A Quote by Leonhard Euler
After exponential quantities the circular functions, sine and cosine, should be considered because they arise when imaginary quantities are involved in the exponential.
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Our principal constraints are cultural. During the last two centuries we have known nothing but exponential growth and in parallel we have evolved what amounts to an exponential-growth culture, a culture so heavily dependent upon the continuance of exponential growth for its stability that it is incapable of reckoning with problems of non-growth.
And what are these fluxions? The velocities of evanescent increments. And what are these same evanescent increments? They are neither finite quantities, nor quantities infinitely small, nor yet nothing. May we not call them the ghosts of departed quantities...?
That's the case with these exponential technologies; our brains, they struggle with it. We live in a world that is global and exponential, and our brains evolved in a world that was linear and local.
It is generally believed that our science is empirical and that we draw our concepts and our mathematical constructs from the empirical data. If this were the whole truth, we should, when entering into a new field, introduce only such quantities as can directly be observed, and formulate natural laws only by means of these quantities.
If the population curve is on an exponential growth, and the resources are on an exponential decline, what happens first is you get increases in wealth discrepancy, which means that you get rich pockets of gated communities with security guards outside them, and you get more and more poverty outside that area.
By the help of God and with His precious assistance, I say that Algebra is a scientific art. The objects with which it deals are absolute numbers and measurable quantities which, though themselves unknown, are related to "things" which are known, whereby the determination of the unknown quantities is possible.
It seems sensible to discard all hope of observing hitherto unobservable quantities, such as the position and period of the electron... Instead it seems more reasonable to try to establish a theoretical quantum mechanics, analogous to classical mechanics, but in which only relations between observable quantities occur.
The danger of dioxins in our environment, our food chain, and our bodies is difficult to illustrate, since they are not visible to the naked eye. My time in Vietnam allowed me to see the result of large quantities of them and therefore understand better the insidiousness of the smaller quantities that have found their way into our lives and bodies.
The difficulties in the study of the infinite arise because we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited; but this... is wrong, for we cannot speak of infinite quantities as being the one greater or less than or equal to another.
Compare ... the various quantities of the same element contained in the molecule of the free substance and in those of all its different compounds and you will not be able to escape the following law: The different quantities of the same element contained in different molecules are all whole multiples of one and the same quantity, which always being entire, has the right to be called an atom.
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.
Life itself is exponential.
We cannot forbear suggesting one practical result which it appears to us must be greatly facilitated by the independent manner in which the engine orders and combines its operations: we allude to the attainment of those combinations into which imaginary quantities enter.
Speculation in oil stock companies was another great evil ... From the first, oil men had to contend with wild fluctuations in the price of oil. ... Such fluctuations were the natural element of the speculator, and he came early, buying in quantities and holding in storage tanks for higher prices. If enough oil was held, or if the production fell off, up went the price, only to be knocked down by the throwing of great quantities of stocks on the market.
I have a glass of hot water with honey and lime in it right after I wake up. I eat in small quantities every two hours and make it a point not to eat anything after 8 P.M. in the evening.
It's impracticable to halt the exponential advancement of technology.
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