The Greatest Magic Trick Ever
...is this one, by Derren Brown.
So how does it work? Quite simple really. The brain tells itself:
Hey, this isn't the guy I was talking to just before! I was talking to Derren Brown!
Then the brain goes:
No no, I've just confused myself because someone walked past me with a poster of Derren Brown. I was never talking to Derren Brown.
Perhaps not in so many words. But that's the meat of it.
The trick doesn't lie in the switch - to switch two people behind a large poster is easy. All the magic takes place in the mind of the target, prompted by the image of Derren Brown.
While most magic tricks are designed to do the seemlingly impossible and leave the audience to try to figure it out, in this one, figuring it out is fairly straightforward. Nobody is left stupified.
Not us, the audience; there is no sleight of hand, no secret.
Nor the target; they don't even see the magic - not right away at least. A bit like how children sometimes miss the magic because for them, levitation and disappearing acts aren't impossible, but entirely ordinary.
It is very elegant.
But why do I think it is the best magic trick ever? Well, I'm not going to tell you.
This post is itself a magic trick - but while you are probably the target, you are not necessarily the audience.
where p is the probability distribution, q is the old probability distribution, and M is the transition matrix. In order to find the optimal transition matrix, we minimize the variance
where d is the dimensionality and E is the size of the statistical ensemble over time and space to which p and q belong. The index of the ensemble e is suppressed. We find the differential
Setting the differential to zero we get
which, assuming Maj is known for all j ≠ b gives the solution
Our strategy then is to iteratively increase the size of the ensemble of observations and compute the transition matrix for each iteration. For j ≠ b we use the value Maj from the previous iteration. For the initial matrix there are many possible choices. We will use
