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The third criteria of immediate feedback seems too stringent. In chess, feedback is often not immediate. If one were to run a reinforcement learning algorithm on chess with no human coded rewards, the only objective feedback would come at the end of the game (win, loss, draw).

Certainly the more immediate the feedback the better though.

Something that has been disturbing to me has been the rise of the phrase "freedom of speech does not mean freedom from consequences."

On some level, this is true. People can of course legally react in certain ways to someone's speech, such as deciding not to associate with them.

However, I feel like the phrase is a bit deceiving because it seems give the impression that "freedom" and "consequence" are unrelated. It's designed to give people the feeling that they are justified to impose more and more "consequences" (such as blacklists or even threats of violence).

Here's the definition of the phrase from the dictionary: "the right of people to express their opinions publicly without governmental interference, subject to the laws against libel, incitement to violence or rebellion, etc"

In this definition, "freedom" is directly identified with protection from a certain consequence, i.e "governmental interference." I think it should be obvious that "freedom" isn't really about the ability to move ones' mouth and make noises, but rather the freedom one has is DIRECTLY related to ones' protection from consequences. Extralegal actions to increase the "consequences" of certain types of speech directly reduce free speech.

This isn't a black or white thing, but based on what I've been seeing in social media, the possibility of some people internalizing the mantra "freedom of speech does not mean freedom from consequences" to the point that they justify violent action against speech they dislike doesn't seem implausible.

If M ~ N(u,v_m) and W ~ N(u,v_w) [where N refers to the normal distribution], with v_m > v_w, then P(M > T) > P(W > T) for all T > u. I.e if the trait is approximately normally distributed with equal means among two groups, the group with the higher variance will exhibit more extreme values. Why is this a change in argument?

Just to respond to a few specific points:

>Despite that unjustified leap, the document goes on to suggest strongly that women working at Google are less qualified than men

Can you elaborate on this? Just because FEWER women may be qualified to work at Google doesn't mean that the ones that are are any less qualified than the men. The fact that fewer women are tall doesn't mean that tall women aren't tall for example.

>I could argue "water is composed of two hydrogen molecules and one oxygen molecule, so women are bad at software development", and my argument would just be a difference of degree worse than hers.

I fail to see how the science discussed in the memo is as irrelevant as you make it out to be. Is it really that far fetched that psychological makeup (as expressed in big-5 characteristics) and interests play a role in what people choose to pursue and what they like to do? Because software engineering is different than other occupations (such as law and medicine), it makes sense to think about what might attract one to one profession over another. Many intelligent women I know chose careers such as medicine over cs. And why not? It pays better and doesn't involve staring at a computer all day (something that not everybody enjoys). The same could be said for law and finance (investment banking, private equity).

>Among all STEM fields, computer science is distinguished for losing the participation of women over the last 10 years.

http://www.pbs.org/newshour/making-sense/truth-women-stem-ca...

If you scroll down to the two bar charts in the link above, you'll notice that while the % of bachelor degrees earned by women in CS has gone down, the % of PHD degrees earned has actually gone up (looks to be about 40% higher compared to 1991)! I think you would agree that earning a phd in CS is much more difficult than a BS, and I think this actually shows that women are being given more opportunity to excel academically in the subject.

As for bachelor degrees in CS, it seems like it has converged more to the % awarded in engineering. Speaking more on the differences between CS (i.e Bachelors level CS that leads to SWE jobs) and Math, I would say there is a qualitative difference between the two, and certainly one can have personal preferences. Software engineering is much more about creating systems that work and solve real-world problems. It also involves a lot of programming. Pure math (and theoretical CS) is more about investigating an abstract world and looking into interesting patterns and connections. It actually has a lot of similarities with philosophy in this regard. Some of the female math/science majors I knew actually didn't really like programming and ended up being highly successful in other fields even if they went into industry (medicine/finance/business).

>There's a reason she does that: if you don't stipulate that correlation, the argument against gender bias in computer science has to confront another damning fact, which is that gender disparity in the field isn't global. Unless women in Asia are somehow biologically different than those of the US, her argument needs some way to address the fact that women make up the majority of STEM majors in many of those cultures.

In fact, people have done cross-cultural studies. https://www.researchgate.net/publication/23179757_Sex_Differ...

"Regression analyses explored the power of sex, gender equality, and their interaction to predict men's and women's 106 national trait means for each of the four traits. Only sex predicted means for all four traits, and sex predicted trait means much more strongly than did gender equality or the interaction between sex and gender equality. These results suggest that biological factors may contribute to sex differences in personality and that culture plays a negligible to small role in moderating sex differences in personality."

From my personal experience (which I agree is less convincing than the numerous empirical studies that have been done on the topic), I'll say that many women in asian countries are pushed into studying cs/programming even if they don't like it, because those fields often provide a straightforward path to making a decent income.

Seems like a lot of the controversy around these types of discussions comes from the consequences of bayesian inference.

If you know that men and women differ in a distributional sense with respect to some trait, that gives you a prior to work off-of when you meet a new individual. This is rational from bayes theorem, so simply saying "you should treat everyone as an individual" is not nuanced enough.

However, as you acquire more information about a particular individual (such as passing a difficult google interview, or knowing that they've succeeded in a reputable CS curriculum), this should quickly "swamp" the prior, causing it to contribute very little to the final inference.

The problem is the humans are not great at adjusting like this: we're not perfect at applying bayes theorem in our heads. We tend to overstate the influence of various priors when there are stronger signals at hand. Nevertheless, incorporating prior distributional information is NOT irrational, but generally overdone.

Therefore, it seems like the approach of some is to shout down information that would suggest biological distributional differences, to try guarantee that people don't overuse prior information.

I think that's being too results driven and doesn't take into account the risk that was taken. As another example, suppose your uber driver drove you home while intoxicated. Even if the trip ended up being fine (no accidents, smooth ride), you would still have valid justification for complaining about this.

Just because his investors made money doesn't excuse him.

Suppose you lent 10,000 to a friend and the friend promised to return it within a year. A year later, your friend doesn't pay you back and makes a bunch of excuses. Instead, he takes the 5,000 he has left to the casino, gambles it on the roulette wheel and by luck manages to turn that into 30,000 and pays you back 1.5 years later. I don't think you would be happy with that situation...

All the stats stuff you mentioned (and more) is laid out very nicely in the second chapter of "Elements of Statistical Learning" https://web.stanford.edu/~hastie/Papers/ESLII.pdf

It's hard to know if the returns are statistically significant given annual returns, but I'm sure he's providing more granular statistics to investors. Kinda annoying how the articles hypes this by distinguishing it from statistical models since he is obviously running some sort of statistical model as well.

In general, people have a poor understanding of how to evaluate an investment manager. It's not enough to just look at absolute returns and compare them to the S&P, you need to correct for market exposure (the beta). Even then, it is not that straightforward: this is one of the best overviews I've seen (the author of the blog, Robert Frey, was a former managing director at Renaissance Technologies, the most successful hedge fund of all time)

http://keplerianfinance.com/2013/07/alpha-and-evaluating-inv...

To make the "correcting for exposure" aspect concrete, suppose you have the opportunity to invest in a poker player that generates a 10% return on capital per year. It wouldn't really make sense to compare this return to the S&P 500 returns, because the beta is very close to 0.

My suggestion would be to slow down when reading math or about math. Let's take Wikipedia's integer factorization for example: https://en.wikipedia.org/wiki/Integer_factorization

First paragraph is:

"In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these integers are further restricted to prime numbers, the process is called prime factorization."

This is a clear and precise statement of the problem. There are some key words that one might need to look up which takes time, but that's what I mean by slowing down.

Doug Polk is completely right and the binary "statistically significant or not" way of thinking is often stupid

Really nice proof! The "clearly" thing isn't too hard to see even if you aren't aware of the "alternating series theorem":

Consider the sequence a1, a2, a3... with the sum being a1 - a2 + a3..., note we can write the sum as: a1 + (-a2 + a3) + (-a4 + a5) hence the sum is less than a1.

We can also write it as: (a1-a2) + (a3-a4) + (a5-a6) .... hence the sum is greater than (a1-a2).

Well properly understanding why certain number systems work (fractions, negative numbers) requires some understanding of set theory, and the great mathematicians of the past struggled with a lot of these concepts we take for granted (negative numbers, complex numbers). It's unrealistic to expect high school teachers to understand these foundations.

What is disagreeable about his comment? Do you disagree that examining a statistic by subgroup could provide more insight into the question?

Growth comes from reinvestment of capital into the business. This makes sense from a shareholder perspective when the risk-adjusted return on this invested capital outweighs the returns capital could get elsewhere (other stocks).

Some companies will actually stop growing and start paying dividends/sharebuybacks for this reason.

Why not both? Both preparation and inherent ability are important. I find it implausible that everything can be explained by "mindset." Perfect pitch is a good example, it's a useful ability and cannot really be developed through training. Other factors are more subtle but are also fixed.

Yeah but the money he made from this doesn't sound like flow, sounds like a large directional bet (similar to the london whale event, except this one happened to work)

Whether or not it's a "fundamental principle of democracy" , the hyperbole and moral policing sets an extremely dangerous precedent. Yes, trump would be a terrible president but he's not Hitler (I know you didn't compare him to Hitler but it was a very common comparison in the media for a while).

Yes, preparation makes a big difference in math olympiad but most of those competing at a high level are already very talented to begin with. The problem is when a parent expects their kid to achieve similar performance when they don't have the raw skills. By attributing no role to inherent ability, blame is always put solely on the child for not trying hard enough. Even within a given family, you'll notice that some kids are better much more talented than their brothers or sisters at a given task, and the difference is not really preparation (especially since these differences can often be seen at a very young age).

In my experience, asian parents tend to vastly underestimate the importance of genetics that predetermine a child's strengths and dispositions. Kids that are born with some combination of great working memory, processing speed, and abstract reasoning ability will do fine at math and science with an order of magnitude less effort than others. For these kids, being pushed to perfection in school can be beneficial. For others, the expectation that they need to do as well as the other kid on the SATs or in engineering or medicine or whatever often leads to the problems the author describes (suicidal ideation, depression, etc...). Sure, everyone should be encouraged to try their best but there needs to be more focus on cultivating everyone's unique strengths. Often times the people getting perfect SAT scores aren't studying any more than others (in my experience, less), yet asian parents will tend to believe that their kid's imperfect score is due merely to a lack of effort.

The desire to "keep up with the Jones's" is one of the strongest human motivators in my opinion and very hard to fight. Most people want to feel respected or on par with their social circle. And even if one can resist the urge, there is often pressure from others (wife is a big one)

This can be mitigated by evaluating all the models on a hold-out test set (similar to what kaggle does and what was done in the netflix prize). The multiple comparisons problem is also mitigated by the fact that the models wont be completely random, there will likely be some positive correlation between them.

edit: Also, by hoeffding's inequality the number of training examples needed for a given level of confidence is only logarithmic in the number of models (even assuming they are independent). See page 6 here: http://cs229.stanford.edu/notes/cs229-notes4.pdf

it's r^2 in the denominator. one idea is to think of the geometry: the surface area of a sphere is proportional to r^2. therefore if you think of a constant "influence" at a given distance, you might divide it by the surface area (to get r^2 in the denominator)

of course they wouldn't have sued if theranos had scored, that doesn't make their lawsuit invalid. companies should be accountable for the statements they make (see Enron)

absolutely agree with 0xfffafaCrash on this, just because a measure is imperfect and has varying levels of validity depending on the person doesn't mean it has no signal.

i'm pretty sure someone who has gotten INTP every single test in his life will behave differently on average than someone who has always gotten ESFJ

Maybe this is an unpopular view, but I think there is something unnatural about mathematics for most people. It tends to be much more abstract than other subjects. I say this as someone who has always enjoyed math and majored in it.

And it does make sense to have "math for mathematicians" or "physics for physicists" classes. You see this a lot in college (often intro classes are divided into different "levels"). This allows some students to accelerate and others to still learn relevant materials but at a more appropriate pace.

well I can only speak to my own experience. personally I really enjoyed geometry but can't say the same for most students

Unfortunately, probability and stats are not easy to teach, and even many professional scientists / researchers have major confusions about the subjects. Common sense actually provides a decent enough guide for most people (i.e a baseball player with a high batting average is more likely to hit the ball).

Euclidean geometry as taught in school does seem rather archaic and out of place though. Some people say it's an introduction to "proofs/rigorous thinking", but it seems to me that that purpose could be better served with a first order logic class.

The problems he suggests overall seem too difficult for the average non-mathematically inclined student. And they also require quite a skilled teacher to teach.

I'm not sure stuff beyond "algebra 1" needs to be taught to everyone in high school. Even the concept of using "x" to stand for an unknown is very difficult for some to grasp. Instead, schools should make sure all students can properly understand how to use addition, subtraction, multiplication, and division, with applications to things like personal finance. In my experience, even many college graduates have trouble understanding when to multiply, divide, etc...

That's a great example and I don't disagree with you.

The way I think about "intelligence" is not to mull over what it "really means" but to think about lots of common "intellectual" tasks (in which aptitude can be measured) that people are interested in: reading, writing, math, programming, solving puzzles, etc. Or ideally, theoretical "potential" in each of these tasks, since one person may put more or less effort into another field.

What's supported by research and anectodal evidence is that if you did principal components analysis on these measured "aptitudes", there would be a principal component explaining a lot of the variation. A good test can try to measure this principal component.

But when you're talking about the very highest levels of specific tasks like cycling or swimming, it would be reasonable to expect that amongst the population of already "elite athletes" there would be less of a dominant first principal component