Powers are algebraic expressions which are based on the idea of repeated products of some symbol with itself.

Example: the third power of x is x^3 = x * x * x.

This idea can be extended to fraction powers, so that x^(1/2) is equal to that y such that y^2 = x. Then more subtle trickery can be used to extend the idea of powers to irrational numbers.

In mathematics, this is a synonym for "exponent", as in "ten to the power of six" (10⁶, or 1,000,000) or "powers of ten".

There are three main types of power, described by where they derive from:

Positional power

Positional power, or authority, is the power to exert control over the behaviour or actions of another person. This type of power is conferred by a position or role within an organisation. People respond to this kind of power because the person exerting it is able, by virtue of what they are, and the role they fill, to direct the behaviour of others and to `punish' any resistance of the power. The use of this type of power is commonly associated with business managers, and authority figures such as policemen or teachers.

Personal power

Personal power or influence is the power to affect the behaviour of another person indirectly or intangibly. This type of power may be exerted by individuals irrespective of the position they hold or the authority they are able to wield. It is also often called charisma People respond to this type of power largely because they acknowledge the value of the relationship they have with the person exerting it, and understand that failing to respond may have a detrimental effect on that relationship. This type of power is associated with 'natural leaders' in all walks of society, but particularly with entertainers and politicians.

Knowledge power

Knowledge power is based in the expertise of the person using it. Like personal power it can be wielded by individuals with, or without any real authority, and it affects the behaviour and actions of others both directly, and indirectly through the application of reason and logic. People respond to this type of power because they accept the greater knowledge or experience the other person has gives them the right to guide the actions of others, in areas relating to their expertise. They are also inclined to listen to and emulate the expert out of respect for their expertise and success. This type of power is seen largely amongst scientists, sportsmen and specialists in all fields .

Michel Foucault's Five Postulates
On the Nature of Power
(pouvoir)

1: Power is not a "thing" -- it is exercised in an interplay of force relations. Power is not something you "hold," "take," or that can "slip away" from you. It is something that you are either exercising, or not.

2: All relationships are inherently power relationships. Power relationships result from divisions and inequalities that occur in other forms of relationships. Conversely, power relationships determine the divisions and inequalities which occur in these relationships. Power relationships are not primarily negative or restrictive, but rather they always have generative roles. In other words, every assertion of power actually establishes something, rather than repressing something, as we normally conceive.

3: Power comes from below, not from above. Power is not fundamentally about ruler vs. ruled, or even ruler:ruled. Rather, these distinctions are merely perpetuated in the power interplays which take form in the institutions of everyone's life of every class. Ongoing domination is merely the residual and cumulative effect of countless confrontations in everyone's life, every day.

4: Power relations have an objective intention all their own. All power relations are exercised to bring about certain aims and objectives. However, this is not because of the choice or decision of any one person or caste; rather, it simply happens that, as power relations cascade against one another, they form themselves into systems which are perfectly comprehensible. No one invents them; but from the smallest to the greatest scope, they fit into a clear tactical schema with decipherable goals and an almost inherent calculation.

Noder's Note: Although it's tempting to compare Foucault's conception of power to the functioning of an organism, this would be misleading -- not least because organisms themselves are constituted by complex systems of power relations. Organisms are constituted as by analogy with power, not vice versa. 5: Power always, and only ever, overcomes some form of resistance. The continuum of power revolves around innumerable resistances. Resistance is the atomic opposite of power. A resistance is the foil, target, adversary, or support of a certain power relation. Although the distribution of resistances through history is not homogeneous, with some eras and regions being notably more volatile than others, resistance is present everywhere, of some sort, to some capacity. Occasionally, this will manifest as a huge, society-wide bifurcation, but usually power cuts through and remoulds societal apparati, institutions, and even individuals.

Noder's Note: Of course, the idea of "resistance" vs. "power" is completely relative, since resistances themselves are constituted by, for, and within the continuum of power itself. In other words, resistance to power is a product of power.

Foucault's conception of power is clearly very different from the received opinion. Nonetheless, it is within this conception that Foucault mounts his analyses of history and society. His views are extremely compelling and intriguing; they force me to call into question the very idea of "The Man," the bourgeoisie, the proletariat, everything. There's no such thing as repression -- only a power matrix with a certain current.

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Although Foucault draws on these postulates throughout his career (especially towards the end, when they were more thoroughly formulated in his head), I'm condensing this stuff from:

Foucault, Michel. The History of Sexuality, Volume 1: An Introduction. Trans. Robert Hurley. Vintage Books, New York: 1978, pp 94-96.

Power is the rate at which energy can be utilized and work can be done. Mathematically, P = dW/dt. Power is not the same as energy; a truckload of wood and a tank of rocket fuel may have the same chemical energy, but the second can release that energy (when burned) at a much greater rate than the first, and hence provide more power.

The greatest power, however, is produced from nuclear reactions of the fission and fusion varieties, which release the binding energy of the nuclei themselves, rather than just the chemical bonds between molecules. In practice, of course, you'd want to limit the rate of the reaction by containing it in a reactor.

The SI unit of power is the Watt, defined as one Joule per second. This has almost totally replaced the old units of foot-pounds, but the power of American automobile engines is usually expressed in terms of horsepower, which can converted to SI units by 1hp = 746W. The idea of having "two hundred horses under the hood" seems "powerful" in the conventional sense and has a much greater appeal to American machismo than the geeky "kilowatts" used in Europe.

Electrical power can be expressed as current times voltage, P = IV, but voltage and current are also related by Ohm's Law,V = IR. Substitute the second equation in the first, and you get P = I²R. The power, or energy dissipated by whatever's carrying a current, is a function of the medium's resistance. Run electricity through something that's not a superconductor, and electrical energy will be converted to thermal energy and released. It'll produce heat which, depending on the situation, can be used to make toast, destroy a CPU, or turn the head of a condemned prisoner into something out of Ghost Rider. In this case at least, the political definition of a term (see item 5 in Cletus The Foetus' writeup above) very nearly matches the scientific definition.

Foucault formulates the analysis of power in two schemes: that of contract-oppression and domination-repression/war-repression. Contract-oppression is reminiscent of Hobbesian theory; a social contract is forged amongst a populace, and governing capacity is given to a sovereign leader. The sovereign is dependent upon the people because as leader he is made up of their expressed wishes; conversely, the people depend upon the sovereign for order. In this model, called the classic or juridical conception, power is of an economic nature. This means that power is taken to be a right, which one is able to possess like a commodity, and which one can in consequence transfer or alienate¹.

Power is generally of a binary nature, and its binary opposites are that of the powerful, and the subjugated. Foucault also refers to this dualism as that of the legitimate and illegitimate². This is the traditional mode in which we analyze power: we see a singular entity holding and wielding power, a massive collective which confers (by will or otherwise) power upon that entity, and both the entity and the collectivity are inextricably tied to one another.

The second schema is the domination/war-repression hypothesis. Where the first schema is more or less continuous and stable (the citizens are usually subject to the same conditions of law under any sovereign), the second schema appears to be rooted in uncertainty and displacement. It is not static, but rather is essentially active. Its nature is that of struggle and submission³. There are structures in place which define, identify, involve and place citizens (think of Louis Althusser's ideological state apparatuses) in such a way that they have to adhere to at least some social structures and become entangled in power relations. This is where the war analogy comes in; there is constant conflict between various agencies in which the only possible outcomes are dominance or submission.It is interesting to note that the two concepts are not entirely symmetrical, which may the be the impression that one gets at first glance. Repression is not abuse, like oppression, but is, on the contrary, the mere effect and continuation of a relation of domination.⁴

Again, we must remember as well, that while the contract-oppression schema denotes something of a binary relationship, the domination-repression schema represents multifaceted, oscillatory relations between social factions (who all are existing within a plethora of social structures). Foucault admits that while he has generally worked within the domination-repression thesis for several years previous to Two Lectures, it is not adequate for accurately portraying the reality of power struggles. This is because it does not reflect the social minutiae and micro-processes which cluster together to make the social webs and structures in which we live.

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¹Michel Foucault, Power/Knowledge, ed. Colin Gordon (New York: Pantheon, 1980) 88.
²Foucault, 92.
³Foucault, 92.
⁴Foucault, 92.

Power Factor

We were all¹ taught in the electicity module of our Physics class that:

P = VI (Power = Volts × Amps)

This is true, but with a clarification which is glossed over in all but the most advanced courses.

For AC power, I and V are vector quantities, not scalar. The peak current may not be drawn at the same time as the potential difference peaks, especially if the load is reactive, rather than just resistive.

Imagine two sine waves which may or may not be out of phase with each other. If the waves are in phase, then our P=IV equation holds. If the waves are exactly out of phase, then P=0. However much power we supply, no work will get done. All electrical equipment has a power factor between these extremes, with motors generally being worse than solid-state equipment.

This power factor is very important in machines which use a large amount of electricity; but can generally be ignored on small equipment. A low power factor means that the power station has to supply current at times when potential is low, and can damage their equipment. For this reason, large factories have to measure and declare their power factor.

Equipment Rating

Electrical equipment may be rated in one or more ways.

• VA (Volt-amps) - The peak voltage × peak current of the supply.
• W (watts) - The power dissipated within the unit. This can be useful for measuring the expected heat generated if you're designing an air conditioning system.

If the power factor is supplied, then one value can be deduced from the other.

W = PowerFactor × VA

If VA, but not the power factor is supplied, then we can still work out a worst-case heat dissipation; it will always be VA or better.

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¹ Those who took Physics, at any rate.

I thought I should read some of that Michel Foucault before writing this node, but really, that baldhead is really only stating some views that any gang member, politician or reader of Sweet Valley High can tell you. However, much like his less intellectual fellow travellers, he misses a point about power. That is, power can be divided into an effective sense, and a formal sense.

To say that "All people want power" in the effective sense is of course totally true. It is true because it is a tautology. If we define power as the ability to get what you want, then by definition everyone wants to be able to get what they want.

However, if we say that everyone wants formal power, the statement is much less convincing. Formal power means not that people want what they want, but that they want to be able to get things they theoretically want. At this point, it is not the desired object or situation that is important, but the the theoretical mastery over any given object of situation. People who would be heavily interested in this would mostly be doing it from a psychological standpoint, because they are psychologically immature. What formal power can mean is so many things: having people address you as sir, being able to write your name on things, being able to press little buttons that relate to imaginary points on a website, or else just having a nice, big mahagony table to pound your gavel on. Formal power can be everything from a mild comfort to a total obsession for people. For most people it lies somewhere inbetween.

That formal power is not always important to people can be seen in many situations. One of the reason politics goes as it does is that people don't really care about the forms of power, who is making the decisions, as long as those decisions go their way, and they get what they effectively want. Also, for that matter, if we look at BDSM, people can find being on the other end of a formal power situation quite pleasurable, because they have not actually lost any effective power.

Of course, the vortices of the two types of powers and other human goals, such as sexuality, economy and self-esteem are not at all straightforward; but that just furthers my point that to say "people seek power" is such a generalization to be meaningless.

History is littered with those who have had great power (Alexander the Great and his empire), those who wanted to define it (Machiavelli in "The Prince"), and even some who have been forced to relinquish it (George W. Bush while undergoing a colonoscopy).

Few have come to realize the before you get the power, you must first get the sugar (C₆H₁₂O₆). Known to the science community as glucose - and to a few as white gold or Texas tea . . . sweetener - this compound, if properly used, can be a significant source of energy (roughly 30 ATP, which is worth roughly 1,600 kcal/mol) and, thus, power. One only needs to employ the intricacies of cellular metabolism.

What to do with all