## Respect their authoritah!

You might recall my post named Latent fascism in education?

Yesterday I watched a talk show with an interesting topic: Corruption (bribery) in higher education. Two things caught my eye in a bad way, and one in a good way.

1. The students’ representative, president of the Students parliament kept saying that every possible case of bribery goes to the district attorney or the honor comity, while asking a person in the audience to stop exposing the bribing system – “please, don’t shake the authority of our professors”, he said. That is hypocrisy!

2. Now, what about the professor in the show? He pointed out that the bribery is inherent in every society, and that it is institutionalized in the US via high tuition fees – paying $42k in Harvard guarantees the student to pass the year – he claims that the percent of students failing to pass a school year in the US is less than 1%. After that he made a claim that the Yale dean said that when Yale professors give a student grade E, it is a sign to the employers not to give him/her the job. Oh yes, he also said that our senior year undergraduates are much better than those in top US universities and that we do much harder projects and write much more serious theses.

3. The young T.A. from a private university has told him that his every argument is false (grade E – at Yale?). His reply was that there is an E grade at every school in the US. After she said she graduated in the US, his reply was – maybe you graduated at a lousy institution such as University of Hawaii, Honolulu.

Is that a person whose authoritah I should respect?

## Now this one is for you, Steve

After writing a post for Bill, it is about time Steve gets one. Why am I writing this post? Well, what would you do with a business offer in Mac-oriented development team? In my case, the decision was simple – turn down the offer. I like programming, but I am an algorithmic type of guy, not OO. On the other hand, if I have to choose between getting familiar with a new operating system, a new framework and a new language on one side, and complex networks, topology, or even Russian language on the other side, my choice is the list number two, even though they would pay me for the list number one.

Of course, there is one more aspect: the principles of Free Software – I don’t think I could ever write code for a proprietary piece of software.

## A convoluted post about Feynman, Mach, Pauli and Captain Obvious

Yesterday I had much fun at the university asking people what happens after Captain Obvious leaves the Blue Eye Island. Each time someone had the answer, no matter what it was, I would choose the other answer and persuade him/her that answer was more logical. That experiment reminded me of Feynman sprinkler. Let me quote Feynman:

I once did an experiment in the cyclotron laboratory at Princeton that had some startling results. There was a problem in a hydrodynamics book that was being discussed by all the physics students. The problem is this: You have an S-shaped lawn sprinkler–an S-shaped pipe on a pivot–and the water squirts out at right angles to the axis and makes it spin in a certain direction. Everybody knows which way it goes around; it backs away from the outgoing water. Now the question is this: If you had a lake, or swimming pool–a big supply of water–and you put the sprinkler completely under water, and sucked the water in, instead of squirting it out, which way would it turn? Would it turn the same way as it does when you squirt water out into the air, or would it turn the other way? The answer is perfectly clear at first sight. The trouble was, some guy would think it was perfectly clear one way, and another guy would think it was perfectly clear the other way. So everybody was discussing it. I remember at one particular seminar, or tea, somebody went nip to Prof John Wheeler and said, “Which way do you think it goes around?” Wheeler said, “Yesterday, Feynman convinced me that it went backwards. Today, he’s convinced me equally well that it goes around the other way. I don’t know what he’ll convince me of tomorrow!” I’ll tell you an argument that will make you think it’s one way, and another argument that will make you think it’s the other way, OK? One argument is that when you’re sucking water in, you’re sort of pulling the water with the nozzle, so it will go forward, towards the incoming water. But then another guy comes along and says, “Suppose we hold it still and ask what kind of a torque we need to hold it still. In the case of the water going out, we all know you have to hold it on the outside of the curve, because of the centrifugal force of the water going around the curve. Now, when the water goes around the same curve the other way, it still makes the same centrifugal force toward the outside of the curve. Therefore the two cases are the same, and the sprinkler will go around the same way, whether you’re squirting water out or sucking it in.”

Now, the problem was first treated in Ernst Mach’s book Die Mechanik in ihrer Entwicklung. Ernst Mach was Wolfgang Ernst Pauli’s godfather (note Pauli’s middle name). Today is the anniversary of Pauli’s death – and a quote from Pauli that everyone remembers

It is not even wrong!

resembles the conclusion most people yesterday made after I convinced them that both solutions of blue-islanders problem have sense (of course, I know the holes in the argument, but it is still fun to argue).

## Мой русский становится все лучше и лучше!

As the title says: my Russian is getting better every day – I haven’t really noticed it until today I read something on the blackboard in my Nonlinear Control class and realized it was wrong. Surname of A. I. Lurʹe was spelled wrong in Cyrillic: it said Лур**ъ**е instead of Лурье. It’s not a big deal, I agree – but I was quite surprised I recognize the difference.

## Did Captain Obvious visit the Blue Eye island?

You have probably heard about the blue-eyed islanders puzzle. If not, take a look at Terry Tao’s blog post here. Just like people often tell the Monty Hall problem to a class or a group of non-mathematician friends and add the story about Marilyn vos Savant receiving 10,000 letters after revealing the solution in her column, I like to show the blue-eyed islanders puzzle to people I know and wait for their answers. Knowing how subtle differences in wording of the problem can lead to different answers (if you browse the web, you might find people proving all possible outcomes – death of all blue-eyed people, death of all people, or the ‘nothing happens’ outcome) I always enjoy the way their logic works.

They always start with the same question: what’s the purpose of the visitor? They already knew that there are blue-eyed people on the island! Well, the concept of common knowledge sheds some light on that.

P.S. Does anyone know the origin of the puzzle? It would be nice to know who formulated it first.

## Everybody hates Haskell

Anecdote time: this Monday we had a presentation at the university – a US software company (no need for names) has vacant places for programmers and developers. On one of their posters I found an interesting challenge problem (solve the problem and get a job)

First n positive integers are randomly placed in an array of length n. One of integers does not appear in the array – instead of it, one of the integers in the array appears twice. What is the simplest algorithm for finding the number omitted and the number repeated in the array without sorting it?

Minute I read it, I got the half of the solution – but the other half puzzled me for 15 minutes or so. I was on my way home when it struck me – I got it! Then I just turned 180° and went back. I reported the solution to their representative – it was indeed the one they expected. Now, during the Q&A session he asked the students in the room what is their favorite programming language. I answered honestly: Haskell. He just smiled. After 10 minutes a colleague of mine asked him whether the company would finance PhD for their eventual employees. “Yes, but we need to know what they plan to study. We won’t finance them if they want to get a PhD studying Haskell, for instance”.

Darn.

P.S. I didn’t want to spoil the fun of algorithm making to my readers by writing the solution for the problem given above. Still, if you get stuck, the solution is written under this post, white font color (select it to see it).

If you sum first n positive integers and subtract the sum of all numbers in the array, the result is x-y where x is the number omitted and y is the number doubled. On the other hand, if you divide the product of first n positive integers with the product of elements in the array, the result is x/y. Two equations, two unknowns, you’re done. In order to save time, don’t multiply and sum the elements in different loops, take just one loop, before that initialize D=0, Q=1 (D for difference, Q for quotient) and in a for loop with counter i going from 1 to n make D=D+i-array(i) and Q=Q*i/array(i).

## WolframAlpha – answering the unanswerable

I had a funny experience with WolframAlpha recently. I typed in:

differentiate (t-t^2/2)Heaviside(t) at t=0

and the result was (as you can probably see in the link):

$\theta(0)\approx\theta(0.)$, alternate form $1$

Surprise, surprise. The function obviously doesn’t have a derivative in that point, but WolframAlpha bravely calculates it. I tested Mathematica 7 with the same question, using both UnitStep and HeavisideTheta for the unit step function. The difference between these two is that HeavisideTheta implemented in Mathematica is undefined at 0, while the UnitStep’s value at 0 is 1.

Heaviside theta case:

In[1]:= D[HeavisideTheta[t] (t – t^2/2), t]

Out[1]:= (t – t^2/2) DiracDelta[t] + (1 – t) HeavisideTheta[t]

In[2]:= % /. t -> 0

Out[2]:= HeavisideTheta[0]

As noted, HeavisideTheta[0] has no defined value.

Unit step case:

In[1]:= D[UnitStep[t] (t – t^2/2), t]

Out[1]:=(t – t^2/2) (\[Piecewise] {{Indeterminate, t == 0},{0, \!\(\*TagBox[“True”,”PiecewiseDefault”,AutoDelete->False, DeletionWarning->True]\)} }) + (1 – t) UnitStep[t]

In[2]:= %/.t->0

Out[2]:=Indeterminate

This opens few other questions about these calculations, but I’ll stop right here.