There is a comment on the r/slatestarcodex subreddit with supposedly true information about him (which I found googling 'who is gwern'), but it left me with even more questions.
> Gwern was the first patient to successfully complete a medical transition to the gender he was originally assigned at birth... his older brother died of a Nuvigil overdose in 2001... his (rather tasteful) neck tattoo of the modafinil molecule
The only concrete things we know about gwern are that he's a world-renowned breeder of Maine Coons and that he is the sole known survivor of a transverse cerebral bifurcation.
He does have a neck tattoo, but it's actually a QR code containing the minimal weights to label MNIST at 99% accuracy.
> The only concrete things we know about gwern are that he's a world-renowned breeder of Maine Coons and that he is the sole known survivor of a transverse cerebral bifurcation.
There's some articles on his site about these attempts and they claim that they are all wrong. If it would be that "easily found" I'd guess we wouldn't be having these discussions: https://gwern.net/blackmail#pseudonymity-bounty
He's making showing that the m'th derivative of p(x) = x^n (a-bx)^n / n! is an integer at 0 and pi for 0 <= m <= 2m way harder than it needs to be.
He notes that p(x) is a polynomial of degree 2n, and then applies that general formula for multiple derivatives of a product that he proves at the start of the video. That involves a bunch of fiddling with binomial coefficients. He does this so he can write down an exact equation for the polynomial and its derivatives as a sum of powers of x. Around 20% of the video is spend on proving that general derivative formula and later applying it.
That's overkill because we do not need to know the exact coefficient of each power of x.
Simpler is to note that since p(x) is a polynomial of degree 2n and the whole thing is divided by n! it is a sum of terms of the form Ci x^i / n! for i = 0...2n. Also note that because it has a factor of x^n, Ci = 0 for i < n.
Consider then some arbitrary term of the polynomial, Ci x^i / n!, i >= n.
When x = 0, that term is 0 because of x^i.
Differentiating lowers the exponent of x by 1, so the first i-1 derivates all still have a factor of x in them, so are all 0 at x = 0.
The i'th derivative finally gets rid of the x. In particular, the i'th derivative of x^i is i!, so the i'th derivative of the term is Ci i! / n!. Remember that i >= n, so i!/n! is an integer and so is Ci i! / n!.
Further derivatives of the term are all 0 because they are derivatives of a constant.
In summary, the polynomial is 0 at x = 0, because all terms have a factor of x in them. As you repeatedly differentiate the polynomial each individual term of the derivative is 0 at x = 0 until you've differentiated enough times to get rid of all its factors of x. At that point the term is a constant integer. Further derivatives of the term are derivatives of a constant which is 0.
To show that the polynomial and its derivatives are integers at pi note that f(x) = f(pi-x), and so f'(x) = - f'(pi-x), f''(x) = f''(pi-x), ..., f^(m)(x) = (-1)^m f^(m)(pi-x). The polynomial and all its derivatives at pi are either the same as they are at 0 or the negative of what they are at 0, and since they are all integers at 0 they are also all integers at pi.
Symbolic mathematics is severely underexplored in undergraduate studies, and the little exposure I had was generally tied to proprietary software such as Mathematica and MATLAB. I learned to use it as an imperfect extension of pen-and-paper thinking, and source code for more advanced stuff gets shaky the deeper into abstraction one goes. For example, I work in a field of mathematics/engineering that requires heavy use of tensor calculations. My go-to tool for that is Maxima, however, it has limited and cumbersome packages for it (see [0]). Now for more sophisticated calculations I resort to SymPy, not necessarily because of better handling of symbolics but because of the abstractions that Python already has. Maybe someday I'll get to read the Principles by Norvig and fix Maxima to suit my needs (if anyone has better references to read Maxima's source code/implementation of tensor computations/symbolic (tensor, geometric) algebra I would be grateful to know).
For great justice, does anyone know of any applications (other than Maple) that support WYSIWYG typeset input (not output) like Maple does?
As far as I know, Wolfram/Mathematica, LaTex, SymPy, Jupyter, Sage etc all rely on typewriter text for composing and inputting math. For this (and only this) reason, Maple is the only application that ever resonated with me, because input may be written in the same form it's written by hand, and it's baffling this capability isn't more commonplace. Is this a barrier to anyone else?
a close friend of mine used to tell me about these production Mathematica Notebooks he'd author at his company Coherence to do all these optical and thermal calculations with. It was a regular workhorse for him.
A very long time ago I used to play around with Derive5 in my youth. It was the most affordable Computer Algebra System (CAS) of the time and I learned to program in that funky one liner programming language where I had to strip all the white space from my editor and always be careful to balance parenthesis. I should dig up those old files and upload them to my github. I've been actually meaning to reimplement those operations in a more modern CAS system and see if I can more densely plot these curves I was studying with some iso-arc-length families of exponentials about the point (0,1).
The moments captured in my images are fresh, but my perspective on them changes.
I am doing an experiment in memory and trying to memorize the name of every U.S. county, with the aid of a map. Several months in I can say that the brain inexorably will tie names together (wether by geographical proximity or etymology, e.g. Imperial-Riverside-San Diego or Redwood-Greenwood), and the addition of new names affects the perception of the ones before, or the perception of words which happen to be county names. I could write an entire essay on the limits of memory, but it would hardly be better than Jorge Luis Borges's story Funes, the memorius.
For anyone curious I can name 80% of U.S. counties with the aid of a blank map, and my geographic intuition has improved greatly. Every county (and county name) has a history attached to it, and sometimes when someone tells me where they grew up, I can guess their ancestry more or less, especially if they come from rural areas. It surprises them, sometimes even more when they know I'm not american.
Memory seems to be cemented when theres some type of value assigned to it, like a useful memory peg I find.
A major battle, a geomarker, usually there is SOMETHING noteworthy historical. I may not have put the labor into the volume of counties as you, but I've lived in so many places, and I index local histories of everywhere I live, and it cements so much.
Love the effort you put into testing your cognitive faculties!
This is fascinating. I’m working on a memory project and would really like to get in touch and hear your insights on limits and especially counters to interference with memorization. I’ll put my email in my profile; pure gratitude if you can spare some time to share your wisdom with me.
In order to have a mature discussion about this topic, it's necessary for people to know about the economic and political history of Argentina. It's impossible to understand their current situation without going back to the 1940s. Bad faith arguments look over the fact that Argentina has had decades of incredible economic distortions as a consequence of political rot, and that undoing those distortions is not achieved in the time Milei has been president (I personally don't believe they could be undone in less than a presidential term).
He is known by all members of the Chilean Navy [1], he is not obscure in this part of the world. By the way, I am chilean and lived most of my childhood just a block away from Lord Cochrane street [0], in downtown Santiago, which is one the busiest places in the whole country (and those adjacent blocks have seen some history).
In case you're interested, here is a photo I took in the Museo Marítimo Nacional, Valparaíso, Chile - a full-length stained glass portrait of him: https://i.imgur.com/XSr6wwG.jpg
Don't forget that he indirectly and in hindsight contributed to the independence of Peru as well. Most of the fighting of course did not happen on the seas, but just as air superiority matters a great deal, naval superiority in the 1820s mattered as well, and the upper hand he gave to the expedition from Chile/Argentina made it a war that was effectively centered on the land war aspect and led to in part and a few years down the line, Peru's independence from Spain as well.
Somewhat ironically, the Irish diaspora (the Flight of the Wild Geese, which happened in 1691 and scattered the Irish Catholic military aristoracy across Catholic Europe and their descendants, just Europe in general, likely had a larger cumulative role in effectuating much of the independence movements. After all, O'Higgins is not exactly a native Spanish surname. Informally the scions of Irish Catholic families of importance, with their paths of advancing in Britain blocked, filtered out across the continent for the next hundred years or so and ended up having certainly an outsized influence on the makeup of military administration and colonial administration by way of the makeup of the officer corps of the nations where they ended up settling, stretching from Spain to France to Austria to Russia. They were not exactly mercenaries but really a true diaspora before the concept really solidified in today's terms. One can argue that it was certainly an early and self-inflicted 'brain-drain' through policies instituted by the post-Williamite British state that may have had longer term consequences (the loss of Minorca and the loss of America came in fairly rapid succession, for example) to the British and the distinct and separate traditions allowing them to be less attached to a sovereign but a cause. Much more on this needs studying, but what is certain is that policies made out of fear undermined the British and aided continental powers for generations. Look at the names etched on the Arc de Triomphe and you'll notice how many of the names are distinctly not French, including that of Dillion (Arthur Dillion, related to the Viscount Dillion, who also fought for the American side during the revolution), Clarke (whose father served in the Dillion Regiment), MacDonald (whose ties to Flora Macdonald during the Jacobite Rising precipitated his family's exile, but nevertheless served as officers first under Dillon before later siding with Napoleon and taking independent command, primarily in Switzerland) are just some of the prominent names inscribed. Sectarianism's long tail etched in stone right there.
As an occasional general aviation pilot (I found this HOWTO after trying to find tools to aid in flight plan calculations), I think it would be great if we took it a step further and make a full-fledged Linux avionics system, but it seems unlikely [0]. And Garmin will likely not be replaced in a dozen years.
The creator of Asterisk (the linux-based PBX) has been building a modern modular avionics system which I believe is Linux-based. From what I can tell they have plans for certification.
The link you posted doesn’t make it seem unlikely inasmuch as it completely pillories even the notion of using Linux for avionics on both technical and economic merits, completely counter to your claim that it would “be great”. So why would it be great?
In practice most pilots use an iPad app for flight planning and navigation. No technical reason why open source hardware/software could be used for that if it had good UX (which is pretty uncommon in the Linux desktop space)
I think you and the link in OP are talking about two different things. The link talks about "safety-critical avionics" and answers mention that they use proprietary RTOS. Certainly, anything that can be done on iPad could be done on Linux, and Linux is quite common for non-real time embedded things.
These answers seem to be quite out of date, as the aerospace industry (most notably SpaceX) has been using Linux as part of their rocket control systems for quite a while now.
Ooo, what did it look like? A Mach kernel oops (aka "just start painting text from the top-left"), a BSOD (more structured), a dialog box over the top, or...?
Also what info was printed? An inscrutable Guru Meditation, a register dump, or...?
Just idly fascinated to figure out how much info would be dumped by a piece of avionics running in end-user production mode.
I went on a bit of a rabbithole trying to look for firmware downloads for the G1000 to run `strings` on but sadly they're not publicly available anywhere.
No amount of quote-googling got me any further though, which was why I went firmware hunting. Now at least I have a good conversation starter for anyone who looks like they might have a dealer account next time I'm at a hangar though...
I read the two first or so papers of the book and understood them, but I coulnd't get past because I lack the sufficient probability theory (I'm a functional analyst). Now it's been in my queue for some time but I hope to get to it after finishing the references I'm reading now.
Didn't the german chancellor say recently that Germany would have to take in 1.5 million immigrants a year so that its pension system wouln't collapse? I personally don't think that is the solution but Spain is going through a similar phenomenon (pensions-low TFR).
Spain has the advantage of having an entire continent who speak Spanish, are generally Catholic, and were former colonies / have overlapping culture. Failing that, British expats might suffice.
German politics/demographics seem balanced carefully between {need for immigrants to maintain population growth} and {cultural reaction to immigrants}.
Although, credit to Germans, at least they're talking about the problem like adults. Mostly. Or moreso than other countries.
Cool! I've just contributed several examples. If anyone is interested in the sheer amount of identities that have been discovered, good books are (many of them gigantic references spanning thousands of pages). When bored, try proving some of those facts, examples build on top of each other. These are not the only examples, as there are
many texts like these in other areas of mathematics and engineering, be it numerical analysis, optimization and variational analysis, statistics, abstract algebra, control theory, geometry and so on.
Table of Integrals, Series, and Products, Gradshteyn & Ryzhik.
Special Integrals of Gradshteyn and Ryzhik, Vols. I and II, Moll for some proofs of the above.
Handbook of Integral Equations, Polyanin & Manzhirov.
Scalar, Vector, and Matrix Mathematics, Bernstein.
Handbook of Number Theory I and II, Sandor, Crstici & Mitrinovic.
Wikipedia also has a plethora of pages with mathematical identities. Some of them:
Can't have a list like that without a mention of Abramowitz & Stegun [0], or its successor, the NIST Digital Library of Mathematical Functions [1]. It's about as comprehensive as it gets.
EDIT: grammar