A literal quantum leap is a discrete change, typically extremely small [1]. A metaphorical quantum leap is a sudden, large change. I can’t think of a good metaphor for a small but discrete change. I was reaching for such a metaphor recently and my first thought was “quantum leap,” though that would imply something much […]

# Author: John

## Professional, amateur, and something else

I opened a blog posts a while back by saying One of the differences between amateur and professional software development is whether you’re writing software for yourself or for someone else. It’s like the difference between keeping a journal and being a journalist. This morning I saw where someone pulled that quote and I thought […]

## Easter and exponential sums

For the last couple years, the exponential sum of the day for Easter Sunday has been a cross. This was not planned, since the image each day is determined by the numbers that make up the date, as explained here. This was the exponential sum for last Easter last year, April 1, 2018: and this […]

## Groups in categories

The first time I saw a reference to a “group in a category” I misread it as something in the category of groups. But that’s not what it means. Due to an unfortunately choice of terminology, “in” is more subtle than just membership in a class. This is related to another potentially misleading term, algebraic […]

## What is an isogeny?

The previous post said that isogenies between elliptic curves are the basis for a quantum-resistant encryption method, but we didn’t say what an isogeny is. It’s difficult to look up what an isogeny is. You’ll find several definitions, and they seem incomplete or incompatible. If you go to Wikipedia, you’ll read “an isogeny is a […]

## Isogeny-based encryption

If and when large quantum computers become practical, all currently widely deployed method for public key cryptography will break. Even the most optimistic proponents of quantum computing believe such computers are years away, maybe decades. But it also takes years, maybe decades, to develop, test, and deploy new encryption methods, and so researchers are working […]

## Calling Python from Mathematica

The Mathematica function ExternalEvalute lets you call Python from Mathematica. However, there are a few wrinkles. I first pasted in an example from the Mathematica documentation and it failed. ExternalEvaluate[ “Python”, {“def f(x): return x**2”, “f(3)”} ] It turns out you (may) have to tell Mathematica where to find Python. I ran the following, tried […]

## Random projection

Last night after dinner, the conversation turned to high-dimensional geometry. (I realize how odd that sentence sounds; I was with some unusual company.) Someone brought up the fact that two randomly chosen vectors in a high-dimensional space are very likely to be nearly orthogonal. This is a surprising but well known fact. Next the conversation […]

## A truly horrible random number generator

I needed a bad random number generator for an illustration, and chose RANDU, possibly the worst random number generator that was ever widely deployed. Donald Knuth comments on RANDU in the second volume of his magnum opus. When this chapter was first written in the late 1960’s, a truly horrible random number generator called RANDU […]

## Maybe you should’t script it after all

Programmers have an easier time scaling up than scaling down. You could call this foresight or over-engineering, depending on how things work out. Scaling is a matter of placing bets. Experienced programmers are rightfully suspicious of claims that something only needs to be done once, or that quick-and-dirty will be OK [*]. They’ve been burned […]

## Squircle perimeter and the isoparametric problem

If you have a fixed length of rope and you want to enclose the most area inside the rope, make it into a circle. This is the solution to the so-called isoparametric problem. Dido’s problem is similar. If one side of your bounded area is given by a straight line, make your rope into a […]

## Taking the derivative of a muscle car

I’ve been getting a lot of spam lately saying my web site does not rank well on “certain keywords.” This is of course true: no web site ranks well for every keyword. I was joking about this on Twitter, saying that my site does not rank well for women’s shoes, muscle cars, or snails because […]

## Safe Harbor and the calendar rollover problem

Data privacy is subtle and difficult to regulate. The lawmakers who wrote the HIPAA privacy regulations took a stab at what would protect privacy when they crafted the “Safe Harbor” list. The list is neither necessary or sufficient, depending on context, but it’s a start. Extreme values of any measurement are more likely to lead […]

## Data privacy Twitter account

My newest Twitter account is Data Privacy (@data_tip). There I post tweets about ways to protect your privacy, statistical disclosure limitation, etc. I had a clever idea for the icon, or so I thought. I started with the default Twitter icon, a sort of stylized anonymous person, and colored it with the same blue and […]

## Ratio of Lebesgue norm ball volumes

As dimension increases, the ratio of volume between a unit ball and a unit cube goes to zero. Said another way, if you have a high-dimensional ball inside a high-dimensional box, nearly all the volume is in the corners. This is a surprising result when you first see it, but it’s well known among people […]

## Higher dimensional squircles

The previous post looked at what exponent makes the area of a squircle midway between the area of a square and circle of the same radius. We could ask the analogous question in three dimensions, or in any dimension. (Is a shape between a cube and a sphere a cuere?) In more conventional mathematical terminology, […]

## History of the term “Squircle”

Architect Peter Panholzer coined the term “squircle” in the summer of 1966 while working for Gerald Robinson. Robinson had seen a Scientific American article on the superellipse shape popularized by Piet Hein and suggested Panholzer use the shape in a project. Piet Hein used the term superellipse for a compromise between an ellipse and a […]

## Covered entities: TMPRA extends HIPAA

The US HIPAA law only protects the privacy of health data held by “covered entities,” which essentially means health care providers and insurance companies. If you give your heart monitoring data or DNA to your doctor, it comes under HIPAA. If you give it to Fitbit or 23andMe, it does not. Government entities are not […]

## Inferring religion from fitness data

Fitness monitors reveal more information than most people realize. For example, it may be possible to infer someone’s religious beliefs from their heart rate data. If you have location data, it’s trivial to tell whether someone is attending religious services. But you could make a reasonable guess from respiration data alone. Muslim prayers occur at […]

## Putting topological data analysis in context

I got a review copy of The Mathematics of Data recently. Five of the six chapters are relatively conventional, a mixture of topics in numerical linear algebra, optimization, and probability. The final chapter, written by Robert Ghrist, is entitled Homological Algebra and Data. Those who grew up with Sesame Street may recall the song “Which […]