P versus NP

The Greatest Unsolved Problem You’ve Never Heard Of – a Movie Review – and Two Methods to Achieve Financial Independence

This week I’m gonna take a break from personal finance and review a math movie. There, I’ve said it. You’ll either stick with me on this post or I’ve significantly alienated a portion of my readers.

But if you wanna stick around (and I sincerely hope you do) then pull up a chair and let’s talk cerebral, math thriller flicks with a good dose of existential soul-searching.

Have you read the important notes before proceeding any further?

P versus NP and Math Thriller Movies

The Travelling Salesman is a movie released in 2012 and now available online for streaming. It’s a sort of cross between A Beautiful Mind and the Bourne Conspiracy, but don’t get your hopes up for the thrills. Most of the action consists of earnest dialog from tense characters stuck in a room.

The story follows a group of mathematicians who have solved the famously unsolved problem “P versus NP” from the field of computational complexity. I can forgive you if you have not heard of this problem, or aren’t familiar with this technical area of mathematical research. However, this problem underpins the integrity of our internet-based society, encompassing online shopping, national security and even crypto-currency.

The problem “P versus NP” is unsolved and is of such importance, and is so fiendishly difficult, that the Clay Mathematics Institute of Cambridge Massachusetts has included it among their seven problems that attract a cool $1m prize for any solution (or disproof).

So that could answer your financial independence problems – simply solve the P versus NP problem and collect your prize. [Method 1 to achieve financial independence. Solve P versus NP problem and collect $1m prize!]

But be careful if you do…

The Ramifications of Solving versus NP

In the movie the mathematicians with the solution are pursued by shady government agents and then have to wrestle with the moral repercussions and ethical dilemma of whether to make the solution public.

So what’s the big deal?

In this context “P” refers to problems that can be solved in a reasonable time with an algorithm. These are ‘easy’ problems. Whereas “NP” refers to problems that might be extremely hard to solve, but if you are given a potential solution then it is quick to check. Think of “NP” problems as like a lock. It’s really hard to create the key to open it, but if you are given a possible key then it’s quick to check whether it will work. The issue is that mathematicians do not know for sure that an “NP” problem is not actually a “P” problem. It might be the case that an NP problem is fundamentally difficult. However, it could be possible that an NP problem has a straightforward solution, but nobody has been smart enough to find it.

The solution of “P versus NP” would have a major impact on cryptography among other areas.

P versus NP
P versus NP

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Cryptography

Cryptography relies on being able to quickly encode and decode messages if you have the right key. It’s no good having a code that would take a computer years to encode and decode the messages. However if you don’t have the key then a code should be super-hard to crack and ideally take a computer several millennia to solve.

But here is the thing – if you could prove that P versus NP was true then cryptographic codes could be easily crackable, and this is why the ramifications of this unsolved puzzle are so important in modern life.

Almost all the internet runs on digital cryptography – think online shopping and any credit card transaction. None of these things can function without secure codes. In other words solving P versus NP could open the door for massive fraud and the demise of modern banking and the internet as we know it. If P=NP was proven to be true then it would be possible to instantaneously mine bitcoin and re-write the blockchain to your own advantage.

If you want to make a killing on Bitcoin then short BTC and start a credible rumor that P=NP has been solved. It’s value will plummet to zero. [Method 2 to achieve financial independence – short Bitcoin and create a rumor that P versus NP has been solved!]

Other Implications

This is really just scratching the surface of the implications of solving P versus NP. Certain computationally difficult problems, such as searching for proteins in biotech, could be quickly solved, curing a number of diseases and conditions. Additionally many algorithms in computer vision could be perfected, resulting in error free face recognition.  This would give a complete loss in anonymity as all faces and movements could be tracked without error.

So you can see that solving P versus NP would be big news.

Movie

I won’t spoil the end of the movie for you but you might want to think twice before selecting it for a date-night. (Unless of course your date is a mathematician). It’s attracted some pretty polar voting on IMDB with most votes swinging between 9/10 and 1/10 giving an average of 5.9. However, I enjoyed it. But bear in minds that’s coming from an actuary with a penchant for personal finance and personally holding a few mathematics degrees.

Whadya think? Do you want less of the math and more of the personal finance? Do you think my two suggested methods to achieve personal finance are achievable? What about having a Travelling Salesman party, get some Buffalo Chicken dip, and enjoy some cerebral conversation on the finer points of computational complexity?

11 thoughts on “The Greatest Unsolved Problem You’ve Never Heard Of – a Movie Review – and Two Methods to Achieve Financial Independence”

  1. Hmmm so things like the reverse discrete logarithmic function that underpin encryption. Very cool stuff, I might have to make my wife watch that one. Then again she has part of an masters in electrical engineering degree so she might enjoy it as well.

    1. My wife is a mathematician as well as me, so we really enjoyed it! Whatever floats your boat -right?
      [I’m not totally sure that hashing algorithms fall under the NP group, but I didn’t want to let that get in the way of a good post 😉 ]

  2. haltcatchfireblogger

    Cool article, however had to google the description of the problem on my mother language and it still did not help a lot 🙂 I remember, when the teacher presented this problem back at the university, but I never really liked higher level mathematics. I adore the ones who understand all this stuff, but I assume my imagination is too poor to process this kind of data. Will check the movie anyway. Have you seen “Gifted”? (not an equally hardcore math background story, but it is cute and includes the seven problems and probably better for a date night when no mathematicians are included). Thanks for sharing 🙂

    1. Hey, thanks for visiting. There is no doubt that P versus NP is a real head-wrecker! I shall check out the movie Gifted, sounds like it is right up my street!

  3. you might enjoy scott aaronson’s blog, shtetl optimized. it’s mostly serious stuff these days, but older posts were a lot of fun.

  4. btw, aaronson was the guy who achieved 15 minutes of very low level fame when, as a then-jr faculty person at m.i.t. he bet his house that a publicized paper on p vs np was wrong, sight unseen.

    1. jk – I was not aware of that blog so thanks for bringing it to my notice – it’s awesome! Although I hope Scott doesn’t stumble on my post, as I simplified a number of things in the interests of trying to make it a bit simpler. I found a post on his site where he said that he thought P probably was equal to NP (and provable under reasonable axioms) but that any kind of proof is a long, long way out of reach for the time being. One thing I glossed over in my post was that even if you could prove that P equals NP, the proof would likely be “non-constructive”. So you might know that your hard problem *has* a simpler solution, but you have no information as to how to construct that solution. That’s the view of Donald Knuth, one of my heroes. Thanks for stopping by, and hope to see you around again.

  5. This problem was proposed by John Nash to the NSA in the 1950’s. So does John Nash’s life provide a solution? He started as rational, descended into irrationality for years, and came back to rationality after some decades through a decision to leave irrationality and become rational again. He died rational. If P=NP he should not have had to leave rationality in order to explore irrationality. The solution should have been accessible through rationality if P=NP I could see him devoting his actual “time” to explore the boundaries of this problem. I never heard of anyone ever “deciding” to become rational and actually accomplishing that.

    Thanks for the article

    1. I had forgotten about Nash, good reminder. As is usually the case the real story is more interesting than the Hollywood rendition. I really don’t know much about his rehabilitation from mental illness, but it sounds extraordinary and unprecedented. And the fact that he was able to reflect so lucidly on his experiences and provide meta-commentary is amazing.

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