I am a big fan of a TV show called Doctor Who, I’m sure a lot of you will know it too, but for those of you that don’t, don’t leave yet! The show revolves around a character called The Doctor who travels through space and time in a craft called the Tardis. Every time someone new enters the Tardis, they notice something. From the outside, the Tardis takes the form of a circa 1954 police box, but once you go inside it is much bigger! Even for those of you that do not watch the show, there is some interesting physics that could explain this behavior, so stick around!
Let there be light: Maxwell’s equations and electromagnetism
A couple of weeks ago, it was my birthday. And for my birthday, one of my friends decided to give me a delightful T-Shirt, seen below expertly modelled by yours truly.
The t-shirt references Maxwell’s equations, four equations created by James Clerk Maxwell, a Scottish physicist and mathematician, and were first published in 1873.
Today, we are lucky enough to have a guest post from none other than a finalist of a nation-wide Pokemon Championship, who has agreed to write on the maths behind this game, and a perfect strategy to capture the game’s hardest Pokemon. We’re sure that if you love either Pokemon or Maths (or both!), then you’ll love Bryn Brunnstrom’s article.
Like many other people born in the late 90s, the Pokemon franchise was a large part of my childhood. I watched the show, bought the toys, and played the video games. And like most people who played the Pokemon games, I was constantly infuriated by how many pokeballs it took to catch a legendary Pokemon. It was when I was trying to catch a mewtwo, somewhere around my 30th ultra ball that I stopped and thought “there has to be a better way.” Now, most people at this point would just go out, buy a gameshark, and give themselves infinite master balls, but I was guided by some misplaced sense of honour to do something infinitely geekier, and instead tried to figure out a perfect strategy.
Recently, we were lucky enough to attend a lecture by Imre Leader, Professor of Combinatorics at Trinity College, Cambridge, on “Pursuit and Evasion” games. In this post we will talk a bit about these games, Game Theory, and some of the problems that he came up with.
First let us explain the premise of “Pursuit and Evasion” games. It is essentially a mathematical version of Cops and Robbers. There are a number of points in a defined space, and some of these points are trying to “catch” other points by moving to exactly the same point, and others are trying to avoid being “caught.” I don’t like anthropomorphising the points by using the word “try,” so it may help if I then explain that one can formulate a series of problems based on the scenarios, and the most common problems are to come up with perfect strategies for either party in the game, or to prove who will win if both use a perfect strategy. Obviously the points themselves make no sort of effort or indeed care, but they act as pieces in a theoretical game played by mathematicians.
8 years after NASA asked for experiments and equipment for the mission, 3 years after the proposed launch and 8 months after the real launch, in August, 2012, we landed something on Mars. That thing was going to use its vast array of instruments to analyze all aspects of our closest planetary neighbor. That thing is a rover, and its name is Curiosity.
The mission has several aims, but its main goal is simple: to determine whether Mars has ever sustained life, or had the potential to sustain life. To do this, it is aiming to do several things.
- Gain a better understanding of radiation at the surface of Mars
- Investigate the mineral and chemical composition of Martian air and soil
- Discover the processes that have modified rocks and soil
- Investigate long-term atmospheric evolutionary processes
- Investigate the Martian water cycle and Carbon cycle
- Identify and analyse any organic compounds
- Investigate “building blocks of life”
- Identify any material that may be biological waste
Take a look around you. Anything you can see, the walls of the room you are in, the computer (or phone) you are looking at, even you, everything in you, is made of atoms. Little bundles of quarks and electrons. Lets zoom out a little. Look at the moon, atoms, look at the sun (don’t really, that is dangerous!), parts of atoms, everything you can see is made of atoms, or a least parts of atoms. So let me tell you something pretty amazing. Those atoms, and every other particle we have every discovered are only 4% of all the matter in the universe.
4 percent! That is a tiny number. So where is all the rest of it? Well, as it turns out, it just seems to be floating about the universe. The more complicated question is what it is. In fact, I chose to write about this because actually, we aren’t quite sure, but I will get to that later.
Last week, the news broke that Shinichi Mochizuki, a Japanese mathematician, has claimed a proof of the abc conjecture, otherwise known as the Oesterlé-Masser conjecture, causing widespread excitement among the mathematical community. But what exactly is the conjecture, and what does its proof mean?
The abc conjecture was, until last week, seen as one of mathematics’ greatest unsolved problems, and sometimes seen as the “Holy Grail” of Number Theory: so many open problems in Number Theory follow as nearly a direct consequence of the abc conjecture or can be reduced to it. Like many Number Theory problems, it can be stated in (relatively) simple terms, and you don’t need to be a highly specialised and educated mathematical genius to understand what the problem is. However, its proof is far from simple, and is only understandable to a handful of mathematicians in the world, and at the moment most likely only to Mochizuki himself. It may take a considerable amount of time for the 500 page document to be fully verified and confirmed correct, but today I’m going to discuss the problem and some of its consequences.
Today, as requested by Oscar Smith (@F15hb0wl) on twitter, we’re going to have a look at Tupper’s self-referential formula: what is it, how does it work, and is it really as amazing as it seems?
Let’s just start by saying what the formula is. It was devised by Jeff Tupper, and goes as follows:
And when this is plotted as a graph starting with N on the Y axis (N is a very large number printed below!), it produces the following graph.
N = 9609393799189588849716729621278527547150043396601293066515055192717028023952664246896428421743 507181212671537827706233559932372808741443078913259639413377234878577357498239266297155171737 1699516523289053822161240323885586618401323558513604882869333790249145422928866708109
863465033159410054974700593138339226497249461751545728366702369745461014655997933798537483143 786841806593422227898388722980000748404719 (a 543-digit number).
This week, we asked you to tweet us or send us a message on Facebook with questions you had about physics and maths. They could be anything, a term you had heard someone use before and didn’t understand or just something that had been puzzling you. You guys sent us a load and today we are going to answer some of them. Please keep the questions coming as we will continue to do question posts from time to time.
What is Quantum Physics?
(Asked by: Olivia Astles)
This seems to be a very common question when I tell people that I am interested in, and write a blog about, physics. Most people are familiar with the most basic physics. You drop something and it falls is an easy example we can give of physics in action, but once we add a fancy adjective, no one seems to have any idea. So let me give you the short and simple answer, before I go and tell you the long, complicated and definitely the more exciting one: Quantum Physics is the study of small things. Really it is called Quantum Mechanics, because it is the study, no not of small mechanics, but of the movement of small things. But isn’t the movement of small things pretty much the same as the movement of large things? If I throw a table-tennis ball, it will fall to the ground in the same way as a football would, after all.
In the lead up and throughout the London 2012 Olympics, one phrase stuck out: “Inspire a generation,” London’s motto and vision for the Games. There is no doubt that the Games can have a great effect on the nation that plays host to the world for that fortnight, but how long does this last? And does this “inspiration” turn itself into medals?
It is a well-known and publicised fact that a “home advantage” exists in the Olympics. Without fail, every host has performed better at their own Olympics than they could expect to at any other. This happens for a few reasons: extra motivation for the athletes to train in order to perform in front of a home crowd, increased investment in funding programmes by the government, and the support of the crowd on the day. However, Lord Coe’s vision for these Olympics have not been simply about the present, but about the future: to inspire youngsters to get involved in sports and push themselves to new heights. At every Olympics Games, the word ‘legacy’ is thrown about, but do the Summer Olympics create a legacy in terms of Olympics performance? And if so how long does it last?