As is often noted, the map is not the territory.[1] But what is usually missed is that, when we attempt to think of how they differ, we most often slip into specifics such that what we really compare is not the map with the territory, but the thing first recognized to be a map with a mental map of the territory.

Our efforts to think about how models differ from reality are usually likewise characterized by comparisons between some model and some other model not recognized to be a model. When we abandon specifics, and attempt to think of reality in the abstract, we almost always think of what amounts not to reality but to a hypothetical, unknown, perfect model of reality.

[1] with Alfred Habdank Skarbek Korzybski being the first to put it just that way

In ordinary discussion of limitation on the time that a political office may be held, two points are not made directly as often as they should be.

Opponents of term limits should not contrast the outcomes expected to obtain under term limits with those imagined to result under an idealized representative government. Ostensibly representative government is regularly not very representative; many participants in the political process — including individual voters — work actively to subvert the extent to which it is representative; and it can never be close to being perfectly representative. Illustrating the first of these points, note how often most voters feel compelled to select a least detestable candidate amongst a field of knaves and of fools, and note that major programmes opposed by a majority of voters are adopted by legislatures. Illustrating the second point, note people who vote in open primaries of the party they disfavor, hoping to effect selection of a weaker candidate for that party. To understand the third point, consider what would be required to select representatives whose preferences operationally mirrored those of the more general public.

Term limits change the incentive system for political officials and for would-be political officials. They can no longer make life-time careers in holding one office. If meaningful term-limits became the norm across all elected offices, it would no longer be practical for the typical elected official to make a life-time career of holding a series of elected offices. Those who held office would be less beholden to political machines and cartels, they would have less to sell, they would have to be proficient at more than office-seeking. More of them would be more representative than now, albeït still quite imperfectly so.

I'm engaged in a fight with a corporation[1] in which I note its agents practice two, somewhat intertangled behaviors which are common to large or corporate enterprises, but which should be opposed whenever encountered.

The first of these is for the agent of the enterprise to confuse his or her rôle. For example: I gave agents of this corporation the same information repeatedly in the course of one phone call. In a later phone call, I told another agent that I'd given that information to you repeatedly, to which the agent replied, as if I were delusional, that she had never spoken with me before. This might be read as deliberate or incompetent misunderstanding of the word you (which of course must serve as a plural as well as a singular[2]), but it fits another pattern, in which the agent speaks as representative when it suits his or her immediate purpose, but instead as just an individual when that immediate purpose changes, and in which the agent doesn't announce changes in the entity for whom he or she speaks. I immediately told the agent in this case that, since she was representing the corporation in the conversation, you are the corporation, and that since I'd repeatedly given the information to the corporation, I had repeatedly given it to you.

The second behavior is to confuse endogenous policy with necessity, to represent the association as unable to do something simply because they have made a deliberate habit of not doing it. Actually, one sees people in general, in or out of a corporate frame-work, doing attempting this confusion. But the misrepresentation is more likely to be effective in the context of a formal, multi-personal institution, and the word policy is more likely to be invoked as if it represents something endogenous and fixed. (Does one often hear a neighbor insist that keeping his dog out of one's garden would be against policy?) And the misrepresentation is even more effective when the agent of the institution confuses the issue of whether he or she is speaking for the corporation or for his- or herself. Speaking for myself, I don't let an individual or association pretend that its chosen policy is not a choice, and I don't let the agents of an association off the hook of being its representatives when they try to claim that something cannot be done because it is against policy.

[1] Sprint Nextel Corporation.

[2] In standard English. And I'm not about to adopt y'all or youse or even you guys to humor a corporate agent.

A while back, I got a copy of Circuit Analysis by Robbins and Miller, to review material that I'd forgot, and to fill-in lacunæ here and there. On the whole, I think that it's a pretty good book, though somewhat slow-moving for my tastes.

But to-day I hit a passage that bugs me:

Although we use phasors to represent sinusoidal waveforms, it should be noted that sine waves and phasors are not the same thing. Sinusoidal voltages and currents are real — they are actual quantities that you measure with meters and whose waveforms you see on oscilloscopes. Phasors, on the other hand, are mathematical abstractions that we use to help visualize relationships and solve problems.

Okay, now, for those of you unfamiliar with phasors, these are two-dimensional vectors or complex numbers whose magnitude corresponds to the amplitude of a sinus wave, and whose direction corresponds to the phase of the wave. In the case of a wave with an amplitude of 1 unit, a phasor would be a radial line on a unit circle, bearing the familiar relationship to a sine wave.

There is an isomorphism between the set of phasors and any representation of sinus waves. That is to say that for every representation of sinus waves and operations thereüpon, one can find equivalent phasors and operations thereüpon, and vice versa, such that a one-to-one correspondence between operands and results is maintained. From the perspective of mathematics, a phasor just is a representation of a sinus wave.

This last point does not contradict what Robbins and Miller have said, but now consider how and why we see wave-forms on an oscilloscope. The most familiar graphical representation of sinus waves looks very much like some of the waves that we observe in water, but electricity isn't water. We cannot look at an ordinary circuit and see its voltage or current; instead, we use devices whose visible behaviour changes to represent voltage or current. These devices might represent that behaviour in various ways; the ways in which they do are determined by various cost considerations (including cultural expectations).

An oscilloscope is designed to present a particular sort of graphical representation of wave-forms. It could instead be designed to present a different sort of graphical representation. If it only had to represent sinus waves, then it could do this with stable phasors. And if it had to represent non-sinus waves, then it could perhaps do this with time-varying phasors (giving the viewer an animated Fourier analysis), though I don't know that this would be as helpful to us.

The representation of the oscilloscope is a map. As Korzybski noted, the map is not the territory. The phasor is not the voltage or the current, but neither is the representation on the oscilloscope; neither is more or less real than is the other.