Let’s win $1,000,000!
Good Morning All! Today we shall endeavor to win $1m by
solving a really tough mathematical problem. There are 7 so-called millennial
problems, the solution of each of them merit’s a $1m prize. I’ve picked the first on the list, a seemingly
easy problem called P=NP. Right then chaps, let’s solve it!
P=NP
Problem = No Problem!
Wait, that’s not right… erm, P must be a variable, that’s
it. And, the N must stand for Not. So… some number P is equal to some other
number Not P?
P=NP……. 1=2? But how could 1=2? That’s already been
disproven, hasn’t it? Okay, how about in Modular arithmetic, or Non-Euclidean
Geometry? *Consults* Well, those branches of math have their own problems, let’s
leave them alone. Okay, another approach, suppose were looking for something
universal? That all problems which have no solutions actually have solutions??
Hmm, obviously were not getting anywhere. Let’s try looking
this problem up:
*45 minutes pass* The office is a mess of crumpled papers,
scribbled notes, and half the walls are covered in print-outs. Sheepdogs wilted
to the floor, and the bunnys have poured cocoa on his furry head in efforts to
revive him.
*Ahem* No thanks to the bunnies, we may finally have some
answers. P=NP states that if a computational solution to a problem can be verified, there exists an algorithm to solve the problem. P represents the problem,
where a solution may exist, and NP represents the verified solution.
Buy why call them P and NP, you ask? Trust me on this one,
you don’t really want to know. P stands for “The existence of an algorithm for
a task that runs in polynomial time. The
general class of such questions is called class
p, whereas NP is an answer that can be verified in polynomial time, and stands for nondeterministic
polynomial time.” See? I told you that you didn’t want to know.
Suppose you ask, as I once did, what polynomial time is. Again, you don’t really want to know. An
algorithm is said to be of polynomial
time if its running time is upper bounded by a polynomial expression of the
same type as the input for the algorithm. From here we get into multiple rabbit
trails, including strong and weak polynomial time, super polynomial time, and
exponential time. And from there the spiral continues down computational
complexity theory.
Anyway, we just wanted to solve this and earn $1m, but how can we solve it if we don’t even
understand the question???
Let’s break down all the technical jargon, and see if we can
wrap our brains around this concept of P=NP without trying to traverse all of
time and space to do it.
Suppose we went to Disneyland! And once we are there, we
want to know where the teacups ride is. We walk up to the information desk, and
there is a line of people about 10 people in front of us. We still don’t know
where the teacups ride is, but we have a pretty good idea how long it will take
to find the answer: namely 2 minutes per person times 10 people: or 20 minutes.
This is what polynomial time is. It’s a way to determine how long it could take
to find the answer.
The information desk here is the algorithm, or solution to our problem. He or she knows where everything
is in the park. This is P.
But suppose we don’t go to information. Suppose we ask Mickey
Mouse to point us in the direction of the teacups. Mickey doesn’t know where
they are, but he knows it’s not in his section of the park. He just verified our guess that it was in a
different section of the park. So Mickey is NP.
Now of course, we know in Disneyland, there is an
information desk, or algorithm solution to our question. P=NP suggests there is
always an information desk anytime
there is a Mickey. Can we prove this? Well in any department store, or hotel
there seems to be. But what about a Saturday Market of sorts? Any clerk or
booth can tell us a piece of the puzzle, like where the broccoli stand is, but
can they tell us where everything is? Most likely not. But then, suppose there
exists a booth somewhere that is an information booth and we just haven’t found
it yet…
In this last case, we don’t know for sure if there even is
and information booth. And that is P=NP.
Quick! Go and solve it! And you could earn $1m!!!! Frankly,
I may be better off to publish this paper under humor and take my $3 publishing
fee. *hehe*
Sheepdog
References to all those big words I wrote:
2 comments:
Brain has been fed. Please enter junk food to wind down.
ooops! erm, sorry about that! *looks about for suitable junk food*. Here you go! https://www.youtube.com/watch?v=kTcRRaXV-fg
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