The Monty Hall problem is to me one of the most fascinating probability problem (for it's simpleness and unintuitive results) that got my mind blown since I learned about it in high school.
One day in high school, in my Math class, the teacher told us about that famous problem.
Monty Hall was an old and popular TV show in the states were you had to choose a door to open from three different ones. Behind one of them was a car, behind the two others were goats. Obviously, the goal of the game was to win the car (except if you were really into goats, but then I guess you could have bought a lot of those with a car).
Anyway, the tricky part was that when you made a choice, the host asked you to wait before opening it and would open another door, revealing a goat. Then he would give you the opportunity to waive your initial choice and swap door one last time.
Here lies the probability problem. Do you think you would have more chance of winning if you changed your choice?
My math teacher said yes, and I could not believe that, I remember loudly objecting, telling the teacher it was not possible, that it was not logical. I declined what seemed grotesque at the time, I refused to acknowledge such an unintuitive result, such a simple thing, my brain could do the calculation easily so why would you tell me I was wrong on such a trivial thing.
But yes, I was wrong. I knew I was wrong. I was upset at my own mind. I didn't understand how I could be so convinced that changing choice wouldn't change my chances of winning the car. The problem was simple, so simple. And yet my mind couldn't make its way around it.
After many years of training my brain to think differently about probabilities, I can know see how this problem works. 7 years after my first introduction to this problem, I can now grasp a part of it. I understand it, I know the probabilities enrolled in the resolution of this problem, I've learned them at uni and I made the effort to think about that problem quite a lot during those last years. I actually often ask that problem to my friends, to blow their mind.
But still, 7 years after being introduced to that problem, I still have troubles finding its probabilities "natural". My brain still cannot process the fact that it HAS to work that way, that the world is turning in that direction and no others.
I hope I didn't send you to sleep with this. If you want to know more about the mathematician who published this result and got insulted by numerous math PHD for being wrong, you can take a stroll on the wikipedia page.
My technique to wire my brain on the right path? Thinking about a hundred doors, 1 car, 99 goats. I open one door, the host closes 98 others.
It feels easier to process when told this way, but there is still a part of me, somewhere, that tells me it wouldn't change a thing. Even with 98 doors opened. What is wrong with my brain?
If you still don't believe me, there is a short and visually clear explanation here.
PS: this is one of my go to when I want to be amazed at how unintuitive or how little we know about how things work. If you like that kind of thing, you can also check the twin paradox or the biography of Milton H. Erickson.
The last things we studied in Arithmetic are the Reed-Solomon codes. It's a type of code you use to, not encrypt your information, but create redundant information in your final code. So when you read your code, if there are errors or missing parts, you can still decode it. It's not perfectly redundant like dog's ADN is. The redundant code is changed in a certain way so you can guess what the missing parts are.
A few days ago I was on the road to La Fête des Lumières (in Lyon) with 4 germans I met in Bordeaux. The driver had an old CD with a few mainstream and german songs on it that he wanted to play, problem, the CD was damaged, solution? None. Didn't need a solution. The CD still played, although sometimes it was indeed jumping, most of the time it was playing correctly. How is that?
Well, the information burned on the CD is coded thanks to Reed-Solomon's algorithm so that you can still guess what was burned on it through particular redundant code. This redundant code is (and I'm taking a guess here) what is used when your computer asks you "do you want to check if there was no error?" right after burning your CD.
more info on wikipedia
In my quest to better support to learn, I've again stumbled into a complicated, badly explained and unclear paper from my prof about discreet and time-memoryless channels.
Although it might be just me, but when I don't understand something from one source I like to diversify, and papers from Polytechnique (in french) are always a good snack :
Learning about Shannon's theorem in class I got curious and googled the guy.
One extract I found interesting in his wikipedia biography :
Shannon and his wife Betty also used to go on weekends to Las Vegas with M.I.T. mathematician Ed Thorp, and made very successful forays in blackjack using game theory type methods co-developed with fellow Bell Labs associate, physicist John L. Kelly Jr. based on principles of information theory. They made a fortune, as detailed in the book Fortune's Formula by William Poundstone and corroborated by the writings of Elwyn Berlekamp, Kelly's research assistant in 1960 and 1962. Shannon and Thorp also applied the same theory, later known as the Kelly criterion, to the stock market with even better results. Claude Shannon's card count techniques were explained in Bringing Down the House, the best-selling book published in 2003 about the MIT Blackjack Team by Ben Mezrich. In 2008, the book was adapted into a drama film titled 21.
Apart for inventing most of cryptography concepts, and doing chess IA, he also made a fortune from gambling and playing with stocks. Interesting.
My portfolio/vitrine/online resume... call it what you want, which is available on davidwong.fr, is now available on david.wong.emi.u-bordeaux1.fr as well. I thought that was pretty cool to have a bordeaux1.fr url. I think I can also have a univ-lyon1.fr since my account is still active but I can't be bothered looking at where it is.
Anyway, just this small piece of news in the ocean of bitcoin/litecoin news I've been posting here. Exams are coming soon and I should blog more about them than cryptocoins but yeah...
posted November 2013
So after a long night staying up and coding I finally handed in my project including my report in LaTeX.
I'm not really proud of what I did, I felt like I could have done much better if given more time (okay I slacked and I had enough time).
BUT, as I already said earlier, I've accomplished a lot and even though I'm done with this project I still kinda want to keep working on it.
Things that I've learned doing this class :
- C is awful. But now I know the basics. I wish we had one more project to code in C to really get it though.
- Makefile? Headers? I still don't really get the structure of a C project (and I'm ashamed).
- I know Linux! Okay I don't know Linux that much, but I'm getting really causy there. I installed debian on a VM and I'm considering setting up a dual boot on my laptop now.
- Emacs emacs! I was postponing learning it because I was afraid, and just forced myself to use it for this project and goshh am I fast when I use it. When I go back to Sublime Text I just want to C-M-F, C-A, C-K, C-Y...
- LaTeX! As a Math major I've always been ashamed not knowing it. Now that I got a taste of it I'm wondering if I should use it to write my book on.
- Svn and Git. I'm not a stranger anymore! And I use them for all my websites as well now :)
I think that's it, but I feel like I've learned a lot and I wished this course was a year thing rather than a semester thing.
The course is not over yet though and next week we'll dive into java for... a quick swim since it will be our last week.
I feel like I've been doing a hackaton these past few days trying to finish my sudoku solver. I had to hand it in 2 hours ago but still haven't finished... I really hope this won't affect my grade too much.
I've been learning a lot of Emacs, C, using gcov, gprof, LaTeX... I'm so confused right now and my code has became so dense that it's hard for me to debug it.
Yesterday, suddenly, I found something really stupid in my sudoku grid generation that I couldn't fix. A day after, I found the solution, randomly, fixing it created a huge load of other issues. I have been re-inspecting my whole code all day long and I'm stressed by this deadline that I already passed.
Gosh that is a hard course.
And... because of this, I missed a day writing on my new application. I was on a 9-day strike :(