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Re: CAUSATION IN PHYSICS



At 08:55 AM 10/14/00 -0500, John M. Clement wrote:
... it makes sense to say the following. Bob pushed on the car, as a
result it accelerated. However, "The car accelerated, as a result Bob
pushed on it" does not make sense. Yes, the math does not recognize the
illogicality of the second statement. And yes the push and the
acceleration are simultaneous and the equation does not recognize
causation. However to push Bob had to first move his hand prior to the
acceleration, thus establishing causality.

1) That's a cute argument, but it is
a) out of context,
b) incorrect regardless of context, and
c) highly misleading.

a) The original context asked whether F=ma expressed causation. A "guilt
by association" argument that merely juxtaposes F=ma with something that
involves causation does not change the fact that F=ma does not express
causation.

In the scenario described above, there are a lot of things going on, some
of which involve causation and some of which do not. The part of the
scenario that involves F=ma does not involve causation. Specifically:

-- We agree the data is consistent with a causal connection from
hand-motion to force:
Bob's volition ==> hand motion ==> F ==> ma ==> other consequences

-- OTOH the data is equally consistent with a causal connection from
hand-motion to acceleration:
Bob's volition ==> hand motion ==> ma ==> F ==> other consequences

The scenario has absolutely nothing to say about the causal relationship
between force and acceleration.

b) The statement labelled "illogical" is not particularly illogical; it is
merely false and misleading. It is false because it is not an accurate
paraphrase of F=ma, and misleading because it purports to be something it's
not.

c) We can equally well cook up a scenario that suggests that ma causes
F: Suppose Bob is blindfolded and initially stationary. The cart is
moving toward Bob's hand. We observe that the cart decelerates. The
deceleration must have "caused" a force on Bob's hand. This statement is
more plausible than JMC's causation statements quoted above.

Causation is a judgement, and not necessarily a mathematical fact.

2) Really? Is there any basis for saying that?

If we allow the assertion that
a) causation is a judgement, not a mathematical fact,
we should equally allow the assertions that
b) energy is a judgement, not a mathematical fact,
c) distance is a judgement, not a mathematical fact, and
d) logic is a judgement, not a mathematical fact.

Of course I disagree with all the itemized assertions (a)..(d).

The real reason for establishing the causation link between forces and
acceleration is ultimately pedagogical. Students who do not establish
this link usually exhibit very fuzzy thinking.

3) That is a classic fallacy.

3a) Remember the ancient principle of logic:
If a fuzzy-thinking student tells you the sun rises in the east,
that doesn't prove the sun rises in the west.

3b) In this case, the sun does in fact rise in the east. Whoever (student
or otherwise) "establishes" a causation-link that does not in fact exist is
the one who is exhibiting the fuzziest thinking.

Unfortunately they do not think in terms of math relationships.
...not formal thinkers.
...do not really understand equations with 3 variables.

4) F=ma is a mathematical relationship. It involves the mathematical
operations of "multiplication" and "equivalence".

I don't see how introducing a new and more complex mathematical operation
("causation") -- and making false statements about it -- will improve
students' understanding of multiplication and equivalence.

They must first make a link that acceleration is caused by force, then
they must make the reverse link that when you observe acceleration, you
know there must have been a force. Making one link does not automatically
establish the other.

5a) I agree that if you have a situation where X causes Y, then it is quite
true that you cannot conclude from this that Y causes X.

5b) The choice of tense communicates a misunderstanding of the physics. It
says "observe" (present tense) acceleration and "have been" (perfect tense)
a force. Real physics says if there is a present-tense acceleration there
must be a present-tense force.

If the difference in tense reflected an actual difference in time, you
could make an argument for causation, but that is not the case.

Note that at 09:21 PM 10/14/00 +0530, D.V.N.Sarma wrote:
Do not cause and effect form a temporal sequence.
If cause and effect are simultaneous naming one as
cause and the other as effect does not make sense.

I agree with Sarma.

Returning to what John M. Clement wrote at 08:55 AM 10/14/00 -0500:
Later on in a very advanced course they might understand that the
mathematical description does not need causation.

6a) Why call the correct description the "mathematical" description? Let's
just call it the correct description.

6b) What is the point of starting out with an incorrect description and
then waiting until an advanced course to rectify the error?
-- Why not give the correct description on day one, or
-- Better yet, why not omit from the first course any discussion of
causation. Why not just say "You can't have F without ma, and vice
versa" and be done with it.


=============================
7) Here's a definition of a Causal Network, based on
http://www.cs.wisc.edu/~dyer/cs540/notes/uncertainty.html
with slight modifications.

"Reasoning Under Uncertainty"

Causal Networks, also known as Bayesian Networks, Belief
Nets, and Probability Nets:

a- are a space-efficient data structure for encoding all of the
information in the joint probability distribution for the
set of random variables defining a domain. That is, from
the Net one can compute any value in the
joint probability distribution of the set of random
variables.
b- Represents all of the direct causal relationships between
variables
c- Intuitively, to construct a Bayesian net for a given set of
variables, draw arcs from cause variables to immediate
effects.
d- Space efficient because it exploits the fact that in many
real-world problem domains the dependencies between
variables are generally local, so there are a lot of
conditionally independent variables
e- Captures both qualitative and quantitative relationships
between variables
f- Can be used to reason
Forward (top-down) from causes to effects --
predictive reasoning (aka causal reasoning)
Backward (bottom-up) from effects to causes --
diagnostic reasoning

g- Formally, a Bayesian Net is a directed, acyclic graph (DAG)
h- There there is a node for each random variable,
i- There is a directed arc from A to B whenever A is
a direct causal influence on B.
j- Each node A in a net is conditionally independent of
any subset of nodes that are not descendants of A
given the parents ("immediate causes") of A.

k- Thus the arcs represent
direct causal relationships and the nodes represent
states of affairs. The occurrence of A provides support
for B, and vice versa. The backward influence is call
"diagnostic" or "evidential" support for A due to the
occurrence of B.

=============

8) Note that it is _not_ possible to have a network that expresses both
F ==> ma
and
ma ==> F
because the graph must be acyclic.

You could arbitrarily choose one or the other, but that would be merely an
opinion, and there cannot possibly be any data that favors one choice over
the other.

Rather than having multiple incompatible Belief Nets running around, my
recommendation is to use a network that expresses _neither_ F ==> ma nor
the reverse, but rather collapses both F and ma into a single node:

(Bob's volition) ==> (hand motion) ==> (F=ma) ==> (other consequences)