Welcome to European Tribune. It's gone a bit quiet around here these days, but it's still going.
Display:
European Tribune - Positive & Negative
My question to ETers is:

Can anyone offer me a mental model such that when I see

+

I don't immediately think, "Ah!  That's the positive sign--two plus two equals five, etc.--so something positive is going on, which means some addition is happening". . .

(An atom becomes positively charged when it loses an electron)

And if I see the following sign:

-

I don't think "Ah!  Take something away!"

(An atom becomes negatively charged when it gains an electron)

Like your friend said, your problem is that you need to eliminate any moral associations from the operation of addition. Maybe the history of the concept of Electric charge might help?
One of the foremost experts on electricity in the 18th century was Benjamin Franklin, who argued in favour of a one-fluid theory of electricity. Franklin imagined electricity as being a type of invisible fluid present in all matter; for example he believed that it was the glass in a Leyden jar that held the accumulated charge. He posited that rubbing insulating surfaces together caused this fluid to change location, and that a flow of this fluid constitutes an electric current. He also posited that when matter contained too little of the fluid it was "negatively" charged, and when it had an excess it was "positively" charged. Arbitrarily (or for a reason that was not recorded) he identified the term "positive" with vitreous electricity and "negative" with resinous electricity. William Watson arrived at the same explanation at about the same time.

We now know that the Franklin/Watson model was fundamentally correct. There is only one kind of electrical charge, and only one variable is required to keep track of the amount of charge.[2] On the other hand, just knowing the charge is not a complete description of the situation. Matter is composed of several kinds of electrically charged particles, and these particles have many properties, not just charge.

The problem was that Franklin made the wrong choice of sign: ordinary moving charges are negative charges, so when there is electrical current going in one direction the actual charge carriers are moving in the opposite direction... In fact, the only way to determine the sign of the fundamental moving charge is the Hall effect
The Hall effect refers to the potential difference (Hall voltage) on the opposite sides of an electrical conductor through which an electric current is flowing, created by a magnetic field applied perpendicular to the current. Edwin Hall discovered this effect in 1879.[1]
Of course, life is never that simple and there are some substances in which the elementary charge carriers are positive (the conductor then displays an anomalous Hall effect). In fact, electric current is not carried by particles at all, but by quasiparticles.
In physics, a quasiparticle refers to a particle-like entity arising in certain systems of interacting particles. It can be thought of as a single particle moving through the system, surrounded by a cloud of other particles that are being pushed out of the way or dragged along by its motion, so that the entire entity moves along somewhat like a free particle. The quasiparticle concept is one of the most important in condensed matter physics, because it is one of the few known ways of simplifying the quantum mechanical many-body problem, and is applicable to an extremely wide range of many-body systems.
The again, I think your psychological hangup is with the aritmetical operation of addition, and with negative numbers. So leave 20th century chemistry aside for a while and let's consider why you have a problem with renaissance-time negative numbers. Given that you want to do things in a logical as opposed to historical way, maybe we need to do Galois theory for dummies to eliminate the psychological hangup about negativity.

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris
by Migeru (migeru at eurotrib dot com) on Sat Mar 22nd, 2008 at 02:19:13 PM EST
I gave Galois theory a quick google and....it looks way out of my league, but if you can create a dummies version--I'm all for it!

Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Sat Mar 22nd, 2008 at 05:22:00 PM EST
[ Parent ]
At the moment your comment is the only text containing the string "quantum" -- and in a quotation, at that. Enough with the negatives, let's move on to the imaginaries!

Words and ideas I offer here may be used freely and without attribution.
by technopolitical on Sun Mar 23rd, 2008 at 01:33:14 AM EST
[ Parent ]
Actually, you can do a lot of quantum mechanics in an arbitrary Rig (Ring without negatives). And a lot of graph theory and statistical mechanics and is also quantum mechanics in a Rig.

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris
by Migeru (migeru at eurotrib dot com) on Sun Mar 23rd, 2008 at 08:14:53 AM EST
[ Parent ]
Ack. Semirings. Yet another bunch of algebras I didn't know about (as such). Now you've made me curious:
  • "A lot of quantum mechanics" omits what?
  • An "arbitrary rig", not non-negative reals? (Is this all about counting states, not describing them or their transitions?)
  • Do you intend that "a lot of graph theory and statistical mechanics and is also quantum mechanics in a Rig" be read as saying that "a lot of graph theory...is also quantum mechanics"?
  • Are complex numbers uniquely necessary for quantum mechanics, or just a convenience?
  • Why do I keep reading about so many mathematical structures that I can't remotely claim to understand?
  • How can anyone (other than a Republican) still support the Clinton candidacy?
I see that Baez has (of course) touched on some of the earlier questions in this list.

Words and ideas I offer here may be used freely and without attribution.
by technopolitical on Sun Mar 23rd, 2008 at 03:12:24 PM EST
[ Parent ]
Well, where do you think I got this stuff from? You think I invented it?
  • "A lot of quantum mechanics" omits squaring the result to get a probability.
  • There are more Rigs that just the nonnegative reals, basically subsets (closed under addition and multiplication) of matrices with nonnegative real entries.
  • No, I intend to say that the mathematical structure of flow in networks, of minimal paths in networks, of statistical mechanics at finite and zero temperature, and quantum mechanics, is that of combinatorics on Rigs.
  • I have no idea whether complex numbers are necessary for quantum mechanics, but given their algebraic completeness once you have characteristic zero you might as well assume your Rig consists of matrices with complex entries. I guess, for convenience.
  • Where do you keep reading about mathematical structures you can't remotely claim to understand?
  • There will always be people who identify with her over the other candidates.
BTW, did you get my e-mail?


It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris
by Migeru (migeru at eurotrib dot com) on Sun Mar 23rd, 2008 at 03:25:34 PM EST
[ Parent ]
After reading a bit on the web, I assumed that you had invented this stuff at a time when you were incredibly young, but gotten no credit. The sufferings of genius.

  • "'A lot of quantum mechanics' omits squaring the result to get a probability." Fair enough, but with a chemical mindset in this diary, one would miss having wavefunctions and amplitudes. On the other hand, given the vast amount of quantum mechanics, I suppose that omitting lot leaves a lot that is not omitted. Just not the sort of QM that I crunch on this machine.

  • "There are more Rigs than just the nonnegative reals..." Indeed, and some of them are, well, cheesy. (To speak non-technically for a moment.) At the bottom of the barrel, "The simplest example of a semiring which is not a ring is the commutative semiring B formed by the two-element Boolean algebra," and nearby are other lame Rigs mentioned in Wikipedia

  • "Where do you keep reading..."? TWF, of course, for starters!

  • "No, I intend to say..." What you say is, I expect, entirely correct and, in principle, enlightening.

Re. your e-mail: Did you get my response? After the conversation I promised, she suggested considering citizen sector options, and minimizing the gap, on strategic/marketing grounds.

Words and ideas I offer here may be used freely and without attribution.
by technopolitical on Tue Mar 25th, 2008 at 02:46:22 AM EST
[ Parent ]
  • You still get "diffusion of states" and "probability densities", just not wave propagation (you need i for that, I think).
  • What can I say, mathematicians tend to use lame examples when asked to make arcane structures concrete. I think matrices or nonnegative reals are a better meta-example, with the advantage of being universal.
  • TWF? I can't be held responsible for that.
  • "You expect" and "in principle"? Ask some questions!
I replied to your e-mail.

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris
by Migeru (migeru at eurotrib dot com) on Tue Mar 25th, 2008 at 09:32:58 AM EST
[ Parent ]
Technically, you could do away with i entirely in QM and not lose generality. But then you'd be stuck with 4th order differential equations. At least that's what one of our Optics profs claimed. I never checked myself, because you do not want to do 4th order PDEs anyway, unless you're a mathmatician or some (other) kind of masochist.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Tue Mar 25th, 2008 at 02:41:11 PM EST
[ Parent ]
Well, a complex differential equation can always be written as a real differential equation of twice the order.

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris
by Migeru (migeru at eurotrib dot com) on Wed Mar 26th, 2008 at 03:07:01 AM EST
[ Parent ]
maybe we need to do Galois theory for dummies to eliminate the psychological hangup about negativity.

I was thinking more along the lines of a short course of Jungian analysis  ;)

by Sassafras on Sun Mar 23rd, 2008 at 04:02:11 PM EST
[ Parent ]

Display:

Occasional Series