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The choice of pi as a number whose sequence of digits is random is a bit of a weak point of the argument in the post. It is not even known whether every digit 0-9 appears infinitely many times in pi (a weak version of the normal number conjecture). So we do not really know (but strongly believe) that the sequence of pi digits would truly appear random. This of course does not detract from beautiful arguments and the general ideas in this post.

His definition of Kolmogorov complexity is a bit loose. The rigorous definition uses Turing machines (or Minsky, or Post, or some sort of lambda expression, etc.) so the size is something specific. Different versions of complexity defined this way may give different values but have the same properties and asymptotics so one might just as well stick with the Turing kind. Chaitin's theorem (about the limit of Kolmogorov's complexity being just entropy) holds for all versions as well.

With all due respect, no, it isn't. His drivel against set theory shows that he didn't even read the basic axiomatic set theory texts. In one of his papers, he is ranting against the axiom of infinity saying that 'there exists an infinite set' is not a precise mathematical statement. However, the axiom of infinity does not say any such thing! It precisely states the existence of some object than can be thought of as infinite but does not assign any semantics to it. Ironically, if he looked deeper, he would realize that the most interesting set theoretic proofs (independence results) are really the results in basic arithmetic (although covered in a lot of abstractions) and thus no less 'constructive' than his rational trigonometry.

I have a couple of EB6s to show to my students but ever since scientific calculators were allowed in written tests, I have never used one myself. Law of cosines is good enough for wind triangles :). Worked for a commercial test as well as the ATP. It is a beautiful device though ...

I am not sure why you are being downvoted but you are absolutely right: it is even in the name (WD stands for 'Water Displacement'). My reaction to this article was a huge: 'why?'. WD-40 is at best mediocre at everything it is used for. Wurth makes much more capable compounds for the came purposes. Their penetrating oil is unmatched. I guess as part of the popular culture, WD-40 has its value but I am not sure its chemical properties are all that unique.

Also, possessive pronouns are exactly like in English, concording in gender with the owner, not the object.

This is only true in third person singular. For example, in first person singular: 'моя чашка' (my cup, 'cup' is feminine) vs. 'мой ключ' (my key, 'key' is masculine). Third person plural: 'ихнее дело' (their business, neuter) vs. 'ихняя забота' (their concern, feminine) although most educated Russian speakers would object to these pronouns as a bit too colloquial (although not as colloquial as 'евойная'). Same in second person singular: 'твой друг' (your friend, masculine) vs. 'твоя подруга' (your friend, feminine). In all of the examples above, the gender of the speaker/owner cannot even be determined (grammatically speaking).

Army PIT? Ah, this is not a good name...

This is a fine opinion, here is another one. Calling everyone who uses LaTeX cultists is a bit insulting. I do not particularly like LaTeX and use it only when a journal requires it in which case it is pretty much painless as I simply follow the provided template. TeX, on the other hand pretty much satisfies all my typesetting needs and I use it daily. I wish everyone would use TeX or LaTeX but I would not force it on everyone. Typst seems like a fine if a bit immature system but I truly hope it goes away, the sooner the better. Not because it is bad at what it does but because it solves a problem that does not exist and distracts from a standard that may not be perfect but has proved itself again and again. I am also weary of any piece of software that is controlled by a private entity, no matter how good the initial intentions are. Being open source is not really a guarantee of anything.

With all due respect to your perspective on TeX, isn't it the whole point? There are weaknesses in TeX (like using $ for both beginning and ending the math mode) but they are quite minor. Quirkiness is not a weakness but being a standard (since 1986!) is a major strength. The fact that it does not change is a blessing, truly. Python may be a fine language with a great community of supporters and I use it because I pretty much must but programming in something that is essentially a moving target is no fun. And I would take TeX macros over Python ugly syntax any day, no offense. Not to say I am right just to point out that taste is not necessarily a reliable guide.

On the other hand here is a Long-EZ that gets 40 mpg flying at over 250 mph (so not quite 250 knots but still). The actual savings will be higher since one can fly in a straight line most of the time. It also avoids congestion and ... is simply more fun than driving. Also an auto-pilot in aircraft has been a real thing for quite some time while same in a car ... is still quite pathetic. I have eaten plenty of lunches comfortably while flying a plane while I would not be comfortable doing it while driving.

Long EZ reference: https://generalaviationnews.com/2016/05/25/going-fast-on-les...

I was wandering the same thing. Quite often the insurance sets a much higher standard than what is legal. I had a lot of fun flying a local police helicopter as a commercial helicopter pilot with the police pilot (who only had a private certificate at the time) simply because insurance required a commercial pilot to be present in the cockpit.

In my experience a more appropriate title for this book would be: 'Linear algebra done ok if this is your second time doing it'. I have seen way too many students who, after having taken a course that used this textbook, could not give an example of a linear operator (yes, I literally asked, show me an example of a linear operator in R^3) because they literally do not have the language for it (because 'matrices are bad').

I have the same sentiment about TeX. The fact that the language has been stable for over 30 years is incredibly important to me. I also feel like I can do anything in TeX: I have written a C compiler in TeX as an academic exercise so I cannot take complaints about TeX's macros seriously.

I am also doubting his claim that he had several students land without assistance on the first try. I have had a few students land with minimal assistance on the first try but I am quite sure that the airplane would be damaged had I refrained from making a couple of minor corrections. Some of those students were very talented (one soloed at 7 hours and went on to fly for Jet Blue eventually, of course this had little to do with my instruction) but they still needed a little bit of help the first time.

I understand this is a (good) attempt at humor but this might be an interesting idea to see if Bluetooth leaks from inside the microwave oven (or from the outside in). Of course, the microwave has to stay off, naturally :)

True, though this may mean many things. The only part of CFR 14 that mentions that a certificate is required for operating aircraft is CFR 14 61.3 which states that an unexpired certificate is required to `exercise the privileges' of that certificate. So if the PAO does not require the certificate to begin with, this part does not apply and one only has to comply with part 91 rules. Again, feel free to disagree, the sheriff told me this so who knows:)

As I mentioned above it is not that the FAA waves their requirements as much as the FAA does not have jurisdiction over such operations (under appropriate circumctances).

Here is a quote from AC No: 00-1.1A (Public Aircraft Operations): What Oversight of PAO Does the FAA Have? The FAA has limited oversight of PAO, though such operations must continue to comply with the regulations applicable to all aircraft operating in the NAS. The government entity conducting the PAO is responsible for oversight of the operation, including aircraft airworthiness and any operational requirements imposed by the government entity. The government agency contracting for the service assumes the responsibility for oversight of a PAO.

The military is another entity that operates aircraft outside of FAA jurisdiction. Even military airman certificates have to be `converted' to civilian ones i a military pilot wants to become a civilian pilot.

Police in the US do not have to have a license to operate anything, including aircraft. In this case, insurance requirements take over though. They may have a legal right to fly but no insurance company would approve operation by anyone but a commercial pilot. I got a few hours in a local police Bell 206 because they needed a commercial pilot to fly while their official pilot only had a private license. Fun!

This is indeed a nice idea, unfortunately the university (mine) gets kick backs from the book store. At the beginning of every semester every faculty gets an email asking us to 'encourage' students to buy their materials at the book store. Every semester I do what I always do and tell the students that the ($250!) book will not be used in class (although mine is just one in a sequence and the book is chosen by the whole department for the whole sequence) and give a half a dozen references to (excellent) free online books. Even then some students for whom the class is the terminal one in a sequence buy their books. Must be human nature at play. On a different note, as a flight instructor, when a future student asks me what to bring to the intro flight, I usually say 'lunch', since I provide everything else, including headsets. Yet half of them bring $500 worth of useless gadgets and expensive books (not, strangely enough, headsets) to 'be prepared'.

Just wanted to say thanks as well. I host a private Jitsi server for my online teaching. It took a bit of effort to set up but worked well for me since.

From what I have seen in TeXmacs documentation, they have implemented pretty much every feature of TeX's linebreaking algorithm and more (microtypography, global page breaking, etc) so my claim above was not to say that the documents TeXmacs outputs have suboptimal aesthetics (to be fair, modern versions of TeX have all of these features, as well, although not the original TeX, alas). What I meant to say was there is no (even theoretically) possible way to have a perfect WYSIWYG editor if global paragraph/page breaking is desired. For example, due to global page breaking, one may be editing a line in the middle of the document and its position on the page (and the page number, left/right headers, etc) will be constantly changing---not good for the visual experience. I do not know how TeXmacs deals with these (extremely rare, admittedly) cases but the discussion was about the true WYSIWYG vs not so take it with a grain of salt. Let me say this again: TeXmacs is an outstanding piece of software. If in thirty years, a TeXmacs file format is still readable by the newest version (possibly with some easy tweaks), I will consider switching from TeX :). My other (minor) concern is that the LaTeX files that TeXmacs exports do not render at all as the pdf files TeXmacs produces itself. So as a WYSIWYG frontend to LaTeX, TeXmacs is ... not quite. Which they never claimed to be so I cannot fault them for this.

As a fellow mathematician you may then appreciate the fact that local and global maxima may differ dramatically which pretty much precludes true WYSIWYG (not just in TeX) in that you have to settle for one of the two: visual output with suboptimal aesthetics (TeXmacs, and, to some extent, LyX) or perfect results that you have to compile with some delay. It has nothing to do with the computational power available but rather with the occasional highly unstable line breaking. Even in MS Word it is annoying sometimes to see it resize a current line even though it uses a rather lame line breaking routine. TeX does have facilities for almost real time WYSIWYG (SyncTeX was added specifically for that purpose) although they take some effort to set up. As far as concentrating on the work at hand I have written whole papers without compiling the document once before everything was complete. I admit it takes some getting used to but I prefer something I can grep through to a mere pretty picture. I admit if my work was heavy on large commutative diagrams I might have had a different view. One thing I totally agree with you on is that TeXmacs is an outstanding piece of software. I would just prefer to keep my documents in TeX (which TeXmacs can export, kinda).

It tells me that beauty is in the eyes of the beholder, i.e. what one may perceive as ugliness, countless others will view as beauty or, at least functionality. I personally think that the ugliest design in existence is Python but I admit my opinion is not common. Moreover, I use Python myself, since syntax is not the only important thing in a language (the ecosystem is Python's undisputable strength). It is also unclear to me what specific 'ugliness' in TeX is fixed by, say TeXmacs. Is TeXmacs internal language dramatically (or any) better than TeX? Does not seem so. The WYSIWYG option? There are WYSIWYG editors for TeX as well.

This would be impossible unless the reader have my LaTeX source code and compile it themselves. But it is super simple for epub, or html webpage (by modifying the css).

Well ..., wouldn't the html page be the source code in this case? Also, in most cases changing the look of a LaTeX document is as simple as changing the docuent class or switching to a different package. Also, modifying CSS is anything but simple in some cases, especially when the original style is not ideal.

I have heard HTML/CSS mentioned as an alternative and I pray every day this time will never come. Even taking all the complaints leveled at LaTeX at face value, using HTML/CSS looks like pure hell to me. Allow me to elaborate.

1. You mentioned forgiving. One may not like the style of TeX error messages but its tracing facilities are extensive and given enough time and perseverance one can track nearly any layout issue down an correct it. Compare this to CSS silently ignoring incorrect syntax, having different syntax across browsers, etc. I would take strict syntax checking over this mess any day.

2. Many complained that LaTeX has more than one way of achieving the same result. True but how many ways are there of centering a div on a page? I can list six off the top of my head and there are probably more.

3. You casually mentioned '...except for maths things...' but this is far from minor. I cringe when I read engineering papers not written in TeX: the formulas are so ugly that they border on unreadable.

4. CSS may be wider known but unlike TeX CSS is a moving target. Being designed by a committee it carries all the flaws, like kludgy design in the name of 'compatibility', poor choices of syntax to make it appeal to a wider audience, etc. The designers of CSS are so enamored with the 'cascade' but in practice it is rarely used as intended. The 'important!' kludge as a perfect testament to this.

5. LaTeX syntax may be unappealing to some but HTML takes it to a whole other level: whitespace that affects the layout yet no easy way of getting rid of it (HTML style comments are a torture device); too verbose... one may not like the backslash but what about <...> </...> ? Five extra symbols!

6. LaTeX engines produce full featured PDF so hyperlinks are not a problem (most LaTeX documents have them). Yes, CSS has so called 3D graphics but it is anything but programmer friendly. What good are 3D transforms if one cannot even use simple lighting effects programmatically; c'mon, at least give me Lambert reflection! Incidentally, inline JavaScript can be included in pdf documents produced by LateX as well (although ... why?)

The way I see it, this only proves my point. As you write: '...None of them have become the standard...' and this is at the center of the argument. TeX may not be ideal but it strikes the correct balance to become and stay standard for so many years. One can do pretty much anything in bare Postscript (and I am ashamed to admit, I have) or even 'handmade' PDF but it does not make it a good alternative to TeX. I have experimented with alternative syntaxes (apologies it this is not the correct plural of 'syntax') but had to give all of them up due to a number of flaws. These experiments gave me a new appreciation for Knuth's choices.

What a great summary! Unfortunately, many discussions of TeX vs alternatives are somewhat thin on details and are instead trading on emotions. As you mentioned in your comment, the choices made by Knuth are far from random. He even made it possible for anyone to change them! Not many people using TeX know that the choice of the backslash as an 'escape' character may be easily changed. Even the necessity of curly braces may be avoided using carefully designed macros. LaTeX took a different path but it is only one possible choice. It is telling that no real alternatives have emerged during the 40+ years of TeX's existence.

TeXmacs is a great project, no doubt, but you have mentioned WYSIWYG as one of the advantages. This is the main reason I do not use TeXmacs to create documents (I do use it to create online lectures). You may like or dislike LaTeX/TeX (and the discussion is usually too emotionally charged for my taste) but the fact that it is a text format (not as verbose as, say, XML, at that) which is more or less standard is a deciding factor for many people, including myself. On a personal level, while I slightly dislike LaTeX style macros, I absolutely adore TeX's design (yes, including syntax). It is a matter of taste, of course. I am aware that TeXmacs can export LaTeX, it is not quite the same. LyX is another (better in my view) WYSIWYG option, if one is desired.

You may think so but this would be going against the facts. In reality, there are two major goals each US university has: 1. attracting funds (in the form of tuition, grants, etc) 2. improving educational statistics for the state The second goal is related to the first and, in the case of a public school, dominates. The more diplomas the university awards, the more funding it usually gets (since it improves 'retention').

Universities certainly have great facilities for learning and if a student wants to learn, s*he certainly can but this is irrelevant from the point of view of the administration.

Lest you think this is another conspiracy theory, I have heard these two exact statements in every faculty meeting we had at the university level. How can I care about grade inflation (as a faculty) if I am penalized for the excessive number of withdrawals from my classes. Think about it: the students have realized that they were not ready for the class early, and decided to save themselves the headache and take a lower level class. This is counted against the faculty. Now what incentive do I have to give objective grades?