Walking Randomly

It won’t be long before I give up Windows Mobile for good in favour of the HTC Hero and the Android operating system but before I do I thought I would take one last look at what’s out there in terms of mathematical software for the Windows Mobile platform.  I last looked at this back in early 2008 but one or two things have changed since then.

SMath studio is a very nice free maths application that is being developed by Andrey Ivashov for Windows and Linux (via Mono) desktops  as well as Windows Mobile handhelds.  It installed perfectly on my HTC TyTn II and offers an experience very similar to a simplified version of PTC’s Mathcad and can even handle Mathcad’s .xmcd file format in some cases.  One cool feature to consider is that you can develop calculations on the desktop version (screen shot below) and then carry them around, edit and run them on your Windows Mobile phone (screenshot above).

Andrey has recently released version 0.82 of the software and there are some active forums over at his website in both English and Russian where you can discuss it.  This software is well worth watching in my opinion.  Although I won’t be able to follow the Windows Mobile versions after next week, I’ll definitely be keeping an eye on SMath for Linux and Windows and hope to bring a more detailed review to you at some point in the future.

Some links that I found interesting recently:

Scientific Computing

• Getting started with the SciPy (Scientific Python) library
• Wolfram Demonstrations exceeds 5000 submissions
• Thesaurus of Mathematical Languages

General geekery

• 100 things your kid may never know about
• The periodic table of awesome

It never ceases to amaze me how researchers manage to find connections between the most seemingly disconnected of things.  A researcher at Manchester University, Bill Lionheart, conducts research into the mathematics of ‘seeing inside things with electricty’ and over at his blog he has a great story which basically says that a certain breed of fish are significantly better at this particular branch of mathematics than we are.

One particular quote I love is “Weakly electric fish are really interesting to us because they have the ability to solve a challenging mathematical problem when catching their food.” as it made me wonder how students would feel if they had to solve challenging mathematical problems in order to get their food :)

As I navigate through the twists and turns that life brings, I occasionally come across people who seem to be working on some higher plane to everyone else.  Richard Feynman was one of those people.  Richard Kac couldn’t have put it better when he said of Feynman

There are two kinds of geniuses: the ‘ordinary’ and the ‘magicians’. An ordinary genius is a fellow whom you and I would be just as good as, if we were only many times better. There is no mystery as to how his mind works. Once we understand what they’ve done, we feel certain that we, too, could have done it. It is different with the magicians. Even after we understand what they have done it is completely dark. Richard Feynman is a magician of the highest calibre.

I never met Feynman of course as he died of cancer back in 1988 when I was only 10 but I have read masses about him.  I first learned about him from my high school physics teacher who lent me a book called Surely You’re Joking Mr Feynman which contained hardly any physics but a lot of stories about a man who was intensely interested in the world about him.  I’ve bought that book several times now because I keep lending it to people who go on to lend it to people!

Not only was Feynman a Nobel prize winner but he was also a first class physics teacher and over 40 years ago he delivered a set of introductory lectures at Caltech which are widely considered to be among the best ever written.  These were later converted to a set of books that have been continuously in print ever since and tend to be on the bookshelves of many people interested in physics.

In 1964 Feynman delivered a different set of lectures called The Character of Physical Law at Cornell University.  This set of lectures was recorded by the BBC and it turns out that Bill Gates recently bought the rights to them.  In a wonderful display of philanthropy Mr Gates has made these lectures freely available to the world on Microsoft’s Project Tuva site.

Sadly, however, the lectures have been delivered via Microsoft’s proprietary Silverlight system.  This is just fine if you are a user of Windows or Mac OS X but Microsoft hasn’t released Silverlight for Linux operating systems.  The practical upshot of this is that if you run Linux on your computer then you can’t watch the lectures.  There is a community effort which is producing a free version of Silverlight (called Moonlight) but sadly Project Tuva doesn’t work on systems running Moonlight (at the time of writing at least).

Not all is lost though thanks to YouTube.  Many of the Feynman lectures have been split up into bite sized chunks and made available by users such as this one.  I’ve just finished watching the first lecture and loved it :)

I’m a lucky guy!  I work for a major UK University and one of the perks of the job is that I (along with every other member of the University) get access to a massive array of academic journals and this is close to priceless as far as I am concerned.  I’d rather take a salary cut than lose that particular perk (shhhh, don’t mention this to my bosses) and I don’t even do any formal research!

I have been blogging for almost two years now and one thing I have learned from the whole experience is that the world contains legions of amateur scholars – people who do research for personal rather than professional reasons.  These scholars (and I like to think I am one of them) don’t want to publish papers or get qualifications, they simply want to learn about and discuss whatever subject takes their fancy.  In my case I focus on subjects such as mathematics and physics since they are (and always have been) the subjects that float my boat and they are also the subjects I studied both at school and at University.

Without having the journal access that I get via my employer I would find this hobby significantly more difficult and expensive to pursue.  Occasionally I get to see just how expensive it would be when I come across a journal which my University doesn’t have a subscription to.   One such journal is Physics Teacher and earlier today I wanted to get hold of a 2 page article published back in 1981 – almost 30 years ago.  The cost was $18.

$18 for two pages of work almost 3 decades old and I wasn’t even asking for it to be sent to me printed on gilt edged paper.  All I wanted was a pdf file which would cost almost nothing to send me.  For comparison, that $18 could get me one of several different maths books on my Amazon wish list.  If the journal had made it $5 or less then I wouldn’t be writing this – I would have just bought it.

I know that journals aren’t charities but surely this kind of asking price is simply too high.  If the work had only been published recently then I might be able to understand it – that $18 would go towards paying for editorial staff, peer review, publication etc but surely older articles aren’t worth this amount since all of their costs were covered years ago.

Why not learn from something like iTunes and make the cost of many articles so low that people don’t even stop to think if they want to spend the money or not?  If every article in Physics Teacher more than 25 years old only cost $1 then I (and probably many others) would buy lots of them and the journal would get a decent amount of cash.  Bandwidth is cheap so it wouldn’t really cost any more to send 20 files then it would to send 1 but I am a lot more likely to spend $20 on 20 files than $18 on 1.  Would it be better to charge the higher prices for the first 10 or 20 years from the publication date and then drop to $1 or so for older articles?

I’m not just picking on Physics Teacher though – many other journals seem to have a similar policy.  What do you think?  What would the best business model be?  Would you buy more journal articles if they only cost a dollar?

While tidying up the attic the other day I came across a very nice looking wooden set of tri-Dominos that someone had given me as a Christmas gift many years ago. I have no idea where it came from but it looks identical to the set below.

I enjoy playing traditional board games whenever I have the time and so my wife and I took a quick look at the instructions and played a couple of games.  It turned out to be good fun – much more interesting than traditional Dominos which we also play from time to time. The scoring involves a reasonable amount of simple arithmetic so if you have a child and want to get them to practise addition by stealth then it might be worth buying a set.

Amazon sell a Tri-ominos set (pictured below) that isn’t as nice as the wooden set I have but it’s quite cheap and probably worth buying if you’re curious. Let me know if you’ve played and enjoyed this game.

Finally, does anyone know of any computer implementations of tri-ominos in any format (Windows, Linux, Android, Windows Mobile, iPhone..whatever) – I couldn’t find one at the time of writing.

Resources

• Buy Tri-ominos from Amazon (and help support Walking Randomly)
• How to play Tri-ominos from Pressman Toys
• Triominoes on Wikipedia

My favourite free mathematics package has seen yet another relase. Released back on Thursday June 9th, version 4.1 of SAGE Math includes a nice array of new features, speed-ups and bug-fixes. Head over to the version 4.1 release tour for more details.

One of the things that I like about each new release of SAGE is that there is always something for everyone – no matter what their level of mathematics. For example, release 4.1 includes advanced functionality for constructing elliptic curves and also adds support for constructing irreducible representations of the symmetric group. On the other hand it also includes some new Sudoku solvers, faster integer division and improved histograms.

If you are a user of SAGE then feel free to say hi in the comments section and let me know what you use it for.

I had a query from a MATLAB user the other day and I thought I would share it with the world just in case it turned out to be useful to someone.  She had some data in a cell array that appeared as follows

data =

    '-0.000252594'
    '-0.788638'
    '-1.14636'
    '-1.15374'
    '-1.15474'

I’m not sure how she ended up with her data in this form but that’s not important here. What is important is that she couldn’t calculate with it in all the ways she was used to so what she asked was ‘how do I convert this cell array to a matrix?‘

It turns out that this is relatively easy to do since this particular cell array has a very simple form.  If you want to follow along then you can create an identical cell array as follows

data={'-0.000252594'; '-0.788638'; '-1.14636' ;'-1.15374' ;'-1.15474'}

data =

    '-0.000252594'
    '-0.788638'
    '-1.14636'
    '-1.15374'
    '-1.15474'

Let’s check that this really is a cell array using the iscell() function

iscell(data)

ans =
     1

Looks good so far. So, to convert this to a matrix all you need to do is

matdata=cellfun(@str2num,data)

matdata =
   -0.0003
   -0.7886
   -1.1464
   -1.1537
   -1.1547

the variable matdata is a standard MATLAB matrix and to prove it I’ll add 1 to all of the elements in the usual fashion

matdata+1

ans =
    0.9997
    0.2114
   -0.1464
   -0.1537
   -0.1547

That’s it! If only all queries were that simple :)

A commercial statistical package called Genstat appeared on my radar fairly recently and I have just discovered that a new version of it was released last month.  The list of new features is here.

My knowledge of stats is pitiful at the moment (I am working on it though) so I won’t even attempt a review but will, instead, point you to one by John Wass over at ScientificComputing.com.

A full 30 day trial is available from Genstat’s website (you’ll need to watch a video before getting access to the trial).  Feel free to drop me a comment about this software if you know anything about it.

Update 9th July 2009: As someone pointed out to me via email – Genstat 11 was released in June 2008 and not last month as I stated above.  Sorry for any confusion this might have caused.

Take a wheel of radius 1 and set it rotating about its axis with a frequency of 1 turn per second. Attach a second wheel, of radius 1/2, to the circumference of the first and set this second wheel rotating about its axis at a frequency of 7 turns per second. Finally, attach a third wheel to the circumference of the second and set this wheel to rotate about it’s axis at a frequency of 17 turns per second.

Now, consider a point on the circumference of the third wheel. What pattern will it trace out as the three wheels rotate?  Click on the video below to find out.

I first came across this idea in a Wolfram demonstration by Daniel de Souza Carvalho.  Daniel’s demonstration focused on the fact that you could write down the equations of these curves in two different ways. If the wheels are rotating with frequencies a, b and c respectively then you can either describe the corresponding curve with a pair of parametric equations as follows:

or as a complex valued equation:

This was a nice demonstration but I wanted to see what sort of patterns I could get by changing the frequencies of the wheels. So, I downloaded Daniel’s demonstration, added some sliders and tick boxes and then uploaded the result. Wolfram Research cleaned up my code a bit and the result was published as the Wolfram Demonstration Wheels on Wheels on Wheels.

It turns out that you can get a LOT of different patterns out of this system as you can see below.

These systems were considered in the paper “Wheels on Wheels on Wheels—Surprising Symmetry,” Mathematics Magazine 69(3), 1996 pp. 185–189 by F. A. Farris. In this paper, Farris showed that the resulting curve exhibits m-fold symmetry if the three frequencies are congruent (mod m).

Can you think of any interesting variations to this system?

Update (6th July 2009): Taki has written another version of this demonstration which includes an animation of the wheels and also looked at an example with four wheels over at his blog, Mesh Mess.