Don Quixote tilts at Zeta functions

October 11, 2011

A friend of mine, Rohit Gupta (@fadesingh) has been doing some of the most creative mathematics communication out there. Using myths, stories, puzzles and poetry he has been making deep questions of mathematics accessible to others in online workshops and now a newspaper column in India. He is about to start a crazy and fascinating project, taking on possibly the greatest challenge of modern mathematics, the Riemann Hypothesis, which plunges the depths of the mysterious structure of the prime numbers. This would be an ambitious project for a group of mathematicians to take on. Current wisdom is probably that there are not even realistic routes to solve the problem. For a group with little or no mathematical training it is just crazy. That is what I love about the project.

Regular readers of this blog will know that I am a fan of impossible quests, and this one comes damn close. In the classic tradition of Don Quixote (which even mentions prime numbers) the value of a quest lies in the seeking, not the goal. Why should the privilege of failing to prove the Riemann Hypothesis be reserved to mathematicians? At worst a group of people will learn a lot, just getting an idea of the prime number theorem, or a clue about what a zeta function even is, is already an achievement. Can that be bad?

Even better the project emphasises that whatever your philosophy of mathematics, its actual study is a very human process. Baring some fairly extreme situations, if the Riemann Hypothesis is proved it will be by humans. Possible special and weird humans, but humans nonetheless. Just as the problem itself was discovered/dreamt up/found by one. Changing the perception of mathematicians as priests with almost magical abilities, to smart, professionals who have been through a tough training again cannot be a bad thing.

I am therefore proud to be part of this project, and see my role as that of Sancho Panza, sometimes bringing the flights of fancy down to earth, but increasingly fascinated and invested in the quest and where it might lead.

Of course it doesn’t hurt that the first stage of the project is playing with quasi-crystals, which have been a large part of my research life.


The Academy: Axiom 1

September 3, 2011

The rule

This post is not trying to do anything clever. It is making a statement that seems self-evident:

There are three ways to gain understanding of the world:

  • Personal experience
  • Systems of rules
  • Stories

All are equally important, and each has its strengths and weaknesses.

The important point is not the content of the statement but the stating of it. This is not just something that feels correct (to me) but something that feels fundamental. This mirrors one of the quests of mathematics to find the simplest statements on which to build the whole subject. I have my suspicions that the same thing would not work completely here, though writing the “Elements of the Academy” with this as one of the axioms might make a curious exercise!

This axiom maps onto the world of academia. The Sciences are primarily concerned with the use of rules to understand the world; the Arts centred on the creation of objects that attempt to transfer personal experience; and the Humanities write, dissect and try to understand the stories of the world.

All three areas, of course, do and should take advantage of the strengths of the other two methods as well as their primary concern.

The story

As a mathematician I obviously come from the grand tradition of finding rules to understand the world. For much of human history this was known to be rather limited in its scope. It was applicable to commerce, certainly; but also to questions of measurement, and to the study of the stars and music. Then, with the acceptance of arguments based on infinitesimals and the genius of Newton and Liebniz, the models of calculus opened up a vast array of phenomena to understanding through rules. It was so successful that many started to believe that it would eventually explain everything.

I do not believe this to be the case. Chaos theory shows that even perfect models can be severely limited by small, unavoidable, measurement errors. The work of Gödel and Turing shows that even in the purely theoretical world, there are unanswerable questions. Some even believe that as fundamental a system as arithmetic might contain contradictions. Before we even get to these hard limits we must deal with the soft limits imposed by the great ideas that we have yet to have.

Unfortunately, or fortunately depending on situation and personal preference,  the world offers many questions that we cannot answer with a systematic, rules based approach. Questions we cannot ignore. I wanted to define for myself the other options, and place them in some imagined framework.

The personal experience

I don’t believe I have said much here. It is, as I stated, self-evident. I also think it is important. It has been useful and practical to me. So, if you have managed to read this far, I thank you, but ask one further thing. Think about it yourself and see if it is a useful for you too.

Acknowledgements

This post grew out of a string of tweets, out of which grew very valuable discussion with  Colin Wright (@ColinTheMathmo) and Daniel Colquitt (@danielcolquitt), on twitter and elsewhere.


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.



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