[PRL] Newton's Laws of Computation?

[Mitchell Wand]

Thanks Joe, that was very interesting.  I've been contemplating questions
like this.  It's easy to show the fallacy of reductionism: for example,
Gerry Sussman showed years ago that the motion of the solar system is
chaotic (ie, numerically unstable, if I understand the problem correctly).

I will have to think about your comments some more.

--Mitch

On 3/27/07, Joe Marshall <jmarshall at alum.mit.edu> wrote:
>
> On 3/21/07, Matthias Felleisen <matthias at ccs.neu.edu> wrote:
> >
> > 6. I like Joe's suggestion but I will frankly admit that I am not
> > sure how to use it. Perhaps the program synthesis people are the
> > answer to this quest for the Floyd-Hoare world and HtDP plus NUPRL
> > are the pieces of the puzzle for the Gödel-Church world.
> >
> > 6a. Joe: I take "Newton's laws" as a metaphorical question here, not
> > as a full-fledged distinction. But it's worth thinking about
> > Hamiltonian and Lagrangian. Perhaps the way engineers use it suggests
> > something for the constructive part.
>
> I thought that it might be metaphorical, but let me try another metaphor.
>
> Suppose I posited the `laws of physics' as these:
>
>   1.  F = ma
>
>   2. Maxwell's equations
>
>   3. The Navier-Stokes equation
>
> These are all fine laws, all fundamental, all true, and almost
> completely useless
> in the context presented here.  You really can't go anywhere by trying
> to combine
> the Navier-Stokes equation with Maxwell's equation unless you already have
> a
> very deep background in physics and a truly perverse desire to increase
> complexity.
>
> Instead of collecting a bunch of unrelated laws together, it is *much*
> more
> interesting to contrast and compare unrelated *systems* of laws.  We learn
> Newton's laws in high school, we may learn Lagrangian mechanics in
> college.
> Newton's laws are based on a fundamental concept of force acting upon
> objects
> with mass.  Lagrangian mechanics is based on the fundamental concept of
> `least action' (minimizing the difference between the kinetic and
> potential
> energy over time).  We can derive Newton's laws from the principle of
> least action.
> We learn a small amount of quantum mechanics in college.  We find that
> Newton's laws are no longer valid when the quantities involved are
> extremely
> small, so we have a different set of laws.  If we go further, we find
> that we can
> derive both Newton's laws and quantum mechanical laws from Hamiltonian
> physics.  Going even further we end up with Noether's theorem, which gives
> us
> some truly profound truths about physics that cannot be captured by simply
> listing our favorite fundamental laws.
>
> So I'm going to claim that you don't want to identify `Newton's laws
> of computing'.
> It is the wrong level of abstraction.  You want to identify the major
> systems of
> computational theory.  *Then* in each theory, you want to find the
> fundamental
> laws of that theory.  Finally, you want to compare and contrast the laws.
>
> --
> ~jrm
>
>
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