Program logic bugs vs input/environmental errors

[Timon Gehr via Digitalmars-d]

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+dlang at 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!