Cosmic Horizons

OK, it's been a very good week (for reasons that will become clearer in the near future) and so I am going to take a breather for half an hour for a little recreational mathematics. The question is all about catching the bus. One good thing about living in Sydney, which I've noted before, is that it easy to get to see international rugby at the Olympic Park. An excellent free bus service is provided to bring people in from the far-reaches of Sydney, and then take them home again. It is quite impressive that it works, with tens of thousands of people pouring out of the grounds and onto buses quite efficiently. So, I've been thinking - If people turn up at a bus stop at a certain rate, and buses arrive at a certain rate, then what do we expect the number of people on each bus to be? OK, the question is easy if the people arrive at a fixed regular intervals, as do the buses. But we are not here to do the easy things. Being a physicist, we start by simplifying the p...

A very quick post tonight, but I've had an article published in The Conversation titled Open-access science: be careful what you wish for . This is a word of caution on the push to make all science, bother the publications and data paid for with public money, available to all. To cut a long story short, I fully support this move. I would love my science to be read by all (well, at least those who are interested :). The caution is, however, that doing this costs. The current funding model is a bit busted; scientists need to publish in established journals, as articles that do not appear in the "highest impact journals" are not considered as important. But the journals are owned by big publishing houses, and so libraries need to pay for access to the papers, often to see the science generated by their own researchers. It's a bit of a complex mess. Anyway, my caution is that while the funding for open source science has to come from somewhere, it is not good...

The newspapers are ringing with the latest exploits of "magician" David Blaine. To a physicist, hopefully those who recently completed my first year course on electromagnetism, it is obvious that this story is little more than "man sits in a fancy Faraday cage for a while". But that's not the point of the post. It's the text accompanying the image. And specifically the phrase "a million volts of fiery electric current"! ARGH!!! I know Joe Public does not care, but such a sentence causes the inner guts of those with a passing knowledge of physics to twist in an awful pain. Put simply, voltage (measured in volts) is not the same as current (measured in amps). If you are being electrocuted, the difference may not bother you, but the fact that smoke is coming out of your ears is not an excuse for physics illiteracy. Right. This is going to be a short post, as I have lots to do, but let's use a gravitational analogy. Let's imagine...

I've written before about The German Tank Problem . Basically, it's a problem in which you try and estimate the number of tanks being produced by the enemy, based upon the serial numbers of the ones that were knocked out. This was a real problem from World War II, but is now often sold as the taxi problem, in case you are too sensitive to think about tanks. The moral of the story is that the spooks and spies were wrong, and the mathematicians right. Yay!!! I was happy with this until my post on this (which was almost a year ago). My ex-student, and Bayesian extraordinaire, Brendon Brewer , said something that bothered me. Namely, the chance of seeing a tank depends on the number of tanks, with more chance of seeing one if there are more of them (obviously!), and this seems to cancel out the effect of knowing the serial numbers of the tanks. So how could it work. I had a good week and so decided to return to the problem. Let's start you being a battlefield intellig...

It sometimes comes as a surprise to non-astronomers that one of the hardest things to do when you look at the Universe is to measure distances to objects out there. People have head about the almost 100 year battle to measure Hubble's Constant , but what people fail to realise is that all of the uncertainty was in measuring distances; how far is it to that galaxy, or that supernova, or that star. Books have been written about the titanic struggle of measuring and calibrating distances in the Universe, so I am not going to cover that here again. But let's talk about my (and my collaborators) effort in the field. I've written before about some work I've been doing with PhD student, Anthony Conn, using the tip of the Red Giant Branch to measure the distances to the dwarf galaxies orbiting our nearest neighbours, the Andromeda (M31) and Triangulum (M33) galaxies. It's easy to understand the method, basically it says that things are fainter when they are further...

It's early on Sunday morning, and I'm up and about due to the chorus of Sulphur-Crested Cockatoos that often make my suburb sound like the depths of Jurassic Park . While lying there in the din, I was thinking about yesterday's post, and found myself pondering the following: "What would happen if I stopped using a cube, but instead had two parallel sheets? Now, in this case, I don't have a closed surface anymore, but if I make my sheets infinitely large, I am guessing that the total integral over the two sheets would converge to the result expected by Gauss's law." Can you see why? Anyway, this is not going to be a long post, as I haven't had any coffee yet, and have a paper to deal with, but I am very quickly going to scribble down the solution. Basically, I am going to replace my square piece with a circle, and then make the circle infinitely large in radius, and this will be the same as making a square sheet infinitely large. Note to mathmo...

It has been a busy week, with a talk to the Macarthur Astronomical Society on Monday, and to the Astronomical Society of New South Wales last night. And if you were in Blighty on Wednesday at 4am, you would have heard me join dr karl on Radio 5 Live's graveyard shift to talk about why high speed protons don;t become black holes, but that is the topic for another post. As I mentioned, I've recently been teaching electromagnetism, and I like to take a little bit of a side-ways glance at derivations and equations. Why? Because sometimes those given in text books can appear a little too idealized or simplified. One of the things that you have to talk about in electromagnetism is Gauss's law. Mathematically, Gauss's law can seem quite intimidating to a first year student, even those in our advanced class, but let's take a look at what it means in a simplified sense, and then something a little more complicated. Right, the maths (and to our American cousins, it ...