throwawaymath

Not that this is uncommon, as we approach 2020...

No, it doesn't. Category theory is not intrinsic to the development, use or explanation of this technique. Category theory is merely one possible framework for explaining why the technique works the way it does. That's an important distinction, and likewise it's not the most practical framework for understanding this technique by a long shot.

In particular, understanding why certain programming techniques are more performant than others virtually never requires the language and abstractions of category theory. Everything you're saying here is a further demonstration of the complaints others have voiced in this thread. Not because you're wrong - you're not wrong. Rather because it's just not the most practical way of understanding or leveraging most programming techniques, and it injects a significant amount of unnecessary abstraction and foreign mathematical terminology into discussion.

For what it's worth I have taken graduate math courses wholly and partly focused on category theory, so I have the background to follow what you're saying. It's essentially correct. But it's also obtuse and mostly inscrutable to other people. It reduces, rather than increases, the shared context software engineers leverage to understand each other. You can project a vast and magnificent theory of categories onto programming because it adheres to a variety of algebras, but at the end of the day it's just not clarifying anything further. Instead it's miring it in overcomplicated verbiage.

There's basically no reason for you to be explaining why a regular expression is faster than a for loop for this use case with the formalism of category theory, unless it's as an academic exercise just to show you can. Explaining this example with the language of functors and type spaces is like proving that Excel is Turing complete in order to explain how summing arbitrary rows in a column works.

The more pedagogically appropriate way to learn analysis is with heavy emphasis on basic topology (metrics) and with the language of geometry. Geometry is useful in calculus and analysis for intuition. Measure is beautiful and helpfully simplifies/generalized a lot of results, but it's really abstract and (in my opinion) unmotivated if you've never encountered rigorous integration or differentiation before.

I'd recommend Tao's, Pugh's or Stein & Shakarchi's analysis books over this one if the focus is analysis. I agree with your broader point that the structure and presentation of math can substantively change, even if the fundamental content doesn't at the undergraduate and graduate levels.

I feel like I've been drinking the author's life from a cup. Spectating his memories right alongside him. What an engaging style of writing.

And as a followup, if you can generate a synthetic dataset by extrapolating from sufficiently many independent conclusions drawn from the original (as opposed to having access to the original itself), would you still need to use such a dataset for training?

Things like Monte Carlo simulation can be used to approximate real world conditions, but they can't typically capture the full information density of organic data. For example, generating a ton of artificial web traffic for fraud analysis or incident response only captures a few dimensions of what real world user traffic captures.

The author talks about simulating data to focus on edge cases or avoid statistical bias, but I don't see how simulated data actually achieves that.

I still use Chrome. I don't feel the need to "justify" my use of Chrome. I like Chrome. I care about internet privacy - I use ublock origin and have JavaScript disabled by default, and only reenable it for sites I really care about.

But I don't really have strong opinions about internet browsers. I used to use Firefox, but a few years ago I started using Chrome and just found it to be better for my habits. I like the tight integration between Chrome and my Google account.

I use a Google Home and several Nest products at home (granted they're on their own VLAN). I use GSuite for my personal email, and Google domains for my domain names. Chrome is just another drop in the bucket, and I can't be bothered to change it. I also tried using other search engines, and somehow still found Google to be more helpful for me despite everyone saying DuckDuckGo has reached parity.

I guess that makes me morally compromised, or supporting a "toxic evil" or whatever, but I just don't care that much. I'm self-aware in my apathy, I guess.

I used to develop and sell novel earnings forecasts which would outperform analyst consensus. Typically my research would have a <1% margin of error on forecasting a specific KPI directly relevant to corporate revenue and profit for an equity. The best hedge funds were able to successfully trade on this information because they combined it with a significant amount of complementary data.

But I would not want to develop a trading strategy based on that data alone. These guys did very well considering the information they had to work with and how primitive trading earnings is. The real money in insider trading is in more illiquid OTC markets, or in mergers/acquisitions.

Nope! I'm not saying that. Read my reply to a sibling comment here, I think it largely responds to the point you're making. I'll reiterate again: being unable to afford all the luxuries you'd like is not equivalent to any reasonable definition of "scraping by."

As an aside, I find it funny in a meta sort of way that while we're talking about hyperbole, you interpreted my point to be literally about starving people in Africa.

You're talking about things like buying a house and finding non-familial child care; these are people worried about receiving government assistance for food and finding affordable rent with bad credit and almost intractable debt. They're scraping by because they wish they could "stretch" a salary like $200k to afford any home and make day care work. Most Americans do not pay for child care, and wouldn't expect to.

I'm going to double down and reiterate here: just because you can't do all the things you want to do doesn't mean you're scraping by. That's a disingenuous definition of the term. If you consider $200k to be "scraping by", what do you call the people who will actually be looking after your kids in day care? How much do you suppose they earn per year?

What people (especially on HN) think "scraping by" looks like is getting a little nuts. Just because you can't have an opulent lifestyle and a cheap five bedroom house doesn't mean you're struggling. $200k in SFBA is well beyond the point where all your basic needs are met.

In the formal sense of the term, "almost always" means that a property applies to all elements of an infinite set, with all exceptions comprising a subset with a smaller cardinality than the original set.

I usually see this term applied in the sense of measure theory, where the sets under study are uncountably infinite (or greater). Being that the naturals are countably infinite, the only way I can interpret this statement is that Tao has proven all but finitely many elements do not have an orbit terminating in 1 under the Collatz map.

Is that correct? If not, would someone mind clarifying the use of percentages here?

Taxonomy is not a settled question, and I'm not trying to imply it is. But neanderthals exhibited significantly different traits from humans. There is probably a case to be made that modern homo sapiens are a subspecies of neanderthals and another hominid. Hybridization can (and frequently does) result in new species distinct from the forebear species, after many generations. But speciation doesn't preclude interbreeding.

It's not uncommon for two related but different species to be capable of interbreeding with viable offspring. That doesn't detract from distinct speciation.

They are not making the claim that choosing to hire someone better than someone else is discriminatory.

First, this is explicitly a vulnerability compromising SGX itself, so saying SGX has to be enabled is tautological. It's not a vulnerability attacking Intel processors generally, and it's not being billed that way either.

Second, securing memory against untrusted privileged execution is a defining characteristic of SGX, so it's likewise unsurprising that it would be required. That is quite literally the intended purpose of SGX.

The design thesis of SGX is to prevent "all hope is lost" from being true in the context of privileged execution.