One of the worst jobs I ever had involved doing door-to-door sales in both Tampa and Milwaukee, not an ideal task for an anxious and gouty person such as myself.  As much as I dearly love to rant from time to time, though, that is not the sort of traveling salesman I have in mind.  Rather, the traveling salesman problem is one of the classic problems of combinatorial mathematics, where determining the ideal and most efficient route of a traveling salesman or a busy baby-kissing politician is a problem of both immense practical benefit and immense difficulty.  The difficulty is fairly obvious, in that there are simply so many combinations to test that brute force methods are infeasible at figuring out what the best route for people to take.  Of all of the most serious problems in mathematics [1], this is a problem I have a considerable degree of experience in on a practical level.

For several months in 2013 I worked for UPS [2] as a consultant in their ORION project.  At the basis of this project was an effort by UPS to solve the traveling salesman problem as it related to the routes that drivers had.  Given that small improvements would lead to greatly improved costs, there was a high motivation for the logistics company to wrestle with this problem.  While the specifics of how this route optimization was done is secret–the general gist of it was that the accurate design of possible routes–hopefully not including logging routes in the middle of nowhere and the choice of constraints would lead to an optimal route that would, over time, save many millions of dollars and more efficiently organize the time of workers, something most workers are not necessarily the most fond of.  Testing the routes designed then required the effort of people like myself before the routes were handed off to drivers to operate as part of their daily job.  It was interesting work, and certainly provided me with a wealth of material to think about and ponder over relating to the relationship between mathematics and technology and the behavior of businesses as well as the culture within businesses.

There are, of course, larger implications for this view that require additional reflection.  The traveling salesman problem is one that requires an immense amount of computer capacity, and the sheer difficulty of solving a problem with that many combinations has increased security by the use of public codes that offer some defense from brute force attacks on firewalls, for example.  If the traveling salesman problem can be solved, though, by the use of contemporary computing, then it stands to reason that public codes are vulnerable because the same methods that would enable solving the problem by a logistics problem could be adopted by a hacker (or a group of hackers) to take down the computer defenses of a company or a public agency.  Combinations are combinations, and the same resources that one has to solve one problem of combinations can be used to solve others–the techniques have no moral qualms, and one depends on the people involved who do.

This suggests that there are trade-offs when dealing with the concern of probablistic resources.  Appeals to chance give a surface plausibility to theories of undirected evolutionary change that do not bear fruit in reality given the limits of such resources in reality.  Likewise, there are other problems, like the traveling salesman or politician, whose solution would be of benefit to people and companies who are willing to put a lot of resources to the resolution of such problems.  However, just as the refuge of permutations and combinations is one that companies wish to uncover for their own profit, so too is it a refuge for companies and institutions when it comes to protecting their own safety and privacy through the use of public keys.  If the ideal efficient routes for traveling salesmen cannot hide from contemporary searches, then neither can the public keys of companies and institutions.  The same techniques that lead to success in the one endeavor lead to it in another, making the question of how we are to ensure privacy and security in our world all the more serious.

There is an asymmetry about our approach to the world.  We want to see and not be seen.  We want to influence others and be immune from their influence.  We want others to hear us but we are unwilling to listen to them.  We want to rule others but do not accept the legitimacy of those in authority over us.  We want to find and not be found.  We want to teach and refuse to be taught.  From this asymmetry we find ourselves caught between a desire to do what we want to do better and a fear that others will do what they want to do but that we do not want them to do with us or to us.  That which frees us to accomplish our own wishes and desires also threatens our liberties by granting that same power to those whom we do not trust.  At what point will we reflect on the hypocrisies and inconsistencies and wrestle with the problems of trust that make technology such a boon and such a threat to us?

[1] See, for example:

https://edgeinducedcohesion.blog/2017/01/16/book-review-the-great-international-math-on-keys-book/

https://edgeinducedcohesion.blog/2016/02/28/book-review-the-babylonian-theorem/

https://edgeinducedcohesion.blog/2016/02/28/book-review-the-beginnings-evolution-of-algebra/

https://edgeinducedcohesion.blog/2016/01/15/the-mind-is-not-a-machine/

https://edgeinducedcohesion.blog/2014/06/20/common-core-and-the-politics-of-math-education/

https://edgeinducedcohesion.blog/2012/09/14/as-simple-as-abc/

https://edgeinducedcohesion.blog/2011/02/01/mathematical-proof-that-theres-no-such-thing-as-a-free-lunch/

[2] See, for example:

https://edgeinducedcohesion.blog/2013/02/05/divine-providence-in-the-life-of-nathan-the-upser/

https://edgeinducedcohesion.blog/2013/05/10/the-creature-of-a-squirrels-nightmares/