
Is Newtonian physics Newton’s physics? (2016) - Hooke
https://thonyc.wordpress.com/2016/12/25/christmas-trilogy-2016-part-1-is-newtonian-physics-newtons-physics/
======
jamesrcole
I can't help noticing that this article, questioning Newton's role, was posted
by a user named Hooke.

------
Koshkin
TL;DR: Yes.

The article is actually is rather short; it points out the differences in the
mathematical notation used in the development of (then new) calculus, which is
an interesting topic in itself since it has been a source of some confusion up
to this day.

For example, using the dot to denote the (time) derivative is extremely
confusing for many beginning students of analytical mechanics due to the
casual mixing it with the other notation adopted in most of the literature. A
first attempt to parse an expression containing the time derivative of the
partial derivative of a function (the Lagrangian) _by the "time derivative"_
of a generalized coordinate, the latter derivative being denoted by the dot,
may be quite challenging.

My advice is to see the dot, at least in such contexts, merely as some kind of
diacritic which is used to denote another _independent_ variable - with the
reminder that this new variable will, in some other appropriate context, be
taken to be the time derivative of the other one (i.e. the one without the
dot).

~~~
lisper
> to denote another independent variable [which] will ... be taken to be the
> time derivative of [another variable]

That makes no sense to me. If one variable is a function of another then _by
definition_ it is not an independent variable.

And I don't see why the dot notation should be any more confusing than any of
the other myriad arbitrary squiggles, spatial relationships, fontifications,
and punctualizations which are assigned semantic meaning in mathematics. The
whole enterprise is a freakin' mess (referring to the notation, not
mathematics in general).

~~~
Koshkin
I knew that would be confusing! Let me give you an example of the context
where the dot should be seen just as a "reminder" rather than a
differentiation symbol. When talking about a Lagrangian (let's say, in one
dimension), which is a function of _three independent variables_ , these
variables are customarily denoted as _t_ , _q_ , and _q-dot_ , thus obscuring
the fact of their being independent variables, which would be much clearer
conveyed by using, say, _a_ , _b_ , _c_ instead. The even more confusing part
comes later when they _differentiate_ by _q-dot_ , and it is this wrong
impression of "differentiating by a derivative" that also could have been
easily avoided by seeing the dot as just some kind of diacritic.

~~~
lisper
I've never seen the overdot in a presentation of Lagrangian mechanics mean
anything other than a time derivative (i.e. a dependent variable). Can you
point me to an example where it denotes an independent variable? Because that
would be really weird.

~~~
Koshkin
Sure: what I was referring to in the example that I gave was the _q-dot_ that
appears in the denominator of the expression of the _partial_ derivative of
the Lagrangian.

~~~
lisper
Ah. I think I get it now. I misinterpreted what you meant by the word "see"
(in "My advice is to see the dot..."). I thought you meant, "understand that
in fact q-dot is an independent variable" when in fact you meant (AFAICT)
"pretend that q-dot is an independent variable even though in fact it is not."

------
GregBuchholz
Is Newtonian physics nondeterministic?

[http://personal.lse.ac.uk/robert49/teaching/methodologies/pd...](http://personal.lse.ac.uk/robert49/teaching/methodologies/pdf/Norton.pdf)

~~~
danbruc
No, it is not. I can not exactly pin down where the mistake in the linked
paper is after looking at it for five minutes but I am pretty sure it is
related to his choice of r(t) in equation 4 as a piecewise polynomial so that
a t = T there is a discontinuity in the 4th derivative which is non-physical,
i.e. without a force tangential to the dome at the apex the object would never
move away from the apex of the dome. If you only look at lower order
derivatives like velocity and acceleration, then there is no discontinuity and
everything seem superficially fine.

~~~
kurthr
I agree, this is likely a joke paper.

I find it fairly hilarious since at it looks like the standard Divide by Zero
algebra problem, but then error after error compounds the result.

The first error appears to be in an un-numbered equation:

sin(theta)=dh/dr which is equal to 0 at r=0!!

which is then substituted into the differential equation:

F=g dh/dr = sqrt(r) = d^2r/dt^2 again equal to ZERO at r=0

Of course this is also an abuse of Leibniz notation (mathematicians squirm
whenever physicists do this sort of "algebra" on differentials) which is then
integrated twice and then differentiated twice (ignoring constants of
integration) to get the equations for r(t) and a(t).

The second key is the square root, which allows for multiple solutions of the
differential equation (one of which is the normal r=a=0), but that's just part
of the side show. Physics has all sorts of "non-physical" results from
integrations, DiffEq, etc. A classic being a negative time solution to
parabolic trajectories.

I would add the use the statistics of continuos probability distributions to
say that there is in fact ZERO probability that any ball is at r=0 just to
complete the silliness. Perhaps he's willing to co-author a follow up?

