Mugwort

The representation theory of Kac-Moody algebras. There are some issues with integration theories that need clearing up, should we really be ditching the Riemann integral for the Lebesgue integral so quickly without a closer look. Recently someone wrote a good book on linear algebra that puts of "ugly" determinants for as long as possible. Much of the problem is making what we already know cleaner and better. Some theories like set theory don't have a unique set of axioms and have lots of loose ends. General topology is a closed subject but there are still potentially better ways to formulate convergence.

I'll say something regarding string theory which has been accused of leading physicists astray because of its "mathematical beauty". First of all, string theory in its present form is NOT mathematically beautiful. The mathematical theories used in string theory are in fact beautiful but the way they are stitched together is an UGLY Frankenstein mess. It's essentially the same ugly math that particle physics was built upon in the 60s and 70s. Lie algebras, conformal fields, algebraic topology etc. are all very beautiful maths but they rest upon this ugly mess of correlation functions, vertex operators, BRST invariant (gulp) Lagrangians and other brick-a-brack nobody should be proud of but gets the job done.

The problem with string theory is 21st century mathematics is still in its infancy. I have reasonable confidence that string theory is essentially correct only that the present maths and our understanding of QM (which needs improvement) is definitely not up to the task. Many topics like the Penrose singularity theorems in General relativity were impossible until Einstein's theory was formulated correctly with rigorous mathematics. IMHO this is the case with string theory. It simply won't work with the tools we have.

Another thing about String theory is that it very well could be a complete description of physics on anti-deSitter space. That would be progress but it still wouldn't be a unified field theory. We would need to find a more general theory which allows for deSitter space.

So there's my opinion. If anyone doubts mathematical beauty leads us to better things, plain old vanilla Classical mechanics is looking stronger than ever before and is still yielding interesting physics. Part of the reason for this is that the mathematical foundation of CM were still not understood properly until the mid 20th century. Give the other theories time to catch up. Mathematical beauty is the best guide we have. If strings turn out to be wrong then that's fine. Mathematical beauty is still the best guide we have. If we listen closely enough to what the equations are really saying then we'll find something better.

I know people who spend large budgets on Facebook and Google ads. What I hear almost universally is that they aren't effective, yet everyone feels compelled to pay for FB ads and Google ads because they see everyone else doing it. The customers I have spoken too feel that it simply isn't working but they're afraid to stop buying the ads for fear of slipping into online oblivion. Numerous people have shared the same experience with me and nobody is happy. Now there is the chance that I just happen to know only statistical outliers, the people who pay a lot of money and feel they aren't getting anything in return but feel compelled to continue. Maybe I just happen to know a dozen or so very unlucky resentful people. I don't have solid "evidence". It's all anecdotal. That said, this experience I've just described is most likely common and hardly unique.

I have a much harder time reasoning with loops than using map, reduce, recursion etc. I'll just say the whole truth, I can't program with loops, I get a headache and I'm forced to quit.

This is one of my favourite tech talks ever. So very, very true. I agree with everything he says. On the other hand, writing software the same way without changing is hard to do and there is the temptation to try something new for the sake of trying something new. It's very strong with me and I've learned to indulge my urge to play with shiny new toys in a way that doesn't blow the main project to kingdom come. I need to write something that will go nowhere just to get it out of my system.

Sell?

A two dimensional being can't eat. Its digestive tract necessarily divides it into two distinct pieces and the being falls apart.

https://preview.redd.it/8fvwyefjav601.jpg?width=640&crop=sma...

If you can learn one easy piece every day for the next three years, that's over 1000 pieces. If you start small with Bach and play his easiest compositions and play even 1 page per day, in not time flat you'll be playing the entire WTC or art of the Fugue. Obviously, this advice does not suit raw beginners but the "advanced" players I hear struggling with Beethoven and sounding bad, this is exactly the advice I'd give. I'd tell them to play all the easiest Beethoven pieces, pick lots of Haydn. Maybe bring a handfull of these pieces to performance quality but to absolutely be able to play them ALL at least acceptably. Struggling is a bad policy. It leads to stiff unnatural technique. Also, things like trills don't need to be fast. Play trills musically. leave ornaments out the first day when playing a new piece. Add a few in at a time. Make everything sing and dance at the piano. You should NOT be struggling too hard on anything. Also, I can play all 32 Beethoven sonatas but I haven't played op 106 or op 111 in front of an audience. It isn't necessary to do so. I play all the Chopin etudes... at home for myself, to build my chops. It isn't spectacular, but I play them pretty good. Save your best for audiences and only things that are very comfortable. Scarlatti composed 555 sonatas. There is more than enough there to keep me busy and you should you take up my "method".

I've played piano over 40 years. By the time I was 25 I played most of the piano repertoire, all 32 Beethoven sonatas etc. That said, let me offer my since advice on how to climb to the top of piano performance. Anyone can do it and this method works but you won't hear about it much and I'm unaware of anybody promoting this method. OK.. Here goes.... I love playing easy pieces. There is so much excellent low laying fruit which everyone should pick. Here are some examples... 1. Bartok - Mikrokosmos (all 153 pieces - play them all, you can do it!) 2. Prokofiev pieces for children. 3. Schumann 43 pieces for children. 4. Bartok 20 pieces for children. 5. Bach 15 inventions and 15 sinfonias. 6. Bach little fugues. 7. The easiest Mozart sonatas e.g. K282 etc. 8. The first 10 Haydn sonatas (partitas). 9. Well tempered clavier - Bach. etc. 10. Select pieces from the French and English suites. ... well you get it.

The whole point is to start small, learn pieces quickly, but most importantly musically. Make music with them. Learn to read from the score comfortably. After a while reading things at sight isn't such a big deal.

The important thing is to learn music is a way that solid skills are acquired. You certainly can focus work on a Beethoven sonata for several months like at a conservatory but I believe this method of learning vast amounts of music quickly is absolutely indispensable. There are a TON of excellent first rate compositions by the best composers, you have no excuse for not mastering them.

The gap between being able to play Haydn sonatas and the Well Tempered Clavier fluently and say being able to work on the "big pieces" is much smaller than you think.

Don't skip anything. Nobody needs to charge in and start playing Beethoven's sonata op. 57 The Appassionata before they've played at least 20 of the easier sonatas.

The other bit of advice I have is to constantly work your memory. Again with simple pieces learned quickly. Most pieces don't need to be memorized and memorizing everything will hamper your development. You do however need to memorize easily and efficiently. It really helps in developing speed and accuracy. Chopin studies mostly need to be memorized in order to practice effectively. That said, I firmly believe you can learn MORE technique playing finales to Haydn sonatas but with a whole lot of energy and spark than slaving away on virtuoso etudes.

One last thing, practicing without pedal (often but definitely not always) is very helpful. It has been for me.

Oops. One more last thing. Play by ear and improvise in any style you like. You'd be surprised how many super advanced classical musicians there are who can't play Happy Birthday at a moments notice without knowing the song at all just to make a group of children happy. This is a symptom of the lop sided skills not to be able to play songs people like whether it's Carol King or Arcade Fire. You should be able to fake something.

TLDR; Picking all the low laying fruit you can find is the one way to success. You get to focus on enjoying the process of actually making music than to struggle with passage work that always comes on its own anyway.

Good luck.

this... https://www.youtube.com/watch?v=5rXPrfnU3G0

I don't disagree but how much influence did they have? The biggest culprits for swaying the election is none other than the US media by giving Trump billions of dollars worth of free election coverage for profits. They knew the negative coverage was energizing his base but they did it anyone because money. Blaming the US media however is as useless as blaming Wikileaks or Russia. At some point we need to admit we have our own self inflicted problems and quit blaming everyone else for them. Trump is a symptom we have been going down the wrong path for a very long time. I'm not optimistic about the US ever being introspective about its actions but it's the only way forward. The problem is US, not somebody else.

I believe the findings of the Mueller report, that Trump did not collude with the Russians to sway the election. I'm rather relieved about it. The possibility of Russia hacking our elections was a very serious matter and I'm glad the case is closed. Still, I'm very very distressed about Trump being President. At least the Russians aren't involved. Now, regarding war crimes and killing journalists, Soviet Russia had a long history of that. It's very disturbing the US is going down that path.

It's worth keeping in mind that when they say Assange is guilty of violating the espionage act, did illegal hacking etc. what they really means is that he's guilt of publishing video showing US armed forces murdering unarmed journalists and civilians. If people are going to place emphasis on Assange's crimes and make them a high priority then it's hypocrisy of the worst possible kind to ignore the serious war crimes committed by the US armed forces in Baghdad in 2007. The crimes exposed by Assange are far more worthy of attention than any criminality Assange could possibly be found guilty of in exposing those crimes.

Capitalism killed Portal 3 and Half-Life 3.

Then John H. Conway's Surreal Numbers might be of interest to you. Donald Knuth wrote a book about the subject and it's actually in the form of a story with dialogue, not your typical math book. I'll attempt a summary. It is possible to build all number systems at once including all integers, rationals, algebraic, irrational, infinitesimal, hyper-reals and transfinite all at once using a single procedure which resembles Dedekind cuts. From that foundation one can recreate many of the results of non-standard analysis. Conway discovered his Surreal Numbers while investigating Combinatorial Game Theory. He wasn't even trying to create a new foundation for mathematics, he was just playing at his games which many of his colleagues looked down upon as useless. Apparently playing games and having fun can occasionally result in extraordinary discoveries.

Conway's left and right "cuts" look like sets but then again I'm not really sure what they are. Is this alien mathematics accidentally discovered on Earth by perhaps the most intelligent Earthling who ever lived. I don't know. All I can say is I took a detour from my usual math studies to look into Surreal numbers and it was an interesting trip. I'm quite conservative when it comes to math. I don't go around preaching Surreal numbers are the way to do math but it is a curiosity none-the-less worth at least the small price of reading Knuth's short book about it from cover to cover.

He looks skinny.

If you're interested in learning t'Hooft's theory in detail here's a link to download his book for FREE. You have to pay for a physical copy but Springer has decided to make this book open access.

https://www.springer.com/us/book/9783319412849

I don't know about eating itself (possible) but Google might one day not need human employees at all or be very close to 100% AI. Maybe Sergey and Larry will keep their jobs because of seniority. The rest of us are in trouble.

Is simulated hate never hate?

Farewell Joe,

That we might be as good to others as you have been good to us and lead by example.

RIP

This is not at all unusual. Poincare discovered special relativity before Einstein, Hilbert found the correct equations for General relativity one week before Einstein, Hamilton almost discovered quantum mechanics decades before everyone else. Newton found solutions to major mathematical problems and never published them. Gauss discovered hyperbolic geometry before Bolyai and Lobachevski and never bothered publishing his results. I can go on and on in the fields of physics and mathematics which I know best. Certainly, the same thing is true in chemistry, biology, etc. I wouldn't doubt someone got there before even Feynman did. Still in every case, the recognized discoverer not only made their discoveries independently but also managed to convince their communities of their merit, something which is FAR harder to do.

This smells like classic Feynman. He did more things than people realize even coming up with his own ideas about the Riemann hypothesis even though he wasn't a mathematician at all. In a certain sense Feynman didn't discover a single physical law. (arguable) . This little anecdote if true would be Feynman's "single" discovery of an actual new physic law (which happens to not have experimental verification).

Feynman was brilliant. If you have a physics PhD you can still benefit enormously by reading Feynman's lectures on physics. His work on statistical mechanics is essential reading too especially if you already know everything.

I found this rather satisfying answer.

"Socialism never took root in America because the poor see themselves not as an exploited proletariat but as temporarily embarrassed millionaires."

- John Steinbeck

Are you temporarily embarrassed?

You may not realise it, but you could be a temporarily embarrassed millionaire. Do you plan to someday in the future have more money? Are you concerned that your taxes are too high, because someday you might pay too much tax. Do you ride the bus only because this year you can’t afford that luxury car you’re going to have? Do you live pay cheque to pay cheque like most people just because you haven’t had your lucky break.

You aren’t rich and it’s very unlikely you ever will be. The economic and power systems of this planet are not designed for you to get rich. The American dream doesn’t exist and it never did. Stop being a temporarily embarrassed millionaire and just be a person.

They should include Julia in the results.

I hope Amazon, Apple and Google are doing better. How can we know for sure? It's not unreasonable to ask because I would have thought it completely NUTS to think FB used clear text but apparently they did (or still do). What about everyone else? Does anyone know how to find out?

Is it even possible for this to be the result of negligence when Facebook has some of the best programming talent in the world? Maybe, but I don't think so. I think this was INTENTIONAL. The question at least is why? IDK. Some FB employees probably didn't mind because it gave them unbelievable spying powers. Another thing to consider is how the NSA had a strong relationship with FB for years and the odds of them not knowing about FB's clear text practices is zero. They knew. People within law enforcement probably knew as well. Given how nothing happens at FB without Zuck's apporoval there's no doubt he knew as well.

I'll just say this. Anyone who discourages anybody from even TRYING to learn or pursue a career in science is a bully and a jerk. That's the way the world is going and being tech savvy only makes the world a better place. That said our schools and workplaces should still be based on MERIT. I don't care where the science comes from so long as it's good science. If it just so happens to be more men are doing science than women, then we should make sure it's not because somebody is being shut out. Everyone get's to try and I even mean slow learners who are men and maybe even white. I say this because we NEED science and technological know-how going forward. If someone is so inclined educate them, give them a job. Yes we need more women in science, because we need more people in science, badly. It would be a pity if someday we achieve some quota that we're satisfied with and leave it at that. The world demands more people competent in science than can every fill the need, especially going forward. I personally DO NOT CARE wha the sex of the scientist who did XYZ happens to be. If fewer women get into the sciences or lean towards studying biology or something else, I accept that on one condition, that the DOOR is OPEN for EVERYONE. The country with the most technologically capable citizens is probably the one that's going to lead the world. Science education should be given out liberally and not rationed for an elite few. I personally do not care how the final stats and quotas look. Did every woman sincerely interested in a science career have the support and means necessary to pursue her goals? The answer to the question should be a resounding YES. The next thing is that I don't like sexist people but why make an example out of this guy and fire him? It doesn't solve anything. He didn't harass or grope someone. Go ahead and trash his ideas, discredit him, etc. whatever but leave his job alone. It's savage to fire people just because they have opinions you do like.

Vim works fine. I use EMACS. TextMate, Atom and Sublime are OK. Any mainstream editor is fine is all but a few corner cases. Truth be told I would be fine without EMACS but maybe less happy. People unable to exit Vim is just a sign of a larger problem, that a generation of programmer relies more on Google and Stack Overflow than simply READING documentation and EXPERIMENTING by writing short little throw away programs. There is so much Vim material out there on the internet that it makes me afraid these defective programmers can't even use Google properly. I still look shit up on the internet all the time but 99% my answer is right in the documentation. Anyone who can really program is horrified by idiots who can't shut off Vim or use WordPad to write c programs and try to compile them.

How is this even possible? I used EMACS for years and had no trouble understanding Vim. Who's hiring these developers who can't even exit Vim? Is this even a real story or the Onion?!? OK, it's real. I need to go outside and get some fresh air. This is simply too shocking.

Javascript is still missing simplicity, consistency and a unified core set of ideas. It will always be that way too. Javascript will always be something grudgingly accepted or used with some misgiving. ES6 has some very nice features and the good parts of javascript stand out as much as the unfortunate inconsistencies lurking inside the language. People know how to use it. Some use it quite well but I always get the feeling I have to step around carefully and not make a dumb mistake in js which is easier to do than almost any other language except say PHP. Web assembly should open up some badly needed possibilities. All we really need is a consistent API. A world without js? I hope so.

It's nice to have a free book as a supplement. Linear Algebra Done Right by Sheldon Axler is a much better choice and when making an investment in learning, particularly a difficult subject like linear algebra, saving money with a free text is probably the most expensive thing you can do. You might save $40 but end up not really learning and wasting hours you don't have. Above all, find a good teacher.