Prime Numb3rs

Watching the latest episode of Numb3rs, I wanted to find out what Listing's Law was about.

I remembered that I'd heard some time back about a Numb3rs blog, which I had completely forgotten to check out. It's quite good.

Reading through it, I discovered that there's an even better one, set up by Stephen Wolfram (at least, it's hosted on his company's domain).

A Nice Blog

My mate Dave W sent me a link to an article today from Good Math, Bad Math, the blog of Mark Chu-Carroll, a computer scientist who works for Google.

While the specific article didn't get my juices flowing, overall it's a wonderful blog ... well, apart from the name (I hate how Americans abbreviate "mathematics" as "math", rather than "maths").

It's a nice mix of mathematics, computer science and weirdo bashing!

You Want Me To Do What?!

I'm quite amazed that I've not heard of this game show a long time ago. Apparently, it has run for over 4000 episodes across 50 series since 1982.

Called Countdown, it works like this ... the contestants have to concoct a calculation whose answer is a given randomly generated three digit number, using another six numbers of various sizes.

In this episode, the guy on the right comes up with a pretty impressive calculation.

Beautiful Visualisation

This is a short video explaining how Möbius Transformations that appear quite complex in the plane are equivalent to simpler manipulations of a projection from the plane onto a sphere.

Mathematics really can be beautiful sometimes!

This is a nice explanation of how to visualise higher dimensions. Very useful if you're trying to understand String Theory ... although, to do that, you'll also need to be clever, like John Baez :-).

Speaking of John Baez, here's a post of his I found that explains the Millennium Problems, specified by the Clay Mathematics Institute, who will pay $US1M for the solution to each.

Rubik's Cube Solving Robot?

The method to solve Rubik's Cube is well known and based on simple group theory. So, it's quite possible that this robot really does solve it automatically.

However, I can't help but think "What if they had the machine perform a random set of rotations beforehand and then this video is just showing the robot running those rotations in reverse?".

There is a flash and a pause in the action at one point, implying the robot is looking at the current configuration and working out the right moves, but I'm going to take it with a large grain of salt, anyway.

Nixie Tube Clock

The first programming I ever did was on a Canola 167P, when I was at high school ... sometime during the middle ages :-).

It displayed numbers via a set of 16 nixie tubes. So, this clock makes me feel just a little nostalgic!

Maths For Morons

I can't remember what I was actually searching for on YouTube when I came across this video, because the shock has burned away some of my brain cells.

This lady is on a crusade to rid US primary schools of what seem to be some pretty screwed up mathematics textbooks. Watch the video and you'll understand why!

Rudy Rucker

I've been a big fan of Rudy Rucker's work for many years, but I only knew of him as a mathematician, computer scientist and novelist.

In fact, I just received his novel, Mathematicians In Love from Amazon, last week ... and it went straight to the top of my pile of unread fiction. I should get to it around September, when I finish The Contortionist's Handbook, which I started over the Bah Humbug break :-).

Today, via Boing Boing, I discovered that he's also an artist! He currently has a small selection (and discussion) of his paintings on his blog at the moment.

More can be found in his gallery at ImageKind.

Happy 300th Lenny!

Leonhard Euler, the greatest mathematician of the 18th century was born on April 15th, 1707.

His achievements ranged across almost every field of mathematics.

He introduced the idea of function and much of modern notation, including that for trigonometric functions, the letter e for the base of natural logarithms, sigma for summations, and the letter i to represent the square root of negative one.

Euler developed the concept of power series, worked out that the sum of the reciprocal squares was pi squared on six, suggested the law of quadratic reciprocity, created graph theory to solve the Konigsberg bridge problem, defined the Gamma function, did important work in differential equations and the calculus of variations ... the list goes on.

His most well known result is probably

Once again, happy 300^th, Lenny !!

Speaking Of Calculators ...

... I rediscovered this wonderful article the other day.

Grapher is an amazing graphing tool that comes for free with all Mac computers.

The story in the linked article is almost impossible to believe, but true.

This incredible product was created by a couple of guys whose contract at Apple had finished, but they would sneak back into the office to work on it after hours.

In the end, they had an army of people, including various managers, helping them to get it shipped!

Happy Birthday!

According to this article, the HP35 electronic calculator is 35 years old this year.

It was Hewlett-Packard's first hand-held calculator. In fact, it was the first hand-held calculator in the world!

As with all good HP calculators, data entry was via Reverse Polish Notation, the choice of every serious arithmetician the world over.

When I was a young lad, I lusted after the HP67 and then the HP 41CV.

Unfortunately, I couldn't afford the price tag, so I ended up with a TI-59 from Texas Instruments, which was still pretty amazing for its time.

The only HP calculator I ever owned was an HP28S, which was truly amazing, but a bit bulky.

These days, my calculator is an HP emulator called MathU Pro installed on my Treo 680.

Happy birthday, HP35, my little friend!

E8 Has Been Cracked

I first heard about this on Adam Spencer's radio programme in the shower this morning (it's so nice to have a geek on my radio). Here's an article about it.

This is all approximately 7km over my head, but E₈ is a 248-dimensional Lie group, which is a non-finite group with a smooth topological structure ... I'll bet that clears it all up for you :-).

The article I originally cited links to this page that tries to explain what E₈ is in simpler terms.

Solving the problem required 77 hours of time on a supercomputer, working with 60GB of data (compared to approximately 1GB for the Human Genome Project).

This achievement will likely have ramifications in the understanding of String Theory. The image is a depiction of the 248 vectors that make up the root system for E₈.

Post-Pi Day

I'm definitely going to order one of these, ready for next Pi Day.

Also, Paul has a nice article on his blog, including this video. It's very amateur, but still cute.

Happy π Day !!

Today is March 14th or 3 14 as the yanks would write it. It's the closest any date in a calendar year gets to the value of Pi. So, it's been dubbed International π Day.

As it turns out, 2006 is the 300th anniversary of the first use of the symbol π was used to represent the ratio of the circumference of a circle to its diameter, in the publication, “Synopsis Palmariorium Mathesios”, written by William Jones in 1706.

In case you're at a loss as to how to celebrate, take a look at these Pi Day Resources and, of course, the obligatory Wikipedia article on π.

Rubik Cubism

I found this photo of some artwork based on Rubik's Cubes over at Core 77. Assuming they didn't just move the coloured labels, this would be quite hard to achieve.

It's hard enough working out the moves necessary to get a common colour onto a face; imagine what it takes to get some arbitrary set of colours!

This, and other Rubik's Cube based artworks can be found here.

Professor Max Kelly

I was very sad to read this evening that Max Kelly died on Australia Day.

I was lucky enough to have Max as my very first mathematics lecturer at Sydney University in 1979. He was a wonderful expositor and a bit of an eccentric. I have told stories of his lectures to many people.

His particular area of research was Category Theory, which looks at the generic properties of mathematical structures and their interrelationships. It's a subject which I find fascinating, but somewhat impenetrable, although I continue to live in hope that its mysteries will one day become clear.

It was pleasing to read that he was still engaged in mathematics right to the end, working on a number of papers with colleagues, as evidenced by this article over at the n-Category Café. You can tell from those letters that he was much loved.

Fluid Dynamics

I read this on Learning Curves (subtitled "Kind of Smart for a Girl), the blog of someone who appears to be a mathematics lecturer ...

"Recently I learned that my department has a 'Fluid Dynamics' seminar, to which I have not been invited. The 'fluid' in question is beer."

[I got to that blog via a post on Mathematics Under The Microscope]

Dollars & Sense

This recording of a telephone conversation a guy had with a number of staff, including two managers, at Verizon is a bit long, but very amusing.

Basically, he used roaming on his mobile phone while away in Canada. Prior to leaving, he rang Verizon to find out how much he would be charged per kilobyte for data access. They quoted him 0.002 cents per kilobyte.

However, when he received the bill, he had been charged 0.002 dollars per kilobyte. Every time he asked them to do the calulation they were multiplying 0.002 cents per kilobyte by the 35893 kilobytes, but then not reading it as cents, because it was displayed as 71.79 which looks like a dollars and cents figure.

It's not that they charged him the wrong amount (they didn't), but that they originally quoted him the wrong figure (which affected how he used his phone), and two managers, who work with numbers as part of their jobs, couldn't understand the difference.

Royal Institution Lectures

The 2006 Royal Institution Bah Humbug Lectures were given by Marcus du Sautoy, an Oxford professor of mathematics who wrote the book The Music of the Primes. This is, apparently, only the third time the lectures have been directly related to mathematics.

The five lecture series was entitled "The Num8er My5teries" and discussed such things as why cicadas only emerge from their holes every 17 years and sunflowers have 89 petals, the reason bees make honeycomb in the shape of a hexagon, the best tactics for surviving on a game show, the German enigma codes and why weather prediction is so hard ... how can you still believe mathematics is boring :-) ?!

The Guardian's education supplement ran a nice interview with du Sautoy a couple of weeks ago.



Update: I found the article du Sautoy wrote for Seed magazine. In it, he explains the connection between the number 42, mentioned in the Hitchiker's Guide to the Galaxy, quantum mechanics and prime numbers.