How the Universe Was Made

How the Universe Was Made:
Before the Big Bang … and After

by Ken Roberts

One day God was working on his latest project. He was making a perfect
golden sphere. The sphere was so round, that there was nothing rounder. It
was so smooth, that there was nothing smoother. And it was so pure, made
of gold using only one type of atom, that there was nothing purer or more

You may be wondering why I am speaking of God as He. Well, it is a
constraint of the English language that I am using to tell this story. God
does not have a gender; God is He, She, It and everything else. God is plant,
animal, rock, water and air. And time — God is past, present, and future, if
those can be said to exist before the Universe. We will simply have to do the
best we can in order to tell this story, using metaphors and frail vocabulary.

So … God had made a perfect sphere. It was almost done. Only a name was
needed. The sphere was so perfect that only one bit of information would
be needed to describe the sphere. God would call it 1. Or maybe 0. God
hadn’t yet decided.

1 would be a good name, because it suggests One-ness, a Uni-Verse, a Poem
that says everything. 0 would be a good name because it suggests the round-
ness of a perfect sphere, and the syllable Om. Either way, one bit would
suffice for the sphere’s name.

While thinking about his decision, God took a coffee break. There was no
rush … Infinite time, actually. After preparing his coffee, God returned to
his workbench, where he had made the sphere. He set his coffee cup down
on the workbench, and turned to examining the sphere, making sure it was
perfectly smooth and pure.

Well, we’re here, so you know what happened. As God was concentrating
on the sphere, his elbow nudged the coffee cup, which spilled coffee all over
God’s workbench. God grabbed for the coffee cup, and the sphere, without
his full attention, rolled to the edge of the workbench and fell onto the

There was a Big Bang ! The perfect sphere was smashed into millions of
bits. Coffee dripped off the workbench and mixed into the breakage, and
created little bits of dark coffee and light cream. That became empty space
and stary galaxies, and everything else in the Universe. “Oops !”, said God.

What happened after the Big Bang? Well, God is probably working on
another sphere. Or, perhaps, She has a new project.

Pushkin Poem Arion Translation

Yesterday I tried translating a poem from Russian. Arion, by Alexander Pushkin, is a poem he published in 1827, when he was 27-28 years old. I’ve read three other translations, and all are good. However, each seems to miss some aspect of the original. So I tried my own translation. Remarks at end. Here is the translation.


Many men on board the bark.
Some strained the sturdy sail,
others set pace with powerful strokes,
oars drawing deep.
In calm control, our wise helmsman
lightly steered the laden ship.
And I – happy of heart,
careless of concern — sang sweetly.
Wild waves suddenly stopped our song …
All hands and helmsman were lost !
Only I, the singer, cast onto the beach.
I dance, chant songs of deliverance
and dry my garments in the sun.


1. Here are three other translations which I enjoy:

At there are two translations, one by I. Zheleznova, “We many were who filled the boat…”, and the other by an unknown translator, “We sailed in numerous company…”. That site also has Pushkin’s poem in the original Russian.

A translation by Babette Deutsch, “We numbered many in the ship…”, appears on page 63 of “The Poems, Prose and Plays of Alexander Pushkin”. That volume was edited by Avrahm Yarmolinsky, and published by Random House, New York, 1936. It is part of the “Modern Library” collection.

2. Pushkin’s poem is 15 lines long, with a rhyme scheme of ABBA CDDDC EE FGGF. That is a variant of the sonnet form. All three translations also use 15 lines, with a similar rhyme scheme.

I try another approach. Instead of rhyme, I use alliteration to provide rhythmic structure in the poem. There is a tradition of alliterative verse in early English. Arion’s is an old tale and it is suitably respectful of that classic tale, of the poet Arion, and of Pushkin, to use an old form. Arion was the poet who established the dithyrambic poetic form, choral dance and song to be performed in honour of the wine god Dionysus. In telling Arion’s tale, one should not feel confined by the formalities of sonnet.

3. The rhythm is regular at first, then becomes rough when the storm arises. I hope to capture that sea change. In the lines at the end, the structure returns somewhat as the poet offers Thanksgiving and rejoices at his rescue.

4. Pushkin was a young man, age 27-28 when this poem was published, and like many young men held passionate opinions about improvement of the social order.

The classical tale of Arion is that he was captured by pirates, and forced to choose between being killed on-board their ship, or being thrown into the sea – where he would drown. Arion sang while he made his choice, and dolphins gathered around the ship to admire his beautiful song. Arion was thrown into the sea, but was carried safely to shore on the back of a dolphin.

It is not unreasonable to suppose that Pushkin knew that his poem might be read with a political subtext. In Pushkin’s poem, Arion is not a captive, and his shipmates are companions not pirates. However, ships of state can encounter heavy weather. Ambiguity adds to the appeal of “Arion”.

5. Here are some links to articles about Pushkin, Arion, and dithyrambic poetry.

And a link to two readings of the original poem, in Russian. Click on either of the first two “Play” buttons to hear the reading.

6. And finally, to attach an image to this post, here is a painting of Alexander Pushkin.



Best wishes,
Ken Roberts

Solar Cells and the Lambert W Function

Computations for the one-diode model for solar cells, if done using the exact formula with Lambert W function, are likely to produce arithmetic overflow or underflow. That is a constraint on the ability to implement such calculations in Fortran or C, or on microcontrollers. The solution: use a coordinate transformation of the computation problem. If the problem were being solved on graph paper, the coordinate transformation would be achieved by using log-log graph paper.

I gave a talk at a recent conference, “Celebrating 20 years of the Lambert W function”. Title: Solar Cells and the Lambert W function. Joint work with my colleague S. R. Valluri. The slides are available at Researchgate, at this URL:

Best wishes,
Ken R.

Non-Harmonic Fourier Series

2016 is the 200th anniversary of the publication of Joseph Fourier’s ideas for the solution of heat conduction and radiation problems using trigonometric series expansions. What we now call Fourier series. His ideas appeared in book form in 1822, but they first appeared in 1816 in a paper Theorie de la Chaleur (Extrait) which describes the book’s contents. It is appropriate to return to Fourier’s work. And there are gems to be found.

Chapter 5 of his book, The Analytical Theory of Heat (in English translation by Alexander Freeman), discusses the conduction of heat in a solid sphere. Fourier obtains a sine series which solves the differential equation. However, his series is not a harmonic series of the form of a weighted sum of terms sin(k*x) where the k are positive integers. Rather, Fourier’s solution is what we now call a non-harmonic series. It is a weighted sum of terms sin(b*x) where the b values are positive reals, moving steadily out roughly as do the integers. What are those values of b ? They are the solutions to an equation of the form b*cotan(b) = B. Those basic modes can be summed in a linear combination to match other constraints of a particular problem.

We have seen the equation b*cotan(b) = B previously. It is the solution for the bound state energy levels in a quantum mechanics problem, the one-dimensional finite square well.

This looks like fun. Fourier’s solution is very clever. William Thomson (Kelvin) worked on this topic also — it is the subject of Thomson’s first published paper. There is plenty to explore.

Just a heads-up, for anyone else who may be interested in this topic.

Best wishes,
Ken Roberts

ps. Fourier’s book was republished by Dover. It is also online via the website.

Finding Good Recommendations

There are many online services which attempt to recommend movies, books, webpages etc that someone will like. In some implementations, recommendations are based upon finding new items that are liked by other users: If you like A, and someone else likes A and B, then B is perhaps a good recommendation for you. The difficulty is that establishing your profile can be a tedious task, as you have to initially indicate several items that you like. On the order of twenty items, perhaps.

A new algorithm, developed by Evgeny Frolov and Ivan Oseledets of the Skolkovo Institute, provides a much less time consuming, and likely more accurate, way of establishing your preferences. It uses information about items that you do not like, as well as about items that you like. Roughly stated, if you do not like item B, and those who like B also like C, then item C is perhaps not a good suggestion for you.

The details of their algorithm are subtle, and designed for efficient operation. It is not just graph searching. See Arxiv 1607.04228 for their paper — linked below — and a press release also linked below.

Best wishes,
Ken Roberts

Evgeny Frolov and Ivan Oseledets — Fifty Shades of Ratings: How to Benefit from a Negative Feedback in Top-N Recommendations Tasks

Press Release — Skoltech scientists have created an algorithm that improves the quality of recommender systems

Edmund Little — The Fantasts

Decades ago, I became an enthusiastic reader of J. R. R. Tolkien’s Hobbit tale and the Ring trilogy, and later other Tolkien works. Recently I encountered a small book, The Fantasts, by T. Edmund Little, which presents an excellent analysis of the idea of sub-creation and Fairie. Fairie was the subject of Tolkien’s famous 1938 lecture, On Fairy-Stories, which was published as the first half of Tree and Leaf — the second half being the story, Leaf by Niggle, one of my favourites.

Little’s book is worth one’s attention. Little explores Tolkien’s assertion that fantasy involves a process of what is called Sub-creation. Little considers five authors and their fantasy worlds: J. R. R. Tolkien’s Middle Earth, Lewis Carroll’s Wonderland, Mervyn Peake’s Gormenghast, Nicolai Gogol’s town NN depicted in Dead Souls, and Kenneth Grahame’s river bank world depicted in The Wind in the Willows. Little’s book The Fantasts is an extended essay, interesting and stimulating for anyone who has wondered about the process of sub-creation.

I will not attempt to summarize Little’s many insights and observations here. Suffice it that careful consideration of the details of sub-created worlds, as provided by Little in this essay, reveals many subtleties and amendments to the sketch provided by Tolkien in his essay on fairy story. For your enjoyment, and perhaps useful if you are engaged in creative (or sub-creative) writing …

T. Edmund Little died in 2013, and I provide links to two obituaries for your interest. The photo used to introduce this post from the second obit, and was perhaps taken in February 1997.

Best wishes,
Ken Roberts


Bertoia Dandelion Sculpture


This metal dandelion sculpture is by Harry Bertoia, and is one of the most beautiful of his works. There are links below to a Wikipedia page about Bertoia, and to the Milwaukee Art Museum where this dandelion is on display. A visit to the Milwaukee museum is worthwhile, as the building’s entryway is fabulous, and the collection includes many excellent modern works, contributed by Mrs. Bradley who evidently had very good taste.

Best wishes,
Ken Roberts

Wikipedia article about Harry Bertoia:

Milwaukee Art Museum links:
Dandelions and Deck Chairs: Harry Bertoia