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Re: [Phys-L] how research is done : exploring a maze using only local information

I do a lot of work with elementary teachers to help them understand what science is really about because nothing in the education provides that. The foundational idea is the being wrong is an opportunity to learn. It that's them a while to accept that but once they do risk taking becomes much easier



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On Sep 15, 2015, at 2:35 PM, John Denker <jsd@av8n.com> wrote:

On 09/15/2015 05:20 AM, Joseph Bellina wrote:

I'm wondering however if the theory of how best to run the
maze is analogous to theory in science. The later makes claims about
the world not about how to learn about the world whereas the maze
theory is about how to run the maze but makes no claim about the maze
itself

That sounds like an interesting question, but I suspect
I don't fully understand the question. Here's how far
I've gotten trying to get a handle on the issue:

Sometimes it helps to make certain distinctions:
*) Physics is mostly about the natural world. This
includes facts and theories. (The facts help us figure
out the theories, and vice versa.)
*) Educational psychology is mostly about the process
of learning about the world.
*) Discussions of "how research is done" fall into
a third category. This partially overlaps with the
other two categories, but not entirely.

Sometimes such distinctions are helpful, and sometimes not.

Psychology is about the human mind. In contrast,
there are some rules about how to do experiments that
are based on information theory, rules that ought to
be followed by humans and non-humans alike, in order
to gain information efficiently. As an example of
a design-of-experiment issue that has nothing to do
with psychology, see
http://www.av8n.com/physics/twelve-coins.htm

In any case, the maze will never be a perfect model of
how research is done ... but it it can be useful even
when it isn't perfect. The key is getting students to
be less risk-averse. They need to understand that
backing out of a blind alley does *not* mean you made
a mistake or a bad decision. It's part of the cost
of doing business.

Decision-making skills are highly portable from one
field to another. Military planners, farmers, business
leaders, physicists, etc. all need similar skills.

On 09/14/2015 02:20 PM, LaMontagne, Bob wrote:
There are theories to be tested. Most oft time maze runners are aware
of quite a few. The most elementary is that one should always turn in
the same direction at every juncture. This works for 90% of mazes.

That's an interesting point. That's called Harvey's algorithm,
named after Harvey Wallbanger. It's interesting in light of
Einstein's dictum that every theory should be as simple as
possible, but not simpler.

It works 100% of the time for certain types of mazes but fails 100%
of the time for other types. In situations where it works, it has
the virtue of simplicity: You don't need to make any nontrivial
decisions, and you don't need to mark anything or remember anything.

As for my maze game in particular, yes, Harvey's wall-banger
algorithm will find the cheese. However, I could easily modify
the game to ensure that you would need a more sophisticated
algorithm. I'm tempted to do this, in order to more faithfully
model the scientific process, i.e. to require decision-making
and record-keeping.

In any case, this nicely illustrates the point that there are
lots and lots of competing theories, and often it's not a_priori
obvious which one is appropriate.

On 09/14/2015 10:39 AM, rjensen@ualberta.ca wrote:

I see is that, at every juncture, there are only two possible pathways
(or going backwards)

Actually that's "almost" true, but not quite. Here is a maze
where each cell has been marked according to its degree, i.e.
according to the number of links it has.
http://www.av8n.com/physics/img48/maze3-degree.png

Legend:
Red: Degree 1: Dead end.
Yellow: Degree 2: Passage. One way out (other than the way in).
Green: Degree 3: Tee. Two ways out (other than the way in).
Blue: Degree 4: Crossroads. Three ways out (other than the way in).

In this instance, 6 of the 128 cells are of degree 4. Here's the
full histogram:
Degree: 0 1 2 3 4
Count: 0, 42, 52, 28, 6
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