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.
I think it's more important that the input produces an immediate and readily observable change to the state of the world, not necessarily that you must have perfect information in the feedback as well that shows the exact utility of your previous action.
For example, in the stock market it's not even clear to me what the total scope of effects is, immediate or not, that any single action I take as a private investor will have on the market. Before I even can start to learn about the effectiveness of the changes that my actions produce, I am hamstrung by an inability to see an immediate, comprehensive effect to each action.
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?
>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.
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.
"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 don't think many people have a problem with any of the science or the statistics. That's not the problem with the 'manifesto'.
The author of the 'manifesto' seems to think that no one else reads these studies. I can assure you that everyone who is working on these issues has already read and understood the studies. The people in charge of these programs agree with them. He presented absolutely nothing of value. There is not a single new idea in what he wrote.
All the manifesto showed was that he thinks he you can just apply studies to your coworkers. He took a bunch of women he works with and turned them into statistics, into a problem that he alone can solve. It's incredible ignorant and arrogant.
The science, or understanding of statistics is not the problem, it is his approach to solving it that is the problem.
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...
> “I asked Fred where the funds had come from, and he responded, ‘The meeting with the General Dynamics board was a bust and I knew we needed money for Monday, so I took a plane to Las Vegas and won $27,000.’ I said, ‘You mean you took our last $5,000— how could you do that?’ He shrugged his shoulders and said, ‘What difference does it make? Without the funds for the fuel companies, we couldn’t have flown anyway.’ Fred’s luck held again. It was not much, but it came at a critical time and kept us in business for another week.” [0]
Technically, Fred committed a fraud (actually I forget the technical term for the crime where you misuse funds). Its just that he wasn't prosecuted for it.
Could you be thinking of Misappropriation of funds? I'm not a lawyer and I haven't spent a lot of time looking it up but from the few places I looked it doesn't seem that it would fit.
Your analogy is slightly off... suppose you lent $10,000 to an acquaintance known for being able to double it, and they promise to return it doubled in a year. A year later you ask for your money and he gives you $6,000 from someone else he convinced to do the same thing along with $6,000 from a different venture that was taking off and $8,000 work of equity for that startup. You didn't quite get what was promised, it seems a little shady, but at least he didn't rip you off.
The problem is, in most cases, historically the type of actions Shkreli tried often ends in disaster (often done by someone intentionally being malicious, I might add).
Shkreli may have been able to work his pseudo-Ponzi-ish scheme to investors' benefit. But it is pretty easy to look up the sordid history of the vast majority of Ponzi-type schemes, to see why this type of activity is generally illegal.
You don't think intent and net harm should be considered in criminal cases? I'd like this sentencing to send a clear message to fraudsters that:
A. If you get caught, you're going to prison
But more importantly -
B. If, however, you work hard to ensure the people you defrauded are not harmed by your fraud, your sentence will be lighter than if you were the type of fraudster to cut and run.
I don't know about you, but in light of the fact that fraudsters are always going to exist, I'd like to incentivize the "benevolent fraudsters", rather than pretending (through equal sentencing) that there is no difference between the two.
I would be perfectly happy to get more than my 10,000 back (like his investors did) late vs getting less or none back ever.
I'd be joyous if the return was better than I could expect to make otherwise, say > 10-20%.
Investments are risky. They are not automatic.
What I wouldn't be happy about is if I was lied to about the risk of an investment. That is closer to what this case is about. The money gained or lost doesn't really matter.
I don't see why it's disingenuous? Investing is extremely risky, and I'm not convinced that he didn't just get lucky on the second bet.
This isn't ok because the original investor was paid off. That's also how Ponzi schemes work - the original investors are paid off (I know, here the money seems to be generated from Retrophin, but the behavior is the same).
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.
I understand a risk was taken, but gambling has a less than 50% chance of return (by design) while buying a Pharma company that you control is conceivably less risk.
Let me add to this: Buying a company you have a government mandated monopoly on (patent) that owns a product that people will die if they don't take (inelastic demand), and has a huge barrier to entry for new, competing entrants (FDA) is conceivably less risk than throwing chips on a roulette wheel.
What if he lied to you, but then went out and through a combination of talent, hard work, and luck somehow made the money to make you whole and then some?
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)
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.
"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.
Be kind and do this for me: Think of yourself as Sara, an average person in society. Put yourself in her shoes. Now click on the following link and scroll down for a bit.
Scroll as slowly as you want/can. Tell me, do you think that this is a good way to communicate to Sara why this problem is of importance? or even better, do you think Sara will ever give a shit if all she can see is that?
If you want to promote a more scientifically literate society, you should not try to render every single person into a scientists. Rather, try introducing scientific thinking into people's every day lives. The only way that will happen is if those who know the sciences learn to communicate better with the rest of us and help us get it into our daily lives.
can you see where I am coming from? I am not annoyed by math or my ignorance toward the topic. I am trying my best to combat it. But the problem I often encounter is that those who know/can rarely speak the same language as those who cannot. Khan Academy grew big because he knew how to communicate, more people should be like him imo.
The first sentence is perfectly comprehensible (factorization is decomposing an object into factors which, when multipled together, gives back the original). As for the most of the rest of the article... there's really no reason for the average Sara to care about polynomial factorization at all (unless it's just algebraic manipulation for doing homework).
To promote a scientifically literate society, improve the secondary school curriculum to teach statistics: How does conditional probability work? What do sensitivity and specificity mean? When a poll comes out, what does the margin of error mean? What are some common probability fallacies and how to recognize and avoid them?
Etc.
In addition to Khan Academy, also check out the OpenStax textbooks (https://openstax.org/subjects) over the likes of Wikipedia (which is more often a mix of technicalese or a bunch of trivia depending on the subject of the article).
I was with you until you said "there's no reason for the average sarah...unless...homework"
I was the average Sarah, a lot of the people I went to public school with were the below than average sarah and it's the elitist math attitude that's being talked about here that turns kids off from that.
It wasn't until years later, after a career in concept art, then vfx and now programming that I realize..."hey the Fibonacci sequence isn't just some parlor trick for 'math types', it's a thing we can look at to study recursion and integrate in our code to make actual products".
Products that the average sarah uses and maybe even loves and would be supremely interested in learning about but doesn't because she's not a "math person".
I also lament the fact I didn't get into maths and see the beauty of it until years later when it was really too late to get into it at any professional level just because I was always implicitly told I was never meant to be a "math person".
Maybe I'm not, but if we could get more kids into maths, even if they're not geniuses, I think society as a whole and they themselves would greatly benefit from that.
It's not elitist to dismiss polynomial factoring, though, just dismissive. I really can't think of any reason to care about the deeper points of polynomial factorization (anything other than repeated trial division), so maybe it's just ignorance on my part.
Stats? Now there's math you can use and is useful in understanding our world! And yet schools prefer to teach calculus in high school over however much stats you can teach without calculus. No one uses the integration bag of tricks in daily life, but everyone gets lied to with numbers.
Same thing happened to me. I picked up math at 25 after not having done a single math related thing in almost 10 years. I picked it up after realizing that a lot of the things that I do on daily basis are heavily related to concepts such as triangular numbers and other sequences. My life would have been completely different had my teachers communicated math in better ways than simply saying here is an equation, solve!
> Scroll as slowly as you want/can. Tell me, do you think that this is a good way to communicate to Sara why this problem is of importance? or even better, do you think Sara will ever give a shit if all she can see is that?
"In all cases, a product of simpler objects is obtained."
That right there seems like a fairly well-stated explanation of the importance of factorization. As long as you're able to understand that a formula can be composed of objects, which I honestly don't think is that much of an abstraction, the very first paragraph (and in fact the very third sentence, the one that immediately follows two easy-to-understand examples of things that can be factored) tell you that factorization lets you express something in simpler terms.
I think an aspect of the problem is that wikipedia has become a highly technical reference rather than a traditional encyclopedia for a layperson to educate themselves. e.g. Articles often swamp the basic idea with myriad qualifications and connections to other topics.
There's demand for both levels.
I'd also like a wikitorial or wikixtbook... taking a layperson through to solid understanding but I suppose something like Khan is what's needed for that role.
BTW I've found wolfram often better than wikipedia for maths topics.
I agree that there is a demand for both levels. That's why there is also a "Simple English" version of this page. [1]
I agree that discoverability of this feature can be hard, though.
I also miss the fact that this feature is only available to the English language. There could be a "simple article" feature built into the website, I think.
Ah! Right on all counts. I have come across this feature before... but (eg) looking at the ordinary wiki page for factorization, I'm not seeing a link to it...
So, to access the user-friendly, non-technical, layperson version is simple, all you need is to know how to edit the url... that's wot you call ironic, that is.
EDIT It's not even linked under "see also"... ok, your remark on it being only english was a tip-off... it's counted as the language "simple english", and is available under the language icon (a funny looking "A" on the left... which I would never have guessed was for languages). I can see that'a a very easy hack to add an alternate version of a page, since that's what languages are already... but IMHO, layperson versions of a page (or even for experts, wanting to just get the gist) are an essential part of wikipedia's mission and purpose.
Re: simple versions in other languages: they could use the same hack, and have (eg) "simple french", "simple japanese" etc, but because it's so important, I'd suggest another explicit level, something like "https://simple.en.m.wikipedia.org/wiki/Factorization" (BTW that's also a mobile url, since I'm on a phone... I'd say, "simple" is just as important).
I understand wikipedia reached a level of completion a few years back, and the organization consequentally changed in character. A push for simple versions of everything coukd revitalize it.
> Some other fundamental concepts of modern algebra also had their origin in 19th-century work on number theory, particularly in connection with attempts to generalize the theorem of (unique) prime factorization beyond the natural numbers. This theorem asserted that every natural number could be written as a product of its prime factors in a unique way, except perhaps for order (e.g., 24 = 2∙2∙2∙3).
All your examples of the problem you are talking about are from Wikipedia, but you give multiple examples in your posts of explanations of maths done the right way. Feynman, Khan Academy, Project Euler. So I guess some maths related text is written one way and some is written another way?
Sure. But I hope that you can see how little access the average person have to mathematical concepts unless he/she have had years of formal training. Khan academy, Numberphiles and the likes have done wonders for lots of us out here. But it is still not enough and more needs to be done. Especially when talking about concepts that are new or truths that we constantly "take for granted".
But is Khan Academy really so different to formal training? I mean, who is going to understand a Khan Academy video on solutions to 2nd order linear homogeneous differential equations if they have never learned any algebra? There is language in there that is necessary to explain it that they will have had to learn before.
It would be great for there to be more resources for learning maths outside being officially enrolled in formal education, but I don't think this has anything to do with the language used in mathematics being too terse or obtuse. Lots of good undergrad textbooks are no less understandable than a Khan Academy video, try those instead of Wikipedia.
Certainly the more immediate the feedback the better though.