BELIEVE   ME   NOT!    -     A   SKEPTIC's   GUIDE  

... Physics;^6.1

This is partly because everyone is so anxious to "get on to the good stuff" that they are predisposed to give a rather superficial treatment to Mechanics; and partly because most beginning Physics courses are expected to produce graduates who can actually calculate tensions in wires, whether boxes will slide off trucks and other practical things like that. Fortunately, I don't care whether you can do that stuff or not, except for a few simple examples for the sake of illustration and familiarization. This book may help you build a bridge in your back yard, but honestly I think there are much more useful study aids for developing such skills. What I am after is just to get you familiar enough with the paradigms of Mechanics to allow bootstrapping on to the next stage.

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... direction.^6.2

This is also true of distance, velocity and acceleration, which are the topics of this Chapter; but we have to start somewhere.

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... championed^6.3

Often referred to as the "Scientific Method," about which I will have more to say later on.

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... somewhere:^6.4

You real Historians go check this out!

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... views^6.5

Actually they would probably have left him alone if he hadn't been so obnoxious about publicly rubbing their noses in it.

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... Harvard.^6.6

One imagines Galileo's response was, "I'm not that desperate." In those days Harvard had presumably not yet acquired much of a reputation. It is amusing to speculate on how much more classic an example of the Modern Physicist he would have made had Galileo accepted this offer of a New World professorship.

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... side.^6.7

The astronomical observations of Tycho Brahe and Johannes Kepler empirically obliterated the Ptolemaic system in favour of a correct heliocentric model of the Solar system at about the same time as Galileo took on the Church in Italy; I am not certain how much interaction there was between these apparently separate battles. More on this later.

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... "showed"^6.8

There is room for argument over whether he really "showed" this, both from a Popperian purist's point of view [you can never verify a conjecture, only refute it] and from the point of view of the very æsthetic he helped to popularize - namely, that you shouldn't "fudge" your results and that other people should be able to reproduce them. It is, however, certainly true that he made a very persuasive case for the economy and utility of this confessed overidealization; and this is, after all, the true measure of any theory!

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...]^6.9

Why not just call it v, if I am not going to be talking about any of the horizontal stuff? Well, this is a pretty simple equation, so I am going to "stack" it with lessons in notation which will serve to make its meaning absolutely unambiguous (subject to all these explanations) and to introduce fine points I will be needing shortly anyway.

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... initial^6.10

Note: generally any symbol with a subscript ₀ (read "nought" as in x₀ = "x nought") designates an initial value of the subscripted symbol - i.e. the value at t=0. (We stop short of writing t₀ for the initial time, in most cases, because we usually don't need any further redundancy to make the the description completely general.) Thus x may be a variable, a function of time x(t), but its initial value $x_0 \equiv x(0)$ is a constant, a parameter of its evolution in time. Since we will often talk about the final value of some variable (e.g. x_f) at time t_f (at the end of some process), using the subscript _f to designate "final," it is equally logical to use a subscript _i for "initial," so that the value of x(t) at t=0 would be written x_i - this notation is perfectly synonymous with the "nought" notation: $x_0 \equiv x_i$ and the two may be used interchangably according to taste.

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... any,^6.11

Lots of people leave out the v_y0 in order to keep it simpler, but of course that would be tantamount to assuming that we were starting from rest, which ain't necesarily so! Why oversimplify an already simple equation?

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... downward^6.12

Note that the conventional choice of "up" as being the positive y direction forces us to put the acceleration of gravity into the equation with a minus sign, since it is in the "down" direction. Sometimes people try to make this look simpler for beginners by defining down as the +y direction, but I like to get across as early as possible that a negative acceleration simply means an acceleration in the direction opposite to the one we arbitrarily defined to be positive. The same is true of any quantity (e.g. the velocity or the position) that has a direction as well as a magnitude; this idea is vital to an understanding of vectors, which are coming up soon!

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... surface.^6.13

What?! How come I don't give g to a huge number of significant figures, with an uncertainty specified, as one is supposed to do for fundamental constants? Because g is neither fundamental nor constant! Far from it. More on this later.

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... symbol.^6.14

I will soon need the analogous notation $\ddot{x} \equiv d^2x/dt^2$ to signify the second time derivative of x, so that $a_y \equiv dv_y/dt \equiv d^2y/dt^2 \equiv \ddot{y}$. The "double-dot" form is the preferred Physics notation for acceleration, mainly for reasons of economy (it takes so few strokes to write).

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... good:^6.15

This is translated from the Italian by someone else; I can't vouch for the translation but I am confident that it gets the right idea across and I am not much interested in quibbles over the exact wording or what it might have meant about Galileo's "authentic originality."

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... eyes,^6.16

This may well be a good measure of the brilliance of an insight.

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... surface,^6.17

E.g., cannonballs! This sort of "techno doubletalk" is not always used for obfuscation [I, for instance, am simply trying to be general!] but Pentagon aides trying to be Generals are very fond of it too.

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... cannon;^6.18

(This is typical - we always make as many simplifications as the arbitrariness of the notation allows!)

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... nonsense.^6.19

By now, you no longer need to be reminded that such comments are "in my humble opinion."

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... History;^6.20

Why not the Sunset of Recorded History, I sometimes wonder?

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... experiment!^6.21

Newton, whom we often picture as the gardener who brought Galileo's seeds to flower, is also famous for his arrogant statement [a blatant lie], "Hypotheses non fingo," or "I do not make conjectures." (What a jerk!)

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... Hypothesis.^6.22

This is not as easy as it sounds. Most Hunches do not survive close examination; they usually contain irreducible internal inconsistencies or self-contradictions that may, at best, lead the Scientist back to a completely new Hunch.

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... Experiment.^6.23

This is also harder than it sounds. Many Hypotheses have no testable Consequences at all; most of the rest could be tested in principle but might require manipulation of galaxies or reenactments of the Big Bang to produce unambiguous experimental results.

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... Gedankenexperiment^6.24

I.e., a "thought experiment." This term was invented by Albert Einstein, I believe, but the technique is as old as Humanity - this was the approved methodology of Aristotelian science, and is still a great boon to research funding agencies!

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... results^6.25

I.e., those most commensurate with conventional models and paradigms, either pro or con the Predictions of the Hypothesis.

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