Author Archives: zebra

Space Oddity

Just when I was reflecting that a post on the Mule was long overdue and I really should get on to writing something, guest poster James Glover has come to the rescue to share his reflections in a guest post on space jumping.

You may have seen media reports of “Fearless” Felix Baumgartner, an Austrian, who takes BASE jumping to a whole new level (literally). He ascended to a height of 40km over the US in a helium balloon and then free-jumped back to Earth, eventually landing safely and breaking several long held records in the process. What I found curious when I looked at the photos though was how far away from the Earth he looked. You might disagree, after all 40km is a long way up. Curiously it is just under the standard distance for a marathon (42km). Humans though have a curious mental process aberration – vertical heights appear much more significant than horizontal ones. That’s why we get scared at the top of a 20m building but think nothing of that as a horizontal distance. If I said a man had just run 40km you’d think him a marathon runner and not having just completed a singular feat of human daring, unless you were actually at Marathon on Greece in 490BC when the first “marathon” supposedly took place.

In fact given the Earth has a radius of 6,400km, 40km represents less than 1% of that. If the Earth were a globe 30cm across (I hear that such things exist!) then his jump would be from a height of 1mm. From that height the Earth is still pretty up close and in your face. By comparison the International Space Station or ISS has an average height of 360km and that is considered to be only in “near Earth orbit”. That vision you see of astronauts floating around the ISS in zero-g isn’t because they are outside the Earth’s gravitational field. At 360km gravity is 90% what is in on the Earth’s surface. They float because the orbital velocity of the ISS, about 7.7kms^-1, needed to stop it falling, means they are in free fall – albeit on a trajectory that means they don’t head straight down.

I have been on a bit of an Earth geometry kick lately so I applied some trigonometry to this problem. Firstly I worked out that at 40km the angle the Earth subtends to a viewer is 167 degrees, compared to 180 degrees at the surface. By contrast at the moon (distance from Earth approximately 380,000km) the angular width of the earth is 2 degrees. In fact you can also show that the distance Fearless Felix could see on the Earth’s surface from (his) horizon to horizon is 1,400km or about the distance from Adelaide to Sydney. From the top of the Sydney Tower (height 260m) the horizon is about 58km away or approximately the distance to Penrith. This also explained why when in Tokyo you can see about 80% of Mt Fuji (height 3776m), from the ground, even though it is 104km away and hence well over the standard horizon. Actually I tried to see it from the top of Roppongi Tower (height 238m) and from there you can potentially see 96% of Mt Fuji. Unfortunately I got there at midday and to see it you have to get there before the smog thickens, by about 11am.

So what of the picture of the jump by Fearless Felix? Well using the same geometric principles and applying some advanced beer coasterology I think the picture is a fake. Fake in the sense that they have used a special lens to deliberately increase the apparent curvature of the Earth to make it look like he was jumping from deeeeep spaaaaace! It is the astronomical equivalent of photo shopping on a few curves to a model to improve her wow factor (though I understand, in practice, the opposite usually occurs).

To see why consider the image of FF himself. Assuming he was about 2m tall I would estimate that the apparent diameter of the Earth in the photo would be about 5ff (a new astronomical unit I invented). It is possible to show that for that to be a true image the picture must have been taken at a distance of 56cm from Felix. Judging by the craft next to him my guess is it was taken at least 4m away. (If in the picture Earth was only 3ff wide it would need to have been taken at a distance of 34cm)

For that to be a true image, from 4m away, geometry shows, he would have to be not 40km but 500km above the Earth. At that height the Earth would subtend an angle of about 135 degrees which also seems to fit the picture as the human field of vision is about 120 degrees. In fact if the impression they are trying to give with the photo is that he could just see the whole image of the Earth floating in space before him, in his normal field of vision, then he would need to be at least 1,000km above the Earth, not a ground hugging 40km.

My suspicions were confirmed when I saw some vision on the tv news that night shown as FF descended. Whenever the camera pointed to the horizon it was almost flat but when it pointed straight down suddenly the Earth appeared as a ball. It is the camera lens rather than some advanced photo shopping to blame. While this does not detract from the fearlessness of Felix’s jump it is a sad indictment that the organisers of the jump felt the need to up the wow factor so as to make it seem more impressive. I guess they never learned their lesson from when NASA faked the moon landings.

Empire Games

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Many readers have been expecting me to post a follow-up to my Olympic analysis of four years ago. I was in fact expecting it myself and even started collecting data, but somehow it has not happened. Fortunately, regular contributor (and some time beer coaster calculator), James Glover has stepped into the void.

It’s at about this time every four years that the same old boring analysis of Olympic Medals [not for everyone! Ed.] is brought out showing Olympic medals per capita, per GDP, per dollar spent etc. While this is all very useful, this particular Olympics it has failed to show Australia “punching above its weight” and is thus, in reality, the dominant sporting nation not just on the planet, but in the whole of history as well. The Fairfax press has tried to prove this thesis, but there is a spoiler. However you cut it we came out of the top half dozen nations. Personally I don’t think coming 10th in the gold medal count is really that bad. At least we beat the Kiwis right? Hmmm, that gets me thinking…

Actually it also occurs to me that were we just to reach out across the Ditch and extend a filial hand to our beloved New Zealand cousins, combined our trans-Tasman teams and competed under an ANZAC flag we would have finished an even more respectable 5th just behind Russia.

So this got me thinking. How would other groups of nations, alliances or indeed, past empires, have fared in the Games of the XXXth Olympiad? I can’t guarantee my geography is precise (and it is not up for discussion) but here is my best take on it. For these purposes I have not included the US in the British Empire because frankly it was their choice to leave without seeking permission.

In the interests of fairness I have allocated only part of the tally in some cases to take into account that (i) the Romans did not conquer Scotland or Ireland (so 50% of Team GB), and (ii) Quebec is not part of the Anglosphere (so they only get 75% of Canada’s tally – this on advice of a non-Quebecois Canadian). Feel free to continue this game – Axis vs Allies, the French Empire of Bonaparte vs British Empire at the same time. Endless fun now our cold winter days are no longer warmed by the Olympic flame. Interesting to see that in terms of Empires the British come behind the Mongolian Empire and the Roman Empire wins on weighted medals (3,2,1) if not on gold medals alone.

In any event the result proves the strongest alliance of all time is NATO – both the strongest military alliance and, if they wished, the strongest sporting one. Maybe money doesn’t buy you medals but it would seem that missiles do!

Empire/Alliance	Gold	Silver	Bronze	Total	Weighted	% Total
NATO	138	129	139	406	811	45%
EU	95	96	103	294	580	32%
Anglosphere	98	73.75	79	249.5	520	29%
Roman Empire	68	79	72.5	219.5	435	24%
Mongolian Empire	75	54	64	193	397	22%
British Empire	58	58	71	186	361	20%
Soviet Union	45	41	67	153	284	16%
ANZAC	14	18	17	48	95	5.3%

Have wheelchair, will travel…probably

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Spending couple of weeks down the south coast of New South Wales, spotting dolphins and echidnas, has slowed down my blogging. Fortunately, regular contributor James Glover has once more come to the rescue with a guest post. This time his topic is wheelchairs and air-travel.

Perhaps you’ve heard of a recent court case in which a wheelchair user, Sheila King, took Jetstar to court (and lost) on the basis of the Disabilities Discrimination Act? If you are a wheelchair user and you book a flight on one of our airline carriers then a fairly obvious thing won’t happen. Unlike say a bus you won’t be able to board the aircraft in your chair and be strapped in for the journey. What actually happens is that when making the booking you tick a box (or tell the booker on the phone) that you are in a wheelchair. If there are seats available for wheelies when you get to the airport you will give up your chair and be made to use a specially designed “wheelchair” (its a chair, it has wheels) that is designed to be fit the narrow corridor of most planes which I am sure you are aware of – their narrowness, for you, only apparent when the person ahead of you is blocking the aisle loading 3 pieces of carry on luggage into the overhead lockers while chatting to their new friends in the seat they are meant to occupy. We all suffer this situation. These “wheelchairs” are not designed to be used without help, they are more like children’s toy carts and cannot be operated by the user as the wheels are very small and low down. For a wheelchair user to be taken out of their wheelchair in a public place can be quite discombobulating. Many wheelchair users develop a personal relationship with their chair – it is after all a place you spend many of your waking hours.

Digression. The very first time I was in a wheelchair outside the confines of a hospital ward (it was a hospital wheelchair but is the exact same model I now own, like I said it is personal) I was being pushed by none other than the proprietor of this very website! Without going into the details let’s just say it was a pretty dramatic event and we both learned a valuable lesson in wheelchair use and the wheelchair repair workshop at the hospital was kept busy. But I digress.

So here is the thing. According to Google about 1% of the population uses wheelchairs. And a Jetstar plane has about 200 seats so they expect to get about 2 wheelchair users on average per flight. So what is the problem with only allowing this same number on each flight, as some airlines do? Well the problem is that statistically wheelchair users don’t travel in pairs and sometimes there will be less than 2 users and sometimes there will be more. Just as if you toss 10 coins sometimes there will be fewer than 5 heads (the average or expected number) and sometimes there will be more. Only on average will there be 5. In fact it is a simple problem to work out the probability of there being, say, n wheelchair users, given the average of 1% on a 200 seat plane. This is called the Binomial Distribution. If you have access to Excel then the function Binomdist(n,200,1%) will tell you this probability. Before I give you some numbers I admit that the overall population average may not be the same as the average flying on planes. It may be less than 1% due to wheelchair users being put off flying. But maybe on some routes it is higher: but I am guessing the annual “snowbird” migration of retired people from the northern United States to Florida at the start of Winter would track above the 1% rate.

So here are the Binomial probability figures.

Count	Probability
0	13%
1	27%
2	27%
3	18%
4	9%
5	4%
6+	2%

Binomial Probabilities (N=200, p=1%)

For example, assuming a 1% chance of any given passenger a 200 hundred seat plane being in a wheelchair, the probability that there will be exactly 4 wheelchair passengers wanting seats is 9%. To work out the probability of a passenger being denied a seat on their preferred flight, we will assume that we’re dealing with an airline where more than two wheelchair passenges book on a flight, then at least on passenger will have to change their travel plans. From the table above, the chance of the flight only having 0, 1 or 2 wheelchair passengers totals 68%, so there’s a 32% chance that there will be at least one wheelchair passenger who cannot fly. For any one wheelchair passenger, there is a (n-1)/(n+1) chance of being bumped if n other wheelchair passengers book on the flight. Weighting that by the probably that there are n passengers and adding it up for all n>1 gives a probability of 27%. As a frequent flyer in a wheelchair, you can expect to miss out on a seat quite regularly! [Note: these calculations have been updated: the editor’s “corrections” were undone. Ed.]

I am quite fortunate now that I no longer need to travel in my wheelchair. But as I still use a walking stick I wait for everyone else to get off the plane. You sit there, looking behind you to see if everyone else has left. But there are always these strange people who seem to sit there at the back of the plane and wait for 10 minutes or more, after everyone has disembarked, before even moving. You wonder why the airline staff don’t just hurry them off? I assume they aren’t disabled because they are sitting at the back of the plane. If airlines really had a problem with the extra time that getting wheelies off the plane then they could make this up by just moving these people along.

When I first read about this case my initial response was that being disabled and traveling is a bit of challenge anyway and you just get on with it. But the more I thought about it I wondered if the airlines just took it for granted that wheelchair users would change their plans to fit in with the rules. I am glad Sheila King took the issue up!

Roadkill Arithmetic

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Returning for another guest post, James Glover is once again drawn to a beer coaster for some quick, if somewhat morbid, calculations. For those taking to the road over the Christmas period, this post should also serve as a reminder to drive carefully!

Why did the chicken cross the road? To get to The Other Side. This twist on the ending to the iconic joke was based on the observation of a single dead chicken on the road while I was returning by car from Sydney to Melbourne at the end of my recent touring holiday. The holiday in fact started two weeks earlier when I was driving around Tasmania. While there were no chickens, there was a dead sperm whale on the road.

In Tasmania I noted that in addition to its abundance of quality food, beer and wines, it has a remarkable supply of one other thing compared to the mainland: native fauna road kill. If you think that the occasional dead kangaroo (or more likely fox) you see driving in the country is plenty, then you haven’t been to Tassie. We are talking a dead possum or wallaby every kilometre or so, which means if you are driving at 100km/hr means you see one every 36 seconds. While it is unfortunate, particularly for the animals involved, to see so many native animals dead (but no foxes because they have been eradicated from the island), it is actually cause for joy because it indicates a very healthy population of native wildlife.

This got me thinking. Could you actually use the number of road kill to estimate the density of animals living in the bush? The answer is yes, and without any derivation or proof I present it here:

density = road kill ratio/kill zone area

where

road kill ratio = av. distance between cars/
                   av. distance between road kill
kill zone area = 2 x car velocity x time x car width

It’s a surprisingly simple formula, and can also be handy for keeping children occupied on long car trips (at least in Tasmania). The model it is derived from is admittedly fairly simplistic – let’s just call it the “Frogger model of vehicle/animal interaction”. Here the time is important because clearly if we had an infinite amount of time and no method of disposal of road kill then the number would build up without limit. In practice the attendant carrion birds on each road kill and its, shall we say, “freshness” (blood, guts, brains you get the picture) suggests that they were all products of the previous nocturnal period’s collisions. In fact there are road signs indicating to drivers to be particularly careful between dusk and dawn to avoid animals so I take “time” to be 10 hours and assumed all carrion are fresh. Taking the average distance between road kill to be 1km and cars to be 10km gives a road kill ratio of 10. The average car speed was 100 km/hr and my car is about 2.5m wide so putting this all together gives an estimated bush density of 20 animals per square km. That’s about one per 5 hectares. That seems a little on the low side for a densely populated area but as “beer coaster” estimates go, it’s probably not a bad start.

This reasoning got me thinking that there probably true that there are no Tasmanian tigers left, because one would have shown up as road kill by now. Tasmanian rangers patrol the roads every morning looking for Tassie devils to monitor the spread of that awful face tumour disease they get. In fact, I saw two Tassie devils on the road and they were both alive and moving. I also saw three live echidnas: three more than I have seen in my life up to now. As mentioned I also saw a dead sperm whale on the road. Not some replica or whale skeleton either: it had died the day before. It was on the beach near Strahan which I was driving on at the time. So, yes, it was on my road and hence I feel justified classifying it as road kill. And no, I don’t know why the whale crossed the road. Perhaps it mis-heard someone say that in Tasmania there was an abundance of “road krill”.

Train in vain

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James Glover is a regular contributor to the Stubborn Mule who tries, whenever possible, to incorporate back of the beer coaster calculations in his posts. Here his beer coaster helps him skewer the prospects of high speed rail in Australia.

Don’t get me wrong–I love trains. I have caught trains around Europe and even the train from Sydney to Melbourne just for the pleasure of it. My favourite train journey, from London to Edinburgh up the east coast, was made particularly memorable one trip because I was (a) sitting in First Class (as usual), and (b) sharing a booth with two particularly rotund members of the House of Lords including Lord Lawrence “Mad-Eye” Mooney. So, whatever you do please don’t accuse me of trainist tendencies.

With that in mind, you would think I’d be excited by the release of a government report into building a high-speed train line from Melbourne to Sydney and from Sydney to Brisbane, via Newcastle and the Gold Coast. Sadly however the report recommending construction of this train line contains figures which crush any chance of this actually happening. The estimated cost of the build is $100 billion and there would be an estimated 54 million passengers per year. So how does that work out on a beer coaster? To convert $100 billion to an equivalent annual funding cost we just work out how much the government would pay, perpetually, to borrow this amount. At current government long-term yields of 6.00% this represents an annual interest cost of $6 billion. If the government wanted to pay back the capital in 25 years, a typical benchmark for infrastructure projects, the annual payments would increase to about $8 billion. So, calling it 50 million passengers a year, represents a cost per passenger of $160 per trip. That doesn’t seem so bad given that the cost of a one-way plane ticket between Sydney and Melbourne is about $200-400.

Is this just a coincidence? Sadly, no. It appears the planners have flipped the beer coaster over to its dark rum-soaked side to work out how many passengers they would require to make the project commercially feasible and competitive against air travel. It’s a time honoured trick but one that doesn’t stand up to closer scrutiny. In the interest of beercoasternomics and because a Google search failed to find the answer, I estimate the daily number of air passengers between Sydney and Melbourne. Turning to webjet.com, I counted 75 flights from Melbourne to Sydney on a Wednesday. From memory a typical plane on that route has about 40 rows and 6 passengers per row or about 250 passengers. That represents a total of fewer than 20,000 passengers per day. Double that for the return journey and add 25% for the numbers travelling to and from Brisbane. Let’s call it 50,000 passengers per day. Over a whole year our generous estimate of airline passenger numbers Sydney-Melbourne-Brisbane is 20 million. I’m guessing it is really no more than 5 million a year but lets call it 20 million anyway. Even at that figure it falls far short of the 50 million required to make the high-speed rail line economically viable. So why have the planners been so brazen in their estimate? That becomes clear if we used a still optimistic but realistic figure, in my opinion, of say 2 million potential rail passengers a year (which is still over 5000 per day), then the average cost of each passenger, one-way, would be $4,000! I rarely approve the use of ~~“dead dog’s dicks”~~ exclamation marks [strikethrough courtesy of a prudish editor], but really!!! Should this line ever get built I will be a frequent and enthusiastic user of it. $150 for $4,000 value is the sort of bargain that would make a late-night shopping channel host blush.

I suspect by including a few commuter stops at the beginning and end of their trips such as Brisbane to Gold Coast and Sydney to Newcastle and maybe even a new commuter line or two, e.g. Sydney to Epping, they have boosted the overall passenger numbers. But then those people are hardly going to pay over $150 for a short trip. The majority of the cost will still be borne by the (maximum) 2 million intercity travellers. Though even including short trip passengers 50 million seems excessively high until you realise it is really just the figure they need to make the numbers work.

So, sadly, the numbers don’t add up. I won’t comment on the politics except to say the feasibility study is one of promises the Labor Party made to get Greens’ support to form a government. Nor will I comment on the claims that there are hidden environmental and economic benefits. High speed rail in Australia is the classic white elephant which, according to Wikipedia, was a gift made by Thai Kings to obnoxious courtiers to bankrupt them due to the high cost of maintenance of these sacred pachyderms. Some will bring up the precedents of Europe or Asia, but there you have either cheap labour and government requisitioned land or a high density of large cities. Australia has none of these.

As The Clash so prophetically sang: it’s a train in vain.

Gibbons and welfare

Action and reaction on climate change

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Regular guest contributer James Glover (@zebra) takes a closer look at the Coalitions climate change policy.

Malcolm Turnbull, an Australian MP, did a rare and risky thing last week. He actually broke away from the political spin-cycle and explained some figures underlying the cost of the Coalition’s “Real Action on Climate Change” policy. Naturally he was attacked by both the Labor government, who are having trouble selling their own Carbon Tax policy, and his own party colleagues who were horrified that he didn’t stay “on message”. The Coalition quickly bunkered down under orders from the top to avoid discussing Turnbull’s “outburst”. So what was he saying anyway and why was it so controversial?

To see why we need to explain the difference between the Labor Party and conservative Coalition’s policies. There are really only two broad differences. Both policies recognise that anthropogenic climate change is scientific fact, not speculative political fiction. Both recognise the need for action (ie. spending money) on combating climate change. But where they differ is in how global warming should be reversed and how to raise the money to do so. It is not commonly understood but the real difference between the policies is the former.

The Carbon Tax (or its close relative the CPRS) aims to reduce carbon emissions by making carbon pollution relatively more expensive than cleaner, alternate sources of power (and really it’s all about power generation). In order to do this they need to raise the price of carbon powered energy sufficiently to tip the balance in favour of wind, wave, geothermal, biofuels or solar energy (as explained in a recent post here on the Mule). Of the money raised by the Carbon Tax, about half goes back to subsidising the increased power bills of the less well-off. Of the remainder, most goes to developing cleaner sources of energy at lower cost. As explained in the earlier post, when there is no more carbon pollution then there is no more carbon tax to distribute. So ultimately, unless the cost of alternate energy comes down to the levels currently enjoyed by coal, gas or oil based power, in the long run the less well off will be much less well off.

While the Coalition’s “Real Action on Climate Change” has more than a whiff of policy-on-the-run, it can be presented as a respectable alternative. It says that we should ignore the fruitless and expensive attempt to cheapen alternative power and accept carbon pollution as a fact of life. In order to mitigate the effects of carbon pollution, though, we need to remove it from the atmosphere after the pollution has occurred, not at the source. This will cost money. A lot of money. Australia alone currently produces about 0.2 billion tonnes of carbon (not C02) each year. That’s a cubic block of carbon approximately 500m x 500m x 500m*. Each year. Anybody who thinks sequestration is the answer has to find somewhere to put all that carbon for a start. Or plant several million trees a year. The only hope for this reactive approach to reducing carbon is that some method is found which removes large amounts of carbon from the atmosphere at a relatively small cost: and much smaller than the likely Carbon Tax price of $20-40 per tonne. While such methods are conjectured, for example spreading iron filings in the ocean to increase carbon uptake by marine organisms, to say they are untested is an understatement. Equally we could allow carbon to increase in the atmosphere but mitigate the effects of global warming by using giant sunlight reflecting shields. Or paint the Sahara Desert white. Hey, stranger things have happened. But at the moment all these methods remain firmly in the province of science fiction.

So what did Malcolm Turnbull actually say that was so exciting to friend and foe alike? Well, using Treasury forecasts of population and economic growth, that 500m carbon cube will have grown to 850m wide by 2050 (650m tonnes) if we do nothing. Assuming we can mitigate the effects of carbon pollution, or pay someone else to do it for us, the cost could be as low as $15 per tonne or $18bn per year. Assuming the population has doubled by 2050 that’s about $500 per person, or an extra $50 per week on the average household tax bill. Given the extreme rubberiness (definitely not vulcanised rubber) of these figures, that’s pretty much what the Carbon Tax will cost as well. If the initial price of the Carbon Tax is set at $30 per tonne, then over time this should come down as alternate energy becomes actually cheaper due to technology improvements and economies of scale, not just relatively cheaper. Indeed if the Real Action plan involves buying permits from other countries who have set up some sort of CPRS and use alternate energy sources, then the equilibrium cost of both plans is probably pretty much the same, i.e. $15 per tonne. The real action policy really only comes out ahead if one of the fanciful ideas for removing carbon en masse, post production, pays off.

Of course the Coalition’s policy has to be funded somehow, and herein lies the second difference between the two. The Coalition’s policy will involve raising taxes, and probably income taxes as opposed to the Carbon Tax favoured by Labor. So any claim on the Coalition’s part (a point made by Mr Turnbull) that the major benefit of their policy is that it won’t raise electricity prices is totally spurious. Both policies will lessen household discretional spending. By the same amount. That’s all voters ultimately care about. Turnbull also claimed that their policy had the advantage that if “climate change is crap” as Tony Abbot famously is purported to have said, then it can all be dismantled without much cost. For that statement alone, sending a dog-whistle to his party’s climate skeptic supporters, Mr Turnbull deserved the public flaying he got, if not for the right reason.

*Note: in the above I have assumed that 1m cubed of carbon weighs 2 tonnes which is the density of graphite. It obviously depends on the form of carbon used. It is intended as an indicative figure only. Though I wish someone would actually build a structure of that size and point out to everyone this is how much carbon a year we are producing

Carbon tax

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Our regular guest writer James Glover (@zebra) returns to the Stubborn Mule today to look at the real cost of carbon tax…and who pays the cost.

It is no surprise that the latest Newspoll shows the Labor Government sinking under a concerted attack by the Opposition, and its supporters in the media, over the Carbon Tax. The incessant cry of “a great big new tax” was bound to have an effect on the marginal voters who derive their political views in atavistic ways. In fact most of the political arguments lately recently seem to revolve around the distinction between levies and taxes. The trick seems to be if your opponents propose it then it is a tax and if you propose it is a levy—the latter being used by both sides to describe variously the flood levy (Labor) and the parental leave levy (Coalition). Taxes, as opposed to levies, apparently lead to profligate spending and are downright un-Australian. It makes you wonder what they use to fund hospitals, schools and roads.

So how does the Carbon Tax work? And what does it mean to say it is “revenue neutral”? Is it really a tax or “not really a tax” as the Treasurer, Wayne Swan, claims? Suppose the government wants to set up a Carbon Tax for the purposes of reducing carbon emmissions. It does this by imposing a tax (or levy or fee) on the price of goods and services that are deemed to ultimately cause high but avoidable (hence no agriculture) emissions of carbon. This of course raises the price of these goods e.g. electricity. If we impose a Carbon Tax on coal-generated electricity (the sine qua non of carbon emitters) then expect the power companies to pass on all or most of the increase to consumers. Now here’s the thing, the money the tax raises will have gone to subsidise the increased power bills of these very same power consumers. By exactly the same amount as the price should rise. So in effect nothing happens. In other words, at a base level the Carbon Tax does nothing. It has no benefits and no costs. Isn’t it really “a great big snooze tax” and not “a great big new tax”?

The Carbon Tax has one (fully intended) important consequence. If power emitters want to increase their profits they can do so by switching to lower carbon emitting alternatives. These might already be available or they can pay to research and develop them. And because of the tax what was previously uneconomic will now be made viable. Since these alternatives are really more expensive than coal-based power, without the tax, you might ask what is really happening at the cost end. It seems like a tax which costs nobody nothing, magically makes alternatives to carbon emitting industries economic. Voila!

Well that’s what the government would have you believe. On closer examination though it is precisely when the Carbon Tax has its intended effect that the cost gets passed onto consumers. But not when the Carbon tax is first introduced. To see why let’s have a look at an example.

Suppose the cost per unit of producing electricity from coal is $100. The power company charges $110 to consumers and so makes a $10 profit. The Govt introduces a 20% Carbon Tax on the cost of producing electricity using coal. This raises the price to $130 in order for the company to maintain its $10 profit margin. That’s $100 for the coal, $20 for the tax and a profit of $10. The extra $20 gets passed onto the consumer whose bill is now $130 per unit. However after the $20 subsidy (paid for by the $20 proceeds of the tax) they still only pay $110.

In other words: the producers, the consumers, and the government are no better or worse off immediately after a Carbon Tax is introduced. But what happens if the Carbon Tax is successful in reducing emissions? That is when consumers end up paying more. The cost to the company, including the tax, of producing one unit of electricity is $120. Suppose an alternative non carbon-emitting energy source is found which costs $115 per unit. This is more than the coal-based cost before the tax, but less than the cost with the Carbon Tax as this carbon-free energy source, let’s call it “sunshine”, attracts no Carbon Tax. So the company, in order to maintain their profit of $10, charges $125 per unit, less than coal based power with a Carbon Tax. But now the consumer receives no subsidy either so even though their total bill has dropped from $130 (with carbon tax and a subsidy) to $125 without a subsidy. It now actually costs them $125, an increase of $15 over the cost before the carbon tax was introduced and even immediately afterwards. This of course is the extra $15 per unit that it costs to produced electricity from sunshine rather than coal.

That is how the Carbon Tax really works and ends up costing the consumer. You start out with a Carbon Tax which costs nobody anything and end up without a Carbon Tax that everybody ends up paying more for. When it has its intended effect, and there is no coal based power, but also no more money for subsidies. And, in principle, no more carbon pollution.That of course though is really the point. There is a (currently) hidden cost of producing carbon as carbon dioxide and methane in global warming and that is, if the system works, the $15 extra you pay to solve the problem by removing carbon from the economy.

Polls apart on climate change

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Regular Stubborn Mule guest James Glover (@zebra) turns his statistical expertise on some apparently contradictory polls gauging opinions on climate change.

Two polls came out today on the question of whether people believed climate change is real and if so whether it is caused by human activity. The first was a Newspoll published in The Australian and the second was by Essential Media and was commented upon by Essential’s Peter Lewis on ABC’s The Drum. Intriguingly, the Newspoll suggests 73% of Australians believe in climate change with a significant human contribution (so called Anthropogenic Global Warming or AGW). Now The Australian has copped a bit of flak lately for its alleged anti-climate change agenda, but leaving that aside this poll suggests that AGW should be practically a closed book politically as an overwhelming majority believe in it. Essential Media describes themselves as a research tool for progressive political campaigns. Essential’s poll indicates that only 45% of people believe in climate change caused by human activity. In the accepted narrative of such things the results would have been around the other way and the tweetsphere would be apoplectic accusing The Australian and News Corp of once again distorting Newspoll results for their own right-wing political agenda. So what is happening here?

First a note on sampling error. Essential polled 1896 people while Newspoll contacted 1,123 people. For polls where the expected split is approximately 50% a good rule of thumb for margin of error (MoE) is 1/√sample size. In the two polls here this gives MoEs of 2.2% and 3.0% respectively. MoE represents two standard deviations from the sample average so differences of 25% are extremely unlikely (like 10^-10 probability unlikely) to be explained by a unfortunate random choice of sample from the general population.

The most likely explanation is that one or both of these polls suffer from an underlying sampling bias. This would be easy enough to generate artificially—just poll people in Newtown if you want to get more people who believe in AGW or in Bob Katter’s seat for the opposite result (is this a little glib? Maybe, but you know I am right). But legitimate pollsters like Essential and Newspoll rely on the rigour of their sampling technique. Especially as every time you publish a controversial result, a large section of the population who disagree with it will accuse you of bias. There are a number of techniques to reduce bias—one is to ask coquestions whose population statistics are well accepted. For example if in your poll you found that 46% of the respondents were female and 54% were male you can readjust the result to reflect the actual population average of 51:49. I assume both polling organisations follow standard methodologies to minimise bias. Often though their actual methodologies are proprietary so question marks remain. A famous political polling agency was well know to always come up with polling results that reflected the political opinions of its founder after “adjustment for bias”.

Some indication that there isn’t an overwhelming bias are some additional questions about voting intention. Here are the results:

	Essential	Newspoll
Coalition	45%	41%
Labor	38%	34%
Green	11%	14%
Other	6%	11%

I would have to say that the differences in the numbers are on the borderline of being consistent with the MoEs I estimated. In any event the Newspoll which has a higher number believing in AGW has less Coalition voters (though about the same Labor+Green votes). It seems unlikely that the votes for Independents and other alone could account for the 28% difference in the polls on the question of AGW.

So that leaves us with the polls themselves. I have assumed so far that they asked the same questions, but there are major differences. Here are the actual questions and results:

Essential

Climate change is happening and is caused by human activity	45%
We are just witnessing a normal fluctuation in the Earth’s climate	36%
Don’t know	19%

Newspoll

No climate change	18%
Climate change solely caused by human activity	18%
Climate change partly caused by human activity	55%
Climate change not caused by human activity	3%
Believe in climate change but don’t know cause	2%
Don’t know if climate change is real	5%

Now what appears at first to be a headline difference between the polls is more subtle. It is quite hard (I tried) to map the answers between them exactly to compare the results. For example Essential doesn’t ask if the respondents directly if they don’t believe in climate change at all (18% in Newspoll) so presumably the climate skeptics get lumped under “Don’t know” (19%) which will also include those who believe in climate change but don’t know if it is caused by human activity or don’t know if climate change is real. That Newspoll total of “don’t knows” and skeptics is 23%, a bit higher than Essentials “Don’t know” of 19% but within the MoEs as reflected by the voting intention results.

However we can try to compare the two main results which boil down to “Believe climate change is real and human activity is significantly affecting it” of 73% (Newspoll’s headline result combining “solely” and “partly” caused by human activity) vs Essential’s “Climate change is happening and is caused by human activity” of 45%. The difference appears huge. The only thing I can think to explain this is that when not offered the choice of “solely” vs “partly” caused by human activity the Essential respondents threw their lot in with “caused by a normal fluctuation in the Earth’s climate”. In other words the results are consistent if most people who believe that “climate change is real” but don’t believe it is “solely caused by human activity” believe it is “partly caused by human activity” but mostly due to “natural fluctuations in the Earth’s climate”.

What is clear here is that the wording of polls is important and that both polls failed to tease out the subtle distinctions in people’s views on climate change (though Newspoll did a better job of this than Essential). There are also question marks about the sampling bias as shown in the voting intention results. But the headlines of both polls will superficially look like totally different results. And that is a problem when the results are used to support political rather than scientific views on anthropogenic global warming as fact or fiction.

Do your block in!

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Sydney’s property market is a subject that has found its way onto the Stubborn Mule more than once. In this post, regular guest contributor Zebra (James Glover) manages to combine property and television with some now-traditional beer coaster calculations.

Channel 9’s high rating renovation show The Block just finished its successful second series on Wednesday night. It concluded with an auction of the four properties that the contestant couples had spent 8 weeks, and in excess of $80,000 each, renovating. The prize for the contestants was the “profit” of whatever they made at auction in excess of the stated reserve. The reserves were varied to reflect unique features of each apartments such as views, an outdoor living area or double garage. The idea was that the couple with the best renovation skills would see their apartment achieve the most above the reserve. In the end the couple who won, John and Neisha, achieved a price of $1,105,000 with a reserve of $900,000 and so made $205,000 (they also won first prize and an additional $100,000 which we’ll ignore for now). Wow! $205,000! Okay that was for 8 weeks of back-breaking unpaid labour. But still. It makes you think that this renovating lark might be a pretty profitable way for making a living. A couple of apartments like that a year and you’d be in gravy! Or would you?

The first thing to consider is the fact that the other couples didn’t do quite so well, making $87,500 (Jake and Erin), $47,000 (Mark and Duncan) and nix (Brendan and Chez’s apartment passed in below the reserve). Okay, you say, but that is still an average of $85,000 for each couple or $42,500 per person for a couple of months’ work. So take $42,500, divide by 8 weeks times by 52 weeks, carry the 2, take off 20% for holidays less breakages tap, tap, tap, that represents an annual profit of about $200,000 each. Still not bad. Break out the champagne!

But buried in the self-congratulatory articles, no doubt generated by Channel 9’s PR department, are some sobering facts. Put away the Kristal and maybe open a cask of Ben Ean and take a seat. The entire unrenovated apartment block was bought for $3.4m. The total amount spent on renovations (not including the couples’ labour) was $470,000 (including $100,000 on common areas). That makes $3.87m. The total sale price was $3.89m. So the total profit was a pretty modest $20,000. And that doesn’t include stamp duty (about $200,000) or agent’s commission ($78,000 @ 2%) plus, let’s say, legal costs of $2,000. So, in reality, the washup of The Block is a loss of $260,000. They don’t mention that in the publicity.

My back of the beer coaster calculations show John and Neisha were still the “winners” having only lost $60,000 on their reno. Jake and Erin and Mark and Duncan each would have lost $66,000 and, still last, Brendan and Chez’s reno lost $67,000. Perhaps Channel 9 should deduct John and Neisha’s loss from the winners’ prize of $100,000 and present them with a cheque for the $40,000 difference.

More revealing than the illusion that this was a profitable business from a renovators point of view is that the total reserve price was $3.55m. Now I’d expect the total reserve to at least equal the break-even cost of the apartments, or $4.15m. In fact it was $600,000 below the actual cost of buying, renovating and selling The Block. If in a very public show like this, with 1.2m viewers, the agents can so blatantly quote below the break-even reserve then what hope for the tens of thousands of buyers in suburbia struggling to match house ads with reality? It’s enough to do your block in.