# Category Archives: Opinions

My opinions on politics, economics, education, World of Warcraft, and basically whatever comes to mind. Understand these mostly as the inane ramblings of a person.

# The Professional Effect

In a recent discussion with a friend, I talked about why the ability of polls and  markets to predict political outcomes seem to have taken a beating as of late. I described an effect whereas the more faith people place into a certain predictive tool and gain more knowledge of it, the less reliable it becomes. I vaguely remember hearing about it somewhere but when pressed for an academic source, I came up short. I couldn’t even give a name for it, which leads to the disturbing possibility that I simply made it up.

However, weeks later, I found a name for it in a rather unorthodox source: this video on the video game Hearthstone. At around the 11 minute mark, Trump talked about something he named the “professional mage effect”, which I shortened to simply the professional effect, which I believe is one of the main causes in the crumbling of the accuracy of polls and other statistical tools as of late. Trump himself summarized the effect fairly succinctly in the video, but for those of you who don’t know the language of Hearthstone, I will give you an explanation.

In Hearthstone there are nine playable classes. Each class has a distinct set of accessible cards and hero abilities. In the current incarnation of the game, the mage class was given several new cards that gave it a significant advantage over other classes. This meant that every time it was possible to select a mage, people tend to select mage; the difference in win rate between mage and the other 8 classes was staggering. As a consequence, Blizzard decided to introduce some changes to try to balance the game, most notably removing several problematic cards for mages. However, after a month of the changes, it seems that mage still maintained a sizeable lead. Blizzard explained this with the ‘professional mage effect’, where strong players who tend to read the statistics instead of choosing at will or from word of mouth, tend to still prefer mage because its previous high win rate and its current average win rate still gives an above average win rate; and since these players tend to be the strongest, their superior skill allows them to win more, which is conflated with the class being strong.

It appears that a similar phenomenon is at play when it comes to high frequency trading. Whenever too many algorithms use similar methods to choose stocks, a slight advantage is exaggerated and causing many buyers to buy into it, significantly overvaluing the stock. This then creates a lot of uncertainty in the valuation of stocks and makes the market rife for bubbles.

This seems to give a rigorous justification that a diversity of ideas is quantitat

# An ethical question with a concrete answer

Ethics questions often give a scenario (often unrealistic and missing key details) where you have to choose between a set of difficult options. For example, it could be “an old lady who has no family or a young man with a promising career and loved by a lot of people are both admitted to the ER. Who would you prioritize on treating if their probability of survival is the same?”

However, sometimes the answer is quite a bit more straightforward. The question I saw is the following: Suppose that an intelligent machine has the ability to predict, with 99.99% accuracy, whether someone will commit murder. Would it be permissible to arrest people based on the predictions of the machine?

There seems to be no ‘correct’ way to answer this question, but that’s because the person who asked the question doesn’t understand statistics. There is a phenomenon in statistics called the false positive paradox, where even a very accurate test will produce many more false positives than actual positives. This is relevant when the actual probability of a true positive is very low.

Here is an example. You are a unique person, one of say 7 billion. Suppose that there is a machine that can identify someone with 99.9999% accuracy. A person gets scanned by the machine, and the machine says it’s you. What is the probability that the machine is right?

There are two possibilities for the machine to give that reading. Either the person scanned by the machine actually is you and the machine is accurate, or the person scanned by the machine is not you and the machine malfunctioned. The probability that the machine is accurate is 99.9999%, and the probability that the person scanned is you is one in 7 billion. The other possibility is that the machine is wrong and the person being scanned is not you. The probability that the machine is wrong is 0.0001%, and the probability that the person is not you is 6,999,999,999 out of 7 billion. Thus, the probability that the person actually is you, given that the machine says it scanned you, is given by the equation

$\dfrac{\frac{999999}{1000000} \times \frac{1}{7000000000}}{\frac{999999}{7000000000} \times \frac{1}{7000000000} + \frac{1}{1000000} \times \frac{6999999999}{7000000000}}.$

Evaluating, the probability that the machine is right is less than 0.015%. The paradox is caused by the fact that the machine’s accuracy is very poor compared to the astronomically unlikely phenomenon that you would be picked out of 7 billion people.

Now back to the question. Whether it is ethical or not (that is, whether the machine produces a desirable result an acceptable proportion of the time) will depend on the actual murder rate of a place. The global average is currently 6.2 people out of every 100,000, or 31 out of every half a million. Assuming the machine has accuracy 99.99%, the probability that a person identified by the machine as a murderer is actually a murderer is given by

$\dfrac{\frac{9999}{10000} \times \frac{31}{500000}}{\frac{9999}{10000} \times \frac{31}{500000} + \frac{1}{10000} \times \frac{499969}{500000}}$

or roughly 38.3%. Therefore, the machine is right way less than half the time, far below what can be considered reasonable. Therefore this question has a concrete answer and is not really debatable.

# Some thoughts after reading an article on Peter Scholze

Recently the following article appeared on my Facebook feed: https://www.quantamagazine.org/20160628-peter-scholze-arithmetic-geometry-profile/Aside from the usual bland mix of singing praises of an archetypal ‘genius’, the article does contain some genuine insights. The most striking of which is Scholze’s description of him learning the proof of Fermat’s Last Theorem by Sir Andrew Wiles: that he “worked backward, figuring out what he needed to learn to make sense of the proof”. Later he also said things like “I never really learned the basic things like linear algebra, actually – I only assimilated it through learning some other stuff.”

If you have experiences learning mathematics at the senior undergraduate level or post-graduate level, you will likely find that these experiences are orthogonal to your own. We spend an inordinate amount of time learning the ‘basics’ for various things, which very much includes linear algebra for example, in order to do research… or so we are told. If you have passed the part of your career where you do more courses than self-learning, then you have likely reached the epiphany that usually it’s not efficient to learn everything there is to know on a subject before actually doing work on the subject.

Of course, I am but a pebble to the avalanche that is Peter Scholze, so my advice may not be worth much. Nevertheless, I feel like I should say this to all prospective and current graduate students: be bold, and give every difficult paper in your field a read. Don’t be intimidated by them. If you don’t understand something, google it until you find what you need to learn the language of the subject. Don’t feel like you need to understand all of Harthshorne before you can read any research papers related to algebraic geometry. Your future self will thank you for this.

Last night, I had the honour of attending a panel discussion featuring eminent mathematician Manjul Bhargava. During the panel, the moderator, Professor Kumar Murty asked the very productive Fields Medalist to give some advice to graduate students in the audience who may be struggling with their research. Professor Bhargava’s response, paraphrased, is essentially the following:  always work on several problems at a time (at least three), of varying difficulty. There should be a problem which is quite difficult and if you make any progress on it it will be a major breakthrough; there should be one of moderate difficulty, and there should be an ‘easy’ problem that you know you can make progress on eventually. Further, never think too much about a problem at a time and instead rotate between the problems to change your mindset. Sometimes when you approach a problem with a fresh perspective you will gain some insight that would’ve been impossible if you stared at the same problem continuously, since you are subconsciously trying to apply the same techniques.

I thought Professor Bhargava’s advice was very helpful to the graduate students in the audience. It is something I started doing a few years ago, but it wasn’t something that I was aware of consciously. Hopefully heeding this advice will be helpful to your work.

# Elizabeth Keen is not dead

More so than that, it appears that my observations watching the episode where ‘died’ were basically right on the money. Feels good to be right!

# Why Elizabeth Keen is (obviously) not dead

I just watched the latest episode of The Blacklist. MAJOR SPOILERS ARE AHEAD, THIS IS YOUR WARNING.

So in the latest episode, “Mr. Solomon – Conclusion”, there is a cataclysmic plot twist in which Elizabeth Keen, whose mysterious familial background is the driving force of the show, seemingly perished after a medical complication. The shock value of this development cannot be underestimated… however, I claim that she is (obviously) not dead. Here are the clues:

1) When Keen was assessed by the first doctor at the hospital, her diagnosis was fine. There are no indications at that time that she has suffered any serious trauma.

2) When Mr. Kaplan went to pick her up from the hospital, Keen was talking angrily about how she’s in this situation because of Reddington. Mr. Kaplan looked sympathetic. Most likely they planned what to do right after.

3) Notice that Keen started developing medical complications only after being treated at the nightclub. During this time Mr. Kaplan, Keen, and Nick had time to converse in private; Reddington (and therefore the audience) is not aware of what happened. After this conversation, all of a sudden Keen’s medical condition started deteriorating, and Nick asked for additional medical equipment to be brought. Who took care of this? Mr. Kaplan.

4) Mr. Kaplan very squarely blamed Red for Keen’s predicament. It is not at all surprising if she would secretly plan to fake Keen’s death just so that Reddington could not be in Keen’s life any longer.

5) After Keen has been pronounced dead, Mr. Kaplan, who earlier in the episode showed that she obviously cares for Keen, displayed no distress. Reddington almost fell over and Samar balled her eyes out, even Nick was extremely distraught. So why didn’t Mr. Kaplan react at all? Probably because she knows Liz is not really dead. Moreover, she again murmured something to Nick while Dembe was helping Red into the car. Clearly there is something astray here.

The obvious need to ‘kill’ Liz is because Megan Boone is pregnant for real and probably has to go give birth for real, and take some mat leave on top of that. This is a pragmatic solution to this very gnarly logistical issue. Do not be surprised if Keen pops up all of a sudden on episode 20 or earlier.