a consistent set of notation.

Really, be happy with what we have at the moment, choose a convention suitable
to your current field of work[1] and everything will be fine.

[0] Some people started using Arab letters for new mathematical functions. Try
googling for that.

[1] Or even invent the n-th one if you work at the edge of two existing fields
or recognise that you can get stuff done more easily if you choose other
symbols.

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marblar
Relevant xkcd: <http://xkcd.com/927/>

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rdtsc
An interesting side-point -- Python supports imaginary numbers and uses j:

    
    
          In [2]: a=5-4j
    
          In [3]: b=1+2j
    
          In [4]: a+b
          Out[4]: (6-2j)

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jpwright
Another interesting side-point -- MATLAB supports imaginary numbers... unless
of course you redefine i to be something else. Then it doesn't.

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claudius
Fortunately, Mathematica makes that somewhat more difficult (and has a strong
convention of inbuilt ./. user-defined variables in the form of
upper/lowercase).

