Let me tell you about something.

Distractions and amusements, with a sandwich and coffee.

This love's a nameless dream.
•
• try to figure it out

numbers.tgz

1,000,000 digits of π, φ, e and ASN.

All the artwork can be purchased from Fine Art America.

The accidental similarity number is a kind of overlap between numbers. I came up with this concept after creating typographical art about the 4ness of π.

To construct this number for π, φ and e we first write the numbers on top of each other and then identify positions for which the numbers have the same digit.

3.1415926535897932 … 21170679821 … 10270193852 … 1.6180339887498948 … 93911374847 … 08659593958 … 2.7182818284590452 … 51664274274 … 32862794349 …

These digits are then used to create the accidental similarity number. In thise case,

0.979 …

By definition, the decimal is held in place.

The poster shows the accidental similarity number for π, φ and e created from the first 1,000,000 digits of each number. There are 9,997 positions in which these numbers have the same digit, but only 9,996 are shown because the distance between positions is used to color the digit and I was limited by input files with 1M digits.

The distribution of distances follows a Poisson distribution with an average of 100, with about 1-1/e values being smaller than 100.

The font is Neutraface Slab Display Medium.

Any properties are accidental, but curiously ASN(π, φ, e) ≈ 1.

If you find other curiously accidental properties, let me know.

Download the first 9,997 digits of the accidental similarity number. This file provides the ASN digit index, the digit and the position from which it is sampled.

I came up with Accidental Similarity Number immediately after creating this poster of the overlap between π, φ and e.

This thought stream started with the 4ness of π.

I was commissioned by Scientific American to create an information graphic that showed how our genomes are more similar to those of the chimp and bonobo than to the gorilla.

I had about 5 x 5 inches of print space to work with. For 4 genomes? No problem. Bring out the Hilbert curve!

To accompany the piece, I will be posting to the Scientific American blog about the process of creating the figure. And to emphasize that the *genome is not a blueprint*!

As part of this project, I created some Hilbert curve art pieces. And while exploring, found thousands of Hilbertonians!

Celebrate Pi Approximation Day (July 22nd) with the art of arm waving. This year I take the first 10,000 most accurate approximations (*m*/*n*, *m*=1..10,000) and look at their accuracy.

I turned to the spiral again after applying it to stack stacked ring plots of frequency distributions in Pi for the 2014 Pi Day.

Our 10th Points of Significance column! Continuing with our previous discussion about comparative experiments, we introduce ANOVA and blocking. Although this column appears to introduce two new concepts (ANOVA and blocking), you've seen both before, though under a different guise.

If you know the *t*-test you've already applied analysis of variance (ANOVA), though you probably didn't realize it. In ANOVA we ask whether the variation within our samples is compatible with the variation between our samples (sample means). If the samples don't all have the same mean then we expect the latter to be larger. The ANOVA test statistic (*F*) assigns significance to the ratio of these two quantities. When we only have two-samples and apply the *t*-test, *t*^{2} = *F*.

ANOVA naturally incorporates and partitions sources of variation—the effects of variables on the system are determined based on the amount of variation they contribute to the total variation in the data. If this contribution is large, we say that the variation can be "explained" by the variable and infer an effect.

We discuss how data collection can be organized using a randomized complete block design to account for sources of uncertainty in the experiment. This process is called blocking because we are blocking the variation from a known source of uncertainty from interfering with our measurements. You've already seen blocking in the paired *t*-test example, in which the subject (or experimental unit) was the block.

We've worked hard to bring you 20 pages of statistics primers (though it feels more like 200!). The column is taking a month off in August, as we shrink our error bars.

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.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Comparing Samples — Part I — *t*-tests *Nature Methods* **11**:215-216.

Krzywinski, M. & Altman, N. (2013) Points of Significance: Significance, *P* values and *t*-tests *Nature Methods* **10**:1041-1042.

This month, Points of Significance begins a series of articles about experimental design. We start by returning to the two-sample and paired *t*-tests for a discussion of biological and experimental variability.

We introduce the concept of blocking using the paired *t*-test as an example and show how biological and experimental variability can be related using the correlation coefficient, *ρ*, and how its value imapacts the relative performance of the paired and two-sample *t*-tests.

We also emphasize that when reporting data analyzed with the paired t-test, differences in sample means (and their associated 95% CI error bars) should be shown—not the original samples—because the correlation in the samples (and its benefits) cannot be gleaned directly from the sample data.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments *Nature Methods* **11**:597-598.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Comparing Samples — Part I — *t*-tests *Nature Methods* **11**:215-216.

Krzywinski, M. & Altman, N. (2013) Points of Significance: Significance, *P* values and *t*-tests *Nature Methods* **10**:1041-1042.