Ian Televan

from random import *

runs = 100000
S = runs
for _ in range(runs):
   while(randint(1,20) != 1):
       S += 1
print(S/runs)

>>> 20.05751

In my experience teachers tend to only give examples of typical members of a category. I wish they'd also give examples along the category border, both positive and negative. Something like: "this seems to have nothing to do with quadratic equations, but it actually does, this is why" and "this problem looks like it can be solved using quadratic equations but this is misleading because XYZ". This is obvious in subjects like geography, (when you want to describe where China is, don't give a bunch of points around Beijing as examples, but instead draw the border and maybe tell about ongoing territorial conflicts) but for some reason less obvious in concept-heavy subjects like mathematics.

Another point on my wishlist: create sufficient room for ambition. Give bonus points for optional but hard exercises. Tell about some problems that even world's top experts don't know how to solve. 

Thank you very much for posting this! I've been thinking about this topic for a while now and feel like this is criminally overlooked. There are so many resources on how to teach other people effectively, but virtually none on how to learn things effectively from other people (not just from textbooks). Yet we are often surrounded by people who know something that we currently don't and who might not know much about teaching or how to explain things well. Knowing what questions to ask and how to ask them makes these people into great teachers - while you reap the benefits! - this feels like a superpower. 

I don't quite follow why 5/10 example presents a problem.

Conditionals with false antecedents seem nonsensical from the perspective of natural language, but why is this a problem for the formal agent? Since the algorithm as presented doesn't actually try to maximize utility, everything seems to be alright. In particular, there are 4 valid assignments: $p_1:(x=0,y=10,A()=10,U()=10)$, $p_2:(x=5,y=0,A()=5,U()=5)$, $p_3:(x=5,y=10,A()=10,U()=10)$, $p_4:(x=10,y=10,A()=10,U()=10)$

The algorithm doesn't try to select an assignment with largest $U\left(\right)$, but rather just outputs $5$ if there's a valid assignment with $x>y$, and $10$ otherwise. Only $p_2$ fulfills the condition, so it outputs $5$. $p_1$ and $p_4$ also seem nonsensical because of false antecedents but with attached utility $U\left(\right)=10$ - would that be a problem too? 

For this particular problem, you could get rid of assignments with nonsensical values by also considering an algorithm with reversed outputs and then taking the intersection of valid assignments, since only $(x=5,y=10)$ satisfies both algorithms. 

I thought of a slightly different exception for the use of "rational": when we talk about conclusions that someone else would draw from their experiences, which are different from ours. "It's rational for Truman Burbank to believe that he has a normal life." 

Or if I had an extraordinary experience which I couldn't communicate with enough fidelity to you, then it might be rational for you not to believe me. Conversely, if you had the experience and tried to tell me, I might answer with "Based only on the information that I received from you, which is possibly different from what you meant to communicate, it's rational for me not to believe the conclusion." There I might want to highlight the issue with fidelity of communication as a possible explanation for the discrepancy (the alternative being, for example, that the conclusion is unwarranted even if the account of the event is true and compete).

Richard Feynman once said that if you really understand something in physics you should be able to explain it to your grandmother.  I believed him.

Curiously enough, there is a recording of an interview with him where he argues almost exactly the opposite, namely that he can't explain something in sufficient detail to laypeople because of the long inferential distance.

But is the Occam's Razor really circular? The hypothesis "there is no pattern" is strictly simpler than "there is this particular pattern", for any value of 'this particular'.. Occam's Razor may expect simplicity in the world, but it is not the simplest strategy itself.  

Edit: I'm talking about the hypothesis itself, as a logic sequence of some kind, not that, which the hypothesis asserts. It asserts maxentropy - the most complex world.