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
Decision trees classify data by splitting it along the predictor axes into partitions with homogeneous values of the dependent variable. Unlike logistic or linear regression, CART does not develop a prediction equation. Instead, data are predicted by a series of binary decisions based on the boundaries of the splits. Decision trees are very effective and the resulting rules are readily interpreted.
Trees can be built using different metrics that measure how well the splits divide up the data classes: Gini index, entropy or misclassification error.
When the predictor variable is quantitative and not categorical, regression trees are used. Here, the data are still split but now the predictor variable is estimated by the average within the split boundaries. Tree growth can be controlled using the complexity parameter, a measure of the relative improvement of each new split.
Individual trees can be very sensitive to minor changes in the data and even better prediction can be achieved by exploiting this variability. Using ensemble methods, we can grow multiple trees from the same data.
Krzywinski, M. & Altman, N. (2017) Points of Significance: Classification and regression trees. Nature Methods 14:757–758.
Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.
Altman, N. & Krzywinski, M. (2015) Points of Significance: Multiple Linear Regression Nature Methods 12:1103-1104.
Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. Nature Methods 13:603-604.
Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Model Selection and Overfitting. Nature Methods 13:703-704.
Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Regularization. Nature Methods 13:803-804.
The artwork was created in collaboration with my colleagues at the Genome Sciences Center to celebrate the 5 year anniversary of the Personalized Oncogenomics Program (POG).
The Personal Oncogenomics Program (POG) is a collaborative research study including many BC Cancer Agency oncologists, pathologists and other clinicians along with Canada's Michael Smith Genome Sciences Centre with support from BC Cancer Foundation.
The aim of the program is to sequence, analyze and compare the genome of each patient's cancer—the entire DNA and RNA inside tumor cells— in order to understand what is enabling it to identify less toxic and more effective treatment options.
Principal component analysis (PCA) simplifies the complexity in high-dimensional data by reducing its number of dimensions.
To retain trend and patterns in the reduced representation, PCA finds linear combinations of canonical dimensions that maximize the variance of the projection of the data.
PCA is helpful in visualizing high-dimensional data and scatter plots based on 2-dimensional PCA can reveal clusters.
Altman, N. & Krzywinski, M. (2017) Points of Significance: Principal component analysis. Nature Methods 14:641–642.
Altman, N. & Krzywinski, M. (2017) Points of Significance: Clustering. Nature Methods 14:545–546.
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.
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.