throwawaymath

In any case I think it makes me an unenjoyable person to be around. I more or less don't engage in opinionated discussion with people unless I'm intimately familiar with the topic at hand. Then it's no longer discussing opinions but trading facts. When I do engage, it's usually to ask questions of the other person's opinion without really challenging them. While I might agree with their opinions, I'm reluctant to refute them unless I can systematically prove them wrong. That's usually not possible, because they often know more than I do about any given topic. When I am asked questions directly I hedge my answers extensively.

When I was younger I used to take pride in this, but now I find it isolating. It's difficult to relate to people like this.

While reading through the article I found this interesting:

> In terms of insight, higher scorers in intellectual humility were less likely to claim knowledge they didn’t have (the researchers tested this by assessing participants’ willingness to claim familiarity with entirely fictitious facts that they couldn’t possibly know), and they also tended to underestimate their performance on a cognitive ability test.

I can appreciate the reasoning behind asking that question, but the fact that it's so useful for judging intellectual humility saddens me. Why would a person spontaneously respond, "Yes" when asked if they're familiar with a thing they know they aren't? What does that say about us as a species, that this behavior is so prevalent?

This is incorrect. Are you familiar with the inverse-square law? In 3-dimensional Euclidean space, the rate at which any force decays over a distance is inversely proportional to the square of the distance. This generalizes to n dimensions; but instead of the drop off rate being inversely proportional to the square of the distance, it becomes inversely proportional to the n - 1th power of the distance.

Suppose our universe is a 3-dimensional embedding of a n-dimensional manifold. Every local force we could empirically test would adhere to the inverse-square law, i.e. have drop off over distance k of ~ 1/(k^2). But theoretically speaking we could empirically test the dimensions of the manifold we reside in by identifying which power of distance is proportional to the drop off rate of extremely small forces where the compactified dimension can be detected.

For practical purposes this would require us to increase the precision with which we can empirically test (and reason about) forces at the subatomic level.

Given the context I'm guessing you asked this rhetorically, but if not: it is not true in general that a curved n-dimensional object must be embedded in a n + k-dimensional space. Curvature can be intrinsic.

That's not to say it's not useful. It's better than email, leaves a neat record to come back to and supports asynchronous communication. There are advantages. But strictly speaking, no, you cannot capture everything good and useful about in-person conversation using text and video. I don't think it should be controversial that much of the richness of in-person conversation - tone, nuance, body language, facial expression, spontaneity, speed - can't be meaningfully replicated through remote mediums. You can't get all of these things from a message or video chat. You can get some of them well, and a few others decently, but it isn't the same.

I like remote work a lot and wish more companies would support it. That being said, in my experience when people give honest, cogent criticisms of remote work they mostly receive responses which don't speak to the spirit of their point. In this comment thread, for example, the person you responded to is talking about difficulties. You are responding as if the person was talking about impossibilities. It is (emphatically) not impossible to function as a remote team, and very few people will try to make that case. But in the world we live in and with the technology we currently have, there are things about in-person discussion you will not be able to capture on a remote team.

If nothing else people have different values. Some developers enjoy being highly social when they're working, others don't. Some don't mind interruptions, others do. Many people feel a sense of comfort and empowerment by using Slack or Zoom which makes it easier for them to have productive discussion, for a variety of reasons. Likewise many developers do not get any of the same enjoyment out of a Slack or Zoom conversation that they do from face to face communication.

I can't immediately tell from the source NYT cites, but is that 20% of one person's vehicle emission, or 20% of the aggregate vehicle emission of all passengers?

If it's the former, that might not be a great way to frame the problem since cross-country flights typically have hundreds of passengers.

In that sense there's a compelling argument that a revised set theory might be called for, in the sense that it could be a better fit for the way most mathematicians use set theory in practice. But since Leinster's set theory is axiomatically equivalent to ZFC without regularity, there's also a compelling argument that it's not worth it unless it's significantly more expedient or easy to learn.

In 2004 Yahoo acquired several smaller companies which were working on algorithmic search and page linking around the same time that Google was. They released their own ranking algorithm called WebRank which was substantially based on the methods of PageRank.

Evan Chen, a math student at MIT, wrote up what would be considered field notes for higher mathematics. The full PDF is here[1], complete with a dependency graph showing what you need to know before reading any particular section.

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1. https://usamo.files.wordpress.com/2019/02/napkin-v15-2019022...

There's a neat video explaining it here: https://www.youtube.com/watch?v=d0vY0CKYhPY

The basic prerogative of a sophisticated bot is to ensure you believe that.

Having written a variety of sophisticated bots - some from pre-existing libraries, others from scratch; for specific websites and for general purpose - I'm reasonably confident most people who think they've never seen a sophisticated bot are mistaken.

I agree with you that anything more sophisticated or bespoke than a mass-spam bot is rare. But rare things happen often to most websites with nontrivial traffic. The types of bots with the most funding and skill behind them are the ones which don't try to spam anything on a website at all.

At my university the letter grades were

    A+  99.00 - 100.00%
    A   93.00 -  98.99%
    A-  90.00 -  92.99%
    B+  87.00 -  89.99%
    B   83.00 -  86.99%
    B-  80.00 -  82.99%
    C+  77.00 -  79.99%
    C   73.00 -  76.99%

I wasn't sure if the author was making an intentional callout to Fermat's lost marvelous proof he couldn't fit in the margin. But indeed, looks like he was, since he doesn't seem to have really mentioned the length of any other proofs.

If you literally wrote down sequences of definition, theorem, proof, definition, theorem, proof, ... with no exposition or exercises whatsoever, I think you might be able to include most undergraduate math in about 1000 pages. That would include calculus, real analysis, complex analysis, linear algebra, abstract algebra, discrete math. Maybe elementary number theory, topology and probability theory as well. That would be...horrible to learn from, frankly. Imagine a ten volume set of Baby Rudins, with no exercises.

If you really doubled down on the cheat sheet angle and didn't include any proofs - just the theorems, identities and inequalities - I think you could get through all undergrad math in a few hundred pages. But you wouldn't have any of the peripheral content the author included, like physics/economics.

EDIT: Nope, probably intentional. The author doesn't say something similar for any other proof based on a quick CTRL+F :)

I would go a bit further and say most companies should only proceed with a microservice architecture if they have sufficient scale and automation such that decomposing their architecture will result in at least a high double digit number of discrete services.

I didn't pick up any ideology in my reading. My interpretation of the article is that the author wanted to provide tips on how to implement mathematics, for two reasons:

1. People have to implement nontrivial mathematics from time to time, and

2. Most mathematics doesn't concern itself with obstacles to implementation, because it doesn't have to.

Sets? Define a set semantically, then replace "set" with S. Vector spaces? Define a vector space semantically, then replace "vector space" with V. Limits? Define a limit semantically, then replace the word with "lim".

Moreover mathematicians typically use jargon in a more reader-friendly way than simply throwing obtuse equations at them. Expressions, equations, inequalities and identities are complements to the proof, not the proofs themselves. Best practice holds that you present a theorem in plain language alongside the necessary notation, then break its proof down into as many atomic units (lemmas, propositions, corollaries, etc) as possible. Here is a blog post[1] from Terence Tao giving general advice for why that's useful. Tao has written a bunch[2] of these on the theme of emphasizing exposition and clarity.

Also contrary to popular belief, well-written mathematics papers actually have quite a lot of exposition in them. For a famous example, look at Yitang Zhang's proof[3] that there are infinitely many primes with 70 million numbers (or fewer) in between them. He spends a full five pages on introduction, background results used to develop the proof, and (most importantly) notation. He also includes a "sketch" of the proof in broad strokes so that a reader can follow his arguments at both a high level and in gritty detail.

That doesn't mean papers like Zhang's are accessible to most people. The jargon is still there and you can't really change that unless you want papers to become self-contained monographs. But the point is that what you're proposing - concepts defined in a straightforward way before moving on to dense notation - is already the general practice.

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1. https://terrytao.wordpress.com/advice-on-writing-papers/crea...

2. https://terrytao.wordpress.com/advice-on-writing-papers/

3. http://annals.math.princeton.edu/2014/179-3/p07

Do you have an example off the top of your head? I'm assuming that by, "fluency in mathematics (both algebra and analysis)", you mean something beyond basic calculus and linear algebra.

My experience has been that software engineers at the staff, principal and architect levels don't really need to know advanced mathematics at all. From what I've seen they usually have a breadth of experience as generalists and a depth of experience in one or two particular specializations, which may or may not involve any advanced mathematics at all.

s = <s1, s2, ... sn> (Please note that in LaTeX, one should use \langle and \rangle for angle brackets--not less than and greater than.)

The article is pretty good overall, but I find this an little odd. I don't think I've ever seen sequences denoted with angle brackets. You usually see those used for denoting an inner product. I've only ever seen sequences denoted with parentheses, like (a_n) = (a_1, a_2, ..., a_n).

It's kind of humorous to me that we can sort of fingerprint the textbooks/lecturers people learned from by the idiosyncrasies of their notation.

Out of curiosity, what is your hypothesis for explaining this difference in behavior? Would you say it's primarily due to differing contexts in which a link is posted, or differing populations on each platform? Or maybe these both contribute about equally?

Stated another way: would you expect the same individual to behave differently coming from Facebook versus coming from reddit, if they happen to be a user of both?

It's also common for market makers to move the market.

Yodlee almost certainly has a record of the vast majority of your credit/debit transactions. It doesn't sell the ability to advertise to you as a specific demographic, it sells that data directly.

If you log into the free public wireless network available in most areas, your presence at that location will be logged, correlated to your identity and sold. Again, Foursquare sells this data directly, not the ability to advertise to you.

Thasos sells your location history based on mobile data. Slice sells your location data based on mobile SDKs it provides developers in return for your data. I can go on and on.

Is there at least an attempt to anonymize this data? Usually, yes. Does that work in practice? Sometimes, often even. But frequently it does not. You need fewer than 33 bits of independent data to uniquely identify anyone on Earth. There are only so many other people in your area and age demographic who share similar waking hours, interests, habits and location data.

It is a myth that companies don't sell user data directly because it's their golden goose. Facebook and Google don't, but most of the data they have can be reconstructed independently from a variety of other sources that freely advertise it.

I'm not confident I'm correct only because it seems unlikely Google would have a page listing trademarks it doesn't actually own. That being said, I'm pretty sure there's no other place to search for trademarks.

I also don't think there is actually a trademark on the term "Go" based on this USPTO search: http://tmsearch.uspto.gov/bin/showfield?f=toc&state=4809%3Ax.... But admittedly I've only looked through five or six pages; using the option to search for an exact term doesn't seem to cut down the search results at all.