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Showing posts with label politics. Show all posts
Showing posts with label politics. Show all posts
Tuesday, 14 May 2013
Monday, 25 March 2013
The TV show QI is a marvellous source of trivia. A while back I heard them say that Sainsbury's is shrinking the size of the tube through the centre of toilet rolls to save volume, and hence the number of delivery lorry trips needed. A quick Google confirms that this is the case: the diameter of the roll has fallen from 123mm to 112mm, whilst keeping the amount of paper the same. (I hope no makers were relying on the constant diameter of the correspondingly shrinking tube for any long term projects.)
This (123-112)/123 = 1-0.91 = 9% reduction in diameter doesn't look much for a single roll:
However, once you get a lot of rolls, the saving soon adds up:
Assuming that the height of the rolls is the same, the 9% reduction in diameter corresponds to a 1-0.912 = 1-0.83 = 17% reduction in volume. Hence more rolls can be packed in each delivery lorry, with a claimed saving of 500 lorry trips, or 140 tonnes of CO2, per year.
But we could do better, surely? I've shown the rolls on a square grid, because that's how they are packed:
But what about a hexagonal packing?
Now each roll occupies a hexagon of half-height r, not a square of half-height r:
What space does this take? The hexagon is made of 6 equilateral triangles, each of height r. If the side is of length h, then we have r = h sin 60 = h √3 / 2. The area of the triangle = 1/2 x base x perpendicular height = h/2 x r = r2 / √3. The area of the hexagon is 6 times this, or 2√3 r2 = 3.464 r2. The square, meanwhile, has area 4 r2. (And not coincidentally, 3.464 is a better approximation to π than is 4.) Hence hexagonal packing is (4 - 3.464)/4 = 0.134, or a little over 13%, better than square packing.
Doing the sums to combine the percentages properly [viz, 1-(1-17%)(1-13%)=0.28], this means hexagonal packing and smaller rolls combined gives about 28% improvement over the original large, square packed rolls.
So Sainsbury's could save a further 300-odd lorry trips, and a further 90 tonnes CO2, by packing the rolls hexagonally.
Maybe I should write them a letter?
This (123-112)/123 = 1-0.91 = 9% reduction in diameter doesn't look much for a single roll:
 |
| 123mm v 112mm, to scale overlaid for comparison |
 |
| the difference is clear with 40 rolls |
But we could do better, surely? I've shown the rolls on a square grid, because that's how they are packed:
But what about a hexagonal packing?
 |
| smaller rolls, and now hexagonally packed |
 |
| square boundary hexagonal boundary equilateral triangle |
What space does this take? The hexagon is made of 6 equilateral triangles, each of height r. If the side is of length h, then we have r = h sin 60 = h √3 / 2. The area of the triangle = 1/2 x base x perpendicular height = h/2 x r = r2 / √3. The area of the hexagon is 6 times this, or 2√3 r2 = 3.464 r2. The square, meanwhile, has area 4 r2. (And not coincidentally, 3.464 is a better approximation to π than is 4.) Hence hexagonal packing is (4 - 3.464)/4 = 0.134, or a little over 13%, better than square packing.
Doing the sums to combine the percentages properly [viz, 1-(1-17%)(1-13%)=0.28], this means hexagonal packing and smaller rolls combined gives about 28% improvement over the original large, square packed rolls.
So Sainsbury's could save a further 300-odd lorry trips, and a further 90 tonnes CO2, by packing the rolls hexagonally.
Maybe I should write them a letter?
Thursday, 24 May 2012
To all of you who don't realise we are already living in the future (albeit one without jet-packs), here's a thought from Charlie Stross:
"to the extent that mainstream literary fiction is about the perfect microscopic anatomization of everyday mundane life, a true and accurate mainstream literary novel today ought to read like a masterpiece of cyberpunk dystopian SF."
Sunday, 19 February 2012
I had a fine time in Thessalonika, and managed to avoid any olives. Interesting people, good conversation, great food; what more could you ask for?
It was sunny, but cold, with a bracing north wind blowing down from the still-snow-capped mountains. Although the sun shone brightly, there was a low level haze, obscuring the views. However, around lunchtime on the Thursday it was a bit clearer, and my hosts pointed out a mountain visible across the bay: Mount Olympus.
The food was excellent in quality, very varied, and too much in quantity. My hosts wanted to ensure that I experienced a whole range of styles and flavours; this would work best in a tapas-like style setting, but is a little overwhelming when each extra example dish ordered is what I consider to be a full meal in itself. I sampled widely, but could not eat it all, no matter how much I wanted to! And I skipped the breakfasts.
Given all the recent news about troubles in Greece (which some were claiming has been manufactured by the government, in order to frighten the people into accepting the economic cuts), my main impression of Thessalonika is of a calm, peaceful, friendly, and welcoming city. There were large groups of people thronging the streets for the "Burnt Thursday" (Tsiknopempti) festival (with lots of barbecues before Lent), and everyone was good natured and enjoying themselves, with no sign of trouble or anger, and none of the drunken rowdiness one would find in England. I'd love to go back there, with more time to explore, both the city, and the surrounding mountains.
It was sunny, but cold, with a bracing north wind blowing down from the still-snow-capped mountains. Although the sun shone brightly, there was a low level haze, obscuring the views. However, around lunchtime on the Thursday it was a bit clearer, and my hosts pointed out a mountain visible across the bay: Mount Olympus.
The food was excellent in quality, very varied, and too much in quantity. My hosts wanted to ensure that I experienced a whole range of styles and flavours; this would work best in a tapas-like style setting, but is a little overwhelming when each extra example dish ordered is what I consider to be a full meal in itself. I sampled widely, but could not eat it all, no matter how much I wanted to! And I skipped the breakfasts.
Given all the recent news about troubles in Greece (which some were claiming has been manufactured by the government, in order to frighten the people into accepting the economic cuts), my main impression of Thessalonika is of a calm, peaceful, friendly, and welcoming city. There were large groups of people thronging the streets for the "Burnt Thursday" (Tsiknopempti) festival (with lots of barbecues before Lent), and everyone was good natured and enjoying themselves, with no sign of trouble or anger, and none of the drunken rowdiness one would find in England. I'd love to go back there, with more time to explore, both the city, and the surrounding mountains.
Tuesday, 19 April 2011
On the 5th of May, the UK has a referendum on whether to change the way we vote for our MPs from the current "first past the post" (FPTP, the "No" campaign) to the Alternative Vote system (AV, the "Yes" campaign).
I had been intending to vote "Yes" (for AV). Then I saw material from the "No" campaign. That material has swayed my decision –- to absolutely absolutely vote "Yes". The "No" campaign's distortions and/or stupidities are just shocking. (It is interesting to see the campaign, since there are party members from both major parties in each of the Yes and the No camps -– strange bedfellows indeed.)
So, what’s the fuss?
With FPTP, you have a list of N candidates, and put a cross next to one of them; the candidate with the most crosses wins. With the proposed AV, you have a list of N candidates, and rank them, putting 1 for your first choice, 2 for your second. You can go all the way up to N, ranking the lot, or stop sooner, when you don’t care about the ranking of the rest. The first preference (those with a 1) are counted. If someone gets more than half these votes, they win (this is only likely in a "two horse race", or where the further "horses" are rank outsiders). Otherwise, the candidate who came last (the one who fewest voters wanted as first choice) has their second preference votes redistributed to the rest. This carries on (the last candidate’s votes redistributed) until someone has more then 50%, and wins.
AV sounds more complicated than FPTP. Well, it is more complicated than FPTP. But that doesn't necessarily mean it's worse.
Consider the following scenario. There are three main parties, the PolkaDots, the Maroons, and the Turquoises. The PolkaDots are a minority party, but with quite a big following, about 20% of the vote. The Maroons and Turquoises are roughly evenly split: about 40% each. I support the PolkaDots, am tolerant of the Maroons, but really really hate the Turquoises.
Under FPTP, who am I going to vote for? The Maroons, of course. I can hear the campaign now: "a vote for the PolkaDots is a wasted vote"; "a vote for the PolkaDots is really a vote for Turquoise/Maroon" (depending on whether it’s a Maroon or Turquoise statement). So hardly anyone votes for the PolkaDots: 20% of the electorate are in some sense disenfranchised.
Under AV, however, I can safely put PolkaDots first, then Maroons. I probably leave off the Turquoises, or put them third, depending how I decide to indicate my disgust with them. (In fact there's always a smattering of really minority candidates: I hate the Turquoises so much I'll even put the looney StripyParty above them, but I'll put the Turquoises above the CrossHatches, who are just plain evil). My support for the PolkaDots gets counted, even though they come third, and then my second choice is given to the Maroons, who win. I'm not devastated: PolkaDots third again, but at least I got Maroons, who I can live with, and my real support for the PolkaDots got counted.
But maybe, just maybe, enough people do this, and hey, the Turquoises come third. Their votes are redistributed. And since no Turquoise supporter would be seen dead in Maroon, their second choice votes are for the PolkaDots. And we win! And those Turquoise voters aren't devastated either: they came third, but at least the hated Maroons didn't win. The compromise candidate dissatisfies least.
Sounds sensible enough. Maybe there is a hidden problem that makes AV disastrous? After all, there's Arrow's theorem, that basically says, given some axioms desirable in any voting system, the only voting system that obeys those axioms is a dictatorship. So it seems there is no "fair" voting system: maybe AV is less fair than FPTP?
If so, the FPTP "No" campaign will be pointing this out. So, let's look. Oh.
I caught the end of a TV broadcast for the "No" campaign, without knowing what it was. First of all, I thought it was comedy sketch, mocking the stupidity of people who couldn't understand AV. Then I thought it was a slightly tasteless "Yes" campaign broadcast, mocking the stupidity of people who couldn't understand AV. It was only at the end that I realised it was a "No" campaign broadcast (presumably self-mocking their own stupidity?)
Then their campaign leaflet fell through the letterbox.
One: it starts with the slogan "Keep One Person, One Vote". The slogan "One Person, One Vote" is part of the universal suffrage campaign, for people who don't have a vote at all. AV isn't going to remove people from the electoral roll. Fear mongering.
Two: complaints about the cost -– "£250 million", the cost of electronic vote counting machines and education in the new system. This is contrasted with what else the money could be spent on (always a dubious tactic -– just because money isn’t spent on one thing doesn’t mean it will be on something else): "2,503 doctors, 6,297 teachers, 8,107 nurses, 35,885 hip replacements or 69,832 school places". First of all, notice the tiny "or" in there: it's doctors OR teachers OR nurse OR hips OR school places, but formatted to look like them all. Also, is that a salary for a month, a year, the lifetime of the person? Compared to the £250M, is that per year, per election, or what? Bad statistics.
Three: "The second or third best can win under AV" versus "Under our present system, the one who comes first is always the winner". Notice that weasely use of the word "best". Voting for your Parliamentary representative is not at all analogous to a horse race or foot race, where the fastest, the best, is first past the winning post. It's more analogous to a group of people choosing where to go for an evening's entertainment, where 40% love skating, hate football, and are fine with the cinema, and another 40% love football, hate skating, and are fine with the cinema, and the final 20% love the cinema (and they all have to go to the same place, rather than split up). With AV, it's the cinema, and everyone is reasonably happy; with FPTP it's either football or skating, with 40% very unhappy. What then is the "best" choice? Why should the "one who comes first" (is most people's first preference, even though that's a minority of the people) be the winner? After all, under FPTP, just because there is a majority for someting doesn't mean there isn't a bigger majority against it! Undefined (and misleading) terminology, combined with false analogy. (I can’t complain that they use "FPTP" terminology, as this is the standard name for the system; I can complain when they use it as an analogy, poorly).
This is accompanied by a photograph of a foot race, with an arrow to the guy in last place (subtly dressed in black, to boot), saying "The winner under AV", not so subtly implying this it what always happens. (There's also the minor fact that the person who comes last -- has fewest first preference votes -- can never win under AV, as their votes get redistributed first.)
Four: "It is wrong that the person who came second or third can overtake the person with the most votes and be allowed to win because the second, third or even lower choices of supporters of extreme parties such as the BNP are counted again and again and again." More fear mongering, by naming an extremist minority party. What about other, non-extremist, minority parties? If I like the looney StripyParty, so put them first, then the PolkaDots, then the Maroons, then the Turquoise, why shouldn’t my wish for the Maroons-more-than-Turquoise be counted just as much as that of a Maroon-firster? (This argument appears to be the source of the "Keep One Person, One Vote" slogan.)
One argument the No campaigners don't use in their leaflet, but that I have heard others use, is that AV might even allow some nasty extremists to gain power (if they were everyone's second choice, say). Well, there's a name for specially designing an electoral system so that it stops those nasty people you don't like from winning: undemocratic. Rather than squelching all those nasty bigots by disenfranchising them, I'd much prefer a system that helps educate them out of their bigotry, and an electoral system that doesn't encourage extremism in the first place. So I was disappointed by the Electoral Reform Society's otherwise excellent site on AV, for saying that AV "penalises extremist parties, who are unlikely to gain many second-preference votes." I would rather it said that such parties wouldn't end up with an unfair advantage (thereby countering the fear-mongering) rather than "penalises" (which smacks of being undemocratic).
Anyhow, off to vote "Yes" on 5th May. Is the referendum itself FPTP, or AV? Well, it's a "two horse race", so it doesn't matter – the result is the same either way.
I had been intending to vote "Yes" (for AV). Then I saw material from the "No" campaign. That material has swayed my decision –- to absolutely absolutely vote "Yes". The "No" campaign's distortions and/or stupidities are just shocking. (It is interesting to see the campaign, since there are party members from both major parties in each of the Yes and the No camps -– strange bedfellows indeed.)
So, what’s the fuss?
With FPTP, you have a list of N candidates, and put a cross next to one of them; the candidate with the most crosses wins. With the proposed AV, you have a list of N candidates, and rank them, putting 1 for your first choice, 2 for your second. You can go all the way up to N, ranking the lot, or stop sooner, when you don’t care about the ranking of the rest. The first preference (those with a 1) are counted. If someone gets more than half these votes, they win (this is only likely in a "two horse race", or where the further "horses" are rank outsiders). Otherwise, the candidate who came last (the one who fewest voters wanted as first choice) has their second preference votes redistributed to the rest. This carries on (the last candidate’s votes redistributed) until someone has more then 50%, and wins.
AV sounds more complicated than FPTP. Well, it is more complicated than FPTP. But that doesn't necessarily mean it's worse.
Consider the following scenario. There are three main parties, the PolkaDots, the Maroons, and the Turquoises. The PolkaDots are a minority party, but with quite a big following, about 20% of the vote. The Maroons and Turquoises are roughly evenly split: about 40% each. I support the PolkaDots, am tolerant of the Maroons, but really really hate the Turquoises.
Under FPTP, who am I going to vote for? The Maroons, of course. I can hear the campaign now: "a vote for the PolkaDots is a wasted vote"; "a vote for the PolkaDots is really a vote for Turquoise/Maroon" (depending on whether it’s a Maroon or Turquoise statement). So hardly anyone votes for the PolkaDots: 20% of the electorate are in some sense disenfranchised.
Under AV, however, I can safely put PolkaDots first, then Maroons. I probably leave off the Turquoises, or put them third, depending how I decide to indicate my disgust with them. (In fact there's always a smattering of really minority candidates: I hate the Turquoises so much I'll even put the looney StripyParty above them, but I'll put the Turquoises above the CrossHatches, who are just plain evil). My support for the PolkaDots gets counted, even though they come third, and then my second choice is given to the Maroons, who win. I'm not devastated: PolkaDots third again, but at least I got Maroons, who I can live with, and my real support for the PolkaDots got counted.
But maybe, just maybe, enough people do this, and hey, the Turquoises come third. Their votes are redistributed. And since no Turquoise supporter would be seen dead in Maroon, their second choice votes are for the PolkaDots. And we win! And those Turquoise voters aren't devastated either: they came third, but at least the hated Maroons didn't win. The compromise candidate dissatisfies least.
Sounds sensible enough. Maybe there is a hidden problem that makes AV disastrous? After all, there's Arrow's theorem, that basically says, given some axioms desirable in any voting system, the only voting system that obeys those axioms is a dictatorship. So it seems there is no "fair" voting system: maybe AV is less fair than FPTP?
I caught the end of a TV broadcast for the "No" campaign, without knowing what it was. First of all, I thought it was comedy sketch, mocking the stupidity of people who couldn't understand AV. Then I thought it was a slightly tasteless "Yes" campaign broadcast, mocking the stupidity of people who couldn't understand AV. It was only at the end that I realised it was a "No" campaign broadcast (presumably self-mocking their own stupidity?)
Then their campaign leaflet fell through the letterbox.
One: it starts with the slogan "Keep One Person, One Vote". The slogan "One Person, One Vote" is part of the universal suffrage campaign, for people who don't have a vote at all. AV isn't going to remove people from the electoral roll. Fear mongering.
Two: complaints about the cost -– "£250 million", the cost of electronic vote counting machines and education in the new system. This is contrasted with what else the money could be spent on (always a dubious tactic -– just because money isn’t spent on one thing doesn’t mean it will be on something else): "2,503 doctors, 6,297 teachers, 8,107 nurses, 35,885 hip replacements or 69,832 school places". First of all, notice the tiny "or" in there: it's doctors OR teachers OR nurse OR hips OR school places, but formatted to look like them all. Also, is that a salary for a month, a year, the lifetime of the person? Compared to the £250M, is that per year, per election, or what? Bad statistics.
Three: "The second or third best can win under AV" versus "Under our present system, the one who comes first is always the winner". Notice that weasely use of the word "best". Voting for your Parliamentary representative is not at all analogous to a horse race or foot race, where the fastest, the best, is first past the winning post. It's more analogous to a group of people choosing where to go for an evening's entertainment, where 40% love skating, hate football, and are fine with the cinema, and another 40% love football, hate skating, and are fine with the cinema, and the final 20% love the cinema (and they all have to go to the same place, rather than split up). With AV, it's the cinema, and everyone is reasonably happy; with FPTP it's either football or skating, with 40% very unhappy. What then is the "best" choice? Why should the "one who comes first" (is most people's first preference, even though that's a minority of the people) be the winner? After all, under FPTP, just because there is a majority for someting doesn't mean there isn't a bigger majority against it! Undefined (and misleading) terminology, combined with false analogy. (I can’t complain that they use "FPTP" terminology, as this is the standard name for the system; I can complain when they use it as an analogy, poorly).
Four: "It is wrong that the person who came second or third can overtake the person with the most votes and be allowed to win because the second, third or even lower choices of supporters of extreme parties such as the BNP are counted again and again and again." More fear mongering, by naming an extremist minority party. What about other, non-extremist, minority parties? If I like the looney StripyParty, so put them first, then the PolkaDots, then the Maroons, then the Turquoise, why shouldn’t my wish for the Maroons-more-than-Turquoise be counted just as much as that of a Maroon-firster? (This argument appears to be the source of the "Keep One Person, One Vote" slogan.)
One argument the No campaigners don't use in their leaflet, but that I have heard others use, is that AV might even allow some nasty extremists to gain power (if they were everyone's second choice, say). Well, there's a name for specially designing an electoral system so that it stops those nasty people you don't like from winning: undemocratic. Rather than squelching all those nasty bigots by disenfranchising them, I'd much prefer a system that helps educate them out of their bigotry, and an electoral system that doesn't encourage extremism in the first place. So I was disappointed by the Electoral Reform Society's otherwise excellent site on AV, for saying that AV "penalises extremist parties, who are unlikely to gain many second-preference votes." I would rather it said that such parties wouldn't end up with an unfair advantage (thereby countering the fear-mongering) rather than "penalises" (which smacks of being undemocratic).
Anyhow, off to vote "Yes" on 5th May. Is the referendum itself FPTP, or AV? Well, it's a "two horse race", so it doesn't matter – the result is the same either way.
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