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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

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