This episode kicks off the next theme on Data Skeptic: artificial intelligence.  Kyle discusses what's to come for the show in 2018, why this topic is relevant, and how we intend to cover it.

We break format from our regular programming today and bring you an excerpt from Max Tegmark's book "Life 3.0".  The first chapter is a short story titled "The Tale of the Omega Team".  Audio excerpted courtesy of Penguin Random House Audio from LIFE 3.0 by Max Tegmark, narrated by Rob Shapiro.  You can find "Life 3.0" at your favorite bookstore and the audio edition via penguinrandomhouseaudio.com.

Kyle will be giving a talk at the Monterey County SkeptiCamp 2018.

This week, our host Kyle Polich is joined by guest Tim Henderson from Google to talk about the computational complexity foundations of modern cryptography and the complexity issues that underlie the field. A key question that arises during the discussion is whether we should trust the security of modern cryptography.

This episode features an interview with Rigel Smiroldo recorded at NIPS 2017 in Long Beach California.  We discuss data privacy, machine learning use cases, model deployment, and end-to-end machine learning.

When computers became commodity hardware and storage became incredibly cheap, we entered the era of so-call "big" data. Most definitions of big data will include something about not being able to process all the data on a single machine. Distributed computing is required for such large datasets.

Getting an algorithm to run on data spread out over a variety of different machines introduced new challenges for designing large-scale systems. First, there are concerns about the best strategy for spreading that data over many machines in an orderly fashion. Resolving ambiguity or disagreements across sources is sometimes required.

This episode discusses how such algorithms related to the complexity class NC.

In this week's episode, Scott Aaronson, a professor at the University of Texas at Austin, explains what a quantum computer is, various possible applications, the types of problems they are good at solving and much more. Kyle and Scott have a lively discussion about the capabilities and limits of quantum computers and computational complexity.

I sat down with Ali Ghodsi, CEO and found of Databricks, and John Chirapurath, GM for Data Platform Marketing at Microsoft related to the recent announcement of Azure Databricks.

When I heard about the announcement, my first thoughts were two-fold.  First, the possibility of optimized integrations with existing Azure services.  This would be a big benefit to heavy Azure users who also want to use Spark.  Second, the benefits of active directory to control Databricks access for large enterprise.

Hear Ali and JG's thoughts and comments on what makes Azure Databricks a novel offering.

In this episode we discuss the complexity class of EXP-Time which contains algorithms which require $O(2^{p(n)})$ time to run.  In other words, the worst case runtime is exponential in some polynomial of the input size.  Problems in this class are even more difficult than problems in NP since you can't even verify a solution in polynomial time.

We mostly discuss Generalized Chess as an intuitive example of a problem in EXP-Time.  Another well-known problem is determining if a given algorithm will halt in k steps.  That extra condition of restricting it to k steps makes this problem distinct from Turing's original definition of the halting problem which is known to be intractable.

In this week's episode, host Kyle Polich interviews author Lance Fortnow about whether P will ever be equal to NP and solve all of life’s problems. Fortnow begins the discussion with the example question: Are there 100 people on Facebook who are all friends with each other? Even if you were an employee of Facebook and had access to all its data, answering this question naively would require checking more possibilities than any computer, now or in the future, could possibly do. The P/NP question asks whether there exists a more clever and faster algorithm that can answer this problem and others like it.

Algorithms with similar runtimes are said to be in the same complexity class. That runtime is measured in the how many steps an algorithm takes relative to the input size.

The class P contains all algorithms which run in polynomial time (basically, a nested for loop iterating over the input).  NP are algorithms which seem to require brute force.  Brute force search cannot be done in polynomial time, so it seems that problems in NP are more difficult than problems in P.  I say it "seems" this way because, while most people believe it to be true, it has not been proven.  This is the famous P vs. NP conjecture.  It will be discussed in more detail in a future episode.

Given a solution to a particular problem, if it can be verified/checked in polynomial time, that problem might be in NP.  If someone hands you a completed Sudoku puzzle, it's not difficult to see if they made any mistakes.  The effort of developing the solution to the Sudoku game seems to be intrinsically more difficult.  In fact, as far as anyone knows, in the general case of all possible examples of the game, it seems no strategy can do better on average than just random guessing.

This notion of random guessing the solution is where the N in NP comes from: Non-deterministic.  Imagine a machine with a random input already written in its memory.  Given enough such machines, one of them will have the right answer.  If they all ran in parallel, one of them could verify it's input in polynomial time.  This guess / provided input is often called a witness string.

NP is an important concept for many reasons.  To me, the most reason to know about NP is a practical one.  Depending on your goals or the goals of your employer, there are many challenging problems you may attempt to solve.  If a problem you are trying to solve happens to be in NP, then you should consider the implications very carefully.  Perhaps you'll be lucky and discover that your particular instance of the problem is easy.  Sudoku is pretty easy if only 2 remaining squares need to be filled in.  The traveling salesman problem is easy to solve if you live in a country where all roads for a ring with exactly one road in and out.

If the problem you wish to solve is not trivial, or if you will face many instances of the problem and expect some will not be trivial, then it's unlikely you'll be able to find the exact solution.  Sure, maybe you can grab a bunch of commodity servers and try to scale the heck out of your attempt.  Depending on the problem you're solving, that might just work.  If you can out-purchase your problem in computing power, then problems in NP will surrender to you.  But if your input size ever grows, it's unlikely you'll be able to keep up.

If your problem is intractable in this way, all is not lost.  You might be able to find an approximate solution to your problem.  Good enough is better than no solution at all, right?  Most of the time, probably.  However, some tremendous work has also been done studying topics like this.  Are there problems which are not even approximable in polynomial time?  What approximation techniques work best?  Alas, those answers lie elsewhere.

This episode avoids a discussion of a few key points in order to keep the material accessible.  If you find this interesting, you should next familiarize yourself with the notions of NP-Complete, NP-Hard, and co-NP.  These are topics we won't necessarily get to in future episodes.  Michael Sipser's Introduction to the Theory of Computation is a good resource.