Retronyms and Backronyms

gear shift for a car with an automatic transmission

A retronym is a new name created for an old thing, often made necessary by technological changes. For example, we have terms like “postal mail” or “snail mail” for what used to simply be “mail” because email has become the default. What was once called a “transmission” is now called a “manual transmission” since most cars (at least in the US) now have an automatic transmission.

A backronym is sort of a fictional etymology, such as a meaning retrofitted to an acronym. Richard Campbell explains Structured Query Language is a backronym for SQL.

IBM’s first database was not relational. Its second database, DB2, was a sequel to its first database, and so they wanted to call its query language SEQUEL but they were unable to copyright the name. So they dropped the vowels, shortened it to SQL. Later someone came up with the backronym “Structured Query Language.”

The APGAR score for newborns is a mnemonic backronym. Virginia Apgar came up with her scoring system ten years before someone came up with the backronym Appearance, Pulse, Grimace, Activity and Respiration.

Flood control parks

flooded park

The park in the photo above flooded. And that’s a good thing. It’s designed to flood so that homes don’t.

It’s not really a park that flooded. It’s a flood control project that most of the time doubles as a park. Ordinarily the park has a lake, but a few days a year the park is a lake.

Harris County, Texas has an unusually large amount of public recreational land. One reason the county can afford this is that some of the recreational land serves two purposes.

Other Houston-area posts:

Kalman filters and bottom-up learning

radio antennae










More on Kalman filters


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Spectral flatness

White noise has a flat power spectrum. So a reasonable way to measure how close a sound is to being pure noise is to measure how flat its spectrum is.

Spectral flatness is defined as the ratio of the geometric mean to the arithmetic mean of a power spectrum.

The arithmetic mean of a sequence of n items is what you usually think of as a mean or average: add up all the items and divide by n.

The geometric mean of a sequence of n items is the nth root of their product. You could calculate this by taking the arithmetic mean of the logarithms of the items, then taking the exponential of the result. What if some items are negative? Since the power spectrum is the squared absolute value of the FFT, it can’t be negative.

So why should the ratio of the geometric mean to the arithmetic mean measure flatness? And why pure tones have “unflat” power spectra?

If a power spectrum were perfectly flat, i.e. constant, then its arithmetic and geometric means would be equal, so their ratio would be 1. Could the ratio ever be more than 1? No, because the geometric mean is always less than or equal to the arithmetic mean, with equality happening only for constant sequences.

In the continuous realm, the Fourier transform of a sine wave is a pair of delta functions. In the discrete realm, the FFT will be large at two points and small everywhere else. Why should a concentrated function have a small flatness score? If one or two of the components are 1’s and the rest are zeros, the geometric mean is zero. So the ratio of geometric and arithmetic means is zero. If you replace the zero entries with some small ε and take the limit as ε goes to zero, you get 0 flatness as well.

Sometimes flatness is measured on a logarithmic scale, so instead of running from 0 to 1, it would run from -∞ to 0.

Let’s compute the flatness of some examples. We’ll take a mixture of a 440 Hz sine wave and Gaussian white noise with varying proportions, from pure sine wave to pure noise. Here’s what the flatness looks like as a function of the proportions.

spectral flatness

The curve is fairly smooth, though there’s some simulation noise at the right end. This is because we’re working with finite samples.

Here’s what a couple of these signals would sound like. First 30% noise and 70% sine wave:


And now the other way around, 70% noise and 30% sine wave:


Why does the flatness of white noise max out somewhere between 0.5 and 0.6 rather than 1? White noise only has a flat spectrum in expectation. The expected value of the power spectrum at every frequency is the same, but that won’t be true of any particular sample.

Related posts:

Linear or not, random or not, at different levels

Linear vs nonlinear

I’ve run across a lot of ambiguity lately regarding systems described as “nonlinear.” Systems typically have several layers, and are linear at one level and nonlinear at another, and authors are not always clear about which level they’re talking about.

For example, I recently ran across something called a “nonlinear trapezoid filter.” My first instinct was to parse this as

nonlinear (trapezoid filter)

though I didn’t know what that meant. On closer inspection, I think they meant

(nonlinear trapezoid) filter

which is a linear filter, formed by multiplying a spectrum by a “nonlinear trapezoid,” a function whose graph looks like a trapezoid except one of the sides is slightly curved.

One of the things that prompted this post was a discussion with a client about Kalman filters and particle filters. You can have linear methods for tracking nonlinear processes, nonlinear methods for tracking nonlinear processes, etc. You have to be careful in this context when you call something “linear” or not.

Random vs deterministic

There’s a similar ambiguity around whether a system is random or deterministic. Systems are often deterministic at one level and random at another. For example, a bandit design is a deterministic rule for conducting an experiment with random outcomes. Simulations can be even more confusing because there could be several alternating layers of randomness and determinism. People can talk past each other while thinking they’re being clear. They can say something about variance, for example, and other other person nods their head, though they’re thinking about the variance of two different things.

As simple as it sounds, you can often help a team out by asking them to be more explicit when they say something is linear or nonlinear, random or deterministic. In a sense this is nothing new: it helps to be explicit. But I’m saying a little more than that, suggesting a couple particular areas to watch out for, areas where it’s common for people to be vague when they think they’re being clear.

Related posts

Alphamagic squares in French

In earlier blog posts I give examples of alphamagic squares in English and in Spanish. This post looks at French.

French flag

The Wikipedia article on alphamagic squares, quoting The Universal Book of Mathematics, says

French allows just one 3 × 3 alphamagic square involving numbers up to 200, but a further 255 squares if the size of the entries is increased to 300.

My script did not find a French alphamagic with entries no larger than 200, but it did find 254 squares with entries no larger than 300. (For each of these squares there are 7 more variations you can form by rotation and reflection.)

The French alphamagic square with the smallest maximum entry that I found is the following.

[[3, 204, 102], [202, 103, 4], [104, 2, 203]]

When spelled out in French we get

[[trois, deux cent quatre, cent deux], [deux cent deux, cent trois, quatre], [cent quatre, deux, deux cent trois]]

And when we replace each cell with its number of letters we get the following magic square:

[[ 5, 14, 8], [12, 9, 6], [10, , 13]]

A list of all the French magic squares with maximum element 300 that I found is available here.

Acoustic roughness



16 Hz:

30 Hz:


100 Hz:


300 Hz:


293 Hz:




from scipy.io.wavfile import write
from numpy import arange, pi, sin, int16, iinfo

N = 48000 # sampling rate per second

def beats(t, f1, f2):

def to_integer(signal):
    m = iinfo(int16).max
    M = max(abs(signal))
    return int16(signal*m/M)

def write_beat_file(center_freq, delta):
    f1 = center_freq - 0.5*delta
    f2 = center_freq + 0.5*delta    

write_beat_file(440, 4)
write_beat_file(440, 16)
write_beat_file(440, 30)
write_beat_file(440, 100)
write_beat_file(440, 293)


Related: Psychoacoustics consulting

Paying for doughnuts with a phone

At a doughnut shop today, I noticed the people at the head of each line were using their phones, either to pay for an order or to use a coupon. I thought how ridiculous it would sound if I were to go back twenty or thirty years and tell my mother about this.

Me: Some day people are going to pay for doughnuts with a phone.

Mom: You mean like calling up a doughnut shop to place an order? We already do that.

Me: No, they’re going to take their phone into the doughnut shop and pay with it.

Mom: Good grief. Why not just use cash?

Me: Well, they could. But it’ll be easy to use their phones since most people will carry them around all the time anyway.

Mom: People will carry around phones?!

Me: Sorta. More like computers, that can also make phone calls.

Mom: People will carry around computers?!!

old PC

Me: Not really. I was just making that up. But they will drive flying cars.

Mom: OK, I could see that. That’ll be nice.

Coffee after Obama

This morning I had coffee and a generous slice of squash bread at Top Pot Doughnuts in Seattle. When I went to pick up my coffee I saw a large photo of President Obama ordering coffee at the same place.

This is the second time I’ve been at a shop that proudly remembered our president stopping by. The first was a diner in San Juan that I cannot remember the name of. They put a plaque on the table President Obama sat at. If Top Pot did too, I missed it.

I enjoyed a few minutes of quiet this morning, something President Obama certainly did not have a chance to do here. One wall of the shop is lined with old books, so naturally that’s where I sat. I pulled down a small book that bound the December 1942 issues of My Garden magazine.

I find the ads in old magazines interesting for what they say between the lines. The ads are more interesting than the articles, the opposite of contemporary magazines, though that depends on the magazine.

One thing that struck me was the small ratio of advertisement to content. I suppose the original subscribers didn’t notice this, or maybe thought the magazine was putting in too many ads. I imagine they would be shocked by magazines that squeeze articles in between the ads.

Another thing that struck me was the somber but hopeful tone of the ads. Ford had a series of ads entitled “Until then …”. The ads seemed to say “We know nobody is going to be buying a car any time soon. But some day this war will be over, and when it is, we hope you’ll remember us.” Other companies tried to make the best of rationing. For example, one ad for shaving cream said that it was a good thing that their product worked so well since there are limits on how much shaving cream you can buy.

It was a pleasant way to start the day, without Secret Service agents buzzing around and without rationing limits on things like coffee and squash bread.

Visualizing search keyword overlap

The other day someone asked me to look at the search data for Debug Pest Control, a pest management company based in Rhode Island. One of the things I wanted to visualize was how the search terms overlapped with each other.

To do this, I created a graph where the nodes are the keywords and edges join nodes that share a word. (A “keyword” is actually a set of words, whatever someone types into a search.) The result was a solid gray blob be cause the the nodes are so densely connected.

I thinned the graph by first only looking at keywords that have occurred at least twice. Then I made my connection criteria a little stronger. I take the union of the individual words in two keywords and create a connection if at least 1/3 of these words appear in both keywords.


The area of each red dot is proportional to the number of times someone has come to the site using that keyword. You can see that there’s long-tail behavior: while some dots are much larger than others, there are a lot of little dots.

In case you’re curious, these are the top keywords:

  1. pest control
  2. ri
  3. pest control ri
  4. pest control rhode island,
  5. plants that keep bees away
  6. poisonous snakes in ri
  7. plants that keep bees and wasps away
  8. plants to keep bees away
  9. plants that keep wasps away
  10. pest control companies


The keywords were filtered a little before making the graph. Some of the top keywords contained “debug.” These may have been people using the term to refer to eliminating pests from their property, but more likely they were people who knew the company name. By removing “debug” from each of the keywords, the results focus on people searching for the company’s services rather than the company itself.

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