Counter Intuitive Maths
“Math doesn't lie, but our brains are
huge scam artists.”
-
Scott
Adams
Ever since
Newton, maths has become the language of science, especially physics. That
trend only accelerated in the last century to a point that when asked whether
physics would ever again have a theorist like Faraday who could do wonders
without sophisticated maths, Richard Feynman replied:
“I'd say the odds are strongly against
it. For one thing, you need the math just to understand what's been done so
far. Beyond that, the behavior of subnuclear systems is so strange compared to
the ones the brain evolved to deal with that the analysis has to be very
abstract.”
And yet even
physicists (at least the pre- Feynman era ones who were at the cutting edge of
20th century physics) couldn’t believe in their own maths:
1) Physicists of the day, for example, had
to wait for Hubble and his data before they believed what the maths of
Einstein’s relativity could have told them much earlier: the universe was
expanding. Even Einstein himself didn’t believe in what his theory had led him
to!
2) Paul Dirac managed to integrate a part of
quantum mechanics and relativity via his modified equations, but there was a
catch: his maths implied that there must be a new particle out there. No such
particle was known to exist at the time, and so Dirac gave in. A few years
later, that exact particle was found and Dirac acknowledged that his equations
were smarter than him!
So if even
scientists have problem in believing in maths, what hope is there for the rest
of us?
Like take that Monty
Hall problem: it is a game show where you are given a choice of three doors. There’s
a car behind one door, and goats behind the other two. If you pick the door
with the car, you win it. Your odds are 1-in-3.
You pick a door,
but before it opens, the host opens one of the other two doors to reveal a
goat. He asks if you want to switch from the door you initially picked to the
other closed door. It seems like the odds are the same for any closed door, so is
there any benefit of switching? Counter intuitively, yes. The odds are twice as
good if you switch doors.
You can see the
maths of why here.
But even after seeing that, it still feels
wrong: with two closed doors remaining, how can the odds be anything but 50-50?
And yet…
Believing in
maths isn’t easy, is it? But at least, we are in good great company...
Yes.
ReplyDeleteI am getting more and more convinced that maths always has something extra which seems unreal and weird at the start. After a while, it looks clear enough but there is some other extra in maths which floors you!
There are times when physics provides meaning to something in maths, which is not clear as a mathematical entity to start with. Physics so desperately leans on maths for its own elaboration that it seems to actually enhance maths. Strange. With all its un-understandable power, it may not always be maths that has physics at its heels!