Lips that taste of tears, they say, are the best for kissing.get crankymore quotes

# pi: beautiful

In Silico Flurries: Computing a world of snow. Scientific American. 23 December 2017

# visualization + design

The 2018 Pi Day art celebrates the 30th anniversary of $\pi$ day and connects friends stitching road maps from around the world. Pack a sandwich and let's go!

# The art of Pi ($\pi$), Phi ($\phi$) and $e$

2018 $\pi$ day shrinks the world and celebrates road trips by stitching streets from around the world together. In this version, we look at the boonies, burbs and boutique of $\pi$ by drawing progressively denser patches of streets. Let's go places.
2017 $\pi$ day
2016 $\pi$ approximation day
2016 $\pi$ day
2015 $\pi$ day
2014 $\pi$ approx day
2014 $\pi$ day
2013 $\pi$ day
Circular $\pi$ art

Numbers are a lot of fun. They can start conversations—the interesting number paradox is a party favourite: every number must be interesting because the first number that wasn't would be very interesting! Of course, in the wrong company they can just as easily end conversations.

## is π normal?

It is not yet known whether the digits of π are normal—determining this is an important problem in mathematics. In other words, is the distribution of digit frequencies in π uniform? Do each of the digits 0–9 appear exactly 1/10th of the time, does every two-digit string appear exactly 1/100th of the time and so on for every finite-length string1?

1 One interesting finite-length string is the 6-digit Fenyman Point (...999999...) which appears at digit 762 in π. The Feynman Point was the subject of 2014 $\pi$ Day art.

This question can be posed for different representations of π—in different bases. The distribution frequencies of 1/10, 1/100, and so on above refer to the representation of π in base 10. This is the way we're used to seeing numbers. However, if π is encoded as binary (base 2), would all the digits in 11.00100100001111... be normal? The table below shows the first several digits of π in each base from 2 to 16, as well as the natural logarithm base, $e$.

 base, $b$ $\pi_b$ base, $b$ $\pi_b$ 2 11.00100100001111 10 3.14159265358979 3 10.01021101222201 11 3.16150702865A48 4 3.02100333122220 12 3.184809493B9186 5 3.03232214303343 13 3.1AC1049052A2C7 6 3.05033005141512 14 3.1DA75CDA813752 7 3.06636514320361 15 3.21CD1DC46C2B7A 8 3.11037552421026 16 3.243F6A8885A300 $e$ 10.10100202000211 source: virtuescience.com

Because the digits in the numbers are essentially random (this is a conjecture), the essence of the art is based on randomness.

A vexing consequence of π being normal is that, because it is non-terminating, π would contain all patterns. Any word you might think of, encoded into numbers in any way, would appear infinitely many times. The entire works of Shakespeare, too. As well, all his plays in which each sentence is reversed, or has one spelling mistake, or two! In fact, you would eventually find π within π, but only if you have infinite patience.

This is why any attempts to use the digits of $\pi$ to infer meaning about anything is ridiculous. The exact opposite of what you find is also in $\pi$.

#### Stoneham's constant

A number can be normal in one base, but another. For example, Stoneham's constant,

$\alpha_{2,3} = 1/2 + 1/(2^{3^1} 3^1) + 1/(2^{3^2} 3^2) + 1/(2^{3^3} 3^3) + ... + 1/(2^{3^k} 3^k) + ...$

is 0.54188368083150298507... in base 10 and 0.100010101011100011100011100... in base 2.

Stoneham's constant is provably normal in base 2. In some other bases, such 6, Stoneham's constant is provably not normal.

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# Statistics vs Machine Learning

Tue 03-04-2018
We conclude our series on Machine Learning with a comparison of two approaches: classical statistical inference and machine learning. The boundary between them is subject to debate, but important generalizations can be made.

Inference creates a mathematical model of the datageneration process to formalize understanding or test a hypothesis about how the system behaves. Prediction aims at forecasting unobserved outcomes or future behavior. Typically we want to do both and know how biological processes work and what will happen next. Inference and ML are complementary in pointing us to biologically meaningful conclusions.

Nature Methods Points of Significance column: Statistics vs machine learning. (read)

Statistics asks us to choose a model that incorporates our knowledge of the system, and ML requires us to choose a predictive algorithm by relying on its empirical capabilities. Justification for an inference model typically rests on whether we feel it adequately captures the essence of the system. The choice of pattern-learning algorithms often depends on measures of past performance in similar scenarios.

Bzdok, D., Krzywinski, M. & Altman, N. (2018) Points of Significance: Statistics vs machine learning. Nature Methods 15:233–234.

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: supervised methods. Nature Methods 15:5–6.

# Happy 2018 $\pi$ Day—Boonies, burbs and boutiques of $\pi$

Wed 14-03-2018

Celebrate $\pi$ Day (March 14th) and go to brand new places. Together with Jake Lever, this year we shrink the world and play with road maps.

Streets are seamlessly streets from across the world. Finally, a halva shop on the same block!

A great 10 km run loop between Istanbul, Copenhagen, San Francisco and Dublin. Stop off for halva, smørrebrød, espresso and a Guinness on the way. (details)

Intriguing and personal patterns of urban development for each city appear in the Boonies, Burbs and Boutiques series.

In the Boonies, Burbs and Boutiques of $\pi$ we draw progressively denser patches using the digit sequence 159 to inform density. (details)

No color—just lines. Lines from Marrakesh, Prague, Istanbul, Nice and other destinations for the mind and the heart.

Roads from cities rearranged according to the digits of $\pi$. (details)

The art is featured in the Pi City on the Scientific American SA Visual blog.

Check out art from previous years: 2013 $\pi$ Day and 2014 $\pi$ Day, 2015 $\pi$ Day, 2016 $\pi$ Day and 2017 $\pi$ Day.

# Machine learning: supervised methods (SVM & kNN)

Thu 18-01-2018
Supervised learning algorithms extract general principles from observed examples guided by a specific prediction objective.

We examine two very common supervised machine learning methods: linear support vector machines (SVM) and k-nearest neighbors (kNN).

SVM is often less computationally demanding than kNN and is easier to interpret, but it can identify only a limited set of patterns. On the other hand, kNN can find very complex patterns, but its output is more challenging to interpret.

Nature Methods Points of Significance column: Machine learning: supervised methods (SVM & kNN). (read)

We illustrate SVM using a data set in which points fall into two categories, which are separated in SVM by a straight line "margin". SVM can be tuned using a parameter that influences the width and location of the margin, permitting points to fall within the margin or on the wrong side of the margin. We then show how kNN relaxes explicit boundary definitions, such as the straight line in SVM, and how kNN too can be tuned to create more robust classification.

Bzdok, D., Krzywinski, M. & Altman, N. (2018) Points of Significance: Machine learning: a primer. Nature Methods 15:5–6.

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.

# Human Versus Machine

Tue 16-01-2018
Balancing subjective design with objective optimization.

In a Nature graphics blog article, I present my process behind designing the stark black-and-white Nature 10 cover.

Nature 10, 18 December 2017

# Machine learning: a primer

Thu 18-01-2018
Machine learning extracts patterns from data without explicit instructions.

In this primer, we focus on essential ML principles— a modeling strategy to let the data speak for themselves, to the extent possible.

The benefits of ML arise from its use of a large number of tuning parameters or weights, which control the algorithm’s complexity and are estimated from the data using numerical optimization. Often ML algorithms are motivated by heuristics such as models of interacting neurons or natural evolution—even if the underlying mechanism of the biological system being studied is substantially different. The utility of ML algorithms is typically assessed empirically by how well extracted patterns generalize to new observations.

Nature Methods Points of Significance column: Machine learning: a primer. (read)

We present a data scenario in which we fit to a model with 5 predictors using polynomials and show what to expect from ML when noise and sample size vary. We also demonstrate the consequences of excluding an important predictor or including a spurious one.

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.

# Snowflake simulation

Tue 16-01-2018
Symmetric, beautiful and unique.

Just in time for the season, I've simulated a snow-pile of snowflakes based on the Gravner-Griffeath model.

A few of the beautiful snowflakes generated by the Gravner-Griffeath model. (explore)

The work is described as a wintertime tale in In Silico Flurries: Computing a world of snow and co-authored with Jake Lever in the Scientific American SA Blog.

Gravner, J. & Griffeath, D. (2007) Modeling Snow Crystal Growth II: A mesoscopic lattice map with plausible dynamics.