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EMBO Practical Course: Bioinformatics and Genome Analysis, 5–17 June 2017.

fun + amusement

The Ptolemaic Clock — A Proposal

the standard clock

Consider the lowly wall clock. It's practical and generally tells the correct time. It's the same clock everywhere and after a while it gets boring pretty quickly—maybe now?

Non-standard clock with rotating bezel. / Martin Krzywinski @MKrzywinski
In a standard clock, the bezel is fixed and the hands rotate.

In the regular clock the face bezels stay in place and the hands move. Why am I telling you this? Well, maybe you see where I'm going.

the Ptolemaic Clock

Who says it's the hands that have to rotate? Instead of rotating hands and a stationary bezel, consider the clock with stationary hands rotating bezels.

Non-standard clock with rotating bezel. / Martin Krzywinski @MKrzywinski
In the Ptolemaic clock, the hands stay in place while independent minute and hour hand bezels rotate to simulate the movement of the hands.

In the Ptolemaic clock there are two independent bezels and two independent hands. The bezels rotate counterclockwise to simulate the standard clockwise motion of the hands. The hands are not moving but in the frame of reference of the bezels, it's the hands that are rotating. The position of the bezel is always related to the current time and the position of its corresponding hand.

The bezel can move clockwise.

Thanks to Rodrigo Goya for suggesting the name for this kind of clock—Ptolemaic Clock, named so after the geocentric Ptolemaic model of the solar system.

telling time on the Ptolemaic clock

To tell the time on the Ptolemaic clock is a process identical to using the standard clock. You look at the bezel numbers at the ends of the hour and minute hands.

On the fixed bezel layout, most people will take a short cut and tell the time by the position of the hands. This works as long as you have a standard clock. On a Ptolemaic clock the position of the hands tells you nothing.

Here is a Ptolemaic clock telling us it is 6:30. It uses the same position of hands as in the figures above.

You know this because the blue hour hand points to midway between 6 and 7 on the inner hour bezel and the grey minute hand points to 30 on the outer minute bezel.

Non-standard clock with rotating bezel. / Martin Krzywinski @MKrzywinski
It is 6:30 on this Ptolemaic clock.

After 15 minutes, it's 6:45 and our Ptolemaic clock bezels have moved a little bit.

Non-standard clock with rotating bezel. / Martin Krzywinski @MKrzywinski
It is 6:45 on this Ptolemaic clock.

Can you tell what time it is on the Ptolemaic clock below?

Non-standard clock with rotating bezel. / Martin Krzywinski @MKrzywinski
If you answered 8:50, you are correct. It is 8:50.

customizing the Ptolemaic clock

Customizing your Ptolemaic clock is easy. Simply adjust the hands to desired positions and set the time by moving the bezels. The clock below shows the same time as the clock in the above figure — both show 8:50.

Non-standard clock with rotating bezel. / Martin Krzywinski @MKrzywinski
This clock tells us it's 8:50. Compare this to the clock in the figure above, which also tells the same time.

ptolemaic clock — hard layout

In the clock design shown here, the hands are the same size and only differ by color. To make things less confusing, emphasize the hour hand.

To make things more confusing, remove all color and number cues, keeping only a single symbol on each of the bezels to indicate 12 o'clock and 0 minutes. This is shown in the clock below.

Non-standard clock with rotating bezel. / Martin Krzywinski @MKrzywinski
In the hard layout of a Ptolemaic clock, there are fewer cues. I think it's 8:50.

news room parodies

Spice it up with multiple Ptolemaic clocks side-by-side telling the same time with different hand positions.

Suppose it is 2:30 in Vancouver—this is my location. The clocks below all show 2:30, but with hands set to 5:30, 11:30 and 7:30.

Non-standard clock with rotating bezel. / Martin Krzywinski @MKrzywinski
Looks like a wall of clocks in a newsroom. Except these Ptolemaic clocks tell us that it's 2:30, three times over in Vancouver.

These hand positions are those that would appear on a standard clock showing the times in New York (5:30), Paris (11:30) and Tokyo (7:30).

Let's now use the Ptolemaic clock to show times at these three locations but with the hand set to the curiously satisfying layout of 10ish minutes to 2.

Non-standard clock with rotating bezel. / Martin Krzywinski @MKrzywinski
A challenging panel of Ptolemaic clocks.


Set both hand positions to 12 o'clock and then remove the hands; to tell time, read the numbers on the hour and minute bezels at the apex of the clock.


Sophisticated implementations of the Ptolemaic clock could periodically randomize hand positions to keep things interesting; by the time you've figured out the time in the morning, you're wide awake.

Every minute the clock randomly resets its hand positions. The movement is smooth and the bezels follow.

hardware implementation

If you would like to implement the Ptolemaic clock, I would be happy to hear from you. One should be able to take a regular wall clock, reverse the direction of the hand mechanism and rig a freely moving bezel to each of the minute and hour mechanism. The hands should not move and can be fixed to the front glass plate, for example.


It should now be clear that the Ptolemaic clock is superior to the standard clock. The reasons are

  • it's much harder to tell time on the Ptolemaic clock, which makes your brain do more work
  • it tips its hat off to a simpler time when we didn't know anything and hints at the possibility of regression anytime
    • it will confuse everyone
    • you have a great excuse for being late
    • return to geocentric values!
  • you can customize your own Ptolemaic clock by moving the hands to arbitrary locations
    • two Ptolemaic clocks can have their hands and bezels at different positions but still be telling the same time
    • two Ptolemaic clocks can have their hands at the same position but be telling different times

news + thoughts

`k` index: a weightlighting and Crossfit performance measure

Wed 07-06-2017

Similar to the `h` index in publishing, the `k` index is a measure of fitness performance.

To achieve a `k` index for a movement you must perform `k` unbroken reps at `k`% 1RM.

The expected value for the `k` index is probably somewhere in the range of `k = 26` to `k=35`, with higher values progressively more difficult to achieve.

In my `k` index introduction article I provide detailed explanation, rep scheme table and WOD example.

Dark Matter of the English Language—the unwords

Wed 07-06-2017

I've applied the char-rnn recurrent neural network to generate new words, names of drugs and countries.

The effect is intriguing and facetious—yes, those are real words.

But these are not: necronology, abobionalism, gabdologist, and nonerify.

These places only exist in the mind: Conchar and Pobacia, Hzuuland, New Kain, Rabibus and Megee Islands, Sentip and Sitina, Sinistan and Urzenia.

And these are the imaginary afflictions of the imagination: ictophobia, myconomascophobia, and talmatomania.

And these, of the body: ophalosis, icabulosis, mediatopathy and bellotalgia.

Want to name your baby? Or someone else's baby? Try Ginavietta Xilly Anganelel or Ferandulde Hommanloco Kictortick.

When taking new therapeutics, never mix salivac and labromine. And don't forget that abadarone is best taken on an empty stomach.

And nothing increases the chance of getting that grant funded than proposing the study of a new –ome! We really need someone to looking into the femome and manome.

Dark Matter of the Genome—the nullomers

Wed 31-05-2017

An exploration of things that are missing in the human genome. The nullomers.

Julia Herold, Stefan Kurtz and Robert Giegerich. Efficient computation of absent words in genomic sequences. BMC Bioinformatics (2008) 9:167


Wed 31-05-2017
Clustering finds patterns in data—whether they are there or not.

We've already seen how data can be grouped into classes in our series on classifiers. In this column, we look at how data can be grouped by similarity in an unsupervised way.

Martin Krzywinski @MKrzywinski
Nature Methods Points of Significance column: Clustering. (read)

We look at two common clustering approaches: `k`-means and hierarchical clustering. All clustering methods share the same approach: they first calculate similarity and then use it to group objects into clusters. The details of the methods, and outputs, vary widely.

Altman, N. & Krzywinski, M. (2017) Points of Significance: Clustering. Nature Methods 14:545–546.

Background reading

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. Nature Methods 13:603-604.

...more about the Points of Significance column

What's wrong with pie charts?

Thu 25-05-2017

In this redesign of a pie chart figure from a Nature Medicine article [1], I look at how to organize and present a large number of categories.

I first discuss some of the benefits of a pie chart—there are few and specific—and its shortcomings—there are few but fundamental.

I then walk through the redesign process by showing how the tumor categories can be shown more clearly if they are first aggregated into a small number groups.

(bottom left) Figure 2b from Zehir et al. Mutational landscape of metastatic cancer revealed from prospective clinical sequencing of 10,000 patients. (2017) Nature Medicine doi:10.1038/nm.4333

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