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This love loves love. It's a strange love, strange love.Liz Fraserfind a way to lovemore quotes

In Silico Flurries: Computing a world of snow. Scientific American. 23 December 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

Find and snap to colors in an image

Sat 29-12-2018

One of my color tools, the colorsnap application snaps colors in an image to a set of reference colors and reports their proportion.

Below is Times Square rendered using the colors of the MTA subway lines.

Colors used by the New York MTA subway lines.

Martin Krzywinski @MKrzywinski
Times Square in New York City.
Martin Krzywinski @MKrzywinski
Times Square in New York City rendered using colors of the MTA subway lines.
Martin Krzywinski @MKrzywinski
Granger rainbow snapped to subway lines colors from four cities. (zoom)

Take your medicine ... now

Wed 19-12-2018

Drugs could be more effective if taken when the genetic proteins they target are most active.

Design tip: rediscover CMYK primaries.

More of my American Scientific Graphic Science designs

Ruben et al. A database of tissue-specific rhythmically expressed human genes has potential applications in circadian medicine Science Translational Medicine 10 Issue 458, eaat8806.

Predicting with confidence and tolerance

Wed 07-11-2018
I abhor averages. I like the individual case. —J.D. Brandeis.

We focus on the important distinction between confidence intervals, typically used to express uncertainty of a sampling statistic such as the mean and, prediction and tolerance intervals, used to make statements about the next value to be drawn from the population.

Confidence intervals provide coverage of a single point—the population mean—with the assurance that the probability of non-coverage is some acceptable value (e.g. 0.05). On the other hand, prediction and tolerance intervals both give information about typical values from the population and the percentage of the population expected to be in the interval. For example, a tolerance interval can be configured to tell us what fraction of sampled values (e.g. 95%) will fall into an interval some fraction of the time (e.g. 95%).

Martin Krzywinski @MKrzywinski
Nature Methods Points of Significance column: Predicting with confidence and tolerance. (read)

Altman, N. & Krzywinski, M. (2018) Points of significance: Predicting with confidence and tolerance Nature Methods 15:843–844.

Background reading

Krzywinski, M. & Altman, N. (2013) Points of significance: Importance of being uncertain. Nature Methods 10:809–810.

4-day Circos course

Wed 31-10-2018

A 4-day introductory course on genome data parsing and visualization using Circos. Prepared for the Bioinformatics and Genome Analysis course in Institut Pasteur Tunis, Tunis, Tunisia.

Martin Krzywinski @MKrzywinski
Composite of the kinds of images you will learn to make in this course.

Oryza longistaminata genome cake

Mon 24-09-2018

Data visualization should be informative and, where possible, tasty.

Stefan Reuscher from Bioscience and Biotechnology Center at Nagoya University celebrates a publication with a Circos cake.

The cake shows an overview of a de-novo assembled genome of a wild rice species Oryza longistaminata.

Martin Krzywinski @MKrzywinski
Circos cake celebrating Reuscher et al. 2018 publication of the Oryza longistaminata genome.

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