This was the second week of geometry (following on from straight lines last week) and we looked at some of the properties of circles.
The theory of evolution by natural selection is, to my mind, one of the most beautiful and simple ideas that scientists have ever put together. I'm not a biologist - maths and astronomy are my primary interests - but armed with the explanatory power of evolution you begin to see the world around you differently. It explains so much based on so few principles.
Despite the resounding success of evolution and the multiple and independent lines of evidence, there are many people who still don't understand "get it". What they have in their heads is some misunderstood or misrepresented version of evolution. And of course that version isn't going to make sense.
That's when you get people trying to knock down this straw man version of evolution.
In this case evolution is being tied to an attack on atheism. It's a common approach from the religious right. In the video jumbling the lego and pulling out a fully working model helicopter is a variation of Fred Hoyle's attack on evolution. He didn't understand it either. They're attacking a nonsensical version of evolution and claiming it a success of common sense over the real theory.
If you have a few minutes to spare consider heading over to Stated Clearly. They've got a series of short, snappy videos on evolution, natural selection, genes and more. You'll get a clearly picture of how evolution really works. I particularly like the video about the evidence supporting evolution:
It's interesting to note a lack of videos (or websites) trying to knock down the correct version of evolution. They always go for some straw man version.
Usually I take the position that it's pointless arguing with everything (or anything) you see on the internet. But attacks on science and rational thought seem to be becoming more widespread; I'm seeing more videos like the one above being shared on social media than I used to. In an age where critical assessment of theory and data is more important than ever (in light of, for example, climate change and the politics surrounding it) then presenting clear and accurate expositions to the public is more important than ever. I think I must be getting a bit more intolerant of nonsense as I get older.
I took this picture of the Sun with a small telescope fitted with a solar filter earlier today. The giant sunspot group on the left has a dark core easily big enough to swallow the Earth. Astronomers have labelled it AR2192. At around 6am on Sunday AR2192 unleashed a powerful X-class flare. It wasn't Earth directed. However, the rotation of the Sun will carry AR2192 towards and Earth facing position in a few days and any flares of that magnitude are very likely to create good chances to see the aurora soon after that.
Although the Sun is at period of maximum, this has been the weakest solar max for more than a century. Big sunspots have been few and far between and the number of aurorae visible from the UK has not compared to the previous solarmax in 2000. I saw quite a number of auroras between 2000-2005 from Northumberland. There's still time to see more and hopefully the Sun will oblige with a big solar flare or two this week.
The first of two weeks of basic geometry began. Introduction to Cartesian coordinates in 2D and straight line equations and graphs. Click below to read further details!
Astronomers can get a lot of information about stars and galaxies not just by looking at the light coming from them but by "listening" to them as well. In the 20th century astronomers began building radio telescopes in order to tune into the signals coming from distant objects like pulsars (extremely compact stars spinning very quickly and beaming out radio signals) and galaxies. Giant dishes were built all over the world; in the UK the radio telescope at Joddrell Bank is probably the most famous example.
The signals collected by radio astronomers can be assembled into an image: a radio-map showing where powerful and energetic processes are taking place in the object being studied.
The images collected by radio telescopes suffer from blurring and distortion just as images taken with ordinary optical telescopes do. During the 1960s and 1970s astronomers and mathematicians came up with impressive techniques to improve the quality of the images so that more detail could be extracted and perhaps saving the cost of getting better pictures by building a bigger and better telescope. When digital imaging evolved in the 1980s and 1990s ordinary backyard astronomers with smaller telescopes were looking to get more out of their pictures too. For example, one of the tricks employed is to take lots of images of an object and then use a computer to combine them to get a better picture.
Medical radiography is the process by which the internal structures of the human body can be imaged using a source of x-ray radiation. The problems faced by radiographers taking x-ray images are similar to those encountered by astronomers looking deep into the universe. However, where an astronomer might take lots of images of a galaxy and then combine them together to give a better final image, a radiographer can’t do the same. Repeatedly exposing a patient to x-rays to get a better picture is not an option; a good picture has to be taken first time and using the lowest radiation dose possible. Radiographers have to walk a fine line to do this. Too much radiation is bad for the patient (but the x-ray image will be good) and although less radiation is preferable, the image quality will be poorer. The radiographers are also constrained by the x-ray machines themselves. Producing x-rays puts an enormous heat load on the machine components and so the exposure time must not be too long. This could be avoided by illuminating the patient using a larger x-ray source - but that would blur the image to an unacceptable level.
In applications such as mammography, radiographers are typically trying to see tiny microcalcifications less than one tenth of a millimetre in size. Microcalcifications can be often be benign or they can sometimes be the first sign of a process leading to breast cancer; x-ray images need to be as clear and sharp as possible to see microcalcifications. The images produced by radiographers come after a careful balance of factors relating to patient safety and image quality, but even so, some blurring remains.
It's almost ten years since my PhD at Northumbria University ended. For the best part of four years I'd been involved in studying the problems of image quality that I’ve described. The Regional Medical Physics Group at Newcastle General Hospital allowed me to take x-ray images of test objects using a decommissioned machine. I was able to adapt and apply some of the image processing techniques used by radio astronomers to improve x-ray images and make microcalcifications easier to spot. I also showed that the radiation dose to the patient could be reduced without sacrificing image quality.
Having studied image processing techniques I still use sometimes use them on my own pictures of the Moon and planets taken through my telescope with a digital camera. It's s also gratifying to see that the same mathematics can be used to solve problems connected with seeing distant astronomical phenomena as well ash the very small components of our own bodies.
Possibly the least observed meteor shower of the autumn has just begun. They are are the ε (epsilon) Geminids which reach a peak of activity on the 18th/19th. These are not the "Geminids" that astronomers get excited about every December! If you've been out observing during late October evenings then it's possible that you've seen a meteor from this shower already; records show that the Earth encounters the meteor stream from about October 10th to the 27th.
Under perfect conditions (no moonlight, radiant directly overhead, etc) then 1 or 2 meteors per hour can be expected! From the UK the radiant can never be overhead and in 2011 the gibbous moon is near the radiant of the shower...so observed rates will be much lower than 1 or 2 per hour. Also, the Orionid meteor shower (peaking on the 20th/21st) has a radiant nearby so meteors coming from that part of the sky may not necessarily be ε-Geminids.
Before you give up on this as a lost cause it's worth noting that the ε Geminids were probably discovered by local astronomer Thomas William Backhouse (1842 - 1920). That he was able to ascribe a radiant to meteors of such low frequency occurring close to the radiant of the Orionids is evidence of his meticulous observing skills. Backhouse of Sunderland was a renowned visual observer in the late 19th and early 20th century. He was one of the first astronomers to see Noctilucent Clouds and he brought the Gegenschein (a glow of zodiacal light directly opposite the Sun) to the attention of astronomers in the UK. The northeast of England can claim a couple of well known astronomers as its own; Sir George Biddell Airy (born in Alnwick) went on to become a mathematician and the 7th Astronomer Royal. And we adopted Sir William Herschel for the brief period he lived in Sunderland (although to be fair, he wasn't an astronomer at this point. Straws are being clutched.) The contributions of T W Backhouse are numerous but he now seems to be the forgotten astronomer of the Northeast.
Back to the epsilon Geminids. As the name suggests, the radiant is close to the star epsilon Geminorum in the constellation Gemini. See a map here. This year the waning gibbous moon (with 63% phase) is close to the radiant making observation tricky. Higher rates will be seen after midnight - particularly in the hours leading up to dawn when the radiant is high above the southern horizon. Don't hold your breath though.
Stars are classified into two types by astronomers. Population I stars - like the Sun, Betelgeuse, Deneb and many others - are found mostly in the spiral arms of the Galaxy. They are hot, luminous and formed in open clusters. Population II stars are older, less luminous and found in globular clusters and in the bulge at the centre of the Milky Way. Population II stars have fewer heavy elements in them that Population I stars. Since heavy elements are created within stars and scattered across the Galaxy by supernovae, it makes sense that Population I stars which have been around longest were formed in conditions where there was a lot less heavy elements.
The very first stars in the universe - born perhaps 400 million years after the Big Bang (when the universe was about 2% of its current age) would have formed from the raw ingredients created in the Big Bang. Those ingredients were hydrogen, helium and a dash of lithium. This first generation of stars is part of what astronomers call Population III.
The universe was a lot warmer when it was 2% of its current age. That coupled with collapsing regions that were almost entirely hydrogen and helium means that Population III stars could be much more massive than modern day stars. There is an upper limit to stars forming today - thought to be around 150 solar masses. By contrast Population III stars were monsters - with perhaps thousands or tens of thousands of solar masses.
Those first stars not only shone brightly it is thought the intense UV radiation from them shaped the early universe by reionising hydrogen which had previously recombined as the universe expanded and cooled after the Big Bang.
Population III stars would have lived fast and died young. Current theories suggest they would have exploded as violent supernovae within a few million years of forming. Perhaps those stars created black holes which were the seeds for the supermassive black holes in the centres of many galaxies today. Perhaps they didn't and we still need another explanation. There are no Population III stars in our universe now - conditions necessary for their formation don't exist any more.
At present there is no direct evidence of Population III stars. Hardly surprising really. To see them today we'd have to look deep into the universe to collect light which has been travelling from them for well over 13 billion years. During that time their light will have been redshifted so that they now shine in infrared and longer wavelengths. They must be very faint. However, there are hopes the James Webb Space Telescope will be able to see signs of our universe's first stars.
This week has been all about quadratic functions and equations. Read on below the fold for more details.
The first formal week of teaching has ended for my 14th cohort of Foundation students at INTO Newcastle University. The first week often feels like a bit of a drag; we're often skimming through topics that they should be completely familiar with. Not all of my students have arrived in the UK so I'm not launching straight into stuff that'll be assessed on the exams immediately.
Details of each session below the break.
Dr Adrian Jannetta
Guitar strummin' explorer of the universe. Mild mannered maths teacher by day and astronomer by night.