Which, if you look carefully at the paper, you will see that "differential
relationships" is just what we did teach the children a few months before doing
the ball drop experiment.
This is very powerful when you have a computer because you can go directly at
the relationships and let the computer do the incremental additions that
perform the integrations. This gets at the heart of what calculus is actually
about (and of course it is what Babbage aimed at with his first difference
engine).
Both Newton and Einstein liked the idea of exploring mathematical relationships
first, because they form a basis (and a language) for helping to think about
and articulate what one might be observing.
The nice thing is that children can readily deal with 1st and 2nd order
differences and their calculations, and this covers a lot of the practical
calculations of elementary Galilean and Newtonian physics.
Underneath every Etoy object is a turtle, and a turtle is a vector (and there
are vector math operations between objects lurking in the Etoys viewers). But
this problem is one dimensional, and even simple 2D followons such as rolling a
ball off a table, "shoot the alien" etc can easily be handled informally and
also acted out with the children's bodies, etc.
Cheers,
Alan
>________________________________
>From: Ondřej Bílka <nel...@seznam.cz>
>To: Fundamentals of New Computing <fonc@vpri.org>
>Sent: Friday, August 5, 2011 6:13 AM
>Subject: Re: [fonc] Physics and Types
>
>On Fri, Aug 05, 2011 at 03:43:04AM -0700, BGB wrote:
>> On 8/4/2011 6:19 PM, Alan Kay wrote:
>>
>> Here's the link to the paper
>> [1]http://www.vpri.org/pdf/rn2005001_learning.pdf
>>
>> inference:
>> it is not that basic math and physics are fundamentally so difficult to
>> understand...
>> but that many classes portray them as such a confusing and incoherent mess
>> of notation and gobbledygook that no one can really make sense of it...
>>
>> old stale/dead rant follows:
>>
>> it is like, one year, with the help of a physics book,
>> google+wikipedia+mathworld, and good old trial and error, I proceed to
>> write a (basically functional, but not particularly "good") rigid body
>> physics engine.
>>
>> several years later, I took a physics class, with a teacher that comes off
>> like Q (calling everyone stupid, comparing the students with dogs, ...)
>> and writes out esoteric mathematical gobbledygook beyond my abilities to
>> make much sense of (filled with set-notation and other unrecognized
>> symbols and notations, some in common with first-order logic, like the
>> inverted A and backwards E, ..., and others unknown...).
>>
>...
>> granted, I have also seen in introductory programming classes just how
>> poorly many of the students seem to grasp some of the basics of
>> programming (struggling with things like variable declarations, loops,
>> understanding why never-called functions fail to do anything, ...), so I
>> guess ultimately it is kind of similar (in an almost sad way, programming
>> really doesn't seem like it should be all that difficult from the POV of
>> someone with a fair amount of experience with it).
>>
>> but, at the same time, there would also be nothing good to be gained by
>> belittling or being condescending towards newbies...
>>
>Well I faced oposite problem that for classes people unnecesarily
>complicate things by trying to make it accessible for newbies.
>One of my experiences that high school physics could be three times
>easier and simpler if students learned differential equations.
>
>--
>
>Pentium FDIV bug
>
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