I decided to provide my feedback on the paper because judging from some of the comments I've read, some of you did not read it. To those that did read it, remember that the authors are people too and can offer any clarifications or address any concerns you have.

After reading through the paper, I'd like to say the authors did an excellent job addressing a sensitive subject. Part of me likes to think that they, like many of you, thought that enrichment programs were a given positive addition to life. The authors do an excellent job attempting to use mathematics to model human behavior - Sections 2-4 are almost entirely used to explain what they mean and how their equations operate. While reading the paper, I thought about some of the negative comments on this thread about economists. To that, I reasoned that we use mathematics as an attempt to model the world. Physics is our attempt to model the physical world and economics is the closest thing we have to modeling human behavior. If you disagree with that sentiment, become an economist and change the domain or dual major in data science and psychology (or sociology or any other degree used to model humans).

My biggest takeaway from this paper is that additional HOMEWORK does not help in improving a student's cognitive ability. In the paper, enrichment is defined as "investments in children's skills" which 87% of their dataset consisted of homework, reading, or before/after school academic programs. Doing or adding an additional hour of these activities does not provide any benefit to the child. This does not mean that learning is bad, as class time was a separate category, it meant "doing more" didn't help. Again, this is a sensitive subject, and I can agree that the authors don't account for "bad" instruction.

I will say there are limitations to their results, which they do acknowledge. Their dataset is small, but one of the closest datasets we have to mapping long-term human activities. I'd say this limitation grows exponentially because the CDS/PSID dataset they use only addressed 3 days in an individual's life. If I am wrong please correct me, but that is what I assume they used based on the paper. PSID contains 75,000 individuals and they only sampled 4,330 children. However, if you assume a nuclear family (4 people), that means the dataset contains ~18,750 families, which means the sample is ~25%. Again, this is a limitation, but one of the only approximations we have. The other limitation is that they are using self-response surveys, which have limited reliability.

With that, what can we take from this paper? My takeaway is that people are effectively equal but different at the same time. This was addressed with their h(X) value. Using all controllable variables, some h() function exists that produces what they addressed as "ability". This is once again where I, as did the authors, recognize that it is a sensitive topic. It is also one of the additional limitations I would say to their paper - assuming ability is a fixed value.

However, as a discussion point, 'ability' would account for some ugly truths. The g-factor and IQ are methods to address cognitive ability with sensitive undertones. Likewise, it is a commonality that networking is a key factor in successful employment often mentioned on HN. This could be accentuated by their findings that additional enrichment negatively impacted non-cognitive skills. Just because you are smart does not mean you are employable. However, I acknowledge that assessing cognitive ability is a sensitive topic, ripe with misconstruction. Likewise, I think the authors do their best to NOT say your ability is determined at birth.

I would caution against using "ability" as a metric for determining worth. Doing so would encourage early testing to see if someone is "worth the time" and I imagine would be vulnerable to prejudice and confound the features of X, e.g. a low-income child is not worth investing in. Instead, I would argue that this paper doesn't fully address "potential" with their unboservable ε. The job of the individual instead is to identify and maximize their potential (X) or at the very least improve the potential of their future selves (X+1, or children). This would acknowledge the concept of "expertise", or practicing a task makes you better at said task. It still presents an uncomfortable truth that some people aren't able to achieve success in a given task, but does address improving one's self.

I'll end there for some discussion and because it is late.