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May 26 11

Survey notes on fermi algebras and the Jordan-Wigner transform now on GitHub

by Michael Nielsen

Continuing the theme of my last post, I’ve now put my old survey notes on fermi algebras and the Jordan-Wigner transform up on GitHub.

The Jordan-Wigner transform is an amazing tool. It let’s you move back and forth between two seemingly very different ways of describing a physical system, either as a collection of qubits, or as a collection of fermions. To give you an idea of the power of the Jordan-Wigner transform, in his famous 1982 paper on quantum computing, Richard Feynman wrote the following:

could we [use a quantum computer to] imitate every quantum mechanical system which is discrete and has a finite number of degrees of freedom? I know, almost certainly, that we could do that for any quantum mechanical system which involves Bose particles. I’m not sure whether Fermi particles could be described by such a system. So I leave that open.

As shown in the notes, once you understand the Jordan-Wigner transform, the answer to Feynman’s question is obvious: yes, we can use quantum computers to simulate systems of fermions. The reason is that the Jordan-Wigner transforms lets us view the fermi system as a system of qubits which is easy to simulate using standard simulation techniques. Obviously, the point here isn’t that Feynman was silly: it’s that tools like the Jordan-Wigner transform can make formerly hard things very simple.

The notes assume familiarity with elementary quantum mechanics, comfort with elementary linear algebr, and a little familiarity with the basic nomenclature of quantum information science (qubits, the Pauli matrices).

I’m releasing the notes under a Creative Commons Attribution license (CC BY 3.0). That means anyone can copy, distribute, transmit and adapt/remix the work, provided my contribution is attributed. The notes could be used, for example, to help flesh out Wikipedia’s article about the Jordan-Wigner transform. Or perhaps they could usefully be adapted into course notes, or part of a review article.

May 17 11

Notes on expander graphs now on GitHub

by Michael Nielsen

Several years ago I wrote a set of introductory notes (pdf) about expander graphs, an exceptionally useful concept from computer science. I’m not an expert on expanders, but the notes were more popular than I anticipated, and still get a surprising amount of traffic. As an experiment, I’ve put the LaTeX source for the notes up on GitHub, under a Creative Commons Attribution license. That makes it trivial for anyone interested to fork, remix and adapt the notes. I don’t imagine a sudden outbreak of expander graph remixes, but maybe they’ll be useful to someone.

Apr 26 11

Polymath wiki logo

by Michael Nielsen

Many people have contributed striking logos for the Polymath wiki. It seems to me that there’s now enough suggestions to have a good conversation about which logo to use, and (perhaps) how the logos could be improved, if that’s what people want. I suggest having that conversation at the talk page for the logo.

Apr 15 11

Speaking about open science

by Michael Nielsen

Over the next few months, I’ll be giving talks to help raise awareness of open science in many cities in North America and Europe: what open science is, what the benefits are, what the obstacles are, and how we can overcome those obstacles.

If you’re interested in having me speak in your city, I’d like to hear from you. Please drop me an email at

As a sampler of the kind of talk I can give, see my talk at TEDxWaterloo. That talk was for a general audience – I’m also interested in speaking to audiences of scientists in all disciplines, to librarians, to people in technology companies and organizations, to people in government. I’d also love to meet people everywhere who are working on open science projects!

My speaking is being supported through a generous grant from the Information Program of the Open Society Institute, with assistance from York University.

As a result of this support, there will be no speaker’s fee. Furthermore, if your organization does not have a budget to support travel, that should not be a barrier.

Apr 7 11

Open science

by Michael Nielsen

The following talk gives a short introduction to open science, and an explanation of why I believe it’s so important for our society. The talk is intended for a general audience, and was given at the very stimulating and enjoyable TEDxWaterloo event held in the Waterloo region, just outside Toronto, in March of 2011.

Mar 3 11


by Michael Nielsen

I’m speaking today about open science at the TEDxWaterloo event, just outside Toronto. I’m really looking forward to the event, and to all the talks – I’m especially excited to see Abby Sunderland and Roberta Bondar. There will be live streaming for the event. I’m speaking around 1:20 pm (Canadian EST), if you’re interested. I don’t seem to be able to find a schedule for the other speakers.

Feb 28 11

“A change of perspective is worth 80 IQ points”

by Michael Nielsen

I was recently asked to prepare a two minute talk on a topic of my choice, for a small audience of about 10 people. Here’s what I came up with.

This is a one dollar bill [holds one up].

[Picking out two people in the audience] Alice and Bob – later in this talk I’m going to use the word “points”.

Can I ask you to pay close attention to what I’m saying, and when you hear me say “points”, stand up from your seat?

Will you do that for me?


Just to make it a bit competitive, I’ll give the first of you to stand up the dollar bill.

Many of us, myself included, often think of a person’s intellectual capacity as something that’s fixed, a feature of their innate makeup.

Intellectually, we may know that this is not so, but we take it so much for granted that it’s built into our language. We say “she’s very clever” or “he’s a bright guy” to describe people who we believe measure up when it comes to intellectual capacity.

A very different point of view has been put forward by the computer scientist Alan Kay. Kay’s saying is this: “A change of perspective is worth 80 IQ points.”

[We have a winner! Gives out the dollar to Alice]

Hmm. “A change of perspective is worth 80 IQ points.”

This is a saying that repays thought.

I just showed you in a very small way that it’s true: by changing Alice and Bob’s perspective on my talk, I’m betting they paid much closer attention to what I was saying. It’s not an 80 IQ point boost, true, but it’s still magical: a tiny shift in perspective can help us focus better. [* – but see footnote below, added in response to feedback]

It tells us that intellectual capacities aren’t innate, they can be dramatically changed by shifts in our perspective. And we can consciously develop strategies to shift our perspective. I don’t have time to review strategies for doing this, but I can mention one meta strategy, due to the musician Brian Eno and the artist Peter Schmidt. They made up a card deck of oblique strategies. It’s a deck of blank cards on which they’ve written many different strategies for solving problems. Most of the strategies are ways of changing perspective: “What would your closest friend do”; “work at a different speed”, etc. When stuck on a problem you can draw out a card, and get a a new perspective.

I think we should all make up our own decks of oblique strategies that we can use to get new perspectives, and to give our own intelligence an occasional boost.

[*] A commenter on Hacker News makes the good point that offering a dollar may cause some people to screen out everything except the word “points” – they may end up effectively stupider. Unfortunately, I can’t ask my audience members “Alice” and “Bob” if this is the case, because after preparing the talk I was asked instead to give an extemporaneous talk. But the talk can be modified to take account of this observation. Suppose instead that I’d offered a dollar to whoever provided a better summary of the talk at the end of my talk. I’ve been in analogous situations in the past, and know that it made me focus a lot better.

Feb 14 11

A logo for the Polymath wiki

by Michael Nielsen

The Polymath wiki needs a logo. Can you suggest or even design one?

Jan 28 11

The Third & The Seventh

by Michael Nielsen

I’ve watched the video below more than a dozen times over the past year. It’s a nearly fully computer graphics piece, entitled “The Third & The Seventh”, made by one person, Alex Roman (AKA Jorge Seva):

It is, I think, the most beautiful piece of art I’ve seen that was made during my lifetime. It’s not just the technical merit, although there’s plenty that’s jaw dropping. But even if was not CG, I would think it astonishing. He has an eye for beauty, and an ability to show things that I, for one, otherwise wouldn’t see. Amazing.

It’s worth watching in full screen, with headphones on. If you have a projector and a good sound system, I recommend watching it that way. Here’s the vimeo link, where he has links to other videos which share some information about how he made it. There’s lots of commentary about the video around on the web: I found this interview with Roman interesting.

Jan 22 11

Awesome grants

by Michael Nielsen

Beginning this month, every month the Toronto Awesome Foundation will give away $1,000 for someone to do something that’s, well, awesome.

Here’s how to apply.

There’s no reporting, no strings, no oversight. Just $1,000 to the winner to do whatever they think is worth doing.

Deadline for submissions is February 15.

Many questions are addressed in the links at the bottom of the announcement post.

There are other chapters of the Awesome Foundation around the world, and here are a few of the awesome things people have done: grown food to help keep their local food pantry stocked; helped get a Fab Lab started in Washington DC, and made invisible musical instruments. There are many more.

It’s going to happen every month, and you can keep track of announcements at the Toronto Awesome blog. I won’t post updates on my blog every month, but I will on twitter.

The money comes from 10 Trustees (I’m one), who each put up $100 a month. I think it’ll be fun, and it’s a good way of supporting people doing interesting things.

(Yes, it’s the projects funded that are supposed to be Awesome, not the trustees. Hah hah.)