On 10/08/2014 12:10 AM, Nick Sabalausky wrote:
On 10/07/2014 06:47 AM, "Ola Fosheim =?UTF-8?B?R3LDuHN0YWQi?=
<ola.fosheim.grostad+dl...@gmail.com>" wrote:
On Tuesday, 7 October 2014 at 08:19:15 UTC, Nick Sabalausky wrote:
But regardless: Yes, there *is* a theoretical side to logic, but logic
is also *extremely* applicable to ordinary everyday life. Even moreso
than math, I would argue.
Yep, however what the human brain is really bad at is reasoning about
probability.
Yea, true. Probability can be surprisingly unintuitive even for people
well-versed in logic.
...
Really?
Ex: A lot of people have trouble understanding that getting "heads" in a
coinflip many times in a row does *not* increase the likelihood of the
next flip being "tails". And there's a very understandable reason why
that's difficult to grasp.
What is this reason? It would be really spooky if the probability was
actually increased in this way. You could win at 'heads or tails' by
flipping a coin really many times until you got a sufficiently long run
of 'tails', then going to another room and betting that the next flip
will be 'heads', and if people didn't intuitively understand that, some
would actually try to apply this trick. (Do they?)
I've managed to grok it, but yet even I (try
as I may) just cannot truly grok the monty hall problem. I *can*
reliably come up with the correct answer, but *never* through an actual
mental model of the problem, *only* by very, very carefully thinking
through each step of the problem. And that never changes no matter how
many times I think it through.
It is actually entirely straightforward, but it is popular to present
the problem as if it was actually really complicated, and those who like
to present it often seem to understand it poorly as well. The stage is
usually set up to maximise entertainment, not understanding. The
presenter is often trying to impress, by forcing a quick answer, hoping
that you will not think at all and get it wrong. Sometimes, the context
is even set up that such a quick shot is more likely to be wrong,
because of an intended wrong analogy to some other completely obvious
question that came just before. Carefully thinking it through step by
step multiple times afterwards tends to only serve to confuse oneself
into strengthening the belief that something counter-intuitive is going
on, and this is aggravated by the fact that there isn't, because
therefore the part that is supposedly counter-intuitive can never be
pinned down. I.e. I think it is confusing because one approaches the
problem with a wrong set of assumptions.
That said, it's just: When you first randomly choose the door, you would
intuitively rather bet that you guessed wrong. The show master is simply
proposing to tell you behind which of the other doors the car is in case
you indeed guessed wrong.
There's not more to it.
I agree that primary school should cover modus ponens,
modus tollens and how you can define equivalance in terms of two
implications. BUT I think you also need to experiment informally with
probability at the same time and experience how intuition clouds our
thinking. It is important to avoid the fallacies of black/white
reasoning that comes with propositional logic.
Actually, one probably should start with teaching "ad hoc"
object-oriented modelling in primary schools. Turning what humans are
really good at, abstraction, into something structured and visual. That
way you also learn that when you argue a point you are biased, you
always model certain limited projections of the relations that are
present in real world.
Interesting points, I hadn't thought of any of that.
...
I mostly agree, except I wouldn't go object-oriented, but do something
else, because it tends to quickly fail at actually capturing relations
that are present in the real world in a straightforward fashion.
Educational research shows that students can handle theory much better
if it they view it as useful. Students have gone from being very bad at
math, to doing fine when it was applied to something they cared about
(like building something, or predicting the outcome of soccer matches).
Yea, definitely. Self-intimidation has a lot to do with it too. I've talked
to several math teachers who say they've had very good success teaching algebra
to students who struggled with it *just* by replacing the letter-based variables
with empty squares.
People are very good at intimidating themselves into refusing to even think.
It's not just students, it's people in general, heck I've seen both my parents
do it quite a bit: "Nick! Something popped up on my screen! I don't know what
to do!!" "What does it say?" "I dunno! I didn't read it!! How do I get rid of
it?!?"
/facepalm
Sounds familiar. I've last run into this on e.g. category theory
(especially monads) and the monty hall problem. :-P
In fact, I only now realised that those two seem to be rather related
phenomena. Thanks!
