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've posted a writeup about the design and redesign process behind the figures in our Nature Methods Points of Significance column.

I have selected several figures from our past columns and show how they evolved from their draft to published versions.

Clarity, concision and space constraints—we have only 3.4" of horizontal space— all have to be balanced for a figure to be effective.

It's nearly impossible to find case studies of scientific articles (or figures) through the editing and review process. Nobody wants to show their drafts. With this writeup I hope to add to this space and encourage others to reveal their process. Students love this. See whether you agree with my decisions!

Past columns have described experimental designs that mitigate the effect of variation: random assignment, blocking and replication.

The goal of these designs is to observe a reproducible effect that can be due only to the treatment, avoiding confounding and bias. Simultaneously, to sample enough variability to estimate how much we expect the effect to differ if the measurements are repeated with similar but not identical samples (replicates).

We need to distinguish between sources of variation that are nuisance factors in our goal to measure mean biological effects from those that are required to assess how much effects vary in the population.

Altman, N. & Krzywinski, M. (2014) Points of Significance: Two Factor Designs *Nature Methods* **11**:5-6.

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

2. Krzywinski, M. & Altman, N. (2014) Points of Significance: Analysis of variance (ANOVA) and blocking *Nature Methods* **11**:699-700.

3. Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication *Nature Methods* **11**:879-880.

We've previously written about how to analyze the impact of one variable in our ANOVA column. Complex biological systems are rarely so obliging—multiple experimental factors interact and producing effects.

ANOVA is a natural way to analyze multiple factors. It can incorporate the possibility that the factors interact—the effect of one factor depends on the level of another factor. For example, the potency of a drug may depend on the subject's diet.

We can increase the power of the analysis by allowing for interaction, as well as by blocking.

Krzywinski, M., Altman, (2014) Points of Significance: Two Factor Designs *Nature Methods* **11**:1187-1188.

Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication *Nature Methods* **11**:879-880.

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.

Sources of noise in experiments can be mitigated and assessed by nested designs. This kind of experimental design naturally models replication, which was the topic of last month's column.

Nested designs are appropriate when we want to use the data derived from experimental subjects to make general statements about populations. In this case, the subjects are *random* factors in the experiment, in contrast to *fixed* factors, such as we've seen previously.

In ANOVA analysis, random factors provide information about the amount of noise contributed by each factor. This is different from inferences made about fixed factors, which typically deal with a change in mean. Using the F-test, we can determine whether each layer of replication (e.g. animal, tissue, cell) contributes additional variation to the overall measurement.

Krzywinski, M., Altman, N. & Blainey, P. (2014) Points of Significance: Nested designs *Nature Methods* **11**:977-978.

Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication *Nature Methods* **11**:879-880.

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.