tag:blogger.com,1999:blog-71784970755678032072024-02-08T12:00:50.266+11:00First Sign of MadnessA blog about life, music, maths, geekery, and stream of consciousness rambling.Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.comBlogger48125tag:blogger.com,1999:blog-7178497075567803207.post-19686875196150812732016-07-09T09:36:00.002+10:002016-07-09T09:36:42.909+10:00I was Wrong about Cowan - 78 seats now possibleIn my <a href="http://firstsignofmadness.blogspot.com.au/2016/07/battle-of-forde.html">last post</a>, I'd all but assumed Cowan would go to Labor, but in a completely unexpected twist the first absent votes have <a href="http://vtr.aec.gov.au/HouseDivisionPage-20499-237.htm">swung more to the Libs </a>than even the postal votes. My model's now predicting it as more-likely-than-not a Coalition victory, and this is a quite conservative model as it assumes different non-ordinary vote types (e.g. absent and postal votes) will swing together. If this early trend in absent votes isn't just a fluke, it could be a very comfortable LNP victory despite being marked as a probable Labor win by analysts.<br />
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That would mean if Herbert and Flynn fall to the LNP as expected (by me, but I could easily be wrong again!), their promising Capricornia results continue on, Forde goes their way as also <a href="http://www.abc.net.au/news/2016-07-08/antony-green-says-malcolm-turnbull-will-be-returned-as-pm/7580646">expected </a>by <a href="http://www.abc.net.au/news/2016-07-08/election-2016-what-is-barrie-cassidy-saying-today/7579500">analysts</a>, and absent votes get them over the line in Cowan - 78 seats is now looking, if not likely, then at least far more feasible than it did last night.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcicR_cQYrp_0JqQ9sdh3IANysxn7k83rD8e2riec5xCdbGBYxiHNotkQ2DqN9BVPxrp51_NUFjFFJM3Tdox9J2Oc4OzReIERR4ObNTdysKhRGB4pWLD-aIkfGX3MNcS1pRNiId8D7_NNI/s1600/cowan.png" imageanchor="1"><img border="0" height="276" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcicR_cQYrp_0JqQ9sdh3IANysxn7k83rD8e2riec5xCdbGBYxiHNotkQ2DqN9BVPxrp51_NUFjFFJM3Tdox9J2Oc4OzReIERR4ObNTdysKhRGB4pWLD-aIkfGX3MNcS1pRNiId8D7_NNI/s400/cowan.png" width="400" /></a>Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com0tag:blogger.com,1999:blog-7178497075567803207.post-83442723317804816032016-07-08T16:59:00.001+10:002016-07-08T17:16:44.033+10:00Battle of the FordeI'd actually managed to stay away from election stuff today but it drew me back with a couple of articles from the ABC, with <a href="http://www.abc.net.au/news/2016-07-08/antony-green-says-malcolm-turnbull-will-be-returned-as-pm/7580646">Antony Green</a> and <a href="http://www.abc.net.au/news/2016-07-08/election-2016-what-is-barrie-cassidy-saying-today/7579500">Barrie Cassidy</a> weighing in on the situation. My prediction of 76 or 77 seats is looking pretty likely, but the thing that interested me is Green and Cassidy both suggesting that the Coalition is "on track" and "too far ahead" in Forde respectively.<br />
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Now, <b>Herbert </b>and <b>Flynn </b>look to be pretty much wrapped up for the Coalition, and <b>Capricornia </b>is still close but may well head in that direction after a better result their way in recent counting, giving them a likely 76 seats. That is by no means certain though, as the graph below may help demonstrate (as in <a href="http://firstsignofmadness.blogspot.com.au/2016/07/postal-votes-coming-in.html">previous </a><a href="http://firstsignofmadness.blogspot.com.au/2016/07/the-77-seats-scenario.html">posts</a>, the Libs win if the red line is above the <b>black horizontal line</b> at the right side of the graph; current progress based on counting is <b><span style="color: #cc0000;">red </span></b>crosses; simulated possible futures are <b><span style="color: #cc0000;">red </span></b>wibbly lines; results if non-ordinary votes behave like in 2013 relative to the ordinary votes are in <b>black</b>; and the track needed for the Coalition to win in <b><span style="color: #3d85c6;">blue</span></b>)<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-uEwmfNGd4JvmSn0o5JQFj9N3JzaF_DVvEG7b_0MJ0JshRH3bIcymAgnEYOMmjHTkoy6NoHb2bf5tydZyoXuWXtX_OJNSeaoOJkzTLZewDLZCi7NqZu3O9f4Egbkicb4oOQDK5xGnWEvc/s1600/capricornia.png" imageanchor="1"><img border="0" height="271" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-uEwmfNGd4JvmSn0o5JQFj9N3JzaF_DVvEG7b_0MJ0JshRH3bIcymAgnEYOMmjHTkoy6NoHb2bf5tydZyoXuWXtX_OJNSeaoOJkzTLZewDLZCi7NqZu3O9f4Egbkicb4oOQDK5xGnWEvc/s400/capricornia.png" width="400" /></a><br />
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<b>Forde</b>, on the other hand, is looking very interesting. The Coalition is probably more likely than not to win but after a relatively strong showing by the ALP in recently counted absent votes (the downwards red kink) there's not a lot in it, and even with a few data points my simulations are still showing a lot of variation that could easily bounce either way in the remaining votes. So I'm surprised at the analysts' confidence, especially given they've been relatively cagey on other results. Maybe there's something I'm missing?<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7zK7wBCT2dCtTy5vyV9Dkcj2nqWODRwOr-mbwfOJawKzXrhrmy-VCatXhyphenhyphen4xDPGdxAWVVcSzOja8vmdDrcv9TOx3V77Yi_nlMmsIb9fZalQKNsrzfHBNqeyKPriBO5t82_4ufmd2l9Ldk/s1600/forde.png" imageanchor="1"><img border="0" height="267" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7zK7wBCT2dCtTy5vyV9Dkcj2nqWODRwOr-mbwfOJawKzXrhrmy-VCatXhyphenhyphen4xDPGdxAWVVcSzOja8vmdDrcv9TOx3V77Yi_nlMmsIb9fZalQKNsrzfHBNqeyKPriBO5t82_4ufmd2l9Ldk/s400/forde.png" width="400" /></a><br />
<br />
And then there's <b>Hindmarsh</b>, which is expected to go to Labor and is looking good for them, but it's still early days...<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHA8eh_egyGLOgcRmwSu21iZXTQNQ5kYZV4DUsQbtj1flHZeTg8uWuXqSumyRyLbJut2s2HasyZ0ITpvi781R3Hu_kB0IqQsZHkK_dBWMx155xAmmpV8iX7yqmIYUQZzjykja5X0OlBrhE/s1600/hindmarsh.png" imageanchor="1"><img border="0" height="272" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHA8eh_egyGLOgcRmwSu21iZXTQNQ5kYZV4DUsQbtj1flHZeTg8uWuXqSumyRyLbJut2s2HasyZ0ITpvi781R3Hu_kB0IqQsZHkK_dBWMx155xAmmpV8iX7yqmIYUQZzjykja5X0OlBrhE/s400/hindmarsh.png" width="400" /></a><br />
<br />
All of this together means that while the 77 seat scenario is looking likely, any result between 75 and 78 is still very possible depending on these three seats. And then the only close seat not mentioned is <b>Cowan </b>which is an expected Labor win but anything can still happen...Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com3tag:blogger.com,1999:blog-7178497075567803207.post-303154501496371942016-07-07T19:49:00.002+10:002016-07-07T19:49:38.199+10:00Postal votes coming inAs the postal votes trickle in for the remaining seats, the situation seems to be getting firmer (<a href="https://firstsignofmadness.blogspot.com.au/2016/07/the-77-seats-scenario.html">see previous analysis here</a>) on top of the 72 locked-in seats for the Coalition - Capricornia remains on a knife edge but the remaining seats are looking more and more like Coalition wins except for Cowan and Hindmarsh (likely to go to the ALP).<br />
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I've cobbled together simulations for each seat of 100 potential non-ordinary vote futures (thin red lines below), all of which go to the LNP in Flynn, Gilmore (already called for the Coalition on ABC) and Herbert. In Forde it's less clear but still 90 simulations are predicted the LNP's way; in Capricornia, 54 pick the LNP making it a real toss-up, and Hindmarsh has only 31 to the LNP and Cowan 6. I may explain how I put the simulations together in a later post.<br />
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According to this so far (<b>and things can easily change - my assumptions are cobbled-together and by no means rock solid</b>), the Coalition is looking pretty well set for 75 seats, likely for 76 and still <a href="https://firstsignofmadness.blogspot.com.au/2016/07/the-77-seats-scenario.html">very possible for 77 seats</a>.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWnFCLlhaZTPlY76mD5tC4eQ7D0pk2_UHTi_R1DbZSpUqLwi6gc7uvPZwgotu8UEXUZToKn44mEP8maNKaMElcyeKNQWaitFzdpkol9qvBLUwMHkpnPFNnG1viCIO9DHdjbIyn9GM54-5H/s1600/capricornia.png" imageanchor="1"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWnFCLlhaZTPlY76mD5tC4eQ7D0pk2_UHTi_R1DbZSpUqLwi6gc7uvPZwgotu8UEXUZToKn44mEP8maNKaMElcyeKNQWaitFzdpkol9qvBLUwMHkpnPFNnG1viCIO9DHdjbIyn9GM54-5H/s320/capricornia.png" width="320" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2qHTXjGAhQgZV2MTK4VFhpWzXJHkr06jWJwY1D2YM4gROot05YPQEpPAVNOPctRHMN1kR07ANU1Fr4rfnkjx7l3Y_PJl5IJjHGV_-UOkuV78u27QRgdTtD5GwbWX8vSWZc7bpKsrw_548/s1600/cowan.png" imageanchor="1"><img border="0" height="203" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2qHTXjGAhQgZV2MTK4VFhpWzXJHkr06jWJwY1D2YM4gROot05YPQEpPAVNOPctRHMN1kR07ANU1Fr4rfnkjx7l3Y_PJl5IJjHGV_-UOkuV78u27QRgdTtD5GwbWX8vSWZc7bpKsrw_548/s320/cowan.png" width="320" /></a><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKmgH6bpyDVsIkHFdaaxGync-hgpcVlN91hiaQPfxB-6NOaMJARdbdDkICPao17fMaGTFyN6Eq_Dzfd4-XemO5vScEc-0Tg0wxRB8b_5oGBjOsjr7EavBoHRKRDs8leSOQsr5osCbEFILG/s1600/flynn.png" imageanchor="1"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKmgH6bpyDVsIkHFdaaxGync-hgpcVlN91hiaQPfxB-6NOaMJARdbdDkICPao17fMaGTFyN6Eq_Dzfd4-XemO5vScEc-0Tg0wxRB8b_5oGBjOsjr7EavBoHRKRDs8leSOQsr5osCbEFILG/s320/flynn.png" width="320" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcDqhd5fgmFPFhwIOw2TDNwkHNpb_NcisgochHNzPgddIbSq6Tq327CUZXoSfpthIKS28hQUM_58BXzNv5LaH7GswZXpxSdB35Cr8s2npKemZhIsl8RKZKg_3Zy_1n0fa6u31TJYLLluTi/s1600/forde.png" imageanchor="1"><img border="0" height="202" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcDqhd5fgmFPFhwIOw2TDNwkHNpb_NcisgochHNzPgddIbSq6Tq327CUZXoSfpthIKS28hQUM_58BXzNv5LaH7GswZXpxSdB35Cr8s2npKemZhIsl8RKZKg_3Zy_1n0fa6u31TJYLLluTi/s320/forde.png" width="320" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFcKH_XWT6LqeS9u3YL4FPbWmMKJ-zPbboPuDKtRp6r6l4rw97kDMfumTO_ekFQE9-h7nR6JyojeTmt-pvI2EV5UCpX1csV58bJAIn0lsDBQdrzNS2KJu5BBQKX7Q57BjY-XZnS07Q844E/s1600/gilmore.png" imageanchor="1"><img border="0" height="201" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFcKH_XWT6LqeS9u3YL4FPbWmMKJ-zPbboPuDKtRp6r6l4rw97kDMfumTO_ekFQE9-h7nR6JyojeTmt-pvI2EV5UCpX1csV58bJAIn0lsDBQdrzNS2KJu5BBQKX7Q57BjY-XZnS07Q844E/s320/gilmore.png" width="320" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUofrV4N6dENIB44thOpwymFncvHlu_xk2jGLfPN5307wtLXN4eJjzz7D74mmXIzajeRGGsCWnWPyd2MlU9njH-BMvR8wI4IXGZbuoSpQwqwVmo8aeQ-mOs4oTqdWH-YQtToIUz-V23rd4/s1600/herbert.png" imageanchor="1"><img border="0" height="202" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUofrV4N6dENIB44thOpwymFncvHlu_xk2jGLfPN5307wtLXN4eJjzz7D74mmXIzajeRGGsCWnWPyd2MlU9njH-BMvR8wI4IXGZbuoSpQwqwVmo8aeQ-mOs4oTqdWH-YQtToIUz-V23rd4/s320/herbert.png" width="320" /></a><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7ZF8_PhojxFlF0RVNXHSALv2Zl-yDZjGMtGKM5SuI7cJm2BpxcTzTsPVrJULgGCUBU5mIZxXCHukWCmWJoDU6mqL3kj5EJJxpPDm7FAYaBIT55J64Rw3jFZtDyfQDknJCL_7z8L5lHu0e/s1600/hindmarsh.png" imageanchor="1"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7ZF8_PhojxFlF0RVNXHSALv2Zl-yDZjGMtGKM5SuI7cJm2BpxcTzTsPVrJULgGCUBU5mIZxXCHukWCmWJoDU6mqL3kj5EJJxpPDm7FAYaBIT55J64Rw3jFZtDyfQDknJCL_7z8L5lHu0e/s320/hindmarsh.png" width="320" /></a><br />
<br />Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com0tag:blogger.com,1999:blog-7178497075567803207.post-65596271153322681792016-07-06T16:05:00.002+10:002016-07-06T20:06:15.881+10:00The 77 seats scenarioNow the postal votes have started coming in, I've been casting around for a way to visualise what's going on. One way I've found useful is, as in <a href="http://firstsignofmadness.blogspot.com/2016/07/election-results-madness.html">my previous post</a>, by using the predicted swings in non-ordinary votes (postals etc) compared to ordinary votes, using the 2013 results as a guide - these swings tend to go to the Coalition. In the plots below, I've put those predictions in <b>black</b>, the relative overall swing needed on top of the postals swing for the Coalition to hit 50-50 in <b><span style="color: cyan;">blue</span></b>, and the data so far in <b><span style="color: #ea9999;">red</span></b>. I've assumed the postals will come in first (they're all we have so far) and the other vote types afterwards (absent, pre-poll and provisional in that order - this probably isn't accurate!).<br />
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In the seat of Forde, my <a href="http://firstsignofmadness.blogspot.com.au/2016/07/election-results-madness.html">earlier model</a> currently predicts an LNP win by about 400 votes despite them only being ahead by 94 votes after ordinary votes. Though <a href="http://www.smh.com.au/federal-politics/federal-election-2016/federal-election-2016-live-coverage-day-five-slow-progress-on-vote-count-20160705-gpzd0v.html#post_live_1011121422">commentators were surprised</a> by a "Coalition surge" as postal votes started coming in, it's actually quite consistent with 2013 results (see the red cross).<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3ApIH8IabBsg__fv1qkmjsTyKvMR9mpLNKgG94efD7xpS_z4RynmChDQ6RFQpe5pn-oXA5sSUq41PnfXfvDDvHJjyKM-uN5URrE3dN93pQzT96_6FG-MNCVekwoO_dzX3ilRjQ2wafnvo/s1600/forde.png" imageanchor="1"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3ApIH8IabBsg__fv1qkmjsTyKvMR9mpLNKgG94efD7xpS_z4RynmChDQ6RFQpe5pn-oXA5sSUq41PnfXfvDDvHJjyKM-uN5URrE3dN93pQzT96_6FG-MNCVekwoO_dzX3ilRjQ2wafnvo/s400/forde.png" width="282" /></a><br />
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I've checked a bunch of other seats that my model predicted would be close (Batman, Chisholm, Cowan, Flynn, Gilmore, Herbert and Hindmarsh) and most of the other results have been relatively consistent with 2013 patterns as well (if not better for the Coalition), currently confirming my 76 seats prediction - except for one. Herbert seems to be looking particularly good for the Coalition, well above where they need to be to make up the difference (see graph below - they're well above the predicted trend, and even well above the needed blue line).<br />
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<b>I can't stress enough that it's early days</b>, other seats with postals yet to count could well swing the other way to the ALP, and the number of remaining votes could be well out, but if current trends continue, they could pick up an extra seat to make 77. Interesting times ahead...<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhI6dj-l7WSC1BM6MSa5JvY8Kq0Fo4DhuqeWku7opokA2c9dcHl0KMnYnRhgNFnjvrNV2Ylsy0TFVfUtvoYCPrk_wnYZ_qIluVMs5CuylzjmA6GF1z5MAO7u_1BY4dXCopCquCh33-lhJL4/s1600/herbert.png" imageanchor="1"><img border="0" height="337" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhI6dj-l7WSC1BM6MSa5JvY8Kq0Fo4DhuqeWku7opokA2c9dcHl0KMnYnRhgNFnjvrNV2Ylsy0TFVfUtvoYCPrk_wnYZ_qIluVMs5CuylzjmA6GF1z5MAO7u_1BY4dXCopCquCh33-lhJL4/s400/herbert.png" width="400" /></a><br />
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Update #1: Things are looking worse than expected for the Coalition in Capricornia - it looks too close to even guess one way or the other. As it stands currently, on top of the ABC's current 72 to Coalition, 66 to ALP:<br />
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<b>Probable LNP: </b>Flynn, Forde, Gilmore, Herbert<br />
<b>Probable ALP: </b>Cowan, Hindmarsh<br />
<b>Complete guess: </b>Capricornia<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGV3OrcWrPThuobt8sK9zgqQnRHeEk-4QTuVfMRsmAoLAOavpKCRKgGoSDAbtleSFgqx78uI9-Bd5acHLTwT_gK5f-GDJBBBSwfWRdJ8RdCKkTPv17RxOsEFg5WSvdIT7WFoL1v2p1FOEb/s1600/capricornia.png" imageanchor="1"><img border="0" height="241" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGV3OrcWrPThuobt8sK9zgqQnRHeEk-4QTuVfMRsmAoLAOavpKCRKgGoSDAbtleSFgqx78uI9-Bd5acHLTwT_gK5f-GDJBBBSwfWRdJ8RdCKkTPv17RxOsEFg5WSvdIT7WFoL1v2p1FOEb/s400/capricornia.png" width="400" /></a><br />
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For interest, this is why I think Flynn is a probable LNP despite it having been in the ABC election ALP column until recently:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghuVq79PlEHmqEP3ykkauezV-kVA5NnhNrNkJFS0iPnDowSu8z58i_DbMmvln0_EvvNKA927u6Dy7Mq91hU2IdTum2zXBh8hB-Qre_g-n4WnctI1U9bac18icKiVz-abD0UgwO7rAxgk_6/s1600/flynn.png" imageanchor="1"><img border="0" height="285" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghuVq79PlEHmqEP3ykkauezV-kVA5NnhNrNkJFS0iPnDowSu8z58i_DbMmvln0_EvvNKA927u6Dy7Mq91hU2IdTum2zXBh8hB-Qre_g-n4WnctI1U9bac18icKiVz-abD0UgwO7rAxgk_6/s400/flynn.png" width="400" /></a>Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com0tag:blogger.com,1999:blog-7178497075567803207.post-69208431789522618262016-07-05T13:10:00.001+10:002016-07-05T17:02:18.749+10:00Election results madness<span style="font-family: inherit;">With help from the AEC scraping code by Mick McCarthy <a href="https://mickresearch.wordpress.com/2016/06/30/election-fever-hits-again/">here</a>, I've tried to predict the election results once the "non-ordinary" votes (early, pre-poll, postal and provisional) have been counted. These tend to go more for the Liberal party, so seats that Labor is currently ahead in might be lost. </span><br />
<br />
I’ve assumed that:<br />
<ul>
<li>all ordinary votes are in (only non-ordinary votes left), </li>
<li>the proportion of formal votes remains the same as in 2013 for all electorates, </li>
<li>the number of non-ordinary votes all increase proportionally with each other, </li>
<li>and the changes in 2 candidate preferred votes between voting types (I call this "bias") in each electorate stay the same between 2013 and 2016 (e.g. if the Libs get a 2% bounce in postals in Denison in 2013 compared to their ordinary vote result, that same proportion holds in 2016).</li>
</ul>
<div>
It turns out that William Bowe of the Poll Bludger, my favourite election analysis page, pipped me to the post with <a href="https://blogs.crikey.com.au/pollbludger/2016/07/05/late-counting-progressively-updated/">his analysis here</a>, but I thought I'd run mine anyway. And it gave similar results, but importantly <b>different enough to get the Coalition over the line</b>. Here are the number of votes that the LNP (Liberal/Nationals party, well, Coalition) are expected to be ahead or behind in the closest seats:</div>
<div>
<br /></div>
<br />
<div>
Capricornia LNP +547</div>
<div>
<div>
Chisolm LNP +1230</div>
<div>
Cowan LNP -580</div>
<div>
Flynn LNP + 1469</div>
<div>
<b>Forde LNP +86</b></div>
<div>
Gilmore LNP +713</div>
<div>
Herbert LNP -315</div>
<div>
Hindmarsh LNP -786</div>
<div>
Melbourne Ports LNP -1224 (I didn't do 3CP analysis though...)</div>
<div>
Petrie LNP +1447</div>
</div>
<div>
<br />
<br /></div>
<div>
The Poll Bludger's analysis has them behind in Forde by 18 votes - my extra seat gives them 76 seats, a majority in their own right, whereas his 75 seats is not enough.</div>
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<br /></div>
<div>
I then had a play with adding random variation, relaxing the assumptions of the proportion of formal votes staying the same and the amount of bias staying the same. I assumed that the overall variance between electorates for these properties stayed the same, but that a little (10%), half (50%) or all (100%) of the variance was due to random variation and not the specific effect of being in one electorate or another. The less important electorates became, the less likely a Coalition victory - for a little, 66% of simulations resulted in a win; for half, 34% and for full random variation, only 20% of cases.<br />
<br />
<b>Edit: Using 2010 results instead give us similar results, though slightly worse for the Coalition - 76 seats for the Coalition without variation, and 53%, 20% and 16% in the three scenarios described respectively.</b><br />
<b><br /></b>
<b>Edit #2: Using 2007 results is more difficult because of seat redistributions, but we can do it if we assume that Liberals and Nationals will experience the same swings in Capricornia and Flynn. The model also gives 76 seats for the Coalition without variation, and 91%, 49% and 27% for the scenarios.</b></div>
<div>
<br /></div>
<div>
The model also pointed to some seats that could potentially be very close (winning 2PP < 50.2%) in these situations, so watch for these potentially coming into play if things get even more interesting:</div>
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<b>likely:</b></div>
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Batman (VIC) </div>
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Longman (QLD)</div>
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<b>possible:</b></div>
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Banks (NSW)</div>
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Dickson (QLD)</div>
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Dunkley (VIC)</div>
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Griffith (QLD)</div>
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La Trobe (VIC)</div>
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Lindsay (NSW)</div>
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Robertson (NSW)</div>
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Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com4tag:blogger.com,1999:blog-7178497075567803207.post-6873695638404938242015-08-26T15:42:00.002+10:002015-08-26T15:42:21.479+10:00St Petersburg ParadoxI was having lunch with teacher friend <a class="twitter-atreply pretty-link" href="https://twitter.com/FallenBeas" role="presentation" style="background: rgb(0, 0, 0); color: #038543; font-family: Arial, sans-serif; font-size: 14px; line-height: 20px; text-decoration: none !important;"><span style="color: #67b58e;">@</span>FallenBeas</a> the other day, and discussing some interesting examples of how statistics and probability can get kind of weird. He loved the <a href="https://en.wikipedia.org/wiki/Birthday_problem">Birthday Problem</a> and decided to use it for his class, but was particularly fascinated by the more tricky <a href="https://en.wikipedia.org/wiki/St._Petersburg_paradox">St Petersburg Paradox</a>.<br />
<br />
The problem goes thus: there is a game that costs X dollars to play, which simply involves tossing a coin. You start with a pot $2, and every time the coin comes up heads the banker doubles the pot. As soon as the coin comes up tails the game ends, and you get to walk away with the pot. The question is, how much is a reasonable amount of money X to play the game?<br />
<br />
Where the paradox comes in is how statistics defines 'fair'. Usually we calculate the average, or "expected" amount of money to be made from the game, by totalling up all of the possibilities combined with how much we expect to make from them. In this game, we have a 50:50 chance of getting $2 (the first throw being a tail), and then a 1/4 chance of getting $4 (a head, then a tail), then 1/8 chance of getting $8 (heads, heads, tails) and so on. That means we can expect on average $1 from the worst-case scenario (it's $2, and happens half the time, and $2 x 1/2 = 1), and another $1 from the heads-tails scenario ($4 x 1/4 = $1) and so on. This process goes on <b>forever </b>- it's always possible to get more heads - so the average amount we expect to win in this game is $1 + $1 + $1 + .... = <b>infinite money, </b>and that's how much we should apparently spend to play the game.<br />
<b><br /></b>
This obviously doesn't make sense. For a start, you're always going to lose at some point, so it's physically impossible for you to make infinite money no matter how many times you get heads. The problem is that the idea of an expected amount of money depends on the assumption that we want to know what happens in the long run, so it assumes we are playing this game infinitely many times and taking the average. But when we play infinitely many times, we suddenly have access to the end of the rainbow where we're making infinite money - the idea is that infinity is a mathematical construct that we never see in reality. Usually we can deal with it pretty happily without weird things happening, but this is a weird game, and breaks our usual assumptions.<br />
<br />
What we can do instead is see what's most <b>likely</b> to happen to our winnings as we keep playing. For a single game, it's pretty clear that most of the time we'll win either $2 or $4 (with a 50% and 25% chance respectively), and occasionally $8 (12.5%) but we're not likely to win much more than that. If we play two games, then our worst case scenario is that we'll win $4, with a 1/2 x 1/2 = 1/4 chance. There are two ways we can win $6 - we can win $2 then $4, or $4 then $2. Both of these options have a 1/2 x 1/4 = 1/8 chance of happening, so overall we've got 1/4 chance of that happening too. We can calculate the other possibilities that way too - obviously we have to stop at some point, but we can go far enough to get a decent idea. We can then keep going and see what happens when we play more and more games in a row, and getting bigger jackpots gets more and more likely.<br />
<br />
Of course, the best way to do this is with a computer to avoid all those pesky calculations. Here is a graph of the possibilities over the course of 100 games:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjF1vbVZDuYpbxhSGRTXNhGtahC5aboh-dA4KR8WKJedChX6Qek39Y_5StZnSJUs5r5_rENtT3sBbqqtMX_b1Qo3hNJVZuJHcViSvCybNK3MA8RZgfooBBPtjE3UrJQCYx482vUoB7KvLo_/s1600/st+petersburg+dist.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="281" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjF1vbVZDuYpbxhSGRTXNhGtahC5aboh-dA4KR8WKJedChX6Qek39Y_5StZnSJUs5r5_rENtT3sBbqqtMX_b1Qo3hNJVZuJHcViSvCybNK3MA8RZgfooBBPtjE3UrJQCYx482vUoB7KvLo_/s400/st+petersburg+dist.jpg" width="400" /></a></div>
Lighter colours represents where a possibility is relatively likely, and dark colours where it is unlikely. You can see little waves towards the top-left of the graph - this is where after a few games there's a small but decent chance of getting a single big win which overwhelms all of the other winnings. Especially when not many games have been played, it's more likely that you'll get a single big win and a lot of small wins than multiple medium-sized wins.<br />
<br />
The blue line represents the <b>median</b> average win, and is surrounded by red <b>interquartile</b> lines - the idea is that half of the time, your winnings per game after a certain number of games will be between the two red lines. For example, after 50 games, it's 50-50 whether your average winnings are above or below $8.20 (the median), and half the time your average winnings will be between $6.12 and $12.44. So if you paid only $6 a game, you're probably doing pretty well at this point!<br />
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The most important part of this graph is that these numbers are going up as we keep playing games, meaning that the game becomes more and more reliably profitable. Further along the graph, the computer can no longer keep track of the higher numbers of winnings (which is why the red line disappears) so we need to find another way to work out what happens with more than 100 games. Using results cited in <a href="http://www.jstor.org/stable/2160590?seq=1#page_scan_tab_contents">this paper</a>, we can actually estimate the median winnings as<br />
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$2.55 + log<sub>2</sub>(number of games)</div>
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So after 100 games, $9.20 looks like a reasonable price - paying that price, half the time we'll end up ahead, the other half we won't. Note that the distribution is what statisticians call skewed - even though we only come out ahead half the time after 50 games, the "good" half is a lot better than the "bad" half is bad.<br />
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Let's say that we really want to milk this game for all it's worth, and we've found a game online that we can make our computer play for us. If we can play a million games a second, and leave our computer running for a year, that's over 30 trillion games. If we put that into our formula, we get a median win of $47.40 per game. If we paid that much per game to play, we'd expect to lose a lot of money at the start but make it back as the games wore on and we got more and more jackpots, breaking even after a year. However, if we only paid $9.20 as before, we'd expect to be doing ok by 100 games (i.e. after 100 microseconds), and by the time our program had been running for a year, we'd be looking at profits around $1200 trillion dollars - 700 times Australia's GDP and enough to basically rule the world.<br />
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Unfortunately, no casino will ever host this game, online or otherwise, for exactly this reason. Sooner or later, the house will always lose.Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com0tag:blogger.com,1999:blog-7178497075567803207.post-35718835993987219772015-04-23T17:28:00.003+10:002015-04-23T19:28:03.426+10:00Quadruple rainbow!A couple of days ago, someone at a train station in New York tweeted this photo of a quadruple rainbow:<br />
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<blockquote class="twitter-tweet" lang="en">
Quadruple <a href="https://twitter.com/hashtag/Rainbow?src=hash">#Rainbow</a> at <a href="https://twitter.com/hashtag/glencove?src=hash">#glencove</a> ny <a href="https://twitter.com/LIRR">@LIRR</a> station Today will be 4 pots of <a href="https://twitter.com/hashtag/gold?src=hash">#gold</a> <a href="https://twitter.com/hashtag/lucky?src=hash">#lucky</a> <a href="https://twitter.com/hashtag/chasetherainbow?src=hash">#chasetherainbow</a> <a href="https://twitter.com/hashtag/aprilshowers?src=hash">#aprilshowers</a> <a href="http://t.co/4YUUveJuy6">pic.twitter.com/4YUUveJuy6</a><br />
— Amanda Curtis (@amanda_curtis) <a href="https://twitter.com/amanda_curtis/status/590469469467729920">April 21, 2015</a></blockquote>
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Like most people, I'd never even heard of such a thing! Some <a href="http://www.slate.com/blogs/bad_astronomy/2015/04/21/quadruple_rainbow_viral_picture_is_real.html">reasonably reputable sites</a> assured me that such a thing exists, and is caused by the combination of two things:<br />
<br />
<b>The first </b>is that you can get two different paths of reflection of rays of light happening within water droplets, which gives us another "secondary" rainbow.<br />
<br />
<b>The second</b> is the effect of a body of water, usually behind the observer along with the sun, reflecting the sun - it acts just like another (though less bright) sun shining from a different location, and gives us another pair of rainbows. Because the second pair of rainbows is from another "virtual sun", the centre of the rainbow is in a different place so they're offset a bit from the first pair, hence the weird shapes.<br />
<br />
So, that makes sense. But there's water everywhere! Rainbows aren't <i>that</i> uncommon, and even double rainbows are seen occasionally, so why are quadruple rainbows so rare? I've never seen one, and I've seen plenty of double rainbows!<br />
<br />
First, the reason that we don't see rainbows all the time is that we need the sun to be shining behind you, and it to be raining in front of you so we have water droplets for the sunlight to reflect off. Often weather is one or the other - either all rain and clouds (hence no sun) or no rain. Also, if the sun is too high in the sky, a rainbow can't happen - a raindrop has to bend the light a certain amount (40-42° for a normal rainbow, 50-53° for a secondary one), so you can't have the sun <b>and</b> the reflections you need for a rainbow in the sky reaching your eye at the same time if the sun's elevation is more than 40° above the horizon. For a secondary rainbow it only needs to be less than 53° above the horizon, but the reflections are a lot weaker (the rays of light have to pass through the raindrop twice and bounce off the inside once) so it's a lot harder to see unless the conditions are just right.<br />
<br />
Here's a drawing from <a href="http://eo.ucar.edu/rainbows/">this site</a> showing the path of light from the sun (yellow lines) at sunrise or sunset, and how they bounce off raindrops to create rainbows at the blue and red colours (these are reflected at different angles, hence the colours of a rainbow). The higher the sun in the sky, the more downward-pointing those yellow lines will be, and the closer to the horizon and harder to see the rainbow will be (to see the effect, tilt your head to the left and imagine the ground is still horizontal from your perspective).<br />
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<a href="http://eo.ucar.edu/rainbows/rnbw7.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://eo.ucar.edu/rainbows/rnbw7.gif" /></a></div>
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<br />
To get the other two rainbows, we <b>also</b> need to have a body of water the right distance away behind you (it's also possible in front of you, but more difficult) to create another "sun" that will <b>also</b> make two rainbows - this will already be more difficult because the reflected sun will be less bright depending on how good a mirror the water body is.<br />
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<a href="http://eo.ucar.edu/rainbows/rnbw8.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://eo.ucar.edu/rainbows/rnbw8.gif" /></a></div>
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We can do a bit of geometry and work out what the required distances would be. Given the sun is reflecting off a raindrop a certain distance in front of us, this plot gives us the relative distance we'd need the height of the raindrop (above the ground) and water (behind us) for the primary and secondary (dotted in the plot) reflected rainbows to occur:</div>
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We can work out a few things from this. First, the apparent height of the original and secondary rainbows (green) are never much larger than the distance the rain is away - the higher the sun is in the sky, the lower the height relative to distance. As the rain goes right to the ground, this doesn't really restrict us at all until the rainbow goes below the ground and we can't see it.</div>
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However, for the reflected rainbows (black), it's the opposite - the higher the sun is in the sky, the higher we expect the raindrops to be, and they're almost always going to be at least as high as the rain is far away. We'd expect raindrops to usually be less than 6km high based on <a href="http://www.bom.gov.au/weather-services/about/cloud/cloud-types.shtml">this site</a>, so the rain should be closer than that at least.</div>
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Using the timestamp in the Twitter post (changed to New York time, 5:57am) and <a href="http://www.esrl.noaa.gov/gmd/grad/solcalc/azel.html">this site</a>, we can actually work out where the sun was in relation to New York when the picture was posted (and, hopefully, taken). It turns out it was not long after sunrise, so the sun was quite low in the sky at about 8.2° in height. The blue line on the graph represents this. The highest points of our secondary original rainbow (green, dotted) and our primary reflected rainbow (black, plain) should be at around the same place, with the original slightly lower, and this looks to be the case on the image. So far so good! Also the primary original (green plain) and secondary reflected (black dotted) are below and above these two.</div>
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The next thing we need to check is if the water lines up - the water for the primary reflected rainbow should be about 7 times further than the rain, and the secondary reflected about 12 times further. The direction of the sun at that time of morning was about 81°, so just north of east. If we assume the rain was about 1km away, <a href="https://www.google.com.au/maps/place/Glen+Cove/@40.8757195,-73.4959698,13z/data=!4m2!3m1!1s0x89c28505c5418913:0xbd0c1113c1219eec">looking at the map of the location</a> there are two likely-looking patches of shallow, calm water about 7km and 12km in that direction at Oyster Bay and Cold Spring Harbor respectively.</div>
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So after doing some detective work, it looks like not only is the quadruple rainbow plausible, but the combination of a series of unlikely but very possible events!</div>
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Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com0tag:blogger.com,1999:blog-7178497075567803207.post-86379157591466345612014-11-04T12:05:00.000+11:002014-11-04T12:34:09.472+11:00The reality of Melbourne Cup bettingAn interesting proposition just came up on my twitter feed. Tom Waterhouse, the smug git you see on TV spruiking his bookmaking service, is offering $25 million dollars to anyone who can pick the first 10 runners in the Melbourne Cup in order - and it only costs you $10 per try! (apparently you get 10 tries at most, don't get greedy now!)<br />
<br />
Sounds good, right?<br />
<br />
Well, no. Intuitively most people can smell a rat straight away - after all, it's difficult to win the lottery and that's only 6 numbers that need picking (though there are more of them). But it's far worse than that. Even with two horses scratched, if we naively assume each horse has the same chance of winning, then picking the first horse is a 1 in 22 chance. Picking the next horse is then a 1 in 21 chance (as we can eliminate the winner), then so on until the 10th horse is a 1 in 13 chance. All up, the probability of doing this is about <i>1 in 2 million million</i>. Even if the <a href="http://www.abs.gov.au/ausstats/abs@.nsf/0/1647509ef7e25faaca2568a900154b63?OpenDocument">entire population of Australia</a> at about 23.6 million (including children!) put in their 10 bets each, there would be an 0.01% chance that <b>anyone</b> would win.<br />
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The smart gamblers are probably now thinking "well, each horse <b>doesn't</b> have an equal chance of winning - I can exploit that!". And they'd be right! So let's look at the odds of each horse winning (I've used the <a href="https://www.betfair.com.au/racing/thoroughbreds/flemington/race-7/27297811/view/645.2.101060234">fixed odds at Betfair</a> but feel free to substitute your own). We can estimate the probability of each horse winning from the bookmaker's odds, and this is as accurate a representation as we're likely to find without significant effort - after all, it's in the bookmaker's interests to know the probabilities as accurately as they can to make the most amount of money! A formula to estimate the probability of a particular horse winning is:<br />
<br />
1/<the odds for your horse> divided by the sum of (1/odds) for every horse.<br />
<br />
Doing this gives us a probability of about 16% of the favourite, Admire Rakti, winning. So let's put our money on the favourite winning, followed by the second favourite in second place, and so on. Once our favourite goes past the line, we then need the second favourite (either Fawkner or Lucia Valentina) to come next. We can estimate the probability of this happening by dividing its probability of winning (about 13%) by the probability of all the remaining horses' probabilities of winning combined (about 84%), giving us a probability of about 15% of this horse coming second given our favourite has already come first.<br />
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Again, we rinse and repeat until we get through the first ten horses. This gives us a much nicer final probability of <i>1 in 28 million.</i> Again, naively you might think that if everyone in Australia had a go at this, surely with 236 million bets, we'd be able to do it pretty easily.<br />
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Unfortunately though, if everyone in Australia put their bets in here, they're not all going to be able to pick this most likely scenario. If they did then either everyone would win, sharing the $25 million dollars and getting $1 each from their outlay of $100, or nobody would win! Instead, everyone would have to organise to pick the 23.6 million best odds. And then, even if someone managed to win, Tom Waterhouse would still be pocketing $2,360 million dollars and only having to shell out $25 million, making his smug face even more unbearable...Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com2tag:blogger.com,1999:blog-7178497075567803207.post-5605173521743339092014-07-25T17:25:00.000+10:002014-07-25T17:27:55.483+10:00Fruits of procrastinationWinter tends to be a bit slow for me, in terms of work and productivity at least. It gets that little bit harder to concentrate, or stay motivated on tasks that are... the less fun parts of my job as a research scientist.<br />
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To that end, I thought I'd keep this blog alive by sharing some of my afternoon's procrastination, which I thought was kind of cool and a real reflection of how even now in 2014 we're still a fair way away from 'science fiction' in a lot of our endeavours. Artificial intelligence is a big one of these - we've achieved a lot since electronic computers hit the scene not-so-long ago - but our imaginations at least for now far outstrip what we've been able to do. Exactly because it excites people's imaginations, progress is heavily trumpeted - and make no mistake, some cool things have been done, especially in AI-friendly environments such as strategy games (chess is probably the most obvious example here).<br />
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Unfortunately, things get much more difficult for AIs when we go from simple games where the options are finite and often manageable to more realistic real-world tasks where there are numerous things that need to be coordinated at once - something that our human brains are evolved to deal with but computers have no such base to work from. The programmer can of course give the computer insights as to how humans would deal with things, and sheer processing speed can help make up some of the difference - any first-person computer gamer can attest to AIs being potentially very skilful (though often easily fooled by unusual strategies).<br />
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My afternoon's procrastination has involved looking at RoboCup - a series of competitions based around the game of soccer (or football, depending where you're from). The AIs actually look reasonably clever in the simulated 2D version. Keep in mind that to keep some degree of 'realism' each AI player has been given some simulated 'noise' to their sensors so they don't have perfect information, much like players in real life.<br />
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Once you get to 3D though, things start looking seriously clunky. Each virtual robot has 22 different joints to control - and it shows. They're very good at doing set combinations of movements (like a set shot at goal, given enough time) but it's not exactly what you'd call graceful...</div>
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When you convert this to real life robots, things get even worse. Really the only thing these robots can do consistently well is get up after they've fallen over - and after watching this video for any length of time you'll understand why this is a vital necessity:</div>
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The stated goal of RoboCup is that "by the middle of the 21st century, a team of fully autonomous humanoid robot soccer players shall win a soccer game, complying with the official rules of FIFA, against the winner of the most recent World Cup". At the moment that looks kind of optimistic, but when you consider how far computing came from the earliest personal computers in the 80s to the present, then extrapolate to 30 years in the future, their goal doesn't seem quite so unrealistic.</div>
Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com0tag:blogger.com,1999:blog-7178497075567803207.post-2209990771337557502014-04-21T13:21:00.000+10:002014-04-21T13:21:42.541+10:00DIY animal surveys (part 2)<div class="separator" style="clear: both; text-align: center;">
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So after the success of my first forays into using motion detection to film the neighbourhood cats, I thought maybe I'd get a little bolder and set up the equipment next to the house. I originally decided against this because I thought any cats (especially kittens) would be scared off by the proximity to light and humans, but considering how bold the last one was, it'd be worth a try!<br /><br />The next morning, a quick perusal of the food bowl suggested that nothing had been eaten, so I wasn't feeling particularly optimistic as I went to review the footage - yet again, I needn't have worried. This time I picked up not one, but two feline feeders, obviously working together:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi30nFvujvBuLxXqOrKdU4fYGtyPOnAlooJFTooszSlBSJMiayklNfTfvV50U-V01Hugq9d-_ctBwN2ybMIEKj9h8G9tbZKValWmgO8O9k4jg2Af2OAMTfjyMtt_3z0o0dPVOT5EmRvy-vs/s1600/motion_2014-04-21_04.02.24_328.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi30nFvujvBuLxXqOrKdU4fYGtyPOnAlooJFTooszSlBSJMiayklNfTfvV50U-V01Hugq9d-_ctBwN2ybMIEKj9h8G9tbZKValWmgO8O9k4jg2Af2OAMTfjyMtt_3z0o0dPVOT5EmRvy-vs/s1600/motion_2014-04-21_04.02.24_328.jpg" height="240" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj53_mNjEoD9ksrSnLFMiyVsQCO1EJaHxJQUEeD6kHrp0XTJ_YU_pe8l4xOt5G1nmDRT-DH0z2U5w124R5_WSK9ktabGHqsaGG1VLmOq2vDW84Jt4rXJD-O5lTv3JJNPxVbq6P5-SUsFsih/s1600/motion_2014-04-21_04.02.27_359.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj53_mNjEoD9ksrSnLFMiyVsQCO1EJaHxJQUEeD6kHrp0XTJ_YU_pe8l4xOt5G1nmDRT-DH0z2U5w124R5_WSK9ktabGHqsaGG1VLmOq2vDW84Jt4rXJD-O5lTv3JJNPxVbq6P5-SUsFsih/s1600/motion_2014-04-21_04.02.27_359.jpg" height="240" width="320" /></a></div>
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After their first joint perusal of the offerings on display, they individually came back to the bowl...<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYTA9tfoWy5LR-AK2OWPDCT8cf5ToNAQFqj2TA4MKR7Bx-ac1cTDcdOWSkOR3eOqnjy6tvG6vnL3ul20wpUjxrfPdxHz1FQa3Vd1stYEp33gs4ViuGy5xYfsztY7lzYnPKdYcwUgsZmbkV/s1600/motion_2014-04-21_04.02.58_984.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYTA9tfoWy5LR-AK2OWPDCT8cf5ToNAQFqj2TA4MKR7Bx-ac1cTDcdOWSkOR3eOqnjy6tvG6vnL3ul20wpUjxrfPdxHz1FQa3Vd1stYEp33gs4ViuGy5xYfsztY7lzYnPKdYcwUgsZmbkV/s1600/motion_2014-04-21_04.02.58_984.jpg" height="240" width="320" /></a></div>
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... and laptop...<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmKUW6H1qh8sTCFnitBib3klWx-mBMzZXdMTh3TB8yBmU1l4WLX6HMlNkwkChHQZ1bDMy9TK-I9PiyouIRoTF94qyw9yvHDDId6NpnuFIkNw0NHDvHnEkJAV810_916AT2Rt5nlNnYxa50/s1600/motion_2014-04-21_04.03.37_031.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmKUW6H1qh8sTCFnitBib3klWx-mBMzZXdMTh3TB8yBmU1l4WLX6HMlNkwkChHQZ1bDMy9TK-I9PiyouIRoTF94qyw9yvHDDId6NpnuFIkNw0NHDvHnEkJAV810_916AT2Rt5nlNnYxa50/s1600/motion_2014-04-21_04.03.37_031.jpg" height="240" width="320" /></a></div>
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... again...<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZ5lvVDjmjOFEjGK8FaZ6EaUy3FQCBxQPeDziXDrjyizTeHfsBjj989toSgXhlNiXJeDmVEV_wC-nKG7HAEUA0NRX0tem1ElfLWk87kC7EAwTMkN6uVHGB5X1QjN5PaPMKe0GCXipKoTD2/s1600/motion_2014-04-21_04.04.04_437.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZ5lvVDjmjOFEjGK8FaZ6EaUy3FQCBxQPeDziXDrjyizTeHfsBjj989toSgXhlNiXJeDmVEV_wC-nKG7HAEUA0NRX0tem1ElfLWk87kC7EAwTMkN6uVHGB5X1QjN5PaPMKe0GCXipKoTD2/s1600/motion_2014-04-21_04.04.04_437.jpg" height="240" width="320" /></a></div>
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... and again - often looking around curiously at objects (or potentially off-screen cats) as they did so.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsQYGznCpPpXqzCgZTUL7qi3IzxJqGG2gXkFzP5nzGCBJt7_hUmD-tjILeMSFkBLpie9lxcZeejVSFS7qAsRLuQ48v9O8UFxPxQxtXMilPWPXKS9BFLW-65OePuWj6BNPzbWAaH02crVui/s1600/motion_2014-04-21_04.05.06_359.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsQYGznCpPpXqzCgZTUL7qi3IzxJqGG2gXkFzP5nzGCBJt7_hUmD-tjILeMSFkBLpie9lxcZeejVSFS7qAsRLuQ48v9O8UFxPxQxtXMilPWPXKS9BFLW-65OePuWj6BNPzbWAaH02crVui/s1600/motion_2014-04-21_04.05.06_359.jpg" height="240" width="320" /></a></div>
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The black cat was evidently the wilier of the two - while the above photos were all taken in the space of five minutes, it returned a couple of hours later apparently having ditched its companion to see if any tastier food had magically appeared in the bowl that it could have for itself.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgK_ktcUxsm1UoXLfRgdGlmR9kOMGVjnETp-axoF1Pwtkwoa8bEsig7kDWyveh7CxV1liB6avlzHoXDGU0jmNWMIIUTOQKEuFh6b7RoQOQI44qTT4lWUrFAFWvjt51VCR2ykXxpKnzEXNZ1/s1600/motion_2014-04-21_05.38.57_015.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgK_ktcUxsm1UoXLfRgdGlmR9kOMGVjnETp-axoF1Pwtkwoa8bEsig7kDWyveh7CxV1liB6avlzHoXDGU0jmNWMIIUTOQKEuFh6b7RoQOQI44qTT4lWUrFAFWvjt51VCR2ykXxpKnzEXNZ1/s1600/motion_2014-04-21_05.38.57_015.jpg" height="240" width="320" /></a></div>
<br />Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com0tag:blogger.com,1999:blog-7178497075567803207.post-31609473571340006222014-04-15T14:47:00.000+10:002014-04-15T14:47:19.427+10:00DIY animal surveysOur neighbourhood is a cat neighbourhood. Walking along the streets at dusk or after dark, you can see at least a small handful of local cats prowling around or sitting smugly on their owners' driveways soaking up the last bit of heat of the day. So it didn't come as any surprise to me that every time I discarded the scraps outside that our own (indoor) cat for whatever reason didn't eat, they'd invariably be gone the following day.<br />
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I thought it worth investigating exactly which cat was taking these scraps. We've occasionally seen kittens wandering around our yard and more regularly around the neighbourhood, and I was a bit concerned for their welfare - so I thought it would be good to know if they were feeding in our yard and whether they could be collected for a rescue shelter.<br />
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So I got out my old crappy laptop with its old crappy webcam and set it up outside in our garage, somewhere that rain/wind wouldn't bother it (though it's old enough that I wouldn't have been too distraught if something did happen to it), and turned on a motion capture software program (I can thoroughly recommend <a href="http://www.yawcam.com/">yawcam</a> - it's free!). I was unsure whether our nightly visitor would be put off by the outside light I left on for the webcam to be able to see, and my fiancee was understandably cynical as to whether the process would work at all. So come next morning, I rushed out to reclaim my laptop, and after flicking through the images captured during the night, felt vindicated at seeing this photo come up at 12.11am:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV6CbXoQ9dz1DtcZb7zLqfFYlrCs8RCUBlbhiDR_dpd5E4h4Lnz-SGvnmJqGvBPg6PZfzMUYtjmXguDHnff_E5JypI4LJEM-J5Rrb6oxsqCButsg0Yh88mZ_50LytL3KyQbezZja6Itfi0/s1600/motion_2014-04-14_00.11.22_484.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhV6CbXoQ9dz1DtcZb7zLqfFYlrCs8RCUBlbhiDR_dpd5E4h4Lnz-SGvnmJqGvBPg6PZfzMUYtjmXguDHnff_E5JypI4LJEM-J5Rrb6oxsqCButsg0Yh88mZ_50LytL3KyQbezZja6Itfi0/s1600/motion_2014-04-14_00.11.22_484.jpg" height="240" width="320" /></a></div>
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I needn't have worried, though, as I'd forgotten two basic attributes of cats. Firstly, they are curious and attracted to new and interesting objects - and secondly, they're attracted to warm objects. The laptop that had been running all night out in the cold was both of these things! Thus, at 2.23am, the vision went entirely black, followed by images of the cat walking directly in front of the laptop sniffing at it:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZMhnUczNA9AVAoNZ3cwrnCtD2S0SFDdzvdAXCwD7v_nmrmUPu2ksdLsEL8oiq8Yn2joNdaFflPB-HqU08vfCg-3w4Q58n-4rfdKAHyapDRojTRhthm9pbTWq7WQ5L138So409N2-vCJVY/s1600/motion_2014-04-14_02.23.48_203.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZMhnUczNA9AVAoNZ3cwrnCtD2S0SFDdzvdAXCwD7v_nmrmUPu2ksdLsEL8oiq8Yn2joNdaFflPB-HqU08vfCg-3w4Q58n-4rfdKAHyapDRojTRhthm9pbTWq7WQ5L138So409N2-vCJVY/s1600/motion_2014-04-14_02.23.48_203.jpg" height="240" width="320" /></a></div>
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Then an hour later at 3.14am it returned for another look at the laptop before scurrying off, not to be seen again in the footage (though it may well have returned - the laptop stopped recording when Windows decided to restart after downloading a security update... a lesson for anyone wanting to try this at home!)<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjk9J8VWKBjMu29Gs_arS_tmFlo9zaIOipxBHuvalg1gRaZZ7e2fNZhdAztE9yQ6q9zYaKF66PtNjfnCjpRTgZm2bIrYYpDwj2I-F3DYYwwL5I4Jv3TTH_s1mgqCCT5EObbD6b4jR8TTrU7/s1600/motion_2014-04-14_03.14.32_265.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjk9J8VWKBjMu29Gs_arS_tmFlo9zaIOipxBHuvalg1gRaZZ7e2fNZhdAztE9yQ6q9zYaKF66PtNjfnCjpRTgZm2bIrYYpDwj2I-F3DYYwwL5I4Jv3TTH_s1mgqCCT5EObbD6b4jR8TTrU7/s1600/motion_2014-04-14_03.14.32_265.jpg" height="240" width="320" /></a></div>
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It just goes to show that with the modern (and sometimes slightly less modern) technology we have available and take for granted, it's actually pretty easy to set up some fun and interesting projects to see what's just outside your door. It's probably worth noting, though, that the webcam didn't actually pick up any evidence of said cat eating the food left out for it, even though it was definitely gone the next morning!</div>
<br />Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com0tag:blogger.com,1999:blog-7178497075567803207.post-91518055464780518272014-01-07T10:05:00.000+11:002014-01-07T10:21:16.035+11:00Testing the Bechdel Test<div class="separator" style="clear: both; text-align: left;">
So, recently <a href="http://www.vocativ.com/01-2014/hollywood-movies-strong-female-roles-make-money/?utm_content=buffer705ea&utm_source=buffer&utm_medium=twitter&utm_campaign=Buffer">this article</a> came out showing that of the top 50 movies of 2013, those that passed the Bechdel Test made more money overall at the US Box Office than those that didn't. For those not in the know, the Bechdel Test evaluates whether a movie has two or more named women in it who have a conversation about something other than a man. The test seems simple enough to pass, but surprisingly quite a lot of movies don't! Of the 47 top movies that were tested, only 24 passed the test (and <i>at least*</i> seven of those were a bit dubious). Gravity was understandably excluded from the test because it didn't really <i>have</i> more than two named characters**, and apparently no-one has bothered to test the remaining two.</div>
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The article comes with this nifty little infographic:</div>
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I've seen a couple of complaints on the web by people saying that this isn't enough proof - the somewhat ingenuous reasoning I saw was that the infographic shows totals and not averages, so can't prove that the average Bechdel-passing film performs better. Though there are more passes (24) than fails (23), the difference is not nearly enough to account for the almost 60% difference in total gross sales. The averages can quickly be calculated from the infographic above - the average passing film makes $176m, and the average failing film makes $116m, still a very substantial $60m difference!</div>
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A more reasonable criticism is that it may be possible that things just happened this way by chance. Maybe this year a handful of big films happened to be on the passing side, and if they had failed there'd be no appreciable difference? Well, we can test that as well using the information in the infographic. All we need to do is run what's called a <i>randomisation test</i> - this is where we randomly allocate the 50 tested movies in this list to the "pass", "fail" and "excluded" categories in the same numbers as in the real case (so, 24 passes, 23 fails, 3 excluded). We can use a random number generator to do this, or if you're playing along at home, put pieces of paper in a hat, whatever. We repeat this process a large number of times (I did it 10 million times) and see how often we can replicate that $60m difference between passing and failing films <i>or better</i> by chance alone.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEin2U8EooRg4AzwWse_-q7XFp6WMgyjovFo8J9DPzxMvRTsLDxN1GxQX7Bfb1jaLQMJLB3cGlKXqbXiVAA1hf8jVlERkUPUVfKT3y-ULFWgk-d7vn1EnlehA5BjiZE1QmKhgSY17IVnK1YP/s1600/bechdel.hist.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEin2U8EooRg4AzwWse_-q7XFp6WMgyjovFo8J9DPzxMvRTsLDxN1GxQX7Bfb1jaLQMJLB3cGlKXqbXiVAA1hf8jVlERkUPUVfKT3y-ULFWgk-d7vn1EnlehA5BjiZE1QmKhgSY17IVnK1YP/s1600/bechdel.hist.jpeg" height="316" width="400" /></a></div>
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It turns out that when you put your pieces of paper in a hat to make your own test, you'll only be able to beat the actual difference 0.71% of the time, or about 1 in 140 times. This is pretty good evidence that it's not a fluke and that the Bechdel Test really did influence movies' bottom lines this past year. One thing that we <i>can't </i>say based on this is whether this is a direct effect - i.e. that people consciously or subconsciously decided to go watch passing films over failing films. It could be that there is some indirect, or <i>confounding</i> effect, causing this phenomenon. For example, maybe directors who write films that pass the test tend to be better filmmakers in other ways which make people want to watch their films more? Either way, a trend towards more women in substantial roles in films can be no bad thing! (though it's worth mentioning that passing the Bechdel test by no means guarantees a "substantial role", and even failing movies can have their strong points - see <a href="http://www.bust.com/the-mako-mori-test-picking-up-where-the-bechdel-test-left-off.html">this link</a>)</div>
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<span style="font-size: x-small;">* Having watched Man of Steel, I'd argue that it was pretty dubious too - I think the only non-about-a-man conversations between two women were one-sided one liners (hardly a conversation)... in any case, any feminist points it may have gained were swiftly taken away in my book by the female US Air Force Captain being mostly portrayed like a ditz rather than as a dedicated leader of people required for the rank. <a href="http://bechdeltest.com/view/4238/man_of_steel/">More here</a>.</span></div>
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<span style="font-size: x-small;">** So I'm told. I haven't watched it yet.</span></div>
Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com2tag:blogger.com,1999:blog-7178497075567803207.post-83714825156542426032013-09-09T17:34:00.001+10:002013-09-10T08:47:39.966+10:00Senate number crunchingFor those outside Australia, or for those Australians who are living (or, understandably, hiding) under a rock, we've just had our national elections, at which our all of the seats of our government have been decided and half of the seats in our Senate (the house of review).<br />
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Though almost all of the seats in the lower house have been decided, which is normal for election night, the results for the Senate generally take days to weeks to be fully finalised. Though most of the seats are generally worked out fairly quickly - in particular, those seats going to the major parties - the remaining few seats are far less certain.<br />
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The use of the <a href="http://en.wikipedia.org/wiki/Single_transferable_vote">Single Transferable Vote </a>system for the Australian Senate means that votes for minor parties go through a convoluted process of 'transfer' from candidate to candidate, which is further complicated by the <a href="http://en.wikipedia.org/wiki/Group_voting_ticket">Group Voting Ticket</a> system and the deals made by minor parties with each other for preferences. What this means is that a party receiving a very small number of votes can obtain a seat in the Senate simply by the snowballing of preferences from other small parties.<br />
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This has been particularly apparent in this election, with the <a href="http://www.abc.net.au/news/federal-election-2013/results/senate/">current estimated results</a> by the ABC suggesting that as many as 8 seats are likely to go to parties outside of the main three (the Liberal/National coalition, the Australian Labor Party and the Australian Greens), with seats controversially likely to go to members from the Australian Sports Party and <a href="http://www.smh.com.au/federal-politics/federal-election-2013/likely-senator-dodges-questions-about-kangaroo-poo-fight-video-20130909-2tf8j.html">Australian Motoring Enthusiasts Party</a>, which only received a tiny fraction of the initial vote. The popular media has already heavily covered these results even though they are still by no means yet certain.<br />
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Because of the above complexities, it can take only a small variation in voting to change the result for one or more seats. In this sense, the ABC's estimate is fairly naive: they assume that all voters have voted 'above the line', allowing their preferences to be decided by their chosen party (though this is not so far from the truth, with over 95% of voters generally doing so) and that the final results will be accurately represented by the results that have come in so far (between 50-80% of the vote for each state). Working out what potential bias there may be in the remaining votes is possible to a certain extent, as the voting information includes voting breakdowns for smaller regions (and can be compared with past elections), and some regions are known to have regular skews in their voting patterns.<br />
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What I've done here more simply, however, is to look at how much effect there might be in random fluctuations in the remaining votes to be counted. I assumed that the proportions of votes to each party so far were an accurate representation of the electorate's intent - based on those numbers, I randomly generated the remaining expected votes to be counted (based on current enrolment numbers and last election's turnout - around 94% on average).<br />
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For Tasmania, for example, my results usually follow the ABC's results - two each of Labor and Liberal senators are elected, one Greens senator, and one from the Palmer United Party are elected as expected. However, in about 4% of cases (for 1000 election runs) a member of the Sex Party is elected instead of the Palmer United candidate, and in a further 1% of cases a third Liberal Party member is elected.<br />
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Taking into account the other sources of fluctuation mentioned above adds to this uncertainty in the results - <a href="https://www.googledrive.com/host/0BxZwU4bDY5aRbG9mNnE1eXByWWs/senate_results_onthenight_wsnat.html">the Geeklections site</a> and <a href="http://originaltruthseeker.blogspot.com.au/2013/09/senate-results-consolidated-9-9-13-10pm.html">the Truth Seeker blog</a> go into much more detail. This only goes to show that surprises are not only possible but likely as the counting continues...Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com0tag:blogger.com,1999:blog-7178497075567803207.post-2600340599921438202013-08-12T14:59:00.000+10:002013-08-12T14:59:11.870+10:00Why we can't really see the starsIf 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:<br />
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<a href="http://upload.wikimedia.org/wikipedia/commons/thumb/5/5c/R_Doradus_ESO.jpg/250px-R_Doradus_ESO.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://upload.wikimedia.org/wikipedia/commons/thumb/5/5c/R_Doradus_ESO.jpg/250px-R_Doradus_ESO.jpg" /></a></div>
<br />
<br />
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?<br />
<br />
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 <a href="http://en.wikipedia.org/wiki/Airy_disk">Airy disk</a>. 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.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGHtZgPQkmclIZ71Ods5eOxZ6KoX91PdlItbUIyXIv328nBpRyAzb0YAQ9xWvOfrgItQBW_ja4eEMtFpdfg284I3Bzod_4s6PggHEq2-na-v_zA7xmcKIhvK0FkMyQncQsSOOdEeTlkl3l/s1600/stars1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGHtZgPQkmclIZ71Ods5eOxZ6KoX91PdlItbUIyXIv328nBpRyAzb0YAQ9xWvOfrgItQBW_ja4eEMtFpdfg284I3Bzod_4s6PggHEq2-na-v_zA7xmcKIhvK0FkMyQncQsSOOdEeTlkl3l/s320/stars1.png" width="318" /></a></div>
<br />
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.<br />
<br />
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.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfbDOTXw3ExKM5IUDgg4ZLf3wqxtzPN-PE8XGz3lVDRfXs7GxnMEAUf8j61CGCwV42nObbsxkKb2uA-_hMS5jT9zGq79Ko8UrNYLkr-l4ZFNB2w3d3ecq1uGBr8rNAQ2BfPiH7GztnSc2-/s1600/stars2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="318" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfbDOTXw3ExKM5IUDgg4ZLf3wqxtzPN-PE8XGz3lVDRfXs7GxnMEAUf8j61CGCwV42nObbsxkKb2uA-_hMS5jT9zGq79Ko8UrNYLkr-l4ZFNB2w3d3ecq1uGBr8rNAQ2BfPiH7GztnSc2-/s320/stars2.png" width="320" /></a></div>
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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. </div>
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<br /></div>
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So humanity has a long way to go yet before we can <i>really</i> see the stars. Now if only I could afford a telescope...</div>
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<span style="font-size: xx-small;">* the largest, the Herschel Space Telescope, has a diameter of 3.5 metres.</span></div>
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Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com1tag:blogger.com,1999:blog-7178497075567803207.post-63171529523198433002013-07-22T09:07:00.000+10:002013-07-22T10:35:15.430+10:00Crappy daysSome days you just know are going to be long and painful. I have a few strategies to survive mine:<br />
<br />
<b>1. Sugary substances</b><br />
<b><br /></b>
Chocolate in any form is always appreciated, but on cold, miserable winter days a nice warming hot chocolate or <a href="http://en.wikipedia.org/wiki/Milo_(drink)">Milo </a>(link for those not in Milo-drinking countries) can make it all seem a little better.<br />
<br />
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<a href="http://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Australian_milo.jpg/300px-Australian_milo.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Australian_milo.jpg/300px-Australian_milo.jpg" /></a></div>
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<br /></div>
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<b>2. Cute things on the internet</b></div>
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<b><br /></b></div>
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It's an internet cliche because it works - my girlfriend (who now <a href="http://seasofgales.wordpress.com/">has a blog</a>!) 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:</div>
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<br /></div>
<div style="text-align: center;">
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/yNZ8CFnDBfs?feature=player_embedded' frameborder='0'></iframe></div>
<br />
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<br /></div>
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<b>3. Puzzles</b></div>
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<b><br /></b></div>
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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 <a href="http://projecteuler.net/">Project Euler</a> (warning - non-programmers will really struggle!)</div>
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<br /></div>
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<b>4. Music</b></div>
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<b><br /></b></div>
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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 <a href="https://soundcloud.com/irixx">iriXx</a>'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 <a href="http://enolafall.bandcamp.com/">Enola Fall</a>.</div>
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<b>5. Writing</b></div>
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<b><br /></b></div>
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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!</div>
Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com1tag:blogger.com,1999:blog-7178497075567803207.post-60055519580451009102013-07-12T10:28:00.000+10:002013-07-13T14:06:44.943+10:00Mathematically possible - GWS making the AFL finals<span style="font-size: x-small;">(Update: thanks to Gazza White and the <a href="http://www.reddit.com/r/AFL/comments/1i4uj6/the_gws_giants_can_still_make_the_finals/">AFL subreddit</a> for linking my post - it's already by far my most popular blog post!)</span><br />
<br />
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.<br />
<br />
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 <i>is</i> a mathematical possibility.<br />
<br />
Here is the current AFL ladder as of the end of Round 15 (courtesy of <a href="http://www.fanfooty.com.au/game/ladder.php">FanFooty </a>- note that the official AFL ladder is not actually up to date!)<br />
<br />
<table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse; margin-right: 0px; padding-bottom: 0px; padding-top: 0px; width: 639px;">
<colgroup><col style="mso-width-alt: 2304; mso-width-source: userset; width: 47pt;" width="63"></col>
<col span="9" style="width: 48pt;" width="64"></col>
</colgroup><tbody>
<tr height="38" style="height: 28.5pt;">
<td class="xl64" height="38" style="height: 28.5pt; width: 47pt;" width="63"><b>Team</b></td>
<td class="xl65" style="width: 48pt;" width="64"><b>P</b></td>
<td class="xl65" style="width: 48pt;" width="64"><b>W</b></td>
<td class="xl65" style="width: 48pt;" width="64"><b>D</b></td>
<td class="xl65" style="width: 48pt;" width="64"><b>L</b></td>
<td class="xl65" style="width: 48pt;" width="64"><b>For</b></td>
<td class="xl65" style="width: 48pt;" width="64"><b>Agt</b></td>
<td class="xl65" style="width: 48pt;" width="64"><b>Percent.</b></td>
<td class="xl65" style="width: 48pt;" width="64"><b>Pts</b></td>
<td class="xl69" rowspan="20" style="width: 48pt;" width="64"></td>
</tr>
<tr height="20" style="background-position: initial initial; background-repeat: initial initial; height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Hawthorn</td>
<td class="xl66" style="width: 48pt;" width="64">14</td>
<td class="xl66" style="width: 48pt;" width="64">12</td>
<td class="xl66" style="width: 48pt;" width="64">0</td>
<td class="xl66" style="width: 48pt;" width="64">2</td>
<td class="xl66" style="width: 48pt;" width="64">1645</td>
<td class="xl66" style="width: 48pt;" width="64">1167</td>
<td class="xl66" style="width: 48pt;" width="64">141</td>
<td class="xl66" style="width: 48pt;" width="64">48</td>
</tr>
<tr height="20" style="background-position: initial initial; background-repeat: initial initial; height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Geelong</td>
<td class="xl67" style="width: 48pt;" width="64">14</td>
<td class="xl67" style="width: 48pt;" width="64">12</td>
<td class="xl67" style="width: 48pt;" width="64">0</td>
<td class="xl67" style="width: 48pt;" width="64">2</td>
<td class="xl67" style="width: 48pt;" width="64">1556</td>
<td class="xl67" style="width: 48pt;" width="64">1216</td>
<td class="xl67" style="width: 48pt;" width="64">128</td>
<td class="xl67" style="width: 48pt;" width="64">48</td>
</tr>
<tr height="20" style="background-position: initial initial; background-repeat: initial initial; height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Essendon</td>
<td class="xl66" style="width: 48pt;" width="64">14</td>
<td class="xl66" style="width: 48pt;" width="64">11</td>
<td class="xl66" style="width: 48pt;" width="64">0</td>
<td class="xl66" style="width: 48pt;" width="64">3</td>
<td class="xl66" style="width: 48pt;" width="64">1483</td>
<td class="xl66" style="width: 48pt;" width="64">1142</td>
<td class="xl66" style="width: 48pt;" width="64">129.9</td>
<td class="xl66" style="width: 48pt;" width="64">44</td>
</tr>
<tr height="20" style="background-position: initial initial; background-repeat: initial initial; height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Sydney</td>
<td class="xl67" style="width: 48pt;" width="64">14</td>
<td class="xl67" style="width: 48pt;" width="64">10</td>
<td class="xl67" style="width: 48pt;" width="64">1</td>
<td class="xl67" style="width: 48pt;" width="64">3</td>
<td class="xl67" style="width: 48pt;" width="64">1379</td>
<td class="xl67" style="width: 48pt;" width="64">1048</td>
<td class="xl67" style="width: 48pt;" width="64">131.6</td>
<td class="xl67" style="width: 48pt;" width="64">42</td>
</tr>
<tr height="20" style="background-position: initial initial; background-repeat: initial initial; height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Fremantle</td>
<td class="xl66" style="width: 48pt;" width="64">14</td>
<td class="xl66" style="width: 48pt;" width="64">10</td>
<td class="xl66" style="width: 48pt;" width="64">1</td>
<td class="xl66" style="width: 48pt;" width="64">3</td>
<td class="xl66" style="width: 48pt;" width="64">1201</td>
<td class="xl66" style="width: 48pt;" width="64">954</td>
<td class="xl66" style="width: 48pt;" width="64">125.9</td>
<td class="xl66" style="width: 48pt;" width="64">42</td>
</tr>
<tr height="20" style="background-position: initial initial; background-repeat: initial initial; height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Richmond</td>
<td class="xl67" style="width: 48pt;" width="64">14</td>
<td class="xl67" style="width: 48pt;" width="64">9</td>
<td class="xl67" style="width: 48pt;" width="64">0</td>
<td class="xl67" style="width: 48pt;" width="64">5</td>
<td class="xl67" style="width: 48pt;" width="64">1387</td>
<td class="xl67" style="width: 48pt;" width="64">1190</td>
<td class="xl67" style="width: 48pt;" width="64">116.6</td>
<td class="xl67" style="width: 48pt;" width="64">36</td>
</tr>
<tr height="20" style="background-position: initial initial; background-repeat: initial initial; height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Collingwood</td>
<td class="xl66" style="width: 48pt;" width="64">14</td>
<td class="xl66" style="width: 48pt;" width="64">9</td>
<td class="xl66" style="width: 48pt;" width="64">0</td>
<td class="xl66" style="width: 48pt;" width="64">5</td>
<td class="xl66" style="width: 48pt;" width="64">1321</td>
<td class="xl66" style="width: 48pt;" width="64">1225</td>
<td class="xl66" style="width: 48pt;" width="64">107.8</td>
<td class="xl66" style="width: 48pt;" width="64">36</td>
</tr>
<tr height="20" style="background-position: initial initial; background-repeat: initial initial; height: 15.0pt;">
<td height="20" style="height: 15.0pt;"><span style="color: red;">Pt Adelaide</span></td>
<td class="xl67" style="width: 48pt;" width="64"><span style="color: red;">14</span></td>
<td class="xl67" style="width: 48pt;" width="64"><span style="color: red;">8</span></td>
<td class="xl67" style="width: 48pt;" width="64"><span style="color: red;">0</span></td>
<td class="xl67" style="width: 48pt;" width="64"><span style="color: red;">6</span></td>
<td class="xl67" style="width: 48pt;" width="64"><span style="color: red;">1317</span></td>
<td class="xl67" style="width: 48pt;" width="64"><span style="color: red;">1158</span></td>
<td class="xl67" style="width: 48pt;" width="64"><span style="color: red;">113.7</span></td>
<td class="xl67" style="width: 48pt;" width="64"><span style="color: red;">32</span></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td class="xl68" colspan="9" height="20" style="height: 15.0pt; width: 431pt;" width="575"></td></tr>
<tr height="20" style="background-position: initial initial; background-repeat: initial initial; height: 15.0pt;"><td height="20" style="height: 15.0pt;">West Coast</td>
<td class="xl66" style="width: 48pt;" width="64">14</td>
<td class="xl66" style="width: 48pt;" width="64">7</td>
<td class="xl66" style="width: 48pt;" width="64">0</td>
<td class="xl66" style="width: 48pt;" width="64">7</td>
<td class="xl66" style="width: 48pt;" width="64">1404</td>
<td class="xl66" style="width: 48pt;" width="64">1277</td>
<td class="xl66" style="width: 48pt;" width="64">109.9</td>
<td class="xl66" style="width: 48pt;" width="64">28</td>
</tr>
<tr height="20" style="background-position: initial initial; background-repeat: initial initial; height: 15.0pt;">
<td height="20" style="height: 15.0pt;">North Melb.</td>
<td class="xl67" style="width: 48pt;" width="64">14</td>
<td class="xl67" style="width: 48pt;" width="64">6</td>
<td class="xl67" style="width: 48pt;" width="64">0</td>
<td class="xl67" style="width: 48pt;" width="64">8</td>
<td class="xl67" style="width: 48pt;" width="64">1435</td>
<td class="xl67" style="width: 48pt;" width="64">1210</td>
<td class="xl67" style="width: 48pt;" width="64">118.6</td>
<td class="xl67" style="width: 48pt;" width="64">24</td>
</tr>
<tr height="20" style="background-position: initial initial; background-repeat: initial initial; height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Carlton</td>
<td class="xl66" style="width: 48pt;" width="64">14</td>
<td class="xl66" style="width: 48pt;" width="64">6</td>
<td class="xl66" style="width: 48pt;" width="64">0</td>
<td class="xl66" style="width: 48pt;" width="64">8</td>
<td class="xl66" style="width: 48pt;" width="64">1331</td>
<td class="xl66" style="width: 48pt;" width="64">1219</td>
<td class="xl66" style="width: 48pt;" width="64">109.2</td>
<td class="xl66" style="width: 48pt;" width="64">24</td>
</tr>
<tr height="20" style="background-position: initial initial; background-repeat: initial initial; height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Adelaide</td>
<td class="xl67" style="width: 48pt;" width="64">14</td>
<td class="xl67" style="width: 48pt;" width="64">6</td>
<td class="xl67" style="width: 48pt;" width="64">0</td>
<td class="xl67" style="width: 48pt;" width="64">8</td>
<td class="xl67" style="width: 48pt;" width="64">1288</td>
<td class="xl67" style="width: 48pt;" width="64">1228</td>
<td class="xl67" style="width: 48pt;" width="64">104.9</td>
<td class="xl67" style="width: 48pt;" width="64">24</td>
</tr>
<tr height="20" style="background-position: initial initial; background-repeat: initial initial; height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Gold Coast</td>
<td class="xl66" style="width: 48pt;" width="64">14</td>
<td class="xl66" style="width: 48pt;" width="64">5</td>
<td class="xl66" style="width: 48pt;" width="64">0</td>
<td class="xl66" style="width: 48pt;" width="64">9</td>
<td class="xl66" style="width: 48pt;" width="64">1197</td>
<td class="xl66" style="width: 48pt;" width="64">1341</td>
<td class="xl66" style="width: 48pt;" width="64">89.26</td>
<td class="xl66" style="width: 48pt;" width="64">20</td>
</tr>
<tr height="20" style="background-position: initial initial; background-repeat: initial initial; height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Brisbane</td>
<td class="xl67" style="width: 48pt;" width="64">14</td>
<td class="xl67" style="width: 48pt;" width="64">5</td>
<td class="xl67" style="width: 48pt;" width="64">0</td>
<td class="xl67" style="width: 48pt;" width="64">9</td>
<td class="xl67" style="width: 48pt;" width="64">1133</td>
<td class="xl67" style="width: 48pt;" width="64">1451</td>
<td class="xl67" style="width: 48pt;" width="64">78.08</td>
<td class="xl67" style="width: 48pt;" width="64">20</td>
</tr>
<tr height="20" style="background-position: initial initial; background-repeat: initial initial; height: 15.0pt;">
<td height="20" style="height: 15.0pt;">W. Bulldogs</td>
<td class="xl66" style="width: 48pt;" width="64">14</td>
<td class="xl66" style="width: 48pt;" width="64">4</td>
<td class="xl66" style="width: 48pt;" width="64">0</td>
<td class="xl66" style="width: 48pt;" width="64">10</td>
<td class="xl66" style="width: 48pt;" width="64">1102</td>
<td class="xl66" style="width: 48pt;" width="64">1433</td>
<td class="xl66" style="width: 48pt;" width="64">76.9</td>
<td class="xl66" style="width: 48pt;" width="64">16</td>
</tr>
<tr height="20" style="background-position: initial initial; background-repeat: initial initial; height: 15.0pt;">
<td height="20" style="height: 15.0pt;">St Kilda</td>
<td class="xl67" style="width: 48pt;" width="64">14</td>
<td class="xl67" style="width: 48pt;" width="64">3</td>
<td class="xl67" style="width: 48pt;" width="64">0</td>
<td class="xl67" style="width: 48pt;" width="64">11</td>
<td class="xl67" style="width: 48pt;" width="64">1129</td>
<td class="xl67" style="width: 48pt;" width="64">1337</td>
<td class="xl67" style="width: 48pt;" width="64">84.44</td>
<td class="xl67" style="width: 48pt;" width="64">12</td>
</tr>
<tr height="20" style="background-position: initial initial; background-repeat: initial initial; height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Melbourne</td>
<td class="xl66" style="width: 48pt;" width="64">14</td>
<td class="xl66" style="width: 48pt;" width="64">2</td>
<td class="xl66" style="width: 48pt;" width="64">0</td>
<td class="xl66" style="width: 48pt;" width="64">12</td>
<td class="xl66" style="width: 48pt;" width="64">981</td>
<td class="xl66" style="width: 48pt;" width="64">1775</td>
<td class="xl66" style="width: 48pt;" width="64">55.26</td>
<td class="xl66" style="width: 48pt;" width="64">8</td>
</tr>
<tr height="20" style="background-position: initial initial; background-repeat: initial initial; height: 15.0pt;">
<td height="20" style="height: 15.0pt;"><span style="color: lime;">W. Sydney</span></td>
<td class="xl67" style="width: 48pt;" width="64"><span style="color: lime;">14</span></td>
<td class="xl67" style="width: 48pt;" width="64"><span style="color: lime;">0</span></td>
<td class="xl67" style="width: 48pt;" width="64"><span style="color: lime;">0</span></td>
<td class="xl67" style="width: 48pt;" width="64"><span style="color: lime;">14</span></td>
<td class="xl67" style="width: 48pt;" width="64"><span style="color: lime;">1003</span></td>
<td class="xl67" style="width: 48pt;" width="64"><span style="color: lime;">1921</span></td>
<td class="xl67" style="width: 48pt;" width="64"><span style="color: lime;">52.21</span></td>
<td class="xl67" style="width: 48pt;" width="64"><span style="color: lime;">0</span></td>
</tr>
</tbody></table>
<br />
In <span style="color: lime;">green </span>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 <span style="color: red;">red</span>). Unfortunately for GWS, there are also 8 games left in the season, so one thing is immediately clear: GWS must win <b>all 8</b> of their games, and Port Adelaide lose <b>all 8</b> 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:<br />
<br />
<table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse; width: 181px;"><tbody>
<tr height="20" style="height: 15pt;"><td height="20" style="height: 15pt; width: 88pt;" width="117"><b>Team</b></td><td align="right" style="width: 48pt;" width="64"><b>Points</b></td></tr>
</tbody></table>
<table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse; width: 181px;">
<colgroup><col style="mso-width-alt: 4278; mso-width-source: userset; width: 88pt;" width="117"></col>
<col style="width: 48pt;" width="64"></col>
</colgroup><tbody>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt; width: 88pt;" width="117">Hawthorn</td>
<td align="right" style="width: 48pt;" width="64">52</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Geelong</td>
<td align="right">52</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Fremantle</td>
<td align="right">46</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Essendon</td>
<td align="right">44</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Sydney</td>
<td align="right">42</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Richmond</td>
<td align="right">36</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Collingwood</td>
<td align="right">36</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;"><span style="color: red;">Port Adelaide</span></td>
<td align="right"><span style="color: red;">32</span></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;"><span style="color: lime;">GWS</span></td>
<td align="right"><span style="color: lime;">32</span></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">West Coast</td>
<td align="right">28</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Carlton</td>
<td align="right">28</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Adelaide</td>
<td align="right">28</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">North Melbourne</td>
<td align="right">24</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Gold Coast</td>
<td align="right">24</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Brisbane</td>
<td align="right">24</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Western Bulldogs</td>
<td align="right">16</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">St Kilda</td>
<td align="right">16</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Melbourne</td>
<td align="right">8</td>
</tr>
</tbody></table>
<br />
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, <b>none</b> 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 <b>don't</b> 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.<br />
<br />
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 / 2<sup>62</sup> = <b>3.27 in a hundred thousand billion chance</b> of finishing equal 8th on points.<br />
<br />
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 <b>winning both times</b>. Even THAT would be twice as likely as GWS finishing <i>equal </i>8th, on a <i>good day</i>.<br />
<br />
Notice that I've mentioned GWS finishing <i>equal </i>8th. Even this herculean feat doesn't guarantee them a place - in the very <b>best case</b> 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:<br />
<br />
<table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse; width: 181px;">
<colgroup><col style="mso-width-alt: 4278; mso-width-source: userset; width: 88pt;" width="117"></col>
<col style="width: 48pt;" width="64"></col>
</colgroup><tbody>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt; width: 88pt;" width="117"><table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse; width: 181px;"><tbody>
<tr height="20" style="height: 15pt;"><td height="20" style="height: 15pt;"><b>Team</b></td><td align="right"><b>Points</b></td></tr>
</tbody></table>
</td><td style="width: 48pt;" width="64"><br /></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Geelong</td>
<td align="right">76</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Fremantle</td>
<td align="right">66</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Hawthorn</td>
<td align="right">64</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Essendon</td>
<td align="right">60</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Sydney</td>
<td align="right">54</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Collingwood</td>
<td align="right">52</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Richmond</td>
<td align="right">48</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;"><span style="color: red;">Port Adelaide</span></td>
<td align="right"><span style="color: red;">32</span></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;"><span style="color: red;">Carlton</span></td>
<td align="right"><span style="color: red;">32</span></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;"><span style="color: red;">Adelaide</span></td>
<td align="right"><span style="color: red;">32</span></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;"><span style="color: red;">Gold Coast</span></td>
<td align="right"><span style="color: red;">32</span></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;"><span style="color: red;">Western Bulldogs</span></td>
<td align="right"><span style="color: red;">32</span></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;"><span style="color: lime;">GWS</span></td>
<td align="right"><span style="color: lime;">32</span></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">West Coast</td>
<td align="right">28</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">North Melbourne</td>
<td align="right">28</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Brisbane</td>
<td align="right">28</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">St Kilda</td>
<td align="right">28</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt;">Melbourne</td>
<td align="right">28</td>
</tr>
</tbody></table>
<br />
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.<br />
<br />
<a href="http://afl.allthestats.com/?itm=11113519">This informative site</a> 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%.<br />
<br />
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.<br />
<br />
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!<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhM2lcR9AEz7cNdI3UYqMN3Q2ClNo8Htb5lwcKpsC5K90BfWdvfjrERDZo_uhyphenhyphenl5wWg_zzjfOwat80a4q8KgGr74BjJRU4ZiOmfMD0eRUjheuwrS9xKYhlZgHYNRJ_lCsbgLRfdTmMj1Qm4/s1600/giants.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhM2lcR9AEz7cNdI3UYqMN3Q2ClNo8Htb5lwcKpsC5K90BfWdvfjrERDZo_uhyphenhyphenl5wWg_zzjfOwat80a4q8KgGr74BjJRU4ZiOmfMD0eRUjheuwrS9xKYhlZgHYNRJ_lCsbgLRfdTmMj1Qm4/s640/giants.png" width="619" /></a></div>
<br />Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com2tag:blogger.com,1999:blog-7178497075567803207.post-16338412794983877182013-07-08T15:13:00.000+10:002013-07-08T15:18:34.527+10:00MusicAfter 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 (<a href="https://www.facebook.com/thesolutiontheband?fref=ts">The Solution</a>), 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.<br />
<br />
One of these has been the choir I joined last year - the <a href="http://www.tasmaniansongcompany.org.au/">Tasmanian Song Company</a>. 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!<br />
<br />
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.<br />
<br />
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."<br />
<br />
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!Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com0tag:blogger.com,1999:blog-7178497075567803207.post-76556903465124120752012-12-22T10:58:00.000+11:002012-12-22T11:01:14.984+11:00At the End of the Day<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOFqPKaxxL5j5o9jnmom5rWa1VLOyKwCBDb_yv9RG77u8FMZpC2dyZHdGHAhlvdWPSAGkWFnLd5Q2RALy7E-H3ESb6ItTnJrNRSfobCYuAfDrql0gsZIa1QZA8mSGXwKZWI6YJUeQ3KQ4c/s1600/20121221_144137%5B1%5D.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOFqPKaxxL5j5o9jnmom5rWa1VLOyKwCBDb_yv9RG77u8FMZpC2dyZHdGHAhlvdWPSAGkWFnLd5Q2RALy7E-H3ESb6ItTnJrNRSfobCYuAfDrql0gsZIa1QZA8mSGXwKZWI6YJUeQ3KQ4c/s320/20121221_144137%5B1%5D.jpg" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The view from my window</td></tr>
</tbody></table>
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.<br />
<br />
I'm here because I was lucky enough to be awarded the <a href="http://www.britishecologicalsociety.org/grants/honours_awards_prizes/southwood_prize.php">Southwood Prize</a>, 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 <i>human</i> 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.<br />
<br />
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 <a href="http://blog.shuningbian.net/">Steve</a> 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.<br />
<br />
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.<br />
<br />
<span style="font-size: xx-small;">* But hey, at least there's reliable free wi-fi.</span><br />
<span style="font-size: xx-small;">** I admit that after seeing the Arc de Triomphe, the Marble Arch looked very small indeed.</span><br />
<span style="font-size: xx-small;">*** I'd have learned more about the average Frenchperson if I spoke French.</span><br />
<span style="font-size: xx-small;">**** Not so much in the bank account, however.</span>Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com1tag:blogger.com,1999:blog-7178497075567803207.post-17682739072660286482012-09-15T10:55:00.000+10:002012-09-15T10:57:28.046+10:00Launch day!So, it's finally here - the day where I <a href="https://www.facebook.com/events/464325066933256/">launch my EP</a>. 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 <i>all about me</i>.<br />
<br />
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!<br />
<br />
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 <a href="https://www.facebook.com/events/464325066933256/">Facebook page for the launch</a> 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 <i>vocal</i>) crowd.<br />
<br />
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 <b>thank you</b> - everyone who's bought a copy already, asked about it, even <i>considered</i> 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**.<br />
<br />
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 <i>after</i> tonight - planning gigs, writing songs, maybe even recording some. Nearly all of that will be done with my band, <a href="https://www.facebook.com/thesolutiontheband">The Solution</a>, 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!<br />
<br />
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 <a href="http://nickbeeton.bandcamp.com/">bandcamp site</a> 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 <a href="http://nickbeeton.bandcamp.com/">http://nickbeeton.bandcamp.com</a> or press some buttons below!<br />
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<iframe allowtransparency="true" frameborder="0" height="410" src="http://bandcamp.com/EmbeddedPlayer/v=2/album=506724928/size=grande3/bgcol=000000/linkcol=4285BB/" style="display: block; height: 410px; position: relative; width: 300px;" width="300"><a href="http://nickbeeton.bandcamp.com/album/the-longest-night-ep">The Longest Night EP by Nick Beeton</a></iframe>
<span style="font-size: xx-small;">* cliched moment warning</span><br />
<span style="font-size: xx-small;">** I warned you!</span>Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com0tag:blogger.com,1999:blog-7178497075567803207.post-21509906741754117902012-08-20T18:52:00.001+10:002012-08-20T19:08:29.787+10:00Locked and loaded<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVIdFHlvuDxxmG0nwrLCQTTXUK5cDmgpw5OwOQt-PCVmPgp4l_OmdBnnWLOx-x63UqqLHhcM3-H7dKCi0UT2_K3n0bgK2k5cAeqNeJF9S8GO9vXWsyFXP0qu2TZGv34ljqH10oO387B0sZ/s1600/front.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVIdFHlvuDxxmG0nwrLCQTTXUK5cDmgpw5OwOQt-PCVmPgp4l_OmdBnnWLOx-x63UqqLHhcM3-H7dKCi0UT2_K3n0bgK2k5cAeqNeJF9S8GO9vXWsyFXP0qu2TZGv34ljqH10oO387B0sZ/s320/front.jpg" width="320" /></a></div>
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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!<br />
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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 <a href="http://www.therealdavemac.com/">David McEldowney</a> and <a href="http://www.velvetrecordings.com/george/">George Begbie</a>), 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!<br />
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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 <i>available online </i>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*** :)<br />
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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!<br />
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<iframe frameborder="no" height="166" scrolling="no" src="http://w.soundcloud.com/player/?url=http%3A%2F%2Fapi.soundcloud.com%2Ftracks%2F56916601%3Fsecret_token%3Ds-VShVv&show_artwork=true&secret_url=true" width="100%"></iframe><br />
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<span style="font-size: x-small;">* Also, I changed the name. I'm indecisive >_></span><br />
<span style="font-size: x-small;">** Except for a computer, of course. Let's not get crazy here!</span><br />
<span style="font-size: x-small;">*** And maybe <i>they'll</i> buy it, seeing as you won't. Stingy bastard. (kidding!)</span>Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com1tag:blogger.com,1999:blog-7178497075567803207.post-70567178881245792522012-08-04T22:03:00.000+10:002012-08-04T22:05:02.103+10:00An abundance of silverStatistics can be a really useful way to get a feel for when a "strange event" may just be coincidence, and when it is likely to be something more.<br />
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For example, sports fans may have noticed that our gold medal tally is less than stellar so far. Another thing that becomes clear when looking at our medal tally (as of 4th August, 9pm) is that though we have a dearth of gold, we have managed to get quite a lot of silver medals! As it stands, we have 16 medals: 1 gold, 10 silver, and 5 bronze. A curious person might wonder whether there's a reason for that - is it just random chance that it happened that way, or is it something else - maybe our Olympians are psyching themselves up too much and falling at the last hurdle to winning gold?<br />
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As it happens, there is a way to get an idea of this using statistics! According to legend, in the 1920s a statistician called Fisher wanted to test his friend's boast that she could always tell whether the milk or tea was added to first to the cup. He tested her boast by giving her 8 cups of tea - four with the milk added first, and four with tea. She got every one of these right and Fisher - using a test known to this day as Fisher's exact test - calculated that if she had guessed, she would have had a less than 1 in 70 chance of getting all 8 correct.<br />
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We can use Fisher's exact test to work out the probability of getting 10 or more silver medals if there's an equal chance of getting gold, silver, or bronze and we get 16 medals overall. It turns out there are 153 different combinations, and 28 of those involve 10 or more silver medals. Most of these are incredibly unlikely to occur by chance, with the most likely being 3 gold, 10 silver and 3 bronze - this has an 0.4% chance of happening at random!<br />
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All together, the chance of getting at least 10 silver medals at random is 1.6%, or about 1 in 60 - almost as unlikely as the lady having a lucky break with her tea drinking! Most scientific literature counts a value of less than 5% as "statistically significant" - meaning that the result is unlikely to have occurred by chance. Of course, this kind of analysis doesn't tell us why it's happening this way, and unfortunately it sheds even less light on how to fix it...Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com2tag:blogger.com,1999:blog-7178497075567803207.post-16351315367014612232012-07-26T11:35:00.003+10:002012-07-26T11:37:37.376+10:00An end to hoop-jumping<span>Just now, I got the email finally telling me that my thesis has been approved by a meeting of Academic Senate and I can finally graduate. No more hoops! This is the penultimate step in a long series of tiny achievements:</span><br />
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<li>Write final version of PhD thesis (the longest step!)</li>
<li>Send thesis to supervisors (then deal with their comments - this can take months)</li>
<li>Send thesis to School for a final pre-submission check (then deal with <i>those</i> comments)</li>
<li>Send thesis off for examination by two experienced international researchers (ok, so one of them was from New Zealand - still counts!), wait for several months...</li>
<li>Deal with <i>those</i> comments, send through to Head of School (along with evidence that I've actually dealt with those comments and not just ignored them)</li>
<li>Get thesis approved by the Head of School (an important step - it means I never have to edit it again!)</li>
<li>Make <i>realllly</i> sure that I haven't made any typos or formatting mistakes, then send thesis off to be bound in shiny pretty books</li>
<li>Get books signed by the necessary people then give them to the Graduate Research Office</li>
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and, finally,</div>
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<li>Get my final thesis approved by the Senate and be placed in a graduation schedule.</li>
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So now all I have to do is wait for August 11th and graduate! As you can probably see, the main problem with getting a PhD accepted is that there are so many steps that you can never be sure when to go all out and celebrate - in a way, it sucks out a little of the joy because there's no single defined endpoint. Though doing a PhD certainly feels like doing a marathon, the analogy stops at the finishing line because instead of one big ribbon to run through at the end, there are a lot of little finish lines along the way! So I decided a while ago to save the biggest party for graduation day - the day I can finally call myself Doctor.</div>
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I thought I'd try and give some kind of idea what it is I do every day, without sending everyone to sleep. One of the projects I'm doing right now (hopefully) gives a nice little example!</div>
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I'm trying to model how lizards might move through the landscape, in a collaboration with someone who actually knows something about lizards - because there's no point doing modelling if what you're modelling is completely unrealistic!<br />
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One current idea I'm working on is the concept that the landscape contains a set number of basking rocks (in this case: 2000, randomly placed in a square kilometre), which every lizard has to have access to in order to survive. So to over-simplify, let's assume that each established lizard has a territory containing one of these basking rocks. Juvenile lizards disperse from their maternal den in order to find their own territory, and we assume that they sprint off in a random direction (they're not very bright), and don't stop until they either find an unoccupied rock or die without a territory. We arbitrarily set the distance they can travel before keeling over to 20 metres. Using this information, we can then generate a map of which rocks are accessible (i.e. within 20 metres) from other rocks, and connect them with lines:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju-LmSe7AEMd3-ESb9B5CakG8N6oJWt17NmBVyfNDnXkP8YluL4d8IpAubtXd04q2GXrSwWUmk9iIRV3WDm949hlLbRATh30Ni9bOSlh9RcF4-yCJFiBCXghGTUWKMhlZDn0iC1bvJxyRr/s1600/rocks2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju-LmSe7AEMd3-ESb9B5CakG8N6oJWt17NmBVyfNDnXkP8YluL4d8IpAubtXd04q2GXrSwWUmk9iIRV3WDm949hlLbRATh30Ni9bOSlh9RcF4-yCJFiBCXghGTUWKMhlZDn0iC1bvJxyRr/s400/rocks2.png" width="500" /></a></div>
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One thing that immediately becomes clear is that there are quite a few rocks that are more than 20 metres away from <i>any</i> other rock - this means that any baby lizard trying to find another territory from there will inevitably die, unless their mother has died (giving up her claim to the maternal territory) and it is the first of its siblings to claim it. Clearly, setting a hard limit for the distance a juvenile can travel has serious implications for survival!</div>
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The next problem is to work out how likely a juvenile from a given site is to find another rock (assuming there even <i>are</i> any within 20 metres). As they're not very bright, we assume they'll only stumble across a rock if they travel within one metre of it during their dash to freedom - so we can draw lines that show the range of angles they can travel to find each rock, like below. Though most of them are straightforward to get to, in this example, you can see there is a rock directly behind another rock - so the juvenile will always just choose the first one it reaches. There is also a lot of space between rocks, so a juvenile has to be pretty lucky to be able to establish a territory in the first place!</div>
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Things aren't always so straightforward, however. Sometimes a lizard might be lucky and pass one rock just to find another - in the example below, in a couple of places one rock is <i>partially </i>covering the one behind it, but there is a small chance that a lizard will go straight past it and find the rock behind it.</div>
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There are more complicated cases again if two rocks are within a metre of each other!<br />
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Next time on the mathsy part of the blog, I'm thinking of looking at Snakes and Ladders - and how it gets more complicated when you have to choose between moving multiple tokens - or I could go back to looking at Cribbage like I did a while ago <a href="http://firstsignofmadness.blogspot.com.au/2011/01/cribbage-part-1.html">in this post</a>. Any thoughts?Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com1tag:blogger.com,1999:blog-7178497075567803207.post-82652564492381004992012-06-07T09:09:00.002+10:002012-08-20T18:24:32.067+10:00Didn't Know (aka the Duck Song)<div class="separator" style="clear: both; text-align: center;">
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Thanks everyone for your support and comments while I tried out this new gimmick to drum up interest! Voting has now closed and the clear winner was <i>Didn't Know</i>, one of my most often-played songs recently!<br />
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<i>Didn't Know</i> - 6 votes<br />
<i>Green Eyes</i> - 3 votes<br />
<i>The Garden</i> - 1 vote<br />
<i>Survive You</i> - 1 vote<br />
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The very simple riff for this song entered my head in a dream, and persisted after I woke up... I managed to play it on a guitar, and then all I needed to do was add lyrics. I really had trouble with this part of the process, and ended up putting in some placeholder lyrics about an "omnipotent duck" to try and move things along. I fully intended to change them for something more serious later on, but my girlfriend insisted they stay... and so has basically everyone else who's heard the song so far. When recording, I gave <a href="http://www.therealdavemac.com/">Dave</a> completely free rein and told him to add as much messed-up stuff as possible - I think he's done an amazing job of that :)<br />
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So here it is - enjoy!<br />
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<iframe frameborder="no" height="166" scrolling="no" src="http://w.soundcloud.com/player/?url=http%3A%2F%2Fapi.soundcloud.com%2Ftracks%2F48868389%3Fsecret_token%3Ds-1hHGQ&show_artwork=true&secret_url=true" width="100%"></iframe>
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... oh. I guess you want to know who won the free copy of the EP. Well, I used my magical random number generator, and the winner was... Ariel Pascoe (whose fine vocals you'll see featured on the final cut of the EP!). But she's already getting a free copy, so I ran it again and the winner is the first voter, who I happen to know is the infamous <a href="https://www.facebook.com/irixx">IriXx Jorvik</a>! She's planning to write a remix for "the duck song" so I think it's very fitting that she wins the free EP. Congratulations!<br />
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More news will be coming up soon, so stay tuned! Who knows, if you're lucky I'll even release another track before the EP launch and give away another copy!Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com0tag:blogger.com,1999:blog-7178497075567803207.post-49270931725352447862012-06-04T13:59:00.001+10:002012-08-20T19:08:50.469+10:00Return of the prodigal EPHey peeps!<br />
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As my regular followers know, I like to play music and have been slowly putting together an EP of my own songs over the course of the last couple of years. I'm excited to announce that it's nearly done, and I'll hopefully be launching it later this year!<br />
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We have a relatively polished version of each of the tracks, and I'd like to put one of them on here - but I'll let <i>you</i> decide which. I've already posted one of them (<a href="http://firstsignofmadness.blogspot.com.au/2011/01/in-which-things-are-revealed.html">Longest Night</a>), but there are four previously unaired tracks left to choose from:<br />
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Green Eyes<br />
Survive You<br />
Didn't Know<br />
The Garden<br />
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Just mention which track you'd like to hear in the comments below, and after a few days (or once I get enough interest) I'll choose the track with the most comments to publish here on the blog! Just to keep things interesting, I'll<b> randomly choose</b> <b>one of the responses to win a free copy of my EP</b> :) So what have you got to lose?<br />
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<span style="color: red;">(Note: if the site won't let you post a comment, try anonymous mode!)</span>Nickhttp://www.blogger.com/profile/17873678238374563087noreply@blogger.com11