The simple statement of "1 + 1 = 2"... when used as a metaphor describing a formula of government, reflects a dictatorship. Each symbol has an identity and only that identity. Within the context of the statement as it is written, the identities do not change. There is no compromise, no digression, no variance, no no diplomacy and no Anarchy, Communism, Corporatocracy, Democracy, Libertarianism, Oligarchy, Socialism, or any other strictly defined model of government. "It is what it is" as some people are given to say.
It is a metaphor that can be used as an analogy for those interested in attempting some means to think outside the conventional boxes of discussing types of government without reducing them to a discussion of political personalities with respect to any particular nation's current governing practices. It is a valid representation because so much of our lives are micro-governed by the application of numbers. For example, we use numbers for social security designations, badge numbers, employee numbers, telephone numbers, payment schedules, time card calculations for purposes of pay, vacation, and other benefits. We use numbers to schedule medical appointments, recreation times, and how much to spend for food, utilities, gasoline, repairs, etc... In short, our lives are suffused with numbers by which our behavior is dictated to abide by, or else find ourselves in possible problems, such as not having enough money for rent or food because we choose to violate the rules of the assigned dictatorship in order to splurge on something else.
When we live our life by having to comply with the assumed necessity to have a certain credit score, live within a given zip code or a house costing a minimum amount of money; we are living according to the rules of a particular type of dictatorship. While some abide by a strict adherence to a given code of dictatorship where a person feels they must obtain and own a particular "score" (cost of home, car, clothes, etc.,) or social position which attached to various types of scores involving monetary numerical values; others incorporate an ability to practice one or another type of personalized government within the dictatorship. In other words, they want to be able to give the impression of abiding by a strict dictatorial rule, yet be granted a means to effect periodic expressions of Anarchy, Communism, Democracy, Socialism, etc...
People like to be allowed to conduct themselves within the structure of game rules but also cheat. The U.S. government, like so many other governments, is a system by which certain types of cheating are controlled, yet those that make the rules provide provisions that enable some people to cheat by using such rules. Typically, they are referred to as lawyers or accountants. When laws or policies become so restrictive that no one is enabled to cheat, there are those who want to either install a politician who will permit the practice of cheating by altering (such as relaxing) government restrictions; or will resort to some other means such as instigating a national or international conflict in an attempt to force restrictions to be removed. Nonetheless, even when a Nation is embroiled in a war, the presumed disarray of combat conditions is itself another form of dictatorship, though some readers may prefer to label it a monarchy.
Military organizations and activities are largely the functionality of a Communism, with its military posts (bases) seen as communal settings practicing various expressions of Socialism, as are described in the following list:
The military is not the practice of a Democracy, easily noted because no elections for leadership are ever undertaken. And it is of interest to point out that the so-called great and wonderful Democracy being hailed as a one-of-a-kind angelically guarding system of government in America is an illusion, because it actually is a spinelessly degenerate individual (a skeleton), since it needs to be protected by a Communistically run Socialist Military institution. However, it is not fair to describe the purported Democracy of America as a skeletal figure since an Actual Democracy doesn't exist. The problem with many people and their offense to any (other than a democracy) labeled government, is that they don't really know what an Anarchy, Communism, Socialism, etc., is... including a Democracy. They generally assume that the type of government practiced by America, Canada, United Kingdom etc., represents a true democracy... when they actually don't. They think that such governments are reflected in the "1 + 1 = 2" equation, and that such a situation reflects the meaning of a Democracy..., even though Democracy is presently practiced as an illusion, (as the counterpart in a dichotomy between illusion and reality).
But the equation and its symbols are made up. They represent an attempt at understanding, designing and repeating an order.... a particular arrangement that is presented by someone who expects others to accept and agree with. While you may think outside the order as an expression of creativity, originality or genius, you must nonetheless tether your belief in this system as the one and only foundation of all truth. Even if you devise a new type of mathematics, it must comply with the fundamental truth of "1 + 1 = 2", or it is wrong. It is this equation which all mathematics must prove themselves. A presumed truth, or belief, is a dictatorship... at least until such time as a different type of thinking comes along and views it as a mistake, or but a part of a larger, more fundamental truth.
And the truth of the matter that it is foolish to think in terms of an "absolute" or "universal", since humans are adaptable organisms that must strive for some semblance of equilibrium in whatever environmental circumstances prevail. One's "truth", or at least belief there in, is tied to one's efforts for establishing and maintaining some level of relevant equilibrium in the conditions to which it is exposed. In other words, many (if not all) of the so-called truths (beliefs) may only be as valid as the environment to which they were generated in. Truth is a dictatorship that we try to undermine and cheat by creating alternative rationalizations to the beliefs once used to validate our previous acceptance of the truth.
So, we might ask... what then is the equation that would best represent a Democracy (or Anarchy, or Communism, or Socialism, or...)? But in order to construct such an equation, it may be necessary to first describe what a Democracy is... or at least isn't. Since we humans do not routinely practice a democracy in how we interact with others or larger world of both animate and inanimate objects; would we even be able to recognize a mathematically illustrated democracy? Surely one would not describe democracy by writing an equation which illustrates the low percentage of voters who participate in an election, much less the Electoral College. But perhaps more to the point, is there a mathematical equation that could illustrate an Actual Democracy?
If we are one who thinks that society (and hence, humanity) would be better if it was run like a "1 + 1 = 2" equation, are we thinking in terms of an analog array of variable statements, or as digital series of invariable discrete units? Will we force ourselves to abide by a given type of mathematics because it corresponds best to a social structure involving the application of the electron (electricity), or prefer to abide by a social structure that relies on a non-electronic dominance? Or perhaps you would prefer an admixture, thereby creating conditions for social oppositions? Thus, many of our social conflicts are derived from a situation involving those who use a heavy application of electrical components, and those that have a light application thereof... like the conflicts between a horse and buggy and automobile cultures?
Along with trying to devise an equation that might best illustrate a Democracy, we might also strive to devise one which best describes Capitalism. Thus, we come to a situation in which we may want to rely on text-book supplied definitions, even though our own analysis may view such descriptions as being very narrow. The definition of a topic that we are trying to describe analogically, may be written out (or verbalized) in a digital manner. It presents us with a dilemma in that it is like trying to describe Direct Current with Alternating Current, or vice versa, and not using the other as part of the explanation. Whereas, analogically speaking, we can describe a "3" as analogous to three "1's", but digitally speaking, they remain separate (discrete) identities whose "personality" changes according to their placement in a series (repetition). Hence, the statement "01" is different from "10", and "010101" is different from "001001001", though the "0" and the "1" have the same individualized appearance and capacity.
By increasing the population of "0s" and "1's" (let us say females and males); we can have clones that function differently when placed into a group. Hence, a Communism (commonism) is effected in order that the applied usage of the 0s and 1s (in electronic programming), is made more efficient... but demands that this type of governing system remains in tact in order that the commercial enterprise of the electrical component system (computer usage) can be maintained. In order to make the system more efficient and profitable, the human component is forced to serve it, and not the other way around. The lives of people are forced to comply by arranging their perceptions and views so as to validate the system as being the best... and what is thus best for humanity. Those who don't fall into line with the convention, are troublemakers, eccentrics, heretics, miscreants, anti-social, deviant, etc... However, if a new industry arises, as previous industries in history have been supplanted by the development of others, those holding onto beliefs that were developed over many decades by living under the conditions of an older industry; are now viewed as being out of step, out of fashion and perhaps even out of their minds for not wanting to accept the new way of thinking... which may be illustrated as:
...or some other thought-to-be correctness (even though many readers will nonetheless be oblivious to the recurring usage of a "three"-based compartmentalization that is better understood if one reviews the concept of threes at Threesology Research Journal.
Our present usage of Capitalism is not conducive to the development of an Actual Democracy, Communism, nor Socialism... But it's not that Capitalism is bad, it's simply in how it is employed and for what purposes. Beating up on Capitalism doesn't solve human social problems, when many of them are caused by a deteriorating environment caused by the natural processes of planetary, inter-planetary, galactic and Universe decay that are beyond humanity's ability to do anything about except leave the influence thereof by leaving the planet, solar system and galaxy. Because Capitalism is frequently used in ways that cause human suffering, the recurring usage of such an application becomes translated into the dominant definition that achieves an unwarranted solidification when textbook after textbook after dictionary after encyclopedic description says the same thing. Such a recurrence sets up the situation for a self-fulfilling prophesy, whereby Capitalism functions in the way it does because it becomes leashed to a standardized definition that no one tries to alter; and because of which is developed social theories which condemn Capitalism and think to solve social problems if it is (presumably) extricated from social practices.
The problem with this logic is that all forms of commercial governance rely on some model of bartering, of give and take... that may evolve into an enterprise which acquires a sophistication described as THE definition of Capitalism, because those who use it typically engage in a formula that games the system of bartering to favor them. It doesn't have to be this way, but this is the way it is employed by those who will use any method at their disposal to effect this way as the standard by which everyone must play their desired game of commercialization... and they don't care how you define it, or what philosophical brand of logic is used to describe it. By any other name (like Shakespeare's commentary on a rose), Capitalism is the name being applied to a given type of bartering system though the word can just as easily apply to other models of give and take. If you would choose another name to be used to describe current practices of commercialized bartering, what would it be? And for that matter, what mathematical equation would you use if this were the preferred language to communicate with?
Alternatively, in looking at the "1 + 1 = 2" equation, could you use it to describe other human behavior? Whereas it may not be used to describe a male and female couple that produce a baby, it could be used to crudely describe a homosexual or lesbian "relationship". And if one permitted a liberal usage of the numerical symbols to be flexibly variant, any number of associations might be illustrated. Yet, would it realistically describe a democracy? Or is the usage of a mathematical language as a requirement reveal yet another dimension of a dictatorship? If you MUST use a mathematical statement and MUST do so in a particular fashion, and/or Must define it in a certain way, is this not a dictatorship even if a central human figure is seemingly absent? And yet, if we assign any particular definition to anything, is this the practice of a dictatorship... including the usage of the word "dictatorship" in the present context, even though in a philosophical topic as the present one, it has been appropriated from is typical subject area?
Is the definition of a "dictatorship" more rigid than a definition of Communism, Theology, Democracy, Socialism, etc., and thus makes it easier to illustrate with a mathematical statement? And... in order to adequately illustrate the different types of Communism, Democracy, Socialism, etc., we might want to employ an Algebra, geometry or Calculus? Here are some general references to these three types (means) of organizing one's ideas/perceptions:
The principal distinguishing characteristic of algebra is the use of simple symbols to represent numerical quantities and mathematical operations. Following a system that originated with the 17th-century French thinker René Descartes, letters near the beginning of the alphabet (a, b, c,…) typically represent known, but arbitrary, numbers in a problem, while letters near the end of the alphabet, especially x, y, and z, represent unknown quantities, or variables. The + and - signs indicate addition and subtraction of these quantities, but multiplication is simply indicated by adjacent letters. Thus, ax represents the product of a by x. This simple expression can be interpreted, for example, as the interest earned in one year by a sum of a dollars invested at an annual rate of x. It can also be interpreted as the distance traveled in a hours by a car moving at x miles per hour. Such flexibility of representation is what gives algebra its great utility.
John L. Berggren: Professor of Mathematics, Simon Fraser University, Burnaby, British Columbia. Author of Episodes in the Mathematics of Medieval Islam.
Source: "Algebra, Elementary." Encyclopædia Britannica Ultimate Reference Suite, 2013.
The branch of mathematics concerned with the shape of individual objects, spatial relationships among various objects, and the properties of surrounding space. It is one of the oldest branches of mathematics, having arisen in response to such practical problems as those found in surveying, and its name is derived from Greek words meaning “Earth measurement.” Eventually it was realized that geometry need not be limited to the study of flat surfaces (plane geometry) and rigid three-dimensional objects (solid geometry) but that even the most abstract thoughts and images might be represented and developed in geometric terms.
J.L. Heilbron: Senior Research Fellow at the University of Oxford, England. Author of Geometry Civilized and The Sun in the Church among others.
Source: "Geometry." Encyclopædia Britannica Ultimate Reference Suite, 2013.
Branch of mathematics concerned with the calculation of instantaneous rates of change (differential calculus) and the summation of infinitely many small factors to determine some whole (integral calculus). Two mathematicians, Isaac Newton of England and Gottfried Wilhelm Leibniz of Germany, share credit for having independently developed the calculus in the 17th century. Calculus is now the basic entry point for anyone wishing to study physics, chemistry, biology, economics, finance, or actuarial science. Calculus makes it possible to solve problems as diverse as tracking the position of a space shuttle or predicting the pressure building up behind a dam as the water rises. Computers have become a valuable tool for solving calculus problems that were once considered impossibly difficult.
John L. Berggren
Source: "Calculus." Encyclopædia Britannica Ultimate Reference Suite, 2013.
But both simple and complex thinking is not constrained to being illustrated with mathematics, though it is often used because it affords a person (and computers) an ability to think in complex terms with simple expressions that provide a means of analyzing lots of information that would otherwise be too cumbersome if it retained a word-only identity. Such thinking can be found in all subject areas (including the various arts), though in many instances, advanced researchers (practitioners) get caught up in the seemingly infinitesimally occurring variables (called minutiae) that entangle them in a geometry of analogy in which they set up camp... thinking they are on the trail of some treasure trove. While this is of interest in that they join in the journey, some readers are not familiar with those researchers who use metaphor and analogy as a tool by which they doodle while thinking in a wholly different language. Analogy and metaphor are themselves, types of mathematical tools as long as one does not permit oneself to be tethered to conventions of dictionary, or encyclopedia-described definitions... even when they are suggestively focused on presenting a diversity of consideration. Such "diversities" nonetheless involve dictator-like constraints, though one must have ventured their courses in order to denote their dead-ended approximations of a supposed greater universality.
(from Greek ana logon, “according to a ratio”), originally, a similarity in proportional relationships. It may be a similarity between two figures (e.g., triangles) that differ in scale or between two quantities, one of which, though unknown, can be calculated if its relation to the other is known to be similar to that in which two other known quantities stand. Thus, if 2:4::4:x, it can be seen that x = 8. Another form of analogy noted by the Greeks is that of inferring similarity of function, known as “educing the correlate.” Aristotle (Topics, i, 17) stated the formulas of these two kinds of analogy: “As A is to B, so C is to D”; and “As A is in B, so C is in D.”
Plato employed a functional analogy when he argued that the Idea of the Good makes knowledge possible in the intelligible world just as the Sun makes vision possible in the perceptual world. Here a relationship not yet understood is analogous to one already familiar.
In the European Middle Ages it was believed that the universe forms an ordered structure such that the macrocosmic pattern of the whole is reproduced in the microcosmic pattern of the parts so that it is possible to draw inferences by analogy from the one to the other. Thus, the law of nature conceived in the juridical sense, which prescribes the fitting order of human relationships, could be assimilated to the physical sense of law, which describes the order obtaining in the natural world. Because the natural world exhibits hierarchical degrees of subordination, it was argued, human relationships should also exhibit such subordination. Such parallels were held to constitute arguments and not merely allegorical illustrations; it was contended, for instance, that, as there were two luminaries to light the world and two authorities set over man (the papacy and the empire), then, as the Moon's light is reflected from the Sun, so the imperial authority must be derived from the papal. Dante, in his De monarchia (c. 1313), while claiming that it is light and not authority that the empire derives from the papacy, nevertheless accepted the principles on which such arguments are built.
In scientific thinking, analogies or resemblances may be used to suggest hypotheses or the existence of some law or principle, especially if a comparison can be made between the functions of elements in two systems, as when observation of the moons of Jupiter suggested by analogy the modern conception of the solar system. The argument of Thomas Robert Malthus, the English economist, that populations tend to increase in numbers beyond the means of their subsistence suggested to Charles Darwin the evolutionary hypothesis of natural selection. The fruitfulness of such analogies depends on whether any testable consequences can be deduced from them, which is likely to depend on whether the resemblance is of a fundamental or a merely superficial kind. Functional resemblances are more likely to be fundamental than qualitative ones (such as colour). It would not be legitimate, for instance, to conclude from the model of the atomic nucleus as a miniature solar system that the process of nuclear fission is similar to that by which new planetary systems may be formed or disrupted.
In social and political discussion, analogies may elucidate some unfamiliar point in terms of what is more familiar. Thus, biological analogies may suggest that a community has an “organic” relationship. Such analogies are misleading, however, insofar as they overlook the fact that individual members of the community also have purposes, rights, and responsibilities of their own. In employing the method of analogy, it should always be possible to show that the resemblances noted bear relevantly on the point to be established, whereas the differences are irrelevant. In many cases it is difficult to be sure of this distinction, and arguments from analogy are therefore precarious unless supported by considerations that can be established independently.
Source: "analogy." Encyclopædia Britannica Ultimate Reference Suite, 2013.
figure of speech that implies comparison between two unlike entities, as distinguished from simile, an explicit comparison signalled by the words “like” or “as.”
The distinction is not simple. The metaphor makes a qualitative leap from a reasonable, perhaps prosaic comparison, to an identification or fusion of two objects, to make one new entity partaking of the characteristics of both. Many critics regard the making of metaphors as a system of thought antedating or bypassing logic.
Metaphor is the fundamental language of poetry, although it is common on all levels and in all kinds of language. Many words were originally vivid images, although they exist now as dead metaphors whose original aptness has been lost—for example, “daisy” (day's eye). Other words, such as “nightfall,” are dormant images. In addition to single words, everyday language abounds in phrases and expressions that once were metaphors. “Time flies” is an ancient metaphorical expression. When a poet says “The Bird of Time has but a little way / To flutter—and the Bird is on the Wing” (The Rubáiyát of Omar Khayyam), he is constructing a new metaphor on the foundations of an older, stock metaphor. When Tennessee Williams entitles his play Sweet Bird of Youth, he, too, is referring to that Bird of Time that flies. Thus, metaphorical language develops continuously in complexity just as ordinary language does.
In poetry a metaphor may perform varied functions from the mere noting of a likeness to the evocation of a swarm of associations; it may exist as a minor beauty or it may be the central concept and controlling image of the poem. The familiar metaphor “Iron Horse,” for train, for example, becomes the elaborate central concept of one of Emily Dickinson's poems, which begins
I like to see it lap the Miles, And lick the Valleys up, And stop to feed itself at Tanks; And then prodigious step . . .
A mixed metaphor is the linking of two or more disparate elements, which often results in an unintentionally comic effect produced by the writer's insensitivity to the literal meaning of words or by the falseness of the comparison. A mixed metaphor may also be used with great effectiveness, however, as in Hamlet's:
Whether 'tis nobler in the mind to suffer The slings and arrows of outrageous fortune Or to take arms against a sea of troubles . . .
in which “sea” should be replaced by “host” for the strictly correct completion of the metaphor.
Source: "Metaphor." Encyclopædia Britannica Ultimate Reference Suite, 2013.
Yet, if one is a writer and can see the obverse of the adage: "one picture is worth a thousand words", the "one word is a thousand (or million) pictures" comes into play and the foregoing three-lines of Shakespeare could well be related to the conditions of other life forms such as apples, snails, or even cloud formations. However, such thinking runs too far afield for conventional researchers whose thoughts are constrained by a compliance to concepts and perceptions being used by those in authority. It's alright for you to think outside the lines, but you must be tethered to them and get permission from those in a given authoritative position of analysis before you are allowed to venture too far from the dictated path, much less offer a defensible rationale for thinking in such a way. And for those who seem to be naturally inclined to wander from the paths of typical consideration because they make intuitive leaps like many an original thinker found in different subject areas— but are not yet well versed enough in a language with which to adequately articulate what they see and how it may be applied to conventional perspectives; one can only hope they will persevere long enough for them to encounter someone who has a measurable means of comprehending the conventionality of their unconventional thinking.
The type of governments, religions, philosophies, etc., living today, are the products of unconventional thinkers. We need to transgress the presently assumed logic of ideas in order to develop something better. Thus, in a very simple way, the question of how we might describe Democracy by using a mathematical equation is a step in this direction.