resources
visualizations
presentations
lunch break
Distractions and amusements, with a sandwich and coffee.
writing
Writing
Poetry
Inked Sadness is a collection of poems written in that difficult time between being no longer young, but not yet old.
Expressions and Conversations of Love are short heart-breakers.
Scripts
Proverbial Man considers how our names and expectations limit our perceptions and freedoms. No answers are offered. I don't think I finished this.
The Surrogate echoes my own fears of fleeing from Poland in the early 80s. Or at least the fears I retroactively erected, to add drama. Count on the Polish for drama.
Narrative
Thirty Reasons should be enough to decide a place isn't worth returning to.
NeverEnder — Epic Space Poem
By my friend and colleague Emanuele Raffaele Ettore Libertini, the NeverEnder is a voyage through space and words.
news + thoughts
Yearning for the Infinite — Aleph 2
Discover Cantor's transfinite numbers through my music video for the Aleph 2 track of Max Cooper's Yearning for the Infinite (album page, event page).
I discuss the math behind the video and the system I built to create the video.
Hidden Markov Models
Everything we see hides another thing, we always want to see what is hidden by what we see.
—Rene Magritte
A Hidden Markov Model extends a Markov chain to have hidden states. Hidden states are used to model aspects of the system that cannot be directly observed and themselves form a Markov chain and each state may emit one or more observed values.
Hidden states in HMMs do not have to have meaning—they can be used to account for measurement errors, compress multi-modal observational data, or to detect unobservable events.
In this column, we extend the cell growth model from our Markov Chain column to include two hidden states: normal and sedentary.
We show how to calculate forward probabilities that can predict the most likely path through the HMM given an observed sequence.
Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Hidden Markov Models. Nature Methods 16:795–796.
Background reading
Altman, N. & Krzywinski, M. (2019) Points of significance: Markov Chains. Nature Methods 16:663–664.
Hola Mundo Cover
My cover design for Hola Mundo by Hannah Fry. Published by Blackie Books.
Curious how the design was created? Read the full details.
Markov Chains
You can look back there to explain things,
but the explanation disappears.
You'll never find it there.
Things are not explained by the past.
They're explained by what happens now.
—Alan Watts
A Markov chain is a probabilistic model that is used to model how a system changes over time as a series of transitions between states. Each transition is assigned a probability that defines the chance of the system changing from one state to another.
Together with the states, these transitions probabilities define a stochastic model with the Markov property: transition probabilities only depend on the current state—the future is independent of the past if the present is known.
Once the transition probabilities are defined in matrix form, it is easy to predict the distribution of future states of the system. We cover concepts of aperiodicity, irreducibility, limiting and stationary distributions and absorption.
This column is the first part of a series and pairs particularly well with Alan Watts and Blond:ish.
Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Markov Chains. Nature Methods 16:663–664.