Word powers of ten

February 2, 2012

How do we understand the number of words on the internet? Its hard to even grasp how many there are, and the number is growing so rapidly. Trying to understand a similar problem, the size of the universe (or just the observable universe) Charles and Ray Eames came up with the classic Powers of Ten video. Lets try the same for words:

1 (one) word
10 (ten) words a haiku, a sentence or a tweet

100 (hundred) words a paragraph, an abstract, a newsitem

1000 (thousand) words an article or blogpost

10,000 (ten thousand) words an essay or short story

100,000 (hundred thousand) words a book

1,000,000 (million) words an epic, Proust’s “A la recherche de temps perdu” is 1.5 million, the complete Harry Potter Saga is just over 1 million.

10,000,000 (ten million) words  an Encyclopedia, the 2002 Britannica is 44 million

100,000,000 (hundred million) words  a large Encyclopedia, like the Yongle Encyclopedia from fifteenth century China

1,000,000,000 (billion) words  Wikipedia (actually over twice that)

Then there is a gap…

10,000,000,000 (ten billion) words

100,000,000,000 (hundred billion) words

1,000,000,000,000 (trillion) words

10,000,000,000,000 (ten trillion) words

100,000,000,000,000 (hundred trillion) words gives you the internet in 2008

So perhaps soon the internet will surpass the work of a single man. The great french author Raymond Queneaux:

10,000,000,000,000,000 (ten thousand trillion, ten thousand million million, ten million billion) words  the word count (assuming 10 words per line) of the complete text of “Cent mille milliards de poèmes

Having exploded outwards, it is not time to come back down, through encyclopedias, books and stories, back to tweets and the word:

1/10 (tenth) of a word a letter

1/100 (hundredth) of a word gives you a line segment which has an interesting property, it can itself be divided.

1/1000 (thousandth) of a word gives you a shorter line segment, allowing you to dive as deeply as you wish theoretically, in practice you will dive surprisingly quickly through atoms, protons, neutrons and quarks to the lower limits of our understanding.


In memorium: Foyle’s Mathematics room.

May 31, 2011

For years the mathematics books at Foyles bookshop in London had their own room. It was a strange place, to the uninitiated inexplicably yellow. It had its own quirks rules and legends. There were shelves whose books were not for sale and, should you find a book that was for sale, you had to try to sneak it out if you wanted to purchase books elsewhere before leaving.

When I entered the room for the third time I was a PhD student in London. I had the practical purpose of finding a book I needed, but I became entranced. It became a regular place to visit, gaining familiarity and comfort. During hard times in my PhD and later jobs in London it acted as a refuge. At some point earlier memories returned.

Old-School Foyles, but not the mathematics room. Do you have an image?

Of course, the first time I visited I had no idea that this room would become part of my personal mythology. I do not know how old I was,  I cannot even remember the context (a family trip to London?); but I do remember the room, standing out even from the magical L-space1 that Foyles used to epitomise. Years later I returned. I was an undergraduate at Warwick and my love affair with mathematics books was truly beginning. Not just for the knowledge they contain, but for a beauty that I feel but not find words for. Part of this beauty is the esoteric language of their titles, the language that puts so many off mathematics but, it must be admitted, entices others in:

Some books I simply gazed at, others I bought simply for the magic of their titles. Those titles echo in my memory. Today some have become trusted friends, some sit mysteriously on my bookshelves having resisted numerous attempts on their secrets, others turn up like old acquaintances when I visit book shops.

I did that recently, I was once again in Foyles. The mathematics section had moved once more. It was once again in a familiar room at the front of the building on the third floor. Had they come home (albeit sharing the space)? But wasn’t the old maths room on the second floor? To my shame I could not remember clearly. I had grown used to the room being gone; it was a shock to find the details of my memory so weak. My internet skills failing me, I could not even find a record that gave the floor, worse, I could not find mention of the room at all. So I decided to write this.For me it makes concrete memories that seemed routine at the time, but now hold great importance, but perhaps I am not the only one? Maybe there are others who have fond memories of this room. If you do find this and remember please share your memories of this odd, impractical but special room.

I mourn the room, but  do realise that some things have to change. Today the nature of the book itself is changing, and with it the bookshop. Just opposite Foyles the space that used to be Borders bookshop is now taken up with TK Maxx. With the ability of the internet to deliver information and,  electronic readers finally usable, the paper book finds competition it has never had before.  Yet the bookshop, as I adore it, has been under threat for a long time. Borders itself along with Barnes and Noble represented the first assault, opening up the bookshop and making it easy to navigate. Then Amazon opened things up further, making it possible to easily find any book in print. Yet great bookshops, like Foyles, have survived, I have faith, there will be changes, but some of what we love in these stores will survive and perhaps some of what will be lost needs to go. Is it such a bad thing that cheap dectective and romance novels will no longer force trees to be cut for their paper?

For the moment therefore I  try to regularly  visit the bookshops I love and buy books from them. Not just for the books themselves but as a support for those wonderful shops.  It makes a good excuse anyway!

Footnotes

1 BACK TO POST
As a regular visitor to Foyles I learnt certain routes around the building, mixing the stairs and elevators. It felt that a tiny deviation from the correct route could leave you in a different place entirely. It was occasionally a shock to realise that two points, that I had thought were in completely different parts of the building, were actually just around the corner from each other. Terry Pratchett describes this best with the concept of L-space, that all libraries, and bookshops in the world are connected both in space and time and, with the correct path, you can navigate to any of them. In the Discworld version of the burning fire of Alexandria a hairy arm is seem amongst the flames rescuing some of the greatest works.


I find myself looking for a job…

January 22, 2011

I have a weird collection of skills. Mathematics, talking about mathematics, art, making…

I am certainly missing opportunities, maybe because few know the skill set even exists! So its time to advertise myself. Perhaps you are looking for someone who can…

  • Do mathematics at a research level, especially:
    • Geometry, understanding the spaces we live in and more exotic ones.
    • Tilings and patterns.
    • History and culture of Mathematics
  • Talk maths in public.
  • Teach (and be creative at it)
  • Program
  • Use computer manufacturing tools, Laser cutters, 3d printers, 3/5/n-axis routers.
  • Make Art and do Design

You need more evidence? I guess that makes sense. More details are below. If you still need to know more get in touch. I can provide references! (edmund.harriss at mathematicians.org.uk)

More details and evidence…

Mathematics: The heart of what I do, I have been an academic mathematician since getting my PhD from Imperial College in 2004. I have written papers, and been invited far and wide to talk about my work. See my CV for the gory details.


Geometry, Tilings and Patterns: I have a very strong understanding of the space we live in (and more exotic spaces). As this is a mathematical understanding I also have the tools to make this concrete, putting it into the equations and other things that computers can play with. My mathematical research has looked at tilings and patterns. Especially substitution tilings a sort of scaling symmetry, I probably know as much about the Penrose tiling than anyone else alive or dead!

History of Mathematics: It is mostly an amateur interest, though I nearly started a PhD with David Fowler before beginning one on tilings. I also think about the role of mathematics as a subject in the world and its relationship to art.

Talking maths in public: You can understand what I have to say without specialist training! I have explained the beauty and wonder of mathematics from the sacred halls of the Royal Society to primary schools. You can even hear me on the radio (and of course read this blog!). Or dive into the geekiness of prime birthdays.


Teaching: I want to teach people to actually think mathematically, not just get the rules that can be followed to a right answer, and have had success with it. Of course I can teach a traditional maths course and these are often necessary to get the bulk of material across, however I have also worked with more innovative courses. That is why I came to Arkansas. I wanted to teach MATH 2033 the conspiracy or mathematics course designed to corrupt people into the subject by giving a glimpse of  undecidability, game theory, 4 dimensional geometry, hyperbolic geometry, topology, codes, sphere packings… The students then have to come up with their own projects and, as could be expected often get incredibly creative.

3d cog spirographs

Art and Design: I can make pretty pictures, normally using maths. I am on the board of the new Art and Science masters at Central St Martins school of Art in London, and designed the screens for the new Mathematics Learning Centre at Imperial College London. I can do graphic design in 2d and make models and render them in 3d. I can use all the standard software, Adobe Illustrator and Photoshop, Rhino 3d (especially with Grasshopper) etc.

Making: I make things, normally focussing on explaining mathematics. I even have my own Laser cutter! I designed some larger versions of the hexayurt, a simple building made, without waste from 12 sheets of plywood or other materials. I am currently working with the FabLab at the architecture school here at the University of Arkansas, and am writing software to drive their 5-axis router.



Mathematical Scales

November 6, 2010

Thanks to the move to the US, my son has a new piano teacher. He is playing at an advanced level, beyond grade 8 (for the UK audience), with pieces by Bach, Mozart and Chopin often ringing out. Yet for the last couple of months he has been taken right back to the basics. Looking again at simple techniques on how fingers hit the keys and going over scales.

I am in love with this idea of training, taking someone who has proved incredibly able in an area and taking them back to the most basic ideas. I started to wonder what the equivalent might be for mathematics. What exercises should we be giving to starting PhD students?What exercises could we ourselves try in order to gain intuition and insight into the basic workings of our subject. I have a first proposal, but am sure there are others? What do you think? Of the idea itself, or of suggestions of possible exercises?

Multiplication Exercise

Multiply all possible pairs of numbers from 1 to 99, that is 4950 different calculations. At a conservative estimate of 120 per hour (most will be a lot quicker than 30s, some will be longer!) that is just over 40 hours work. That could spread quite nicely over a month, maybe two along with other activities. It would be 40 hours of meditation on the most fundamental of mathematical operations, what might come from that?
Other suggestions

A couple of excellent suggestions from commentors in a lively debate on reddit:

1) Teaching, which of course is already a significant part of graduate training in the US, unfortunately less so in the UK (those being the two systems I have worked in).

2) Deep study of proofs, with mention of this beautiful paper of Dykstra.


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