433 karma · joined July 25, 2015
Research interests: a broad range of applied mathematics topics, generally in the neighborhood of information theory and probability.
Other interests: mathematics in general, computer systems (especially security), FOSS projects, reading, bicycling, and cooking.
Website: gajjanag.github.io
[ my public key: https://keybase.io/gajjanag; my proof: https://keybase.io/gajjanag/sigs/-vv1qyl9QGR_46BS-LPAm3wBVPYna8zjMyUzDBWVKWg ]
An example of a good effort to combat these tendencies is a course by Prof. Bhargava at Princeton, where he introduces good mathematics through card tricks and games: https://www.princeton.edu/main/news/archive/S36/37/98S70/ind...
Not really on topic, but I would like to use this opportunity to express gratitude to the HN community - although this forum is mostly tech-centric, it is wonderful to see things like this post get interest and discussion.
Note that these references have a more "abstract" viewpoint (e.g focusing on "coordinate-free" methods, such as linear operators as opposed to matries as the fundamental object) than that advocated and taught by Strang. I do not know in the end which is better for an absolute beginner. All I can guarantee is that the abstract viewpoint is definitely needed and far more useful for anyone using math beyond its basics. This includes (but is not limited to) machine learning and optimization.
The book also gives copious concrete examples of these dangers. In particular, the book describes the LSI-R (Level of Service Inventory-Revised) questionnaire and how it effectively pinpoints race even though it does not actually ask for the person's race, which is illegal.
"20 years back, everyone wanted CD's for music, today it is flash drives, the upcoming thing is streaming music from the internet. Technologies come and go. What I can say is that the Fourier transform will still be around 200 years from now as a valuable way of understanding the world."
I am of course in no real position to assert that this is a good idea (as I am still in graduate school), but this is the reason why I gravitate towards math and physics classes. Conditional on the assumption that we have a meaningful civilization decades from now (and none of the dangers outlined for instance in the excellent book "Here Be Dragons: Science, Technology and the Future of Humanity" by Olle Haggstrom) cause its utter collapse, I think it is a safe bet to assume "fundamental" topics like Maxwell's equations, Fourier transforms, etc will still be around, alive, and fruitfully studied and applied across a variety of domains. Part of the reason is simply historical: the Fourier transform has had over 200 years to prove its worth time and again across a variety of disciplines.
Maybe deep learning is here to stay, maybe it isn't. I don't know, and I am not willing or interested in making bets either way. I am willing to bet on a time proven framework of understanding, such as the examples above.
Citation needed for this. From a quick look from a paper: https://arxiv.org/pdf/1606.06196.pdf it seems like this statement is true at the undergraduate major level, but certainly not true at the doctoral level.
This is particularly relevant as unlike engineering/tech, where a Bachelor's (or less) suffices for the majority of work, the same is certainly not true in mathematics.
As an illustration of this, note that for many people graduate school in mathematics is spent trying to come up to speed with the current research efforts of the community, unlike engineering where one is (generally) expected to be a "producer" once one hits graduate school.
It is a rigorous treatment that covers a lot of the essentials of Fourier theory, while also covers some very interesting "math applications" (e.g Dirichlet's theorem on primes in arithmetic progressions at the end), as well as "mixed applications" (e.g Radon transforms that are used in imaging but are also of interest from a math perspective).
Note that this book requires an introductory analysis class as a prereq; basically you need to be familiar with the standard Riemann integral theory and rigorous treatment of limits, continuity, and derivatives.
Regardless of that, I find it very puzzling why you don't simply email the authors with your critique, instead of writing a pretty thorough comment on HN that they will likely not read? That would be far more constructive IMHO.
Keep in mind that this is a preprint. From my experiences in this field, preprints are usually very sloppy and are simply a means to lay "first claim" to a discovery. There are usually a ton of typos/other issues to be sorted out, or even worse, bugs in many key proofs - I am not saying this paper is guilty of this, just that expectations should be low regarding exposition quality in preprints.
And yet some of these people can say that they were "dead broke" with a straight face: http://www.politifact.com/truth-o-meter/statements/2014/jun/...
It is a cool function. I remember using it for some testing I did while checking the accuracy of various implementations of basic math functions.
Not an answer to your question, but I found out recently that there is definitely significant interest in ideas like interval arithmetic in hardware among mathematicians. The application I am somewhat familiar with is "brute forcing" proofs of inequalities, which can get very annoying, even for apparently easy stuff like 2 variable ones.
Indeed, "The Princeton Companion to Applied Mathematics" edited by N. Higham et al has an entire article on this (in section II.20). In particular, the article has a reference to a library called filib++ (http://www2.math.uni-wuppertal.de/~xsc/software/filib.html). I unfortunately have no idea how it performs/how good it is.
By the way, thanks a lot for the Unum reference; seems like it is still in too early a stage for inclusion in the book above.
Alternatively, since you mention this above, one can use a Blendtec or Vitamix grade blender to friction-heat the liquid. Apparently this is more energy efficient than microwaving for instance: https://news.ycombinator.com/item?id=11399036 . Obviously this won't work for soups where one desires very coarse pieces of vegetables; nonetheless I often find the above useful.
If you are into this stuff, there is some interesting research on this: https://freedom-to-tinker.com/2016/10/21/bitcoin-is-unstable...
More generally, there is this fantastic repo on github that lists a bunch of such things that can be tweaked in about:config (mostly from a security/privacy standpoint): https://github.com/pyllyukko/user.js
Associated hn discussion: https://news.ycombinator.com/item?id=13371991
The reasons for this are not hard to find. Indeed, you hit the nail on the head in the next paragraph by pointing out the role of governments.
> I'm not sure what can be done on that or what that means, just a bit breathtaking how governments can help people or really screw things up on a scale nothing else even comes close to.
A case study of this in Ethiopia serves as a point in William Easterly's critique of "technocratic aid" in general and Gates's approach specifically: http://www.seattletimes.com/opinion/guest-the-flaw-in-bill-g... He elaborates upon this at length in his book "The Tyranny of Experts: Economists, Dictators, and the Forgotten Rights of the Poor".
The way I like to think of it is that money, especially in large sums like the $50 billion in the foundation, is a potent tactical weapon. However, wars are not won on tactics/technology alone, but also on strategy. Here that amounts to solid leadership/deployment of the capital. I think this letter shows that they have done a pretty good job with it. Nevertheless, it is easy to fall into complacency and arrogance here. I only hope that they continue to listen, observe, and learn.
This depends on a lot on the "consumption basket". The small percentage comment is definitely not true for some categories of products. Concretely, consider cheese. Genuine imported Parmigiano-Reggiano can be had outside Whole Foods for < $14 a pound, with extremes like Costco selling it for $12 I believe. Whole Foods charges $20 for this, a ~ 50% higher price. Similar remarks apply to other high grade cheeses.
More generally, although Whole Foods keeps the pricing of their store brand products competitive (e.g the 365 value stuff), they certainly do mark up many high quality items significantly.
This is an excellent point, whose magnitude I have come to appreciate more recently.
One of my favorite ruminations on the fundamental role that inequality plays in civilized society comes from "Midnight Tides" by Steven Erikson:
"As they walked, Tehol spoke '... the assumption is the foundation stone of Letherii society, perhaps all societies the world over. The notion of inequity, my friends. For from inequity derives the concept of value, whether measured by money or the countless other means of gauging human worth. Simply put, there resides in all of us the un-challenged belief that the poor and the starving are in some way deserving of their fate. In other words, there will always be poor people. A truism to grant structure to the continual task of comparison, the establishment through observation of not our mutual similarities, but our essential differences.
'I know what you're thinking, to which I have no choice but to challenge you both. Like this. Imagine walking down this street, doling out coins by the thousands. Until everyone here is in possession of vast wealth. A solution? No, you say, because among these suddenly rich folk there will be perhaps a majority who will prove wasteful, profligate, and foolish, and before long they will be poor once again. Besides, if wealth were distributed in such a fashion, the coins themselves would lose all value - they would cease being useful. And without such utility, the entire social structure we love so dearly would collapse.
'Ah, but to that I say, so what? There are other ways of measuring self-worth. To which you both heatedly reply: with no value applicable to labour, all sense of worth vanishes! And in answer to that I simply smile and shake my head. Labour and its product become the negotiable commodities. But wait, you object, then value sneaks in after all! Because a man who makes bricks cannot be equated with, say, a man who paints portraits. Material is inherently value-laden, on the basis of our need to assert comparison - but ah, was I not challenging the very assumption that one must proceed with such intricate structures of value?
'And so you ask, what's your point, Tehol? To which I reply with a shrug. Did I say my discourse was a valuable means of using this time? I did not. No, you assumed it was. Thus proving my point!'"
The installation work can be trivially automated with a shell script (note though that the Arch wiki generally discourages this). The benefits of this are that in the process of creating the script, one has a good sense of the installation process and can customize it, unlike the case of Ubuntu and many other distros where a lot of stuff happens behind the scenes. The con is that this script needs to be kept up to date with the (occasional) change in the Arch project.
I have had good success with this method - over the past 2 years and 3 fresh installs on laptops and a desktop. Basically, with a new laptop and a reasonably fast internet connection, I can go from the USB installation medium to a complete desktop environment tailored for my needs with everything configured correctly in ~ 10-15 minutes, with minimal interaction needed during the process (only to set things like the password).
Also note that in most use cases some post installation tweaking gets done, such as the installation of new applications as per interest.
So there are primarily 2 things the script can handle: 1. The annoying "low level work" - network configuration, boot loader configuration, etc. This should be relatively stable and fixed across a variety of hardware.
2. Application specific configuration needs (e.g vimrc, .bashrc). This may evolve over time/usage patterns - for this one can try keeping the script up to date, or not bother and simply focus on 1 above.
> Case in point: many of these same companies that refuse to upgrade systems for a decade or more are still running Windows XP and Server 2003. Due to the negligence of their IT leadership, they are now vulnerable to all types of security vulnerabilities that won't be patched, and have put both their business and their customer's private data at risk.
There are legitimate reasons for this though. The way I understand it, a big chunk of the problem is that many software vendors refuse to properly separate security related updates from regular updates. Firefox at least has an ESR version, AFAIK there is no equivalent for Chrome. See also attitudes like that mentioned in: https://news.ycombinator.com/item?id=9164251
Similar examples can be given for MATLAB - I know of many professors who ask students to run some old and fixed version of MATLAB for many years - they do not want to waste their time dealing with the breakage that inevitably happens with newer releases.
If all vendors actually put in effort into maintaining LTS versions, the situation could be different.
I do agree that the idea of perpetual business value with zero maintenance in a frozen state doesn't make sense - but as a business, I would always be interested in minimizing my maintenance burden.
I noticed just now that there is another hn discussion on recent developments on this front in GCC: https://news.ycombinator.com/item?id=13153320.
I do wish there was a portable solution though (at least across *nix platforms with clang or gcc).
The raw ingredients that are part of classical preparations are extremely cheap. For example, in the United States, rice can be had at ~ $0.50-$0.75 a pound, or in my favorite normalization, < $1 per 2000 calories. Beans can be obtained for ~ $1.00 a pound, or ~ $1.50 per 2000 calories. On the other hand, bread is far more expensive at standard grocery stores, and typically comes in at ~ $3 per 2000 calories. The above is an illustration with respect to carbohydrates, there are similar easy examples with respect to protein/vegetables/fruits that allow significant optimizations as compared to the average diet. The end result is that (dependent on location) balanced meals requiring a minimum of preparation work out to roughly $2.50-4.50 per adult per day.
As for preparation time, again with some thought one can minimize effort (pressure cooking is one concrete example).
The point is that if people thought a bit more deeply about their food choices and the cost tradeoffs made, healthy food budgets should really be very minimal as compared to far more expensive things, like health insurance, rent, etc. Most media outlets instead spread a lot of disinformation - the standard "working" assumption is that healthy food is organic, is found in expensive stores like Whole Foods, and that one needs to pay more for healthy food. A fun experiment that illustrates this point: try looking at the labels of marketed "healthy/organic" stuff at a store geared towards such things and examine the sugar content in them. And this is why such places get away with ridiculousness regarding their prices on basic items.
It is the only book I know of that takes a comprehensive view of a variety of such issues (climate change, extraterrestrials, strong AI, etc) and is written in a scientific manner with numerous citations, and little to no empty statements as is typically found in "popular" books.
I agree with your general point, but note that there are some unfortunate reasons why this can't be done in many cases.
A compiler can only make use of appropriate SIMD instructions if it knows that the target has the appropriate SIMD. Most packages/shipped binaries are "universal" x86-64 binaries, i.e at compilation time, these instructions can't really be used effectively in many cases. Of course, in certain cases, one can get around this issue. For example, if one compiles from source, one can pass -march=native or similar such flags. Another example is in game development, where one can freely assume that the target processor has AVX (or whatever it is based on the "min reqs" listed on the game).
But in the general case, the common solution is to compile in different pieces of code corresponding to the different target CPU levels and do runtime CPU detection. Video coding (e.g FFmpeg) is one illustration of this approach, and to which I don't know of any reasonable portable alternatives.
Otherwise, there is a misalignment of incentives for the elected representatives as you point out.
For an (unrelated) example of this misalignment, N.N Taleb outlines in his works why most financial "news" or "recommendations" are completely useless - the people peddling the "news" are trying to sell a story. If they actually put their own money (like their personal savings account) based off their recommendations, a lot of them would disappear very quickly. At the moment, most of them have no "skin in the game".
Why can't it be viewed as a source of comfort? At a longer time scale, even life on earth won't exist as the sun dies. At a sufficiently long time scale, none of this stuff on earth matters, the universe continues to move on. As these highlight the transitory nature of life on earth, there is no reason for why one can't "let go" after a point. I find that a tremondous source of comfort, as I often face the problem of when to "let go" in many contexts.
I won't get into a detailed discussion of the purpose of existence (a natural counter-question to the above), or why one should still strive in one's own way to tackle issues like climate change up to "one's capacity" (which depends on accepting the purpose of existence).
These fundamental questions are extremely hard to address. It took me a long time and a lot of thought to have a reasonably satisfactory answer to these questions - though of course what answer one is satisfied by will vary from person to person. For me, the bulk of the answer came from a study of the Indian Vedantic tradition (chiefly Adwaita Vedanta) through the "Complete Works of Swami Vivekananda" among other such books, and the works of Leo Tolstoy. Mileage may vary of course.
I am not a biologist, but nevertheless I found out something interesting today regarding the problem of designing good guide RNA via machine learning.
The work that I learnt about today addresses 2 key questions via machine learning approaches: off-target effects of CRISPR (http://biorxiv.org/content/early/2016/10/05/078253) and optimization of the guide RNA sequence to maximize on-target activity and minimize off target effects (http://www.nature.com/nbt/journal/v34/n2/full/nbt.3437.html).
I learnt of this stuff from one of the authors who works at MSR New England (http://nicolofusi.com/).
Also of possible interest is their project page https://www.microsoft.com/en-us/research/project/crispr/, where they are planning to release a cloud-based service for end-to-end guide design by incorporating the approaches developed in the above work.