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Thank you for subscribing to my monthly newsletter. Each month I highlight the posts that have been most popular on my blog, and sometimes I say a little about what I've been up to.

Encryption

Two of the most popular posts this month have been related to encryption. One was encryption that is provably as hard to break as large the products of large primes are to factor. RSA encryption depends on factoring being difficult, but it's possible that breaking RSA is strictly easier than factoring. But being able to break Rabin's variation on RSA would provide an efficient factoring algorithm for factoring. However, it is not used in practice.

The other encryption-related post that has gotten traffic this month is Proving that a choice was made in good faith. It's hard if not logically impossible to prove that a decision was not deliberate. But you can prove that a choice was deliberate by a different criterion.

Technology

We often compare expressiveness and ease of learning. But this post argues we should also consider ease of realearning. Not only do you have to learn a technology before you can use it, you might have to learn it several times, depending on how well it sticks in your head.

Math and statistics

This post makes the simple observation that if two lines are nearly parallel to a third line, they're nearly parallel to each other. That statement is made more precise and applied to statistics. Correlation is not transitive, but high correlation is.

I enjoyed writing this post resolving an apparent contradiction uniform approximation. It wasn't especially popular, probably because it requires more math background to understand than most posts, but it's a post I wish I had read in college.

Sculpting a business

Progress in business is usually described with additive metaphors like expanding and growing, but I've been thinking about subtractive metaphors like sculpting and pruning. I've been looking for ways to make room for growth by cutting things out, such as being more selective in the projects I agree to take on.

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The 3n+1 problem

This month I wrote two posts on the Collatz conjecture, also known as the 3n+1 problem. The post commenting on Tao's new results was popular, but the post pointing out reasons why the conjecture may not be true was not.

Unicode everywhere

This month I also wrote several posts related to Unicode, the most popular being one explaining the number of possible characters. I also wrote about how UTF-8 encoding works and why Unicode faces an impossible task.

Power laws and projects

Though not written this month, a post on power laws and projects was the most popular post this month because it got picked up on Hacker News. The post demonstrates that if project times follow a power law distribution, then the longer a project has taken so far, the longer you can expect for it to drag on into the future. This was just sort of a back-of-the-envelope calculation, but it seems to describe real projects.

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The most popular post this month has been Computational survivalists. There are two strains of computational survivalist. The more extreme form only uses the most widely deployed tools in order to maximally prepared for working in a minimal environment. The more moderate form plans ahead for possibly having to work in a minimal environment, but doesn't live there all the time.

Another post that was popular this month was on hacking passwords using De Bruijn sequences. I'm writing this newsletter just after writing a couple more posts on De Bruijn sequences, one on an algorithm for generating such sequences and another on linear feedback shift registers, a generalization of binary De Bruijn sequences.

I wrote a couple posts this month on curvature, first on the total curvature of a knot and then on a function such that the curvature of its graph is proportional to its values.

My favorite post this month was Binary Surprise, discussing my surprise when a post about exact values of sine led to seeing a fractal pattern in related binary numbers.

I did an interview a few days ago with someone who wanted me to talk about queuing theory. (I'll probably say something here or on my blog when the project containing the interview is released.) That got me to wondering how many other words like "queueing" have four or five consecutive vowels. Results here.

On a personal note, I'm in that narrow zone between being bored and being overwhelmed. It's a great place to be.

Thanks for reading.

-- John

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Here are three quick takes on three short blog posts that were popular this month.

Floating point oddity

The most popular post this month was about an example crafted to show the limitations of floating point arithmetic, even in quadratic precision. The example is admittedly artificial, but instructive. The follow-up post gives another example, also somewhat artificial, but representative of problems that pop up naturally.

Any number can start a factorial

A lot of people like a post looks at the surprising fact that any number can start a factorial. That is, you can take any positive integer you like, say 1492, and tack on more digits so that the result is the factorial of some number. This is related to Benford's law.

Serpentine walls

Undulating walls are not just decorative; they save bricks. They obviously use more bricks than a straight wall of the same thickness, but they don't have to be as thick to be sturdy. A simple integral shows how much the walls save on materials, but the integral cannot be computed in closed form.

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End of year roll

I didn't write a newsletter last month because of the holidays, so this month I look back on the most popular posts of the last two months. Turns out the most popular posts were all ones I wrote just before the end of year, December 28, 30, and 31.

The first of these three posts was a brief blurb pointing out a paper giving a new look at the famous birthday problem. The post explains briefly why the birthday problem is not just a party trick but a matter of practical importance in applications of hash functions.

The next post gives some simple tips on how to minimize context switching costs when calling Python from a shell or calling a shell from Python.

The most popular of the posts, written on New Year's Eve, was a little tutorial on how to do a database-like join on CSV files. I suppose a lot of people need to join CSV files occasionally and don't know about the xsv utility.

Maybe these posts were popular because they were written over the holidays. Not as many people were writing blog posts, and so there was less competition for reader attention.

Data privacy

I expect two things will be big on the data privacy front this year: CCPA and differential privacy.

California's new CCPA privacy law went into effect at the beginning of the year. It's not clear yet what the law will mean in practice, and amendments are still being proposed. One amendment I'm particularly interested in is one which would create an expert determination provision similar to the analogous provision under HIPAA.

The US Census Bureau has committed to using differential privacy to release the results of the 2020 census. I expect this will lead to greater adoption of differential privacy. When I've mentioned the Census Bureau's plans to potential consulting clients, the reaction is often something to the effect of "Wow, this must be ready for prime time."

I expect the Census Bureau will run into major difficulties, but this will not diminish interest in differential privacy. The fact that a project so large and complex is even attempting to use differential privacy suggests that the technology is mature enough for the majority projects that are far smaller and simpler.

Contact info

If you'd like to discuss differential privacy or anything else, you can find all my contact information here.

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Attn: John Cook

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Computational survivalist

Sometimes you only have access to a limited number of software tools and you''re unable to install anything. Maybe you''re used to a graphical interface and you can only access a server through the command line. Or maybe you''re in the opposite situation: you only have access to a graphical interface and cannot use the command line.

I had written about this before, but I revisited the topic after getting a locked-down laptop from an extremely security-conscious client. It''s a Windows machine with lots of consumer conveniences and presumably not many scientific programming tools. I don''t know for sure because I still haven''t gotten everything I need to log in.

A little Hebrew

I have started doing some work for a client in Israel, and that stirred my interest in learning a little Hebrew. I wrote a blog post on how to include Hebrew text inside a LaTeX document for my own future reference.

Whenever I write about how to include non-ASCII characters in LaTeX someone asks why I don''t just use Unicode. The problem is you can''t "just" use Unicode. You have to input the Unicode characters somehow, and LaTeX provides convenient ways to do this using only ASCII characters.

Mathematical posts

One of the more popular mathematical posts this month has been one on permutable polynomials. When can you have a family of polynomials such that for any members p and q, p(q(x)) = q(p(x))? Essentially the only non-trivial family is the Chebyshev polynomials.This is another example of how these polynomials are in some sense natural and inevitable. Many road lead to Chebyshev.

I''ll finish by including links to a couple posts that lead to some interesting images. This post implemented an example I found in HAKMEM, a collection of interesting hacks and tidbits circulating around MIT five decades ago.

That lead to another post plotting contours of a similar function, something I thought looked kinda like a cross section of a tree with ingrown bark.

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Best of the month

Thanks for subscribing to my newsletter where I highlight some of the best posts from my blog.

The best posts this month fall into four different categories: history, math, programming, and productivity.

History

The most popular post this month has been a bit of history, the story behind how a venerable classic in applied math was once a banned book.

Math

On the math front, a lot of people seemed to like the post about how you can create any continuous function out of sums and compositions of continuous functions of one variable. See the post for details.

Programming

The comments to this post are more interesting than the post itself. I posed a little challenge based on numbers in Morse code and got a lot of creative examples of code golf.

Productivity

At one point I believed in the best-tool-for-the-job philosophy. And indeed there are contexts in which you do want to choose the best tool for the job. But there are other factors to consider, such as the cost of changing tools. A few days ago I wrote about why you might want to choose the worst tool for the job.

How can we help you?

If there''s anything my team or I can help you with, let''s talk.

Copyright ? 2020 Singular Value Consulting, LLC, All rights reserved.
You are receiving this email because you opted in at my web site, johndcook.com.

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Singular Value Consulting, LLC

21175 Tomball Parkway #707

Attn: John Cook

Houston, TX 77070

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Best posts of the month

Every month this newsletter highlights some of the most popular posts from my blog. I plan to change my approach slightly, recapping the best posts each month rather than simply the most popular posts.

Best and most popular usually overlap, but page views are heavily skewed by what happens to get picked up on social media. Part of the purpose of this newsletter is to point out posts that you may have missed, and by including the posts picked up on social media, I do the opposite, pointing out the post you''ve most likely seen.

The most popular post this month was a commentary on object oriented programming, and more generally about learning from the past rather than ignoring it. I believe this post is a good example of something that got a lot of page views due to social media but that isn''t necessarily what subscribers to this newsletter most want to read.

Advanced perspective on basics

A few other posts have been popular both in terms of page views and in terms of feedback. The first of these was entitled To integrate the impossible integral. It starts with a homework problem my daughter asked me about and then moves out to a more advanced perspective on the problem, discussing several ways in which an integral may be "possible" or "impossible."

Similar in spirit is my post on the fundamental theorem of algebra. I start with a theorem that most people would have seen in high school and move out to related theorems that most people would not have seen in college. This post is part of a short series of posts on fundamental theorems.

The first fundamental theorem in the series is the fundamental theorem of calculus.It looks at the two fundamental theorems of calculus and how they generalize to measurable functions. The third in the series was on the fundamental theorem of arithmetic. I may do one more fundamental theorem post before moving on to something else.

Work in time of plague

Several people have asked how the ongoing pandemic has effected my business. They said they could imagine work slowing down, as it has for so many, or picking up, due to corona-related projects. Neither has been the case, except for a couple corona-related projects. Business keeps growing, in spite of corona rather than because of it.

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Holiday edition

Tomorrow is Thanksgiving in the US. I would like the US to adopt the Canadian date for Thanksgiving, the second Monday in October, because it more evenly divides the fall. As it is, Thanksgiving here sorta blurs into Christmas with an awkward time in between where people are still showing up to work but it''s hard to get anything done.

Here are a few links you might want to look at if you''re looking for something to read over Thanksgiving.

Divisibility by 7, 11, and 13

The most popular post this month has been one on testing divisibility by 7, 11, and 13 at the same time. The math is pretty basic, but the result is something I imagine many people haven''t seen before. I hadn''t seen in until recently.

Category theory made a little easier

This post argues that it might be better to present category theory the way we teach other areas of math, sweeping some subtle parts under the rug to deal with later.

Circular coordinates

Circular coordinates sound like polar coordinates, but they''re not. They are a strange kind of coordinate system in which ordinary functions lead to interesting graphs. This post gives some examples and includes enough information for you to try your hand at making your own examples if you''re so inclined. If you come up with anything you''d like to share, let me know.

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Reversible computing

I''ve been thinking about reversible computing lately, and that led me to write the most popular post this month: Making a reversible function out of non-reversible parts.Specifically, the post looks at Feistel networks, a framework for designing block ciphers such as DES.

The primary interest in reversible computing is not that it''s reversible but that it requires less energy. Introductions to reversible computing often being with a discussion of the Landauer limit, which I believe is unfortunate. It''s a theoretical limit on energy consumption that inspired an interest in reversible computing, but beginning there implies that reversible computing is purely a theoretical possibility. There are hardware prototypes that show you can lower energy consumption by limiting your hardware to supporting reversible operations.

Regression

Another post that has been popular this month is my remarks on exponential growth vs logistic growth. It is related to pandemic modeling, but only at an abstract level. I have not tried to create my own pandemic model. I''ll leave that up to experts. The experts have done a poor job of predicting what will happen, but I imagine the amateurs have done worse.

Retro computing

I just wrote a post this morning that may end up being one of the more popular posts of the month. It''s a short post (56 words) on the advantages to using software that''s installed locally on your computer and doesn''t require network access.

Rubber bands

One last thing to throw in. A rubber band acts like a spring when you stretch it, but not when you compress it. This asymmetry means that when you combine a spring and a rubber band, you can get complicated results, as explained in this post.

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Thank you

Thank you for subscribing to my monthly newsletter. If you''ve subscribed for a while, you know that I keep these newsletters short and sweet. This month''s newsletter will be even shorter than usual; hopefully you''ll also find it sweeter than usual.

A little knowledge is a dangerous thing

Alexander Pope said a little knowledge is a dangerous thing. (My eighth grade English teacher said that if you don''t know who said something, Alexander Pope is a good guess.) My most popular post this month has a few ideas about why a little knowledge is often a dangerous thing.

A couple inequalities

Two posts this month have been about inequalities. One is the mediant inequlaity. I''d forgotten that it is called that, so I called it the baseball inequality because of seeing it applied to batting averages.

The other inequality post looks at Kantorovich''s inequality relating a random variable and its reciprocal.

The word problem

What mathematicians call "the" word problem is not a word problem in the sense of a real-world application described verbally. Instead, it''s about manipulating "words" in the sense of strings of symbols, subject to algebraic rules. You can think of it and its variations as studying what can and cannot be computed by algorithms.

In this post I describe the word problem and give a few comments regarding my encounters with the problem.

That''s it

As promised, this was short and sweet. Sometimes I conclude this newsletter with a few brief comments about what I''ve been up to. If you''d like to read more along those lines, see my post Doing well.

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The elephant in the room

I had debated whether to say anything about the ongoing pandemic in this month''s newsletter. I thought you might appreciate the normalcy of reading something that makes no mention of the virus. On the other hand, this newsletter presents the most popular posts from the blog each month, and the most popular post this post been the one time I wrote about something related to the pandemic.

I''ve had little to say about the pandemic because I''m not an expert in such things. But I do know something about clinical trials, and I wrote a few comments on a clinical trial of COVID-19 treatments.

We''re all fine and I wish you the same.

Approximation theory

So how do you find the best polynomial approximation to a function over an interval, best in the sense of minimizing the maximum error? You''d use the Remez algorithm. Or if you''re content with having nearly the best polynomial approximation, you can more easily use Chebyshev approximation.

Several articles were spin offs of the Remez post: the Chebyshev approximation post mentioned above, a post on the product of Chebyshev polynomials, and a few words about The Brothers Markov.

Copulas

I wrote a couple of posts about copulas. These are a technical device for modeling the dependence between random variables. I barely mention applications to modeling but instead comment on a couple ways copulas show surprising algebraic structure.

Finding coffee in pi

For Pi Day this year I wrote a post about finding c0ffee in the hexadecimal representation of pi. The normal number theorem implies that you can find anything you''re looking for in the digits of almost every irrational number, so finding a particular sequence in pi is not a surprise. (It has not been proven than pi is a "normal number" but it would be astonishing if it were not.)

You may find the background of the post more interesting than the foreground. While the foreground is about searching for a particular string of digits, the background concerns the LibBF arbitrary precision library, the Chudnovsky algorithm for computing pi, and how to use a couple of the less common options of grep.

Coda

Stay well, everyone. Best wishes to you and yours.

Singular Value Consulting, LLC

21175 Tomball Parkway #707

Attn: John Cook

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Most popular posts

I''ve written a lot about differential equations lately. I started out my career working in differential equations and have been visiting the old neighborhood lately.

The most popular post has been an introduction to stiff equations, followed closely by a post about a periodic orbit for a ship orbiting Earth and the Moon.

This orbit was discovered by Richard Arenstorf and was used as the basis for the path Apollo astronauts took to the moon. In the post I say a few words about my experience sitting in a class by Arenstorf.

Another post that was popular this month was a post on how to efficiently count the number of 1s in a binary number. The function to compute this is traditionally called "popcount" for population count. It seems like a very simple thing, and in a sense it is, but as Feyman said, nearly everything is interesting if you look into it deeply enough.

Idea threads

A few days ago I wrote about the German ADFGVX cipher used in World War I. The name comes from six letters chosen for transmitting messages because they were distinct in Morse code. The post looks at whether better letters could have been chosen. Picking optimal letters in Morse code segued into picking optimal binary code words. This lead to how you could efficiently compute the parity bits needed for these codes, which ties back to popcount mentioned above. The problem of optimizing Morse code representatives lead to this Twitter thread on optimization.

The posts on my blog are often related to my client work, though sometimes indirectly. For example, problems with stability for statistical methods got me to thinking about problems with stability in differential equations, which led to write about Arenstorf''s orbit.

Most popular posts for next month

Of course there''s no way to know yet what will be popular next month, but I can speculate. Probably something moderately technical. I like it, and apparently readers like it, when I find something to write about that''s not too familiar but can be explained quickly. Like popcount. Even better if it leads to an interesting image, like Arenstorf''s orbit.

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Attn: John Cook

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Best blog posts

The blog posts most popular with the world at large might not be your favorite blog posts. As I mentioned last month, I''m starting to select blog posts for this newsletter based on more than just page views. I''m also selecting posts based on interaction and variety.

The post Bit flipping to primes has been fairly popular in terms of page views, and more so in terms of comments and interaction on Twitter. It''s also a very accessible post: if you know what a prime number is and you know what binary notation is, you''ve got the background to read the post. Another accessible blog post describes how to compute the square root of a complex number.

If you''d like to read a post with more mathematical depth, check out Convex functions of diagonals and eigenvalues.

Two posts this month are related to calculating orbits. The first describes the Hohmann transfer orbit, the most efficient way to move between two circular orbits in the same plane. The second describes the numerical method NASA used, and still uses as far as I know, to solve the differential equations related to orbital calculations.

Graphics

I''ve had some fun playing around with graphics lately. A couple days I ago I wrote up one experiment that plots the set of lines orthogonal to an ellipse and to an egg shape. These lines are tangent to a curve called the evolute of the original curve.

If you''d like to see more math-related graphics, you might like to scroll through @AnalysisFact or the Exponential sum of the day.

See you next month.

Singular Value Consulting, LLC

21175 Tomball Parkway #707

Attn: John Cook

Houston, TX 77070

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Validation

Membership Emails

Encryption

Technology

Math and statistics

Sculpting a business

The 3n+1 problem

Unicode everywhere

Power laws and projects

Floating point oddity

Any number can start a factorial

Serpentine walls

End of year roll

Data privacy

Contact info

Computational survivalist

A little Hebrew

Mathematical posts

Best of the month

History

Math

Programming

Productivity

How can we help you?

Best posts of the month

Advanced perspective on basics

Work in time of plague

Holiday edition

Divisibility by 7, 11, and 13

Category theory made a little easier

Circular coordinates

Reversible computing

Regression

Retro computing

Rubber bands

Thank you

A little knowledge is a dangerous thing

A couple inequalities

The word problem

That''s it

The elephant in the room

Approximation theory

Copulas

Finding coffee in pi

Coda

Most popular posts

Idea threads

Most popular posts for next month

Best blog posts

Graphics

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