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?
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.
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.
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.
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.
After 15 minutes, it's 6:45 and our Ptolemaic clock bezels have moved a little bit.
Can you tell what time it is on the Ptolemaic clock below?
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.
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.
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.
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.
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.
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
Outliers can degrade the fit of linear regression models when the estimation is performed using the ordinary least squares. The impact of outliers can be mitigated with methods that provide robust inference and greater reliability in the presence of anomalous values.
We discuss MM-estimation and show how it can be used to keep your fitting sane and reliable.
Greco, L., Luta, G., Krzywinski, M. & Altman, N. (2019) Points of significance: Analyzing outliers: Robust methods to the rescue. Nature Methods 16:275–276.
Altman, N. & Krzywinski, M. (2016) Points of significance: Analyzing outliers: Influential or nuisance. Nature Methods 13:281–282.
Two-level factorial experiments, in which all combinations of multiple factor levels are used, efficiently estimate factor effects and detect interactions—desirable statistical qualities that can provide deep insight into a system.
They offer two benefits over the widely used one-factor-at-a-time (OFAT) experiments: efficiency and ability to detect interactions.
Since the number of factor combinations can quickly increase, one approach is to model only some of the factorial effects using empirically-validated assumptions of effect sparsity and effect hierarchy. Effect sparsity tells us that in factorial experiments most of the factorial terms are likely to be unimportant. Effect hierarchy tells us that low-order terms (e.g. main effects) tend to be larger than higher-order terms (e.g. two-factor or three-factor interactions).
Smucker, B., Krzywinski, M. & Altman, N. (2019) Points of significance: Two-level factorial experiments Nature Methods 16:211–212.
Krzywinski, M. & Altman, N. (2014) Points of significance: Designing comparative experiments.. Nature Methods 11:597–598.
Celebrate `\pi` Day (March 14th) and set out on an exploration explore accents unknown (to you)!
This year is purely typographical, with something for everyone. Hundreds of digits and hundreds of languages.
A special kids' edition merges math with color and fat fonts.
One moment you're
:) and the next you're
Make sense of it all with my Tree of Emotional life—a hierarchical account of how we feel.