(With apologies to those who do not know machine learning)
I had a dream of benzene proportions a few nights ago. For some inexplicable reason,
I was pondering about marriage a lot that night. Not my marriage, but marriage in
general -- why do guys go for it? what is the benefit to both the parties etc? The usual stuff, no biggie. I forgot about it and went to bed thinking about Mount Doom as usual.
Three hours later, I was talking to myself in a dream:
Me1: You know that a single guy is like a very high dimensional vector with high density and very few zeros.
Me2: No kidding! Why?
Me1: A single guy holds a lot of opinions on thousands of issues, is quite dogmatic, has two cents on every problem, and everything is important to him. If you ask him anything, you will rarely draw a blank.
Me2: Hmmm fair enough I guess, go on.
Me1: A girl is like a projection matrix and a marriage is like projecting the guy vector on a low dimensional space with high sparsity.
Me2: I don't get it. Why is marriage a sparse vector in low dimensions?
Me1: Think about it. Marriage means finding commonalities between the two people => low dimensions, and marriage really depends only on a select few solid traits => sparsity. After marriage, the guy lets go (or has to let go) of most of his opinions, 'compromise' and focus only on the important things.
Me2: Ok fine, marriage is a sparse vector in a low dimensional space. Big deal. What's your
point?
Me1 (smiling): My point?
Me2 (impatient): Yes, your point.
Me2: Johnson Lindenstrauss lemma?
Me1: Precisely.
Me2: ??
Me1 (beatific smile):
Me2: OH!!!
Me2: Man! You just blew my mind!
For those of you who are not aware of the lemma, it states that with high probabilily, any random projection matrix can be employed to project a high dimensional vector into a low dimensional one, with small loss in the resulting transformation. For marriage it means that do not think about who you should marry, just pick a random girl, and with high probability the end outcome won't be too bad ;-) I fell into a blissful sleep after that.
Probably the only time in my life when I impressed myself.
PS: Would have loved to see an XKCD cartoon of that.
