A Quote by Leonhard Euler
A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities.
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Numbers are the product of counting. Quantities are the product of measurement. This means that numbers can conceivably be accurate because there is a discontinuity between each integer and the next. Between two and three there is a jump. In the case of quantity, there is no such jump; and because jump is missing in the world of quantity, it is impossible for any quantity to be exact. You can have exactly three tomatoes. You can never have exactly three gallons of water. Always quantity is approximate.
Rather, for all objects and experiences, there is a quantity that has optimum value. Above that quantity, the variable becomes toxic. To fall below that value is to be deprived.
Desired substance, things, patterns, or sequences of experience that are in some sense "good" for the organism - items of diet, conditions of life, temperature, entertainment, sex, and so forth - are never such that more of the something is always better than less of the something. Rather, for all objects and experiences, there is a quantity that has optimum value. Above that quantity, the variable becomes toxic. To fall below that value is to be deprived.
If I were to give a summary of the tendency of our times, I would say, Quantity. The multitude, the mass spirit, dominates everywhere, destroying quality. Our entire life--production, politics, and education--rests on quantity, on numbers. The worker who once took pride in the thoroughness and quality of his work, has been replaced by brainless, incompetent automatons, who turn out enormous quantities of things, valueless to themselves, and generally injurious to the rest of mankind. Thus quantity, instead of adding to life's comforts and peace, has merely increased man's burden.
You can always create a fraction by putting one variable upstairs and another variable downstairs, but that soes not establish any causal relationship between them, nor does the resulting quotient have any necessary relationship to anything in the real world.
In the abstract world of American economists, equations run both ways; they believe that by changing the sign of a variable from plus to minus or from minus to plus or the price and quantity of x or y, the direction of historical movement can be reversed.
The potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has to assume values that either become smaller than any finite limit no matter how small, or greater than any finite limit no matter how great.
Through and through the world is infested with quantity: To talk sense is to talk quantities. It is no use saying the nation is large. . . . How large? It is no use saying the radium is scarce. . . . How scarce? You cannot evade quantity. You may fly to poetry and music, and quantity and number will face you in your rhythms and your octaves.
To reduce modern climate change to one variable, CO2, or a small proportion of one variable - human-induced CO2 - is not science. To try to predict the future based on just one variable (CO2) in extraordinarily complex natural systems is folly. Yet when astronomers have the temerity to show that climate is driven by solar activities rather than CO2 emissions, they are dismissed as dinosaurs undertaking the methods of old-fashioned science.
Complete knowledge of the nature of an analytic function must also include insight into its behavior for imaginary values of the arguments. Often the latter is indispensable even for a proper appreciation of the behavior of the function for real arguments. It is therefore essential that the original determination of the function concept be broadened to a domain of magnitudes which includes both the real and the imaginary quantities, on an equal footing, under the single designation complex numbers.
If you had a robot out here calculating all the variables, I think you could potentially get really close to perfection, but from a human perspective, there's no way to understand all the wind. The wind is the biggest variable, and the grass length is the second biggest variable that we just don't have control over and never will.
Beauty is variable, ugliness is constant.
There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated.
The technology is the independent variable, the social system the dependent variable. Social, systems are therefore determined by systems of technology; as the latter change, so do the former.
Prosperity has nothing to do with the quantity of money that we have in our pockets, but rather with the quantity of goods that we can buy.
General Systems Theory, a related modern concept [to holism], says that each variable in any system interacts with the other variables so thoroughly that cause and effect cannot be separated. A simple variable can be both cause and effect. Reality will not be still. And it cannot be taken apart! You cannot understand a cell, a rat, a brain structure, a family, a culture if you isolate it from its context. Relationship is everything.
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