Vedic Math as a teaching tool

Vedic math has been active for over several hundred years in the Indian subcontinent. This kind of math, a kind of alternative algebra, is nearly unheard-of in the Western world, and is almost never taught in school. One of the reasons it had been nearly unknown is that the first book on its techniques was not published until 1965.

Vedic math a system of reckoning with solving equations which seeks to do the same thing as arithmetic and algebra. It is really a system of techniques and sutras which provide fast and easy ways of reckoning with arithmetic operations which would otherwise be burdensome. A student I know was able to, mentally, without a pen, pencil or calculator, perform multiplications consisting entirely of 3-digit numbers. The same student of Vedic math was also able to mentally find answers to calculus questions that would take over a page of work.

My student had an impressive skill, and certaily taught me quite a bit. But did he “understand” math this way? It turns out that Vedic math reduces math operations to a series of tricks which coax an answer from a problem. It doesn’t require any deep understanding of what is going on. It doesn’t even require you to have even a conceptual understanding of basic arithmetic.

We have tricks too in the Western world. Ever heard of cross-multiplication? Or the FOIL method? Mistakes students make in executing these tricks arise from a misapplication of the trick, not from a misunderstanding of math. Teaching tricks makes a better obstacle to a math education than a passageway. And this is the main objection to Vedic math, and a reason as to why it hadn’t caught on with the western world.

For better or worse, us westerners demand reason, evidence and analysis as a keystone to the understanding of anything, let alone math. Accepting an idea without evidence makes it too easy to reject the idea without evidence. Accepting an idea without analysis makes it easy to reject the idea without analysis. And in this age of “post truth”, it makes it too easy for governments to rule at one’s whim if evidence, analysis and reason are not offered for a decision or policy.

On Media Centrism

A current default chart from Ad Fontes Media.

Ad Fontes Media is “famous” for their “Media Bias Chart”, an ever-changing chart that is now in version 6.0. The charts are customizable, so that you don’t have the thicket of media logos printed on top of each other as in the image you see to the right.

I took a closer look to see if I agree with the chart, and I believe that the spectrum of opinion depicted here is too narrow. Even if you go the the fringes on this chart — what is considered “the far left” and “the far right”, it is my opinion that all media outlets depicted operate within certain paradigms, and offer similar viewpoints. The problem is, though, much of what is “far left” appears to amount to opinion and little actual news; whereas what is on the far right is similar, with an added dose of misrepresentation and fabrication.

The definitions of “left” and “right” themselves are suspect also. Am I to believe that MSNBC is in the nearly identical part of the political spectrum as Democracy Now? I am a fan of both news sources, and I can say that this is a bad comparison on many levels. For one thing, DN! is a single news program dealing with politics, labour and peace issues; while MSNBC is an entire cable news network. Even individual programs within MSNBC will have a range of opinion to the right of DN. I would even consider Rachel Maddow to the right of DN, but not terribly far. DN is a newscast, branding itself variously as “The War and Peace Report”, and “The Quarantine Report”; while MSNBC is more than 70% opinion, and talking heads. DN earns its leftist cred by its choice and angle of its news; not necessarily by  opinion. Where MSNBC, like all major networks, would discuss war by bringing in military generals and politicians; DN will bring in medical personnel, and peace activists.

In addition, DN and MSNBC are lumped together as the “hyper partisan left”. DN hasn’t really had much nice to say about either party; while MSNBC has actually been the Cable News answer to Fox’s Republican cheerleading. MSNBC has advertisers to answer to and have to colour inside the lines; DN is donor-driven, and has its viewership to answer to, and are not answerable to capitalist forces in any important way.

Another curious mention is Jacobin, probably considered “hyper-partisan left” because even their subscription instruction suggests: “If life has treated you well, you should feel guilty about it and subscribe at the high-income rate for the cause. Your help will allow us to subsidize subscriptions for others”, offering separate rates for the financially priveleged and for the disadvantaged. I am given to believe they are what right-wingers often think about as forming “the socialist agenda”. These people, who genuinely are solidly leftist, are lumped in the same “hyper-partisan left” pigeonhole as MSNBC. Would MSNBC have an interview between Noam Chomsky and David Barsamian? Or use the phrase “class struggle” in a sentence? Jacobin did both in their most recent issue.

There are other things that make me scratch my head. Is The Atlantic, a magazine which has on its staff a former Republican presidential speechwriter considered “left of centre”? On what planet? Also not sure what TMZ and Vogue are doing anywhere on this list. Is there now such a thing as “right wing” or “left wing” fashion and celebrity gossip? Also, I see that The Weather Channel is at centre, perfecting the art of telling us the temperature outside while walking the tightrope between left and right. Thank God.

Bloomberg, Financial Times and MarketWatch are considered “dead centre” in this distribution, but I wouldn’t expect articles from these financial market publications to ever publish anything that questions the capitalist system. It is clear what is meant by centrist is just a reporting of business news that does not favour Republican or Democrat. After all, investors need a tolerably balanced news source to know where to invest their money. But partisan balance is not the only kind of balance. Would they give equal time to union leaders in reporting labour disputes? Would they interview wildlife biologists or indigenous leaders when reporting about pipeline construction? Or the construction of anything? Would they give equal time to protestors who have good reason for a project to not go ahead?

Kinky muckraking journalism without the messy controversy.

I decided to be a bit adventurous and go for the looniest lefty publication I could find in the distribution. That would be a website called Wonkette. I never heard of the publication before researching this article, although I have heard of publications on the far right of the spectrum, since their association with Trump had generated much publicity (Brietbart, Fox News, and InfoWars are examples). What can I say about Wonkette? I think it is MSNBC with much more colourful language. They introduce a Trump tweet with: “Here’s old shithead, so you you can see him lying.” Colourful invective and f-bombs aside, their articles appear to show evidence of research from more mainstream sources like Forbes and The New York Times. Their merch suggests support for the usual Democratic party suspects: Face masks depicting Kamala Harris and Ruth Bader Ginsberg, for example. They also sell clothing with messages along Democrat themes. In other words, it appears uncertain whether they really are an alternative voice, once you go past the colorful language referred to earlier. While they are sometimes a hilarious read, I have yet to read an article that uses the phrase “class struggle” in a sentence or read a report on labour issues of any kind.

The numerical nature of the rating system on the Media Bias Chart is also suspect. It gives the illusion of scientific precision to what is essentially subjective data, resulting in a placement on a purportedly partisan basis that is incosistent. They rate individual articles as well. It is also not clear what specific criteria they are using to rate articles and websites.

“Partisanship” is implies support for a political party, but it doesn’t mean the same thing as “balance”. Labour groups, environmental groups, youth groups, civil rights groups, anti-poverty groups, have all been frozen out of public discourse in nearly all major media, whether in print, online, or on television or radio. To read the New York Times, one would be excused for thinking these groups didn’t exist at all. Same for MSNBC, although they will support nearly anything along Democrat party lines. While CNN is less partisan, they are just as silent about groups organized in the public interest such as these.

The only way the major media could be called “left” (as right-wing people love to label them as) is if the voice of the public is shut out of public discourse, reducing news reporting to little more than the he-said-she-said banter between pundits, politicians and other highly paid talking heads, as these media has successfully done.

Websites I wished I created

A wall clock once sold at

I would bet that there are a lot of people who wished they created a website called Faux News. “Faux”, being French for “Fake” (as in “faux fur”), but could be pronounced by un-knowing English speakers as “Fox”. A stroke of genius.

There are actually four sites that I am aware of with the same name:

  •, The “.com” website is a single-page website which has retouched photos intended to parody the political news of the day. There are no articles or text on the site. The “.org” website has “fact-free” satirical news articles and some graphics, but is extremely limited in its output.
  • The same can be said for a third site I found,, which is not much more than a barely-set-up website with test postings and test graphics. The latter one is registered to an owner in Utah; the first two are registered to an owner in Scottsdale, Arizona.
  • There is a fourth domain,, which just generates a blank page. A whois lookup suggests that it is owned and operated by InFaux Holdings of New Jersey.
    At first glance, you could be excused for thinking there was going to be a fivefold increase in taxation in 2013.

    Most of these websites are registered with GoDaddy and are all subject to a legal dispute, according to publically-available registrar information. The content in these sites is pretty much frozen from update, which is sad. There is so much possibility here. It isn’t just making fun of the gaffes of Fox hosts or presenting bizarre bar graphs (much like the real ones on Fox, famous for its mislabelled axes, pie charts that add to more than 100%, bar graphs that don’t start from 0, and other liberties taken with graphs that cause misleading impressions to be made.But Faux News won’t go away, now morphing to a Facebook group, and in at least one subreddit. I have a problem with it in that its full capability is not exploited; most of the humour is juvenile and from a YouTube Faux News video, the delivery could be better. I can say the same for a podcast by this name, which is less satire and more juvenile banter. When it is good, its satire amounts to goofy character sketches. Maybe they are poking fun at some particular interviewer or host, but it is unclear. But that isn’t satire. I can appreciate that satire is

    Honestly, could you have made this bar graph up as a joke?

    sometimes difficult to write. At the “easiest” level, it still requires research, since satire becomes more effective according to how much you know about the topic. But for Fox News parodies, you have to realize that most of this stuff writes itself.

    Faux News can claim some kind of connection to the fact that the online world is rife with “information” on every nutty idea that exists. I am not sure if I need to accuse Fox news of passing on information “because it exists”, since I would accuse them of far worse: of being the ones to creatively conjure up information into existence. In less polite circles, we would call that “bullshitting”. Whether it is misleading with bar graphs, or presenting impossible pie charts, it would appear as if NewsCorp will stop at nothing to present its own view of the world, without much regard for the truth.

Trendy Google Searches of 2020

I have heard about Google’s cataloguing their top search terms. They don’t really curate the “top 10” of all time or anything; rather, they divide their search terms into categories. I have discovered something about myself when I saw these lists: I don’t give a shit about most of it. Here is Google’s finger on the world’s pulse for 2020:

  • Top search:  Coronavirus. Celebrities and politicians have been beat out in the search rankings by a submicroscopic, nonliving viral particle. It was also top in the news category also.
  • Top Actor: Tom Hanks was at the top.
  • Top Athlete: Ryan Newman. This NASCAR guy  survived a grisly crash on the last lap of the Daytona 500 back in February.
  • Top Game: Among Us trended after late August.
  • “Top” Recent Deaths: Kobe Bryant, also the third most frequent search term overall.
  • Top Movie: Parasite is at the top. I saw this movie. It’s about how the protagonists, a servant for a rich family lowers their morals continuously to obtain more of their master’s wealth, to the point of murdering their masters. I thought the idea was supposed to be that a parasite doesn’t kill its host. Personally I don’t like movies where you can’t root for the protagonist.
  • Top TV Show: I have no appreciation of television shows. What’s “Tiger King”? Maybe I should Google it. Oh, I see. It’s a show about cat breeding on Netflix.

If you want a meaningful life, quit filling it with glorified lolcat programming like this and actually take on something intellectually challenging, with the TV shut off. In my case, I do  have the TV on as I type this, but it is tuned to a spotify-like music-only station playing smooth jazz. No words. I can concentrate. I seem to have a low tolerance for mindless programming.

Inverse of a larger matrix and Power Series

Most textbooks I have on Lin Alg discuss finding the inverse of a 2×2 matrix,and appear to have little to say about inverting 3×3 matrices and above. I was trying to invert a 5×5 matrix, but all I could find after looking through two linear algebra textbooks, and the internet was info for 2×2 matrices.

    \begin{equation*} \begin{bmatrix}a & b\\c & d\end{bmatrix}^{-1} = \frac{1}{ad-bc} \begin{bmatrix}d & -b\\-c & a\end{bmatrix} \end{equation*}

… except the web page I read used comic sans. Then there was this really good lin alg textbook I came across that had a technique that used a 3×3 example that could scale to any size. Bingo. The next problem will be presenting this to you as there appears to be no way (after an online lookup) to present the notation to you in a satisfying way. I will separate two matrices with a right arrow (\longrightarrow) instead of using a double matrix with a vertical bar in the middle. I also have to reckon with limitations in using Latex notation in a blog article. So, please excuse any makeshift notation used in this article.

    \begin{equation*} \begin{bmatrix} 1&0&0&0&0 \\ 1&1&0&0&0 \\ 1&2&1&0&0 \\ 1&3&3&1&0 \\ 1&4&6&4&1 \\ \end{bmatrix}\longrightarrow \begin{bmatrix} 1&0&0&0&0 \\ 0&1&0&0&0 \\ 0&0&1&0&0 \\ 0&0&0&1&0 \\ 0&0&0&0&1 \\ \end{bmatrix} \end{equation*}

The idea being, to turn the left matrix into the right matrix, applying the techniques of Gauss-Jordan elimination. Meanwhile, any operation I commit to the left matrix must be also done to the right matrix. It turns out that you don’t necessarily get the same matrix. First, I subtract the first row from the rows below:

    \begin{equation*} \begin{bmatrix} 1&0&0&0&0 \\ 0&1&0&0&0 \\ 0&2&1&0&0 \\ 0&3&3&1&0 \\ 0&4&6&4&1 \end{bmatrix}\longrightarrow \begin{bmatrix} 1&0&0&0&0 \\ -1&1&0&0&0 \\ -1&0&1&0&0 \\ -1&0&0&1&0 \\ -1&0&0&0&1 \\ \end{bmatrix} \end{equation*}

Then, I apply the same thinking with the second row to eliminate variables in the second column of the left matrix, and proceed similarly for subsequent columns of the left-hand matrix:

    \begin{equation*} \begin{bmatrix} 1&0&0&0&0 \\ 0&1&0&0&0 \\ 0&0&1&0&0 \\ 0&0&3&1&0 \\ 0&0&6&4&1 \\ \end{bmatrix} \longrightarrow \begin{bmatrix} 1&0&0&0&0 \\ -1&1&0&0&0 \\ 1&-2&1&0&0 \\ 2&-3&0&1&0 \\ 3&-4&0&0&1 \\ \end{bmatrix} \end{equation*}

    \begin{equation*} \begin{bmatrix} 1&0&0&0&0 \\ 0&1&0&0&0 \\ 0&0&1&0&0 \\ 0&0&0&1&0 \\ 0&0&0&4&1 \\ \end{bmatrix}\longrightarrow \begin{bmatrix} 1&0&0&0&0 \\ -1&1&0&0&0 \\ 1&-2&1&0&0 \\ -1&3&-3&1&0 \\ -3&8&-6&0&1 \\ \end{bmatrix} \end{equation*}

    \begin{equation*} \begin{bmatrix} 1&0&0&0&0 \\ 0&1&0&0&0 \\ 0&0&1&0&0 \\ 0&0&0&1&0 \\ 0&0&0&0&1 \\ \end{bmatrix}\longrightarrow \begin{bmatrix} 1&0&0&0&0 \\ -1&1&0&0&0 \\ 1&-2&1&0&0 \\ -1&3&-3&1&0 \\ 1&-4&6&-4&1 \\ \end{bmatrix} \end{equation*}


    \begin{equation*} \begin{bmatrix} 1&0&0&0&0 \\ 1&1&0&0&0 \\ 1&2&1&0&0 \\ 1&3&3&1&0 \\ 1&4&6&4&1 \\ \end{bmatrix}^{-1} = \begin{bmatrix} 1&0&0&0&0 \\ -1&1&0&0&0 \\ 1&-2&1&0&0 \\ -1&3&-3&1&0 \\ 1&-4&6&-4&1 \\ \end{bmatrix} \end{equation*}

You might recognize number pattern in the very first matrix to resemble part of Pascal’s Triangle:

    \begin{equation*} \begin{bmatrix} 1& 0& 0& 0& 0 \\ 1& 1& 0& 0& 0 \\ 1& 2& 1& 0& 0 \\ 1& 3& 3& 1& 0 \\ 1& 4& 6& 4& 1 \\ \end{bmatrix} \end{equation}

There was a Mathologer video on YouTube which I saw recently which modified this Pascal-triangle based matrix. First, it changed the main diagonal from 1 to 0; then removed the top row; then moved all rows up and added a new row. Then every second diagonal is “decorated” (Burkhard Polster’s words, not mine) with minus signs in the following manner:

    \begin{equation*} \begin{bmatrix} 1& 0& 0& 0& 0 \\ -1& 2& 0& 0& 0 \\ 1& -3& 3& 0& 0 \\ -1& 4& -6& 4& 0 \\ 1& -5&10&-10& 5 \\ \end{bmatrix} \end{equation}

This weird concoction of Pascal’s triangle is based on the coefficients of the expansion of -(1-x)^k, where k is the row number of the matrix counting from 0. Also, the last term, 1, is omitted as stated before. The inverse of this matrix is a fair bit different, but has a special property. When you find the inverse, then multiply by a 5 by 1 matrix consisting of successive powers of n, you get:

    \begin{equation*} \begin{bmatrix} 1& 0& 0& 0& 0 \\ -1& 2& 0& 0& 0 \\ 1& -3& 3& 0& 0 \\ -1& 4& -6& 4& 0 \\ 1& -5&10&-10& 5 \\ \end{bmatrix}^{-1} \times \begin{bmatrix} n \\ n^2 \\ n^3 \\ n^4 \\ n^5 \end{bmatrix} = \begin{bmatrix} 1& 0& 0& 0& 0 \\ \frac{1}{2}& \frac{1}{2}& 0& 0& 0 \\ \frac{1}{6}& \frac{1}{2}& \frac{1}{3}& 0& 0 \\ 0& \frac{1}{4}& \frac{1}{2}& \frac{1}{4}& 0 \\ -\frac{1}{30}& 0& \frac{1}{3}& \frac{1}{2}& \frac{1}{5} \\ \end{bmatrix} \times \begin{bmatrix} n \\ n^2 \\ n^3 \\ n^4 \\ n^5 \end{bmatrix} \end{equation*}

We multiply by the n^r series in order to lead us to the next step, which is to reveal that each row in this matrix make up the coefficients of the sum of a power series after multiplication:

    \begin{align*} S_0 &= \sum_{n=1}^{\infty} 1 = n \\ S_1 &= \sum_{n=1}^{\infty} n = \frac{n}{2} + \frac{n^2}{2} \\ S_2 &= \sum_{n=1}^{\infty} n^2 = \frac{n}{6} + \frac{n^2}{2} + \frac{n^3}{3} \\ S_3 &= \sum_{n=1}^{\infty} n^3 = \frac{n^2}{4} + \frac{n^3}{2} + \frac{n^4}{4} \\ S_4 &= \sum_{n=1}^{\infty} n^4 = -\frac{n}{30} + \frac{n^3}{3} + \frac{n^4}{2} + \frac{n^5}{5} \end{align*}

The payoff here is that you can make a matrix as large as you want to find the summation formulae for all power series ad infinitum. The power series would utilize a 10\times 10 matrix to obtain the power series for S_9:

    \begin{align*} S_9 = \sum_{n=1}^{\infty} n^9 &= 1^9 + 2^9 + 3^9 + 4^9 + ... \\ &= -\frac{3n^2}{20} + \frac{n^4}{2} - \frac{7n^6}{10} + \frac{3n^8}{4} + \frac{n^9}{2} + \frac{n^{10}}{10} \end{align*}

More generally:

    \[ S_m = \sum_{n=1}^{\infty} n^m \]

for any m in the set of integers.

Google Reviews of the Quality of Service at Mount Everest Base Camp IV

A screenshot of what I saw when I looked up Mount Everest. It seems to have a new set of pictures, and gave me the left panel when I clicked on “Everest Base Camp IV” on the map. This is in Sattelite View.

Base Camp IV is the camp nearest to the summit of the tallest mountain in the world. It is situated at 26,000 feet above sea level, in the oxygen-deprived region of the mountain called the “death zone”. It gets its name from the fact that at that altitude your body is consuming oxygen faster than you can breathe it in. When you surf there on Google Maps, you get a map of the summit, and depending on how much screen you have, the snow-encrusted Base Camps III and IV. If you went there on a search, Google likes to present you with a panel with hopefully useful information on the left-hand side.

With that, some rather questionable user options that seem out of place here. One of them is a phone number (do they really have phone service?), and a checkbox to “Claim this business”, making assumptions that are really unsuitable.

But the least suitable of all is that Google Maps offers a “Review” section, as if this is some kind of swanky hotel or neighbourhood restaurant. The people who climb Everest aren’t going there for room service or good food, and are probably assuming that Base Camp IV doesn’t have any kind of entertainment or any other reference to normal urban civilization that most of us are used to. To anyone not in the know: that isn’t why you climb Everest.

The truth is, one-third of climbers never make it to the summit, and 2% never make it back alive. If the weather is unfavourable to climb the rest of the way up after 48 hours at Camp IV, climbers are forced to return, effectively giving up their bid to make it to the top.

Then came the reviews. The authors of the reviews knew that the review section was out of place, and decided to put absurd, obviously fake, reviews which may be found here, and some zingers are given below:

From David Bell: The pool was closed when I checked in and they didn’t know when it would re-open, which was very disappointing. I also found it concerning that there was no bellhop available to help with my luggage and i had to carry it all myself. As for my accommodations Camp IV was rather cold and had a horrible draft. I was also told I would be given sherbet each day, orange is my favorite, yet when I arrived I was assigned a Sherpa who wasn’t sure what I was inquiring about. Pro tip: Don’t bother bringing ice for cocktail hour, there is plenty to be had. Overall I have to rate the local 5 stars for its location and scenery alone., simply majestic views and wildlife. The Yeti were very welcoming!

From Cheyenne Nicole Philips: Broke a nail on the way up! Very long walk from the parking lot! No cell service, wore the wrong shoes. Was told I would get a king size bed. When I showed up they only had sleeping bags. Didn’t pack a colorful enough outfit. Wind messed up my hair. Starbucks was closed! Will have to try again in the summer. Hopefully pool will be open, the views were average too.

From Shawn Speller: It was, well, alright I guess. Complimentary breakfast was alright: toast, jam, various fruits. Played bingo at the pavilion in the afternoon which was fun, although I have to say the sherpa caller was a little hard to hear so it made for a couple false bingos which was a little annoying. As far as the views, I mean, you get what you get. It’s a little cloudy in the mornings by mid day it clears up a bit but all you’re seeing is a rock and yeah I guess it’s a big rock but as other reviewers said too the brochure makes it look a lot bigger (false advertising). I’m giving a 3 star review simply because cell service was not an issue, I got 3 bars at the top of the mountain and was able to chill for a bit and binge watch Game of Thrones.

From Nick Randall-Smith: This is the 21st century and there is absolutely no provision for the disabled at this camp, there was no place to charge the battery on my wheelchair. All was not lost as I persuaded a Sherpa to carry me up to the viewing point at the top of the mountain, thank goodness I remembered my American Express card because the Sherpa charged a fortune with the feeble excuse that he was risking his life to get me up to the summit, and he had a problem getting the card machine to work too. The view was pretty good but I was hoping to see the sea from the top but you can’t so that was a disappointment. When we got down I offered the Sherpa a $5 tip but he rudely told me where to shove my good American dollars, ungrateful brute.

From Justin Mehoni: Bit rocky for sunbathing. I could feel the stones below my beach towel. And when I got up some darned yeti stole all my clothes!

From Martino Keates: No proper rooms, just TENTS!!! Food very boring. Asked for an omelette and salmon, received a biscuit. Worth noting that evenings can get very cold. Bring a cardigan.

From Kelly Zitterkopf: It was pretty cool, but the mountain wasn’t as tall as the brochure made it look. The camp didn’t provide wifi and cell reception was terrible. I was able to get one bar at the top of the mountain, but I found it tedious to walk up to the summit every time I wanted to update my twitter.

A composite of some reviews: No pets allowed. The wi-fi was pretty bad. Also the local CVS said they didn’t sell cigarettes anymore. Poor sea view. You have to go through Everest to the nearest TESCO. Also – I was under the impression that there was to be a “wise man” or some such personage at the summit. There wasn’t; instead I was subjected to the inane yammering of a veterinarian from Brisbane who kept calling me a “tough little sheila” whatever the heck that’s supposed to mean.

More reviews: Too far from the nearest parking lot, and no beer store. Starbucks was open when I came, but they couldn’t fill my order for “Double Ristretto Venti Half-Soy Nonfat Decaf Organic Chocolate Brownie Iced Vanilla Double-Shot Gingerbread Frappuccino Extra Hot With Foam Whipped Cream Upside Down Double Blended, One Sweet’N Low and One Nutrasweet, and Ice”. Oh and there is no cell service or wi-fi. This is the 21st century, how can there be no wi-fi? Won’t go back any time soon.

Still more: OK, I suppose, but the views were ruined by a great big mountain in the way. Also, there is poor signage and no ski lift. When I complained, they said they expected me to walk to the top of Everest! Do you know how freakin’ high Everest is? Apart from that, the toilets smelled and there were no antibacterial wipes either. I misread the equipment manifest and as a result brought tanks of helium rather than oxygen. As a result, the sherpas never took my commands seriously due to my now high-pitched voice. I had to put up with the sherpas, since they wouldn’t let me drive my camper to the summit.

Remarks on LaTeX editors

Nearly three years ago on another blog, I wrote about a comparison of LaTeX editors. Soon after, I began to use a third editor which, if you are a latex expert, you almost certaintly would have heard about, and are probably in fact using TeXStudio, an editor that has been around for close to a decade, but never appeared to show up on Linux installation packages. The editors that showed up, at least for me, were LyX and TeXmacs.

TeXstudio, once I discovered it, I installed it everywhere I could: on my Windows 10 and 7 machines, on my Linux installations, and even on Cygwin, even though they already had a Windows installation. To this day I have not seen any difference in output or functionality. All invocations of TeXstudio require a lot of time and packages for an installation of enough features.

This is TeXstudio, with the horizontal toolbars shown, along with part of the workspace. There are two vertical toolbars there, also partially shown.

First thing’s first: the editor. In LyX and TeXmacs, I needed to bail out of the editor, and export the code to LaTeX whenever I needed to do any serious equation editing or table editing or the like. In contrast, TeXstudio leaves me with no reason to ever leave the editor. First of all, the editor allows for native latex code to be entered. If there are pieces of Latex code that you don’t know, or have a fuzzy knowledge about, there is probably an icon or menu item that covers it. For document formatting, a menu item leads to a form dialog where you can fill in the form with sensible information pertaining to your particular document, default font size, paper size, margins, and so on. The ouput of this dialog is the preamble section to the LaTeX source file. To the rest of that source file, you add your document and formatting codes.  It is a kind of “notepad” for LaTeX, with syntax highlighting and shortcut buttons, menus and dialogs. It comes close to being WYSIWYG, in that “compiling” the code and pressing  the green “play” button brings up a window with the output of the existing code you are editing. It is not a live update, but it saves you the agony of saving, going on the command line compiling the code, and viewing in seeminly endless cycles. Now you can view the formatted document at the press of the play button.

Compiling The Linux Kernel Docs

In the last article, I said that compiling and installing source versions of software was akin to “going rogue”. I must confess that I have compiled from source and installed software that wasn’t in my distribution, most recently TexStudio, as being one of the larger projects, requiring tons of other libraries and whatnot to also be installed (or quite often, compiled from source on the side), since it wasn’t a part of the linux distro I was using at the time. It also wasn’t a part of Cygwin, and I compiled for that too. It was a great way to kill an afternoon.

But there was a time that I had compiled the kernel from source. It was necessary for me, as speed was an issue and I had slow hardware at the time. What I also had was a mixture of hardware pulled from different computers at different times. I researched specs on sound cards, network cards, video cards and the motherboard chipsets, and knew what specs to tweak on the kernel compilation dialogs, so I could get the kernel to do the right thing: which is to be fast and recognize all my hardware. I was doing this before the days of modules, with the version 1.x kernel. It worked, and it was noticeably faster than the stock kernels. X-Windows on my 80486 PC ran quite well with these compiled kernels, but was sluggish to the point of un-useable with a stock kernel running. Every few versions of the kernel, I would re-compile a new kernel for my PC, and pretty soon using the tcl/tk dialogs they had made things pretty easy, and I could answer all the questions from memory.

But then that all ended with version 2. Yes, I compiled a version 2 kernel from source, and yes, it ran OK. But it also had modules. The precompiled kernels were now stripped down and lean, and the modules would only be added as needed when the kernel auto-detected the presence of the appropriate hardware. After compiling a few times, I no longer saw the point from a performance standpoint, and today we are well into kernel version 5.3, and I haven’t compiled my own kernel for a very long time.

For the heck of it, I downloaded the 5.3 kernel, which uncompressed into nearly 1 gigabyte of source code. I studied the config options and the Makefile options, and saw that I could just run “make” to create only the documentation. So that’s what I did.

It created over 8,500 pages of documentation across dozens of PDF files. And 24 of them are zero-length PDFs, which presumably didn’t compile properly, otherwise the pagecount would have easily tipped the scales at 10,000. The pages were generated quickly, the 8,500 or more pages were generated with errors in about 3 minutes. The errors seemed to be manifest in the associated PDFs not showing up under the Documentation directory. I have a fast-ish processor, an Intel 4770k (a 4th generation i7 processor), which I never overclocked, running on what is now a fast-ish gaming motherboard (an ASUS Hero Maximus VI) with 32 gigs of fast-ish RAM. The compilation, even though it was only documentation, seemed to go screamingly fast on this computer, much faster than I was accustomed to (although I guess if I am using 80486’s and early Pentiums as a comparison …). The generated output to standard error of the LaTeX compilation was a veritable blur of underfull hbox’es and page numbers.

For the record, the pagecount was generated using the following code:

#! /bin/bash
list=`ls *.pdf`
for i in $list ; do
        # if the PDF is of non-zero length then ...
        if [ -s "${i}" ] ; then 
                j=`pdfinfo ${i} | grep ^Pages`
                j=`awk '{gsub("Pages:", "");print}' <<< ${j}`
                # give a pagecount/filename/running total
                echo ${j}	    ${i}    ${tot}
                # tally up the total so far
                tot=$(($tot + $j))

echo Total page count: ${tot}

Relitivistic Pedantry

I must say first off, that I teach math and computer science, and was never qualified to teach physics. But I am interested in physics, and got drawn into in a physics discussion about how time does not stretch or compress in the visible world, and this is why in most of science, time is always the independent variable, stuck for most practical purposes on the x axis.

In the macroscopic world, time and mass are pretty reliable and so close to Einstein’s formulas (or those associated with the Special and General Theories of Relativity) at the macroscopic level that we prefer to stick to simpler formulas from classical mechanics, since they are great approximations, so long as things move well below the speed of light.

I am not sure (is anyone?) about how time is influenced by things like gravity and velocity (in particluar, the formulas stating how time is a dependent varable with respect to these things), but I remember an equation for relative mass, which doesn’t use time that would provide some insight into relativity:

    \[ \displaystyle{m(v) = lim_{v \to c^-} \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}} = \infty} \]

Here, the independent variable is velocity, and it is evident that even for bodies that appear to move fast (on the scale of 10 to 20,000 km/h), it doesn’t have much impact on this equation. Rest mass and relative mass are essentially the same, and a body would have to move at nearly the speed of light for the mass of the moving body to change significantly. Indeed, as velocity v gets closer to the speed of light c, mass shoots up to infinity. I understand that Einstein stated that nothing can move faster than light, and this is supported by the above equation, since that would make it negative under the radical.

It does not escape my notice that velocity is supposed to depend on time, making the function m(v(t)), but time warps under things like high velocity also (as well as high gravity), so that time depends on … ? This is where I tell people to “go ask your physics prof” about anything more involved.

Sattelites move within the range of 10,000 to 20,000 km/h, hundreds of kilometres above the Earth’s surface. My assertion that there is not much change here in relativity terms. But this is still is large enough to keep makers of cell phones up at night, since not considering Einstein equations in time calcluations can cause GPS systems to register errors in a person’s position on the globe on the order of several kilometres, rendering the GPS functions on cell phones essentially useless.

My companion was trying to make the latter point, where I was thinking much more generally. We stick to classical mechanics, not because the equations are necessarily the correct ones, but instead because they are simple and lend a great deal of predictive power to the macroscopic world around us.

While you are quarantining and social distancing …

Sir Isaac Newton, along with some personal notes written in Greek.

Other, greater people have done great things in quarantine way before you were born. I already knew that the late Sir Isaac Newton discovered things like optics, gravity, and the rules for Calculus, which he called the study of “fluxions”. But what I didn’t know is that in the two years he did so, he was in his early 20’s, and England suffered an epidemic of The Bubonic Plague, known as The Great Plague, in the years 1665-1666, long before infectious disease were known and understood. It is even worthy of remarking that so little was known of medicine generally that even Sir Isaac believed in alchemy until the day he died.

Prior to his quarantine he was thought of as an unremarkable undergraduate student, according to Wikipedia. But given two years cooped up where he lived and avoiding the Plague gave him time alone to come up with his brilliant theories on classical mechanics, using calculus to explain it mathematically.