A couple of maths videos

In the last two weeks, I've been sent the following two mathematics videos - one serious, one not so much.

Can you conceptualise 10 dimensions? This could help.



Ever wondered what maths is really about? This is hilarious (well I think so...)

Ep 118: Astrobiology and the search for extraterrestrial life

Astrobiology is a fascinating and complex field of science. It is the study of the origin, evolution, distribution, and future of life in the universe, and is a relatively new field of science incorporating astronomy, biology, geology, palaeontology, physics, mathematics and other disciplines. It is even more fascinating given that we have never actually discovered life anywhere else in the universe!

Dr Carol Oliver is a science communication researcher working for the Australian Centre for Astrobioligy, whose key goals include contributing to the understanding of the orgin of life on Earth and to set an Australian life-seeking instrument on the surface of Mars.

I spoke to Carol about astrobiology and the SETI Project - the search for extraterrestrial life. Tune in to the podcast here (or press play below):



We covered a number of topics in our chat including:

• How does SETI actually look for extraterrestrial life?
  

SETI searches for electromagnetic signals from civilizations elsewhere in the universe - but where should they look? It turns out there is a handy hole in the electromagnetic spectrum coined The Water Hole - a band of radio frequencies between 1420 MHz and 1640 MHz. This is the band between the hydrogen line and the strongest hydroxyl spectral line, and is a very quiet region - there is little radio noise from space between these frequencies. It is theorised that alien communications could be found in this range because of its quietness and also because the combination of hydrogen and hydroxyl yields water, something considered vital for life. It is therefore a likely place for other life, which needs water to survive, to try and communicate. 

• The Fermi Paradox - The Fermi paradox asks the question, if there are other civilisations in the universe, why haven't we seen any evidence of their presence?

• Where is the best candidate for life in our Solar System? Is it Mars (more likely for microbial life) or perhaps a moon of Jupiter, like Europa? Was there life on Mars at any stage of its history?

• The concept of panspermia - that life on Earth may have originated elsewhere in the universe before coming to Earth, perhaps on an asteroid;
  

• The Kepler mission - this mission uses a space telescope to look for Earth-like planets and was launched in March 2009;

• The Drake equation - can we predict whether there are other civilisations out there using maths?

You can participate in the search for extraterrestrial life in the SETI@home project. In 1995, David Gedye proposed analysing radio signals from space using a virtual supercomputer composed of large numbers of Internet-connected computers - this is known these days as grid computing. The idea is to use the combination of many networked computers rather than a single supercomputer, and because of the vastness of space, the width of the electromagnetic spectrum and the fine resolution required, there is an awful lot of data to analyse! You can download the software needed at the SETI@home homepage.

Tune in to the podcast here (or press play below):

Swimming with Whales - video from Tonga

A few months back, I spoke to Scott Portelli about his experiences diving with whales in Tonga - see Ep 109: Tongan blowholes and whales. Scott has recently returned from Tonga, and took from breathtaking footage of the whales. Enjoy the video below.

Ep 117: The Science of Superheroes - Mystique (X-men)

Ever wondered whether it is scientifically possible to become a superhero?

In a new series of podcasts, Dr Christopher Pettigrew (aka Dr Boob*) and I are going to tackle this question. Chris is a post-doctoral researcher at the Department of Biochemistry in University College Cork, and in these podcast episodes - which we will publish more than a few times a year - we will uncover whether it is possible now to possess the powers of superheroes, and if we can't, whether in the near future we could engineer ourselves to become superheroes.

The first superhero we are tackling is Mystique from X-Men. X-men get their powers from an "X gene" that normal humans do not possess, and Mystique is a shapeshifter who naturally looks blue. Actress Rebecca Romijn portrayed Mystique in the X-Men films - I know I clearly remember the blue body-paint...

Mystique has a number of powers including:

• The ability to change skin colour;
• The ability to shape-shift - that is, change form;
• She can impersonate other voices;
• She can rapidly grow her hair.

Within nature, chameleons are able to change their skin colour to match their environment. There are also technologies under current development, such as metamaterials, that can be used to make something look invisible. Through a combination of genetic manipulation to activate melanocytes (and possibly chromatophores), and the use of surface coatings, it is not unforeseeable that we could develop human chameleons. The difficulty here lies in whether we can make a skin colour change a conscious decision - how can you wire up the body such that skin colour responds your thoughts?

The challenge of being able to impersonate another person's voice should be easy enough to conquer in the near future through a combination of electronics and simple mimicry. It is also possible to foresee rapid hair growth - this could be accomplished by rapid protein synthesis, such as in spider webs.

The biggest difficulty comes with the shape-shifting - how can one change their 3D shape?

Tune in to the podcast here (or press play below) to discover what scientific techniques we came up with to tackle the problem of scientifically engineering Mystique:



A few extra notes to explain some of the random comments in the show:

• Iva Davies is the front man of Australian band Icehouse;
• Shane Warne, Greg Matthews and Graham Gooch are all cricketers who advertised the hair-loss company Advanced Hair;
  

Let us know your thoughts on how we could scientifically engineer Mystique. We rated this a 7.5 out of 10 possibly for the next 200 years - if someone really wanted to, notwithstanding the ethical concerns along the way.

Also let us know which superheroes you would be interested in us tackling.

* From here on in, Chris will be referred to as Dr Boob - this nickname stems from the fact that Chris's PhD and some of his post-doctoral work has been into the study of breast cancer - yes, someone who is actually changing the world!

Ep 116: Terence Tao and Prime Numbers

Terence Tao is a Professor at the Department of Mathematics, UCLA and one of Australia's most acclaimed mathematicians. Indeed, he is arguably the world's greatest living mathematician. In 2006, he was awarded a Fields Medal, which is the top prize a mathematician can win, and at 24 became the youngest ever full professor at UCLA.

I recently went to Tao's Clay–Mahler Lecturer at UNSW, which was a fascinating look at prime numbers. I managed to grab Terence for a quick chat. Listen to this podcast here:



Primes are integers that can only be divided by themselves and one. For example, the number 10 can be divided by 1, 2, 5 and 10 - whilst the number 11 can only be divided 1 and 11. The first few primes are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 ....

One of the interesting things about the primes is that there is no known formula yielding all of them - you can't simply plug a few numbers into a formula to generate a list of the primes. However, on a large scale, their distribution can be modelled. The primes behave as if they are distributed pseudorandomly - see the picture on the right. Each dot in this Ulam spiral represents a prime number - you start in the middle, and wind outwards like a spiral - each dot is a prime, whilst empty space is a non-prime. Whilst you can see various patterns, nothing is predictable.

The prime number theorem says that the probability of a given number n being prime is inversely proportional to its logarithm. Euclid proved that there are infinitely many prime numbers way back in 300BC - see Euclid's Theorem for more. The current largest known prime was discovered in 2008 by the distributed computing project Great Internet Mersenne Prime Search and has 12,978,189 digits:

2^43,112,609 − 1.

Primes are very important for public-key cryptography - that is, the way your credit card numbers are encrypted in online transactions. The cryptography makes use of the fact that is difficult to factorise large numbers into their prime factors, whilst it is comparatively easy to multiply two large primes together. No efficient integer factorisation algorithm is currently known - in 2005 a 193-digit number was factorised, but it took 5 months.

Terence Tao, along with Ben Green, proved that the sequence of prime numbers contains arbitrarily long arithmetic progressions - this is the Green-Tao theorem. What this means is that for any number k, there is an arithmetic progression of primes k long. An arithmetic progression is one in which the difference between two numbers in the progression is the same. For example, the series 2, 4, 6, 8, 10... is an arithmetic progression with common difference 2. Green and Tao proved that such sequences exist within the primes for any length of series you want. For example, the series 3, 7, 11 is a prime sequence of length 3 with common difference 4. The series 3, 5, 7 is length 3 with common difference 2. The current record is a series of 25 primes.

I have just finished reading the excellent book The Music of the Primes by British author Marcus du Sautoy - I highly recommend it. It details the story of the Riemann hypothesis which is considered by many to be the most important unresolved problem in mathematics. A solution to the Riemann hypothesis could make an immense contribution to our understanding of the distribution of prime numbers. You certainly don't need to be a maths geek to understand this book - it is a great historical tale. You can buy the book from Amazon by clicking on the cover on below.

I chatted to Terence briefly after his talk, but being the amateur journalist I am, my recorder ran out of batteries! Not to fear, I have added an interview Terence did with Australia radio station Triple J's current affair program Hack - this interview has been reproduced with the permission of the executive producer, best brother James West - it's nice to have a proper professional journo in the family! The interviewer is Kate O'Toole. Listen to this podcast here:



God may not play dice with the universe, but something strange is going on with the prime numbers - Paul Erdos