So far we have been discussing the properties of matter from the atomic point of view, trying to understand roughly what will happen if we suppose that things are made of atoms obeying certain laws. However, there are number of relationships among the properties of substances which can be worked out without consideration of the detailed structure of the materials. The determination of the relationships among the various properties of the materials, without knowing their internal structure, is the subject of thermodynamics. Historically, thermodynamics was developed before an understanding of the internal structure of matter was achieved….
We have seen how these two processes, contraction when heated and cooling during relaxation, can be related by the kinetic theory, but it would be a tremendous challenge to determine from the theory the precise relationship between the two. We would have to know how many collisions there were each second and what the chains look like, and we would have to take account of all kinds of other complications. The detailed mechanism is so complex that we cannot, by kinetic theory, really determine exactly what happens; still, a definite relation between the two effects we observe can be worked out without knowing anything about the internal machinery!
The extraordinary thing about algebra is that it provides accurate solutions in advance of intuitive understanding, rather than after it. Normally this only happens with the observation of empirical phenomena. You see that a thing happens and then you try to explain it. But with algebra, too, sometimes you see that a result pops out of your equations, and then you try to explain it. But algebra is pure thought! Herein the facticity of thought.
Climbing the Eiffel Tower is a disappointment. Reaching the moon is a disappointment. Why shouldn’t getting down below the nuclear level be a disappointment? Or getting outside the universe be a disappointment? Why shouldn’t science generally be the Eiffel Tower?
Suppose, for a minute, that God really did mean the universe to be our stage. Wouldn’t we expect its underside, and its backside, to be drab and unadorned, just as they are at the Met or La Scala? And shouldn’t we take the barrenness of the moon, the emptiness of space, and the randomness of quantum mechanics, as signs. Can’t we see the signs?
To follow the plot, keep your eyes on the stage.
Is it the fly who dies behind the window pane, or the fly who fears to enter your house, who retains her dignity?
Either flies don’t enter or people open their windows. By dying, which does the fly make possible?
You are nought but your fortune, as completely empty as chance, from the color of your eyes to the sharpness of your mind. So do not tell me that gambling lacks substance. You lack substance. There is no greater humility than the gambler’s.
In what way are mathematical models that validate our intuition different from specious etymologies? History is sexist because it is his story. Dogs are backward gods. Etc.
I don’t need a book; I can figure it out for myself!
The pervasive problem of absence of information on sellers admits only of a government fix. Only government can extract seller information and present it to consumers in a way that maximizes consumer welfare. Buyers can try to unite, but sellers will never volunteer information. Only an agent wielding the scissors of the law can lay sellers bare.
For the humanist, the mathematical rubber hits the road of thought when she understands that almost all of her supposedly qualitative thought, particularly as it relates to the economy, involves ranking or statements of magnitude. “Invading Iraq set the country back to the stone age,” for example, is the statement that Iraq now has fewer cars, or dollar bills, or hospitals, or whatever, than it had before. Or consider “a dictatorship is better than an occupation.” In the first case you are counting, even if you don’t realize it. And in the second you are ranking, and any ranking can be represented as a counting of units of preference. So implicitly you are doing math.
The rub is that if you don’t actually write down functions and equations to describe your implicitly mathematical arguments, you end up doing very rudimentary and crude math. You are stuck with general mores versus lesses. Once you add the tools of math to your statements, you can multiply and divide your mores, integrate and differentiate your lesses, optimize them all, and so on. You explore your theories with much greater precision and insight than if you stick to just > and <. Moreover, you can compare your statements and harmonize them in ways that you cannot do when you lack the compact mathematical notation that allows you to include many complex ideas on a single line of text. And perhaps most beautifully and powerfully, at least for me, you can go out into the world, and get actual numbers that can be input into your mores and lesses, so that you can say, with extraordinary magic, precisely how much more and how much less, precisely how badly Iraq was injured.
The frightening thing for the humanist is that math, far from being an obfuscation and a superficiality, is something one has been doing crudely all along. It is a humbling that a true humanist should welcome to discover that her humanism is just an ignorance, or perhaps an illiteracy. Indeed, an innumeracy.
Unless you happen to fervently believe in a principle itself, and no one ought to, because principles aren’t real, you should never use one to win an argument, because one day something you love will run counter to the principle, and then you will be forced to watch it die. The argument against the Iraq war was that it was a bad war; it should never have been that military intervention is always wrong as a matter of principle. Now we have a relatively non-interventionist President, and the price is the murder of an entire country.