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 .

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.



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.


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 this power? A good, albeit fragmented, question that has plagued many people. You could take over Europe, force the computer age to abide by your rules, go after the dictator that had the audacity to threaten your father’s life, or maybe demand and endless supply of Mallomars (yummy!). But in the end, all of this will at best chip away at that personal void you’ve attempted to fill.

Well, friend, that’s because chain of events isn’t yet over. For, you see, the next logical step after getting the power is getting (you guessed it) the women. This step should really take car of itself, as can be seen in the Gibb’s Free Energy equation:

G = H – TS

Where G = your unattractiveness towards women.

H = a cosmological constant which stands for the average man’s attractiveness to the average woman. Its value is exactly . . . 3.

T = your amount of power in telomeres. To calculate this, hold your hands in front of you, perpendicular to your chest, and the move them away from each other until they are at a distance which you feel represents the amount of power you have from converting so many pounds of sugar. Make sure to have a friend measure this as it is quite difficult to gauge the distance while maintaining the proper gap.

S = penis size

The lower your value of G, the greater your affinity to women.

Use this information as wisely as I have and you will soon be sleeping on top of large piles of money with many beautiful women.

Pow"er (?), n. Zool.

Same as Poor, the fish.

 

© Webster 1913.


Pow"er, n. [OE. pouer, poer, OF. poeir, pooir, F. pouvoir, n. & v., fr. LL. potere, for L. posse, potesse, to be able, to have power. See Possible, Potent, and cf. Posse comitatus.]

1.

Ability to act, regarded as latent or inherent; the faculty of doing or performing something; capacity for action or performance; capability of producing an effect, whether physical or moral: potency; might; as, a man of great power; the power of capillary attraction; money gives power.

"One next himself in power, and next in crime."

Milton.

2.

Ability, regarded as put forth or exerted; strength, force, or energy in action; as, the power of steam in moving an engine; the power of truth, or of argument, in producing conviction; the power of enthusiasm.

"The power of fancy."

Shak.

3.

Capacity of undergoing or suffering; fitness to be acted upon; susceptibility; -- called also passive power; as, great power of endurance.

Power, then, is active and passive; faculty is active power or capacity; capacity is passive power. Sir W. Hamilton.

4.

The exercise of a faculty; the employment of strength; the exercise of any kind of control; influence; dominion; sway; command; government.

Power is no blessing in itself but when it is employed to protect the innocent. Swift.

5.

The agent exercising an ability to act; an individual invested with authority; an institution, or government, which exercises control; as, the great powers of Europe; hence, often, a superhuman agent; a spirit; a divinity.

"The powers of darkness."

Milton.

And the powers of the heavens shall be shaken. Matt. xxiv. 29.

6.

A military or naval force; an army or navy; a great host.

Spenser.

Never such a power . . . Was levied in the body of a land. Shak.

7.

A large quantity; a great number; as, a power o good things.

[Colloq.]

Richardson.

8. Mech. (a)

The rate at which mechanical energy is exerted or mechanical work performed, as by an engine or other machine, or an animal, working continuously; as, an engine of twenty horse power.

⇒ The English unit of power used most commonly is the horse power. See Horse power.

(b)

A mechanical agent; that from which useful mechanical energy is derived; as, water power; steam power; hand power, etc.

(c)

Applied force; force producing motion or pressure; as, the power applied at one and of a lever to lift a weight at the other end

.

⇒ This use in mechanics, of power as a synonym for force, is improper and is becoming obsolete.

(d)

A machine acted upon by an animal, and serving as a motor to drive other machinery; as, a dog power

.

Power is used adjectively, denoting, driven, or adapted to be driven, by machinery, and not actuated directly by the hand or foot; as, a power lathe; a power loom; a power press.

9. Math.

The product arising from the multiplication of a number into itself; as, a square is the second power, and a cube is third power, of a number.

10. () Metaph.

Mental or moral ability to act; one of the faculties which are possessed by the mind or soul; as, the power of thinking, reasoning, judging, willing, fearing, hoping, etc.

I. Watts.

The guiltiness of my mind, the sudden surprise of my powers, drove the grossness . . . into a received belief. Shak.

11. Optics

The degree to which a lens, mirror, or any optical instrument, magnifies; in the telescope, and usually in the microscope, the number of times it multiplies, or augments, the apparent diameter of an object; sometimes, in microscopes, the number of times it multiplies the apparent surface.

12. Law

An authority enabling a person to dispose of an interest vested either in himself or in another person; ownership by appointment.

Wharton.

13.

Hence, vested authority to act in a given case; as, the business was referred to a committee with power.

Power may be predicated of inanimate agents, like the winds and waves, electricity and magnetism, gravitation, etc., or of animal and intelligent beings; and when predicated of these beings, it may indicate physical, mental, or moral ability or capacity.

Mechanical powers. See under Mechanical. -- Power loom, ∨ Power press. See Def. 8 (d), note. -- Power of attorney. See under Attorney. -- Power of a point (relative to a given curve) Geom., the result of substituting the coordinates of any point in that expression which being put equal to zero forms the equation of the curve; as, x2 + y2 - 100 is the power of the point x, y, relative to the circle x2 + y2 - 100 = 0.

 

© Webster 1913.

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