- ... 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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- ... championed6.3
- 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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- ... views6.5
- 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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- ... initial6.10
- 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
is a constant, a parameter
of its evolution in time.
Since we will often talk about the
final value of some variable (e.g. xf) at time tf
(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 xi - this notation is perfectly synonymous
with the "nought" notation:
and the two may be
used interchangably according to taste.
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- ... any,6.11
- Lots
of people leave out the vy0 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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- ... downward6.12
- 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
to signify the second time derivative of x, so that
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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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- ... Gedankenexperiment6.24
- 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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- ... results6.25
- I.e.,
those most commensurate with conventional models and paradigms,
either pro or con the Predictions of the Hypothesis.
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