Why we can't really see the stars

If you're like me, you enjoy looking up at the stars at night and thinking about how far away they are, and such things. Recently, though, I started wondering why there aren't any high quality images of stars other than our sun. The star with the largest apparent size from Earth (after the sun, again) is currently believed to be R Doradus - and the photograph of that on Wikipedia isn't exactly spectacular:

I don't know anything much about astronomy so this seemed strange to me. If I can see the stars with my naked eye, what's to stop someone with a high powered telescope zooming in and getting good details?

The reason, as I found out, is that stars are much, much further away than they look when viewed with the eye. The main reason for this is that every lens, including the human eye, has a limit to the resolution it can see. This is known as the 'diffraction limit' because once light travels through an aperture (in our case, our pupils), the waves spread out before hitting the detector (our retinas), blurring each point into what is called an Airy disk. For a human with 20/20 vision, the Airy disk is about an arcminute in size - so our sight can resolve something 1 inch in diameter from about 90 metres away. Every star we see looks 'blurred' to about this size - which is why all stars in the sky (except, once more, for the sun) look the same size.

To be able to escape the diffraction limit, we need a much larger lens - which is why we use telescopes. However, once a telescope reaches about 10cm in diameter, another effect stops us from seeing the star - a phenomenon known as 'astronomical seeing'. This is the effect caused by variations in temperature and wind speed in the atmosphere causing the light to bend on the way to the receiver. The 'twinkling' that can sometimes be seen in stars is due to this effect, as the apparent position of the star moves with the constantly changing conditions in the atmosphere.

At a good astronomical site, astronomical seeing will allow for a resolution of around 1 arcsecond. As illustrated above, this is roughly sixty times smaller (in blue) in length than human vision (in white) but even this is not enough to see a star. Below is the resolution with atmospheric seeing in blue again, but with R Doradus pictured in red - with a radius of 0.057 arcseconds. The only reason that ground-based telescopes are able to image R Doradus at all is by using adaptive optics - this attempts to compensate for the atmopsheric effects, and even this technology is currently only just enough to get a picture.

A large enough orbiting telescope would get past both of these effects - the Hubble Space Telescope is still one of the largest with a mirror 2.5 metres in diameter*, which translates to a 0.05 arcsecond resolution for visible light: only just enough to see R Doradus. 

So humanity has a long way to go yet before we can really see the stars. Now if only I could afford a telescope...

* the largest, the Herschel Space Telescope, has a diameter of 3.5 metres.

Crappy days

Some days you just know are going to be long and painful. I have a few strategies to survive mine:

1. Sugary substances

Chocolate in any form is always appreciated, but on cold, miserable winter days a nice warming hot chocolate or Milo (link for those not in Milo-drinking countries) can make it all seem a little better.

2. Cute things on the internet

It's an internet cliche because it works - my girlfriend (who now has a blog!)  is usually my main source of such links. However, I always keep this one on standby for particularly bad days - it takes a cold soul indeed not to find this one cute:

3. Puzzles

When it's hard for me to concentrate on things I should be actually working on, I sometimes find doing some puzzles a good way to keep my brain ticking over. My current favourite is Project Euler (warning - non-programmers will really struggle!)

4. Music

I'm regularly surprised by how much music can help turn a mood around or focus the energies - I've never been much of an electronica fan, but iriXx's work has given me some of my most productive afternoons. I tend to listen to the same music over and over again before moving on to another artist - one on my current high-rotation list is Tasmanian act Enola Fall.

5. Writing

Sometimes it's good just to blow off some steam - as screaming in my office would probably cause some distress in my nearby colleagues, writing things down is a little safer. Chatting to friends online, writing blog posts, writing out to-do lists and plans - it all helps!

Mathematically possible - GWS making the AFL finals

(Update: thanks to Gazza White and the AFL subreddit for linking my post - it's already by far my most popular blog post!)

Towards the end of a sporting season, it's not unusual to hear the commentators call a team a "mathematical" chance to achieve some target - be that winning a premiership, making the finals, avoiding relegation, whatever. What this means is that there is at least one combination of events (usually discounting other teams being disqualified) that could bring it about, but it's almost vanishingly unlikely to occur.

Very seldom is this a more appropriate term than for the current chances of Greater Western Sydney getting into the top 8 and making the AFL finals this year - so much so that commentators probably aren't even aware that it is a mathematical possibility.

Here is the current AFL ladder as of the end of Round 15 (courtesy of FanFooty - note that the official AFL ladder is not actually up to date!)

Team	P	W	D	L	For	Agt	Percent.	Pts
Hawthorn	14	12	0	2	1645	1167	141	48
Geelong	14	12	0	2	1556	1216	128	48
Essendon	14	11	0	3	1483	1142	129.9	44
Sydney	14	10	1	3	1379	1048	131.6	42
Fremantle	14	10	1	3	1201	954	125.9	42
Richmond	14	9	0	5	1387	1190	116.6	36
Collingwood	14	9	0	5	1321	1225	107.8	36
Pt Adelaide	14	8	0	6	1317	1158	113.7	32
West Coast	14	7	0	7	1404	1277	109.9	28
North Melb.	14	6	0	8	1435	1210	118.6	24
Carlton	14	6	0	8	1331	1219	109.2	24
Adelaide	14	6	0	8	1288	1228	104.9	24
Gold Coast	14	5	0	9	1197	1341	89.26	20
Brisbane	14	5	0	9	1133	1451	78.08	20
W. Bulldogs	14	4	0	10	1102	1433	76.9	16
St Kilda	14	3	0	11	1129	1337	84.44	12
Melbourne	14	2	0	12	981	1775	55.26	8
W. Sydney	14	0	0	14	1003	1921	52.21	0

In green is our team of interest - Greater Western Sydney. They are currently winless at the bottom of the ladder, 8 wins behind the lowest top 8 side (Port Adelaide - in red). Unfortunately for GWS, there are also 8 games left in the season, so one thing is immediately clear: GWS must win all 8 of their games, and Port Adelaide lose all 8 of theirs, for GWS to be any chance of making the finals (the two teams do not play each other, so this accounts for 16 separate games). If this happens, the ladder looks like this:

Team

Points

Hawthorn	52
Geelong	52
Fremantle	46
Essendon	44
Sydney	42
Richmond	36
Collingwood	36
Port Adelaide	32
GWS	32
West Coast	28
Carlton	28
Adelaide	28
North Melbourne	24
Gold Coast	24
Brisbane	24
Western Bulldogs	16
St Kilda	16
Melbourne	8

This on its own is still not enough to guarantee GWS a place, however - there are 9 other teams on the ladder that are also striving for a spot in the top 8. For GWS to make the finals, none of these sides can finish with more than 32 points (8 wins) at the end of the season. Therefore every game that involves one of these sides - 46 games, excluding the 16 already accounted for by GWS and Port's games - can make or break GWS's finals chances. In particular, West Coast, Carlton and Adelaide cannot get any more than 1 win for the rest of their remaining games. In fact, there are only 10 games that don't affect GWS's chances - the games between top 7 sides, who already have more wins than GWS can possibly get and are guaranteed to place above them on the ladder.

Using a computer to calculate the possible combinations in which this could happen comes up with 150,744 ways for GWS to place equal 8th. Even assuming that all teams will have a 50-50 chance of winning each game for the rest of the season (discounting draws), an assumption which is very kind to GWS to say the least, this would give them a 150,744 / 2⁶² = 3.27 in a hundred thousand billion chance of finishing equal 8th on points.

To put this into perspective, imagine a lottery where you have to pick which 6 balls out of 40 will be drawn - a 1 in 3.8 million chance. Now imagine only entering that lottery twice in your life - and winning both times. Even THAT would be twice as likely as GWS finishing equal 8th, on a good day.

Notice that I've mentioned GWS finishing equal 8th. Even this herculean feat doesn't guarantee them a place - in the very best case scenario of the 150,744, there will be 6 teams vying for 8th place on 32 points (on average in these scenarios, there will be 9.6). So GWS's best-case scenario looks like this:

Team Points
Geelong	76
Fremantle	66
Hawthorn	64
Essendon	60
Sydney	54
Collingwood	52
Richmond	48
Port Adelaide	32
Carlton	32
Adelaide	32
Gold Coast	32
Western Bulldogs	32
GWS	32
West Coast	28
North Melbourne	28
Brisbane	28
St Kilda	28
Melbourne	28

To make the finals, from this point they need to gain a higher percentage than the other 5 teams. Currently, they are on 52.21%, having scored only 1003 against their opponents' 1921 points. On the other hand, their currently best-placed opposition, Port Adelaide, has a percentage of 113.7%, scoring 1317 to their opponents' 1158.

This informative site tells us that the average score in an AFL this season so far is 92.43, and the average margin for a game is 36.92. So a roughly "average" game of AFL would involve the winner with 110.89 points and the loser with 73.97. If we assume that GWS's 8 winning games follow this scoreline, as well as Port's 8 losing games, then we end up with GWS having an improved percentage of 75.22% and Port with a dented percentage, but still plenty enough for finals, of 93.33%.

So, obviously just winning is not going to be enough for GWS to leapfrog Port and its other finals rivals. Let's assume the same as above, but this time work on the assumption that GWS has somehow found a secret scoring weapon and is able to rack up ridiculous scores while keeping their opponents to an average score of 73.97. They would need to be able to score, on average, 167.78 points in order to beat Port's percentage - an average winning margin of 93.8 on their run home - and hope that none of their other rivals have had a similar late-season percentage boost themselves. I'll leave it to someone else to work out how often a team has won 8 games in a row by an average margin of at least 93.8 in AFL history.

Our conclusion: is it possible for GWS to make the finals? Mathematically, yes. Are they going to make the finals? No. But it'd be a hell of a story if they did!

Music

After the joy of launching an EP (look to the right of screen - that's my EP), my rock music career has quietened down substantially in the last few months. Initially, I wanted to concentrate on writing songs suited more to my band (The Solution), but the band has itself faded into the background a little after our bassist moved to the other end of the state for work. We're still getting the occasional practice session in, and are steadily working towards recording an album, but it's left a lot of time in which to ponder other musical directions.

One of these has been the choir I joined last year - the Tasmanian Song Company. When I joined, I sang in the tenor section but as the number of males in the group has grown (due in part to some of my friends joining!), it became obvious that we needed more basses so I moved there instead. As time's gone on, I've found my involvement growing to the point where I found myself joining the committee and helping out on a regular basis. I've never been on any kind of committee before, but this one involves cake and cups of tea so it can't be all bad!

The other way I'm keeping myself going with music is busking. It had been a long time since I busked, so a month ago I put together a collection of covers and made my way out to Elizabeth Mall - and I've been trying to get out there every week or so. It's a great way to practice performing in front of people - something I sorely needed when I was a beginning musician years ago, but just as useful now that I've got a little more experience and want to keep my skills under pressure fresh.

Though I'm fortunately not broke enough to need the money from busking, I still find it a good way to "keep score" of how well I'm going - of course, it doesn't hurt if I make enough to buy lunch and have some change for parking meters! Over the weeks, though, I've found the money really isn't a good measure of how people are reacting to my music. A couple of weeks ago, I went out on a crowded day and only made a couple of dollars despite singing my heart out, and I was feeling pretty miserable about the whole affair. Then, in the middle of my set, an obviously down-and-out, slightly elderly lady came up to me and said very sincerely "Lovely singing - I'm sorry I don't have any money to give you."

Since then, I've gotten far more joy out of playing music I love out in the winter sun, getting a smile of recognition or a kind word from a passer-by, or watching small children dance gleefully in front of my guitar case. Sometimes it doesn't hurt to be reminded of the old cliché that money doesn't buy happiness!

At the End of the Day

The view from my window

It's amazing that I've avoided posting for three months, thinking I'd have nothing interesting to say, considering how much has happened in this time. This is probably the most appropriate time to break my silence - I'm sitting in a cramped hotel room in London's West End listening to the noises of the city* on the last night of my two week trip to England before coming home for Christmas, and seeing out what has very probably been the most eventful year of my life so far.

I'm here because I was lucky enough to be awarded the Southwood Prize, one of the British Ecological Society's prizes for young scientists publishing in their journals. The very pretty but no less heavy piece of perspex is ensconced in my backpack, along with numerous trinkets, awaiting the trip back home. I've met a lot of wonderful people, and been amazed at just how approachable, friendly and above all human the people occupying the dizzying heights of the academic world are. It's wonderful to know that so many people who, just a few days ago, were strangers in a strange country are now my friends and colleagues.

I've also fallen a little in love with Europe, and England in particular. After a couple of days in London and Paris, I joked about seeing "yet another bloody arch"**, but there's something that never gets old about seeing avenues full of grand old buildings full of character and history everywhere I look. And though while walking around I've seen plenty of homelessness and disenchantment on the streets in Birmingham, London and Paris, I've also experienced a little of the friendly, self-effacing nature of the average Briton***. Staying in Oxford with my friend Steve gave me a taste of a slightly more laid-back, less stressful life that made me wish that I could have discovered more of the UK, particularly the smaller towns in which I feel so much more at home.

And like any good travelling experience, I've learned a little about myself. Mostly I've learned (more than I already knew) that I'm a contrarian, self-contradictory bastard. After a couple of weeks away I long to be home, but at the same time I wish I could stay and explore a little bit more. The most difficult times of the trip have been when I've been alone, wishing I could share the experience with people I care about and for that extra confidence that comes with travelling with others. But when I have had company, I've often been withdrawn and grumpy, and snappy whenever things haven't been done my way (sorry, Steve!). I've chatted confidently for hours with interesting people who have also, helpfully, been very interested in me and what I do - but even now, I'm terrified of being the first to put myself forward and introduce myself (being a prize-winner certainly worked in my favour here!). Possibly most importantly, I've learned once again that I need to let things go and accept my own decisions - maybe I could have seen and done more things, and talked to more people than I did, but at the end of the day I'm richer**** for the experience and life goes on. And tomorrow I'm coming home.

* But hey, at least there's reliable free wi-fi.
** I admit that after seeing the Arc de Triomphe, the Marble Arch looked very small indeed.
*** I'd have learned more about the average Frenchperson if I spoke French.
**** Not so much in the bank account, however.

Launch day!

So, it's finally here - the day where I launch my EP. Part of me feels kind of underwhelmed by the whole affair - after all, I've had plenty of time to get used to doing gigs and at the end of the day, this is just another gig. But the other part - and the part I'm sure will start screaming louder as the day goes on - is quick to remind me that I've intentionally made this particular gig all about me.

Making myself the centre of attention is usually something I actively avoid, but writing an EP demands a launch party, and I'm not going to miss out on an opportunity to party with many of the people who made it possible and supported me through the whole thing. Also, it'd be nice to sell a few copies now it's done!

I've done pretty much everything I've needed to do - putting the CDs together, making posters, drumming up a little bit of publicity, rehearsals, getting audio gear. The Facebook page for the launch is looking pretty healthy as these things go, so hopefully I'll get a decent crowd. But until 7pm tonight - and possibly some time after - I'm going to be terrified that no-one will show up. But at least I can rely on the friends and family who got me here, and even by themselves they make a nice little (but vocal) crowd.

I intentionally didn't put any thanks on my EP itself: mainly because there wasn't much room left. But also because I'd rather do my thanks in person (or... well, in internet). So thank you - everyone who's bought a copy already, asked about it, even considered buying a copy, asked me how things were going along musically (both with the EP and in general), come to (or wanted to come to) my solo gigs or those with the band. If it weren't for all of you, they would have had to drag me out from under the table to get me to perform at all! I said this gig is all about me, but really* it's all about you**.

I'm really looking forward to tonight, and playing a gig that means a lot to me. Even more than that, I'm looking forward to continuing on with music after tonight - planning gigs, writing songs, maybe even recording some. Nearly all of that will be done with my band, The Solution, because - well, because they're awesome, and I find it much more fun and rewarding playing with a band than solo. So look out for us!

For those of you who can't be there tonight (or randomly stumbled upon/were directed to this blog) the EP is now available to download on my bandcamp site for $4, complete with secret bonus tracks! You can listen to all of the tracks live on the bandcamp page and decide for yourself whether I'm worth the price of an overpriced packet of chips ;) Go to http://nickbeeton.bandcamp.com or press some buttons below!


* cliched moment warning
** I warned you!

Locked and loaded

At long last, my EP is done and dusted*. All that's left to do now is get ready to show it to people, which means a launch party! I've booked a venue, organised a support act, burned the music onto CDs, printed CD labels, cajoled my friend and co-star Ariel into providing art, sent away to get CD sleeves printed... I've never been much of an organiser, but somehow it's coming together. I won't say putting this thing together took nearly as much work as my PhD did, but it's taken almost as long - and strangely means almost as much, though in a different way. When I first came to Hobart five years ago, doing something like this was no more than a far-flung fantasy - I could barely manage to sing in front of my friends, let alone record something that anyone might happen upon! It's only been through the support and enthusiasm of my family and friends (you all know who you are!) that I've been able to believe that my voice and my words are something that people might want to hear. Even now it amazes me that people are interested in my stuff - but because they are, I wrote it, because I knew that somebody would want to hear it!

The launch party will be on Saturday, 15th September at Brookfield Margate - we'll most likely be kicking things off around 7pm with Vino (consisting of good friends David McEldowney and George Begbie), and then I'll be taking to the stage with The Solution to play songs for you (and hopefully sell some EPs!). Stay tuned for more info as I get it organised!

The EP will be released under a Creative Commons licence - in short, it means that once you've bought it you can distribute it around as much as you like as long as you give me credit, don't sell it, and share it under the same conditions! Of course, I would love it if you bought my EP - and it'll be available online on bandcamp.com after the launch date for those ascetics who don't believe in the whole "physical objects" thing** - but I'll be just as happy if you listen to it on my blog, enjoy it and share it around with your friends*** :)

So, in the spirit of sharing, here's a third track from the EP for you to listen to - it's called The Garden, and it's the closest thing to a love song I've ever written, dedicated to my girlfriend. Aww. Enjoy!




* Also, I changed the name. I'm indecisive >_>
** Except for a computer, of course. Let's not get crazy here!
*** And maybe they'll buy it, seeing as you won't. Stingy bastard. (kidding!)