Why is a pole called a pole?

Dunno. The two meanings of the word "pole" in English are "stake, tall skinny tree, post" (think "flag pole"), and "pivot, center" (think "north pole").

Either one would be a likely candidate, but I suspect the "pivot" meaning, because one's analysis has to rotate around the pole when one is trying to do math in it's vicinity.

Dnia 29-03-2010 o 18:31:27 Tim Wescott napisa=B3(= a):

Maybe because modulus looks like steep hill. Matlab 'please forgive me' code:

%L=3D(0.3*(1.2-s)/(s^2+s+1)); used during my maximum modulus theorem fun= , =

one zero, two poles

h=3Dinline( '20*log10(abs(0.3* (1.2-Re+j*Im)/ ( (Re+j*Im)^2+(Re+j*Im) +1= ) )) =

','Re','Im'); ezmesh(h)

The term was in wide use in theoretical mathematics well before DSP (or indeed any signal processing) was practiced. See

Jerry

It's because EEs are lazy (*), and say "there's a pole at 1 kHz" rather than -1j kHz. A pole is an infinite singularity in the complex plane, and if you look at a 3-d plot of its magnitude vs x+jy, you'll rapidly see why it's called that.

Cheers

Phil Hobbs

(*) I hasten to add that we physicists are lazy too, but in different ways, e.g. our tendency to put gigaohm resistors on cables.

The question was *why* an infinite singularity is called a pole. It's a language question. There is a horticultural technique known as "layering". Someone who doesn't know the term is unlikely to guess what the technique is. I know the technique, but I don't how it got its name.

Jerry

I answered that. If you look at a 3-d plot, you'll see this big tall spike going off to infinity from a flat background. Looks just like, um, a pole.

Cheers

Phil Hobbs

That may be why you were told that a pole is called a pole -- it's what I was told, too.

But that may not _be_ why the word "pole" was chosen, and in fact that may not be the "pole" that was chosen at all. In the year 1000, budding astronomers were told that the planets were affixed to great crystalline spheres, but just because they were told that didn't make it so. Just because you and I were told -- by mathematicians and engineers, not etymologists, that this is so, doesn't make it so, any more than Copernicus being told that the planets were mounted on crystalline spheres made _that_ so.

Thanks for the replies everyone. I think Jerry and Phil are basically saying the same thing anyway. If you check the link Jerry provides (

), a pole is described as a singularity... that is, a tall skinny spike going to infinity. Looks like a ``pole'' to me.

Comment: I was being rather lazy when I posted my original question, and didn't look at my undergrad text, Feedback Control of Dynamic Systems by Franklin-Powell-Emami. In Ch. 3, Sec. 1.8 (pg 116 in the fourth ed.) there is a footnote that reads

`` The meaning of the pole can also be appreciated by visualized a three-dimensional plot of the transfer function, where the real and imaginary parts of s are plotted on the x and y axes, and the magnitude of the transfer function is plotted on the vertical z axis. For a single pole, the resulting three-dimensional plot will look like a tent with the ``tent-pole'' being located at the pole of the transfer function! '' (exclamation mark included in actual quote).

On one hand I should apologize for bothering everyone. On the other, now we all know!

Phil, did you ever see a pole with a base like that? My guess is that the answer lies in Latin, Greek, or even proto-European.

Jerry

It's OK to have one of these polarizing discussions now and then. :-)

Jerry

Well, it seems to have been introduced by Weierstrass,

and the idea of a pole as a centre of rotation was probably in there too. It's quite an evocative word now that I think of it.

Cheers

Phil Hobbs

The original term was "ausserwesentliche singulaer Stelle", literally "not-essential singular place", although "ausserwesentlich" translates literally to "outside of essential".

The French translation uses 'pole', which more or less means 'place', and comes close to "pole" as in "north pole" or "pole of attraction". It does not mean "perche", "long skinny thing that holds stuff up".

We are victims of the 19th century predilection of English speakers to think that anything French makes one insufferably cool, and to just adopt French words into English as if we were all still being ruled by Normans. Never mind that the four letters p-o-l-e already mean something in English -- we'll just adopt them, and expect folks to remember that we mean the French "pole ay".

Well, enough of this. I'm off to the new French restaurant in town: their chef is from France and can be exceedingly rude to Americans he thinks are pretentious. They've got a new dish on special today. It's called Frites de Merde du Chien. I have no idea what it is, but it's a French dish, so it has to be tasty!

Does he collect the morsels Fr: morceau) in the park? If I lived closer, I could add Mooch's contribution, but I doubt they would allow it through the mail.

Jerry

P.S. Is it served on a shingle?

The Middle Ages were actually pretty civilized and intellectually astute--within certain limitations, which were basically due to an exaggerated and uncritical respect for ancient authors of all sorts--pagan, Christian, and even Muslim.

The crystalline spheres were invented by Eudoxus, a follower of Plato, around 400 BC. And Copernicus didn't get rid of spheres and epicycles and so on, he just moved the centre of the Ptolemaic system to the Sun instead of the Earth.

Cheers

Phil Hobbs

I have read an article (or book -- dang my memory!) that made the point that the transition from the Middle Ages to the Renaissance happened because, in trying to revive the ancient knowledge, western culture managed to exceed it. The author's opinion was that at first, folks didn't realize they had done so -- and when they had, that's what _really_ spurred the Renaissance on.

The 'Renaissance' is really a creation of the 18th Century neoclassicists, who were one of those groups who think that They Know Best. They decided that Latin should be written and spoken as Cicero did, and as a result killed off what was then still a living language. (We suffer from similar busybodies today, but having by now completed the destruction of the humanities, they've moved on to science and politics.) Those folks lumped everything they happened to like under the term 'Renaissance', even though that allegedly coherent historical period was in the 14th Century in Italy and the 16th and 17th Centuries in England--a time span longer than the High Middle Ages.

They also tried to take credit for the 'revival of learning' which was actually due to the Turks having overrun the Byzantine Empire, burned the libraries, and pushed whatever was left of the learning of the ancient world westward into Europe.

Early modern times were just another unsettled period, albeit one in which both modern science and the modern 'occult' (magic and many other kinds of superstition) were born. Frequently it wasn't altogether clear which was which--Kepler cast horoscopes for part of his living, for instance--but it was very largely the real upswing in witchcraft, which was widely believed in at the time that was responsible for the early modern ('Renaissance') witch-burnings.

But don't get me started, or I might go off-topic. ;)

Cheers

Phil Hobbs

You're thinking of Merde sur le Toit -- that's next week's special.