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
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%).
Altman, N. & Krzywinski, M. (2018) Points of significance: Predicting with confidence and tolerance Nature Methods 15:843–844.
Krzywinski, M. & Altman, N. (2013) Points of significance: Importance of being uncertain. Nature Methods 10:809–810.
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.
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.
The presence of constraints in experiments, such as sample size restrictions, awkward blocking or disallowed treatment combinations may make using classical designs very difficult or impossible.
Optimal design is a powerful, general purpose alternative for high quality, statistically grounded designs under nonstandard conditions.
We discuss two types of optimal designs (D-optimal and I-optimal) and show how it can be applied to a scenario with sample size and blocking constraints.
Smucker, B., Krzywinski, M. & Altman, N. (2018) Points of significance: Optimal experimental design Nature Methods 15:599–600.
Krzywinski, M., Altman, N. (2014) Points of significance: Two factor designs. Nature Methods 11:1187–1188.
Krzywinski, M. & Altman, N. (2014) Points of significance: Analysis of variance (ANOVA) and blocking. Nature Methods 11:699–700.
Krzywinski, M. & Altman, N. (2014) Points of significance: Designing comparative experiments. Nature Methods 11:597–598.
An illustration of the Tree of Life, showing some of the key branches.
The tree is drawn as a DNA double helix, with bases colored to encode ribosomal RNA genes from various organisms on the tree.
All living things on earth descended from a single organism called LUCA (last universal common ancestor) and inherited LUCA’s genetic code for basic biological functions, such as translating DNA and creating proteins. Constant genetic mutations shuffled and altered this inheritance and added new genetic material—a process that created the diversity of life we see today. The “tree of life” organizes all organisms based on the extent of shuffling and alteration between them. The full tree has millions of branches and every living organism has its own place at one of the leaves in the tree. The simplified tree shown here depicts all three kingdoms of life: bacteria, archaebacteria and eukaryota. For some organisms a grey bar shows when they first appeared in the tree in millions of years (Ma). The double helix winding around the tree encodes highly conserved ribosomal RNA genes from various organisms.
Johnson, H.L. (2018) The Whole Earth Cataloguer, Sactown, Jun/Jul, p. 89