The Meaning of Life, the Universe, and Everything

Derek Feng

Friday, August 2nd 2019

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From Bridges to Amazon, to Sudoku, to One Million Dollars!

Graphs

We talked about the Konigsberg Bridges problem last lecture.

Question

What are the Practical Applications?

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Applications

I Garbage Collection?

I Postal Service/UPS/FedEx

I Supply Chain Optimization

This is what makes it possible for you to order something on Amazononline today and have it arrive AT YOUR DOORSTEP tomorrow.1

1Not sure about Abkazia...

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Traveling Salesman Problem

Given a list of cities and thedistances between each pair ofcities, what is the shortestpossible route that visits each cityand returns to the origin city?

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What about this graph?

NP-hard: hard to solve, also hard to check the solution.

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Shortest Path Problem

P: easy to solve

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Sudoku

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Sudoku

NP : hard to solve, but easy to check the solution

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Who wants $1,000,000?

All you have to do is show P 6= NP? That doesn’t sound too difficult,right?

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Let’s go back to Graphs and Networks

Traffic

I Suppose you are a Urban Planner and you are in charge ofimproving traffic in your city.

I You see that traffic is bad, and you decide to construct a new road

I Traffic should improve, right?

Question

Is it possible for traffic to actually get worse?

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Braess’ Paradox

I Seoul, Korea, Early 2000s: traffic improved when a centralhighway was removed

I New York City, 1990: the closing of 42nd street reduced theamount of congestion in the area

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Simple Example

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This is an example of the Tragedy of the Commons (more broadly, thefield of Game Theory)

I selfish individual behavior leads to results that are sociallysub-optimal.

Any solutions?

Self-Driving Cars: The Future

I One person is killed every 25 seconds by a Traffic-related accident

I On the other hand, the self-driving cars have driven millions ofmiles in USA, and there has been only 1 confirmed death

I Which is safer?

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Self-Driving Cars

Question

If a self-driving car kills someone, who is to blame?

Question

If you are Uber, and your passenger is in a self-driving car, and the carhas a choice between killing a bystander and killing the passenger, whatis it going to choose?

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Self-Driving Cars

Question

If a self-driving car kills someone, who is to blame?

Question

If you are Uber, and your passenger is in a self-driving car, and the carhas a choice between killing a bystander and killing the passenger, whatis it going to choose?

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Mathematics of Ethics

The Repugnant Conclusion

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Two scenarios:

1. A pregnant mother suffers from an illness which, unless sheundergoes a simple treatment, will cause her child to suffer apermanent handicap. If she receives the treatment and is curedher child will be perfectly normal.

2. A woman suffers from an illness which means that, if she getspregnant now, her child will suffer from a permanent handicap. Ifshe postpones her pregnancy a few months until she hasrecovered, her child will be perfectly normal.

Similar scenario:

I Suppose we who are living now decide to ignore global warming,with the result that the lives of future people are much harder.

I It would seem that we have made things worse for those futurepeople. But, in fact, as long as their lives are worth living this isnot the case—because if we had acted differently, the world wouldhave been different, and those particular people would never haveexisted

The Repugnant Conclusion

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The Repugnant Conclusion

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