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Mathematically Challenged Education Authority

Posted on 23rd October, 2008 by TW

What hope do the children have?

In the UK we suffer a very bad obsession with league tables in which the performance of every public body is graded (on an arbitrary scale) and compared against others - rarely in a like for like but that is another matter.

As you can imagine, schools bear the brunt of this. Parents are understandably determined to get their children the best education possible, often moving across the country to be in the catchment area of their chosen school. Most of this one-upmanship is derived from the school tables, helpfully published on the BBC website.

All the trust has to be placed in what ever body is responsible for collecting these numbers. Are they up to the task?

Idly surfing the web, I came upon this educational report on the BBC. It is the stats for an infants/primary school (ages 3 - 11) in Shrewsbury. All normal. Have a look at the stats and it seems like its a reasonably good school - it performs above the average for its educational authority, which is also above the average nationally.

Then have a look at this:

PERFORMANCE
37 eligible, 18.9% of whom had special educational needs

At first glance it seems normal and slightly low compared to some schools.

Then look at the numbers.

18.9% of 37 is 6.993.

This means that 6.993 students have special educational needs. How is that possible? Is this just a rounding problem? No, because 7 pupils would be 19% in any normal formulation.

Either the organisation who collates the stats is mathematically challenged, or they have massaged the numbers to make it look lower than it is (and are ethically challenged).

Whichever it is, how much faith can you have in this system?

Popularity: 10% [?]


Popularity: 10% [?]

Banks Fumble, Taxpayers Punished

Posted on 29th September, 2008 by TW

The current “banking crisis” has been pretty hard to ignore of late, but here in the WhyDontYou ivory towers, we have tried. Partly this is because both of us are in (largely) economy immune employment sectors and partly (mainly) because neither of us can really fathom the nonsense being thrown about in the news. Given that both of us are required by profession to be mathematically astute (yes, really) it could be taken to imply that the average citizen would be even more lost.

With this in mind, it is entertaining to watch the news about the crisis when it pretty much only shows scared-to-death financial experts going on about weird ways of selling things you dont have (short selling) and how important the banking risk takers are to society. They are so important that the rest of society has to protect them should their risk taking go wrong. Being ignorant of the financial wizardry, this strikes me as being totally insane, let alone unfair. This post (long, sorry) is pretty much a way for me to let off steam about something that is destroying peoples lives and, basically, really annoys me. I would welcome your comments and feedback on my take - if I am wrong, please educate me.

There are two headline examples today (in the UK at least) - The UK Government take ownership of the crap part of Bradford & Bingley, after selling the good bits to a Spanish bank; The American government fails to secure a $700bn line of funding for its banks to keep them safe. (Neither are good news items. Neither are going to reassure people that their future is safe. Do not mistake a light tone here for a lack of concern)

Some Background

UK first. Starting about 20 years ago there was a big rush for building societies to become banks - changing from being basically there for a group of people in one area (eg. Bradford, Halifax) where everyone who paid in was a member to becoming a limited company, where some of the members became shareholders. In the process, especially throughout the 1990s the drive was on for these banks to press hard and return massive profits for the shareholders (often a tiny subset of the Building Societies membership). At the time (and in principle it still does) this seemed a good idea. Most people got a bit of money (sadly for most of the members this was just a bit - around £100) and a few people got lots and lots of money. Everyone was happy.

From this, there was a drive in the finance sector to target more and more high risk trades, where often the winnings were large beyond the avarice of mortal man. City bonuses in the millions ceased to be newsworthy and sales of high end sports cars went through the roof. Being a “risk taker” became the nicest thing you could say about someone. We (the public) were dimly aware that there was a risk it could fall down on the bank (Barings) so we accepted the ostentatious lifestyle of the successful. For some reason we were convinced it was down to skill and intelligence rather than basically throwing dice and hoping for the best. These were people who worked hard predicting the markets and had a rare skill in knowing where the trades were. Or so we thought.

Hidden for most of the time were the downsides to this.

Insane wages in London made the already insane prices there spiral out of control. People began to think that paying £750,000 on a one bedroom apartment was a “good investment.” In turn, this priced even well paid people out of the city, so prices near London went up (often even faster if it was commutable and “nice”). For the last ten years it has been impossible for anyone on less than twice the average wage to even think of buying a house in the south of England, without a hugely fiddling their application - so they did. People overstated their income, understated their expenses, and took insane repayment terms hoping they’d get on the gravy train before they had to pay the capital. Lots of these people had “normal” jobs and were not aware that they were bearing the same risk that the Ferrari driving millionaires living in central London appartments had. The public never benefited from the wins so, rightly you would think, assumed it was safe from the risks.

Wrong. (More on that in a minute)

A similar story in the US (I assume, I have no idea of the background). From my visits, the gulf between rich and poor in America vastly outstrips that in the UK. I have always thought that if you were filthy rich, there is no better place to live than the US, but if you were penniless poor the UK wins. Rich people in America are really rich. I am amazed the poor survive one day to another.

In recent years, the risk loving traders have really had a few field days in the US. Massive windfalls made rich people richer. They took huge risks, which often paid off. People applauded them for having the guts to risk so much, making it hard to condemn them for their salaries and bonuses. As with the UK, most Americans had some fallout from this (house prices going up for example) and people begin to think that property is the best investment, so take some personal risks to buy a house. In turn the bank takes a bit of a risk lending to them, but often at crippling interest rates that will see the bank get its money back in spades.

Eventually, as everyone with hindsight knew it would, the whole system explodes. That is the thing with taking a risk, sometimes you get hurt.

Here is where my understanding and reality part company.

Current events

I have always thought that you took a risk, gambled something for example, sometimes it would pay off and other times it wouldn’t. Some risks are “low risk”: for example, betting that a tossed coin will land on either heads or tails rather than its side is quite a low risk bet - you are a lot more likely to win than lose. Some are “medium risks”: betting on heads in our example. Some are “high risk”: betting the coin will land on its side. They all make sense to us and we live with this sort of understanding on a day to day basis.

The world banks have paid their “High Risk takers” absolute fortunes because they take high risks. This is fair. If I bet £1000 on the coin landing on its side and I won, I would expect to win big, if I bet £1000 on the coin not landing on its side, I would expect to win a tiny amount simply because I wouldn’t expect to lose.

For most of the last two decades, the amazing thing is the risks have (on the whole won). The coin has landed on its side a lot. People have won big.

The problem is people then forgot what a risk it was. If you win something that is high risk enough times, you forget that it is high risk and assume the opposite. The merchant banks have been so successful with high risk ventures, they forgot that “high risk” meant dangerous and plowed more and more money into it. They still throw around the terms, they certainly still paid the bonuses, but everyone assumed it would never happen.

Then the coin came up tails and everyone lost. Everyone who had bet big, lost big.

Oddly, this came as a shock. The great and bold risk takers were mortified. Nothing hits a herd as fast as panic and the trading centres of the west are no different. Contagious fear spread everywhere and a generation of “risk takers” who actually had no idea about risk were the most affected. The less scrupulous traders saw a chance to strip the foundations of fragile structures and asset rich, stable organisations took a massive hit (Bye, bye HBOS). The wonders of a free market allowed short-selling and a few scares to destroy a company with solid resources - can you imagine how scared the rest must have become.

Risk?

So, in the interests of a free market, the government steps in and saves the companies. The government spends billions of the taxpayers money to rescue institutions that have, basically, gambled themselves out into the street.

This is where I am confused.

In the UK, the government has reportedly taken over a £50billion debt on behalf of Bradford and Bingley. That is effectively £1000 per person so that the demutualised, risk taking, company can survive. Although we were not aware of the risk we were taking, nor did we share in the rewards, everyone of us in the UK was involved in the gambles these people were taking.

The US has the same problem. The $700bn bail out (good idea or not) is a phenomenal sum of money. The high flier financial wizz-kids and their high risk lifestyle would cost every one of the 300 million people in the US over $2000. For someone on federal minimum wage, that is 321 hours work - 40 working days - to save the rich from becoming poor (I know it is not quite that simple). Instead, the poor get a little bit poorer. Wonderful.

The US must be the only modern democracy where funding the rich bankers is a more appealing proposition than giving healthcare to the sick. That confuses me.

To confuse me even more, the news today had lots of talking heads on both sides of the Atlantic saying how it might seem strange but it was vital that the taxpayer (poor) bail out the bankers (rich) because. Often simply because. Sometimes there were vague, dire, warnings about the economy, but most of the time it was just a simple statement. We have to do it.

Why?

I don’t doubt that letting one or two banks slip will cause even more panic which will destabilise the economies, but if the US has $700bn and the UK has £20bn going spare, then surely we can weather some rough times. When the average person on the street still has money for shops to take off them, then the economy will still work. In my mind that is where the salvation needs to be pointed.

Equally odd, is this new definition of risk.

If I gamble my house on a high risk deal and lose, I lose my house. Will the government bail me out? (Well, in the UK we have social housing but that is different) It is unlikely. For me, betting on high risk stocks is just that - high risk. I stand to gain but I also stand to lose everything.

If a bank gambles the houses of 20 million people and loses, well they really lose nothing. Poorly paid staff will get laid off but the “risk takers” are immune. The organisation is immune because as long as it cries loudly enough the government helps. For the banks, betting on a high risk is actually risk free. They will either gain a lot, or lose nothing.

Why is this acceptable? Why is this considered normal? Why are we still hearing that it is all down to the taxpayers to save these banks? Why not claw back the multimillion bonuses? Why not fine the fund managers? Why are they allowed to gamble without risk, yet still be thought of as “cool” risk takers?

Crime and Punishment

The most sickening thing about the whole deal is not just that the taxpayer has to suffer.

If, through negligence or design, I caused someone to lose out to the tune of £1000 there are laws that would punish me. If I gambled £1000 of someone else’s money without their knowledge and lost it, I would expect the police to visit me and to end up in jail.

It seems, however, if you do it with enough people then not only does the government step in to cover your debts, but you dont even get punished. In the middle of the credit crunch, UK stockbrokers were still getting massive Christmas bonuses (just not as massive… poor things).

While it often smacks of unscientific voodoo, I accept what the “finance experts” say and that the state has to prop up these failing institutions. However, why should the people who have caused this problem be allowed to walk away? If, for example, the fund managers and directors of each organisation were to be fined in proportion to their participation, the rescue plan’s tax burden would be a sweeter pill.

Alternatively, if this heralds a new era of tightly controlled financial markets, where crazy risks are punished, and these people are not simply able to start ripping the world off again in a few years then, again, it becomes a bit more acceptable.

I think the problem is, this will never happen. The hint that the US bail-out would be followed with government involvement meant that the Republicans stood against the great George Bush and turned down the bill (*). It seems the only way a rescue plan will be approved is if it carries no strings or punishments. Basically, the bankers are free to risk all our money without having to worry…. (Slightly better over here, where we are more accepting of government control and oversight).

What a wonderful world.

(*) This adds an ironic twist. I strongly think that the Republican party expect to lose the next election. McCain/Palin are their idea of a joke. They know the country and the economy is about to tank, and the war in Iraq has gone badly. If they lose the election, Obama will be handed a hospital ball of a presidency. Unless he is truly Odin’s chosen one, come the next elections people will still be smarting from the economic crisis and will be ready to turn to the Republicans once more. Taken in this light, both Bush’s plan to asset strip the country, and the parties refusal to do something that (on the surface) benefits the public makes sense.

Can you be too cynical?

Popularity: 21% [?]


Popularity: 21% [?]

Shares for all

Posted on 14th October, 2007 by Heather

On the BBC Tech pages a blog by Kate Russell recommends a site called Gnu Trade where you can gamble on the world’s stock markets.

Now everyone will have their own take on whether gambling on market movements is a good or bad thing but even if you do not want to risk a penny it is possible to make money here.

That is because the site allows people who bet with cash to back players who are playing for fun. If you attract a real money player to back you and you make a profit - then some of that real cash gets sent to your account.

If you are sh*t hot (belatedly decided to think of family-friendly filters) at online poker you could probably make a lot of money, There are plenty of maths geniuses out there. It’s got to be easier than the lottery,

I can think of a few other potential unforeseen consequences, whether “good” or “bad”.

My grasp of economics is pretty shaky (as witnessed by my lifetime failure to even try to be rich) but I thought the things traded in stock markets related to people’s livelihoods. Food? Manufactured goods? Oil?

Stocks and shares aren’t just numbers. Entire national economies and people’s lives rest on them.

Aren’t international markets supposed to be “sensitive” to the slightest event? Share prices fluctuate within moments with the impact of a mysterious set of forces - from changes of government to the wildest rumours.

Wild rumours on the Internet? Surely not. Bizarre misunderstandings across cultural and language gaps? No, they can’t happen on the Net. The Internet isn’t allowed to lie. It’s like television (It said so in the Simpsons.)

Might not the international markets become ever more volatile? Easier to manipulate? Might not the implications be ever more destabilising?

It’s been so long now that economists have been saying that “free trade” is the answer to everything. Maybe we will soon find out if this is the case. Alternatively, you could think of it as a scientific test of chaos theory.

Popularity: 20% [?]


Popularity: 20% [?]

Moebius strip

Posted on 10th August, 2007 by Heather

Moebius strips are wonderful. There’s an image at http://images.salon.com/comics/tomo/2003/08/29/tomo/story.jpg
showing Bush’s foreign policy as a Mobius strip. I couldn’t save it here so I borrowed this one from mcescher.com

Escher’s mobius strip

Seed magazine says that two mathematicians - Gert van der Heijden and Eugene Starostin - have resolved the shape algebraically. I’ll have to take that on trust. I can’t even grasp what the problem is, so I doubt I’ll understand the solution..

What determines the strip’s shape is its differing areas of “energy density,” they say.
“Energy density” means the stored, elastic energy that is contained in the strip as a result of the folding. Places where the strip is most bent have the highest energy density; conversely, places that are flat and unstressed by a fold have the least energy density.

Popularity: 24% [?]


Popularity: 24% [?]

Stats cant lie

Posted on 19th February, 2007 by TW

Five days ago I talked about the odd statistics which were showing up in my BOINC client for Einstein@Home. Sadly in the intervening five days, nothing has become any clearer.

BOINC Client - User Total 19 Feb BOINC Client - User Average 19 Feb

Now, the BOINC client has been running constantly (with the exception of one 9 hour period) for the last five days, yet the increase seems minimal and the average is plummeting like a stone. Looking at the client stats page there are still 82 work units “pending” credit (at around 53.4 credits per unit) so eventually this should change.

Even so, I am still not sure how the two sets of numbers compare to each other. I cant work out how the averages are calculated at all. Any comments welcome.

Popularity: 23% [?]


Popularity: 23% [?]

Statistics and Averages

Posted on 14th February, 2007 by TW

I am far from an expert on these subjects, but it covers something which has been intriguing me over the last few days. The Einstein@HOME program is described as follows:

Einstein@Home is a program that uses your computer’s idle time to search for spinning neutron stars (also called pulsars) using data from the LIGO and GEO gravitational wave detectors. Einstein@Home is a World Year of Physics 2005 project supported by the American Physical Society (APS)and by a number of international organizations.

(A bit like Seti@Home but that seems to have lost some popularity of late)

Now this is a nice bit of software which runs from something called the BOINC manager, where you can get to view your current work unit, see stats, visit the forums etc.

The question I have, is about the “user statistics” it shows. As you can see in the screen shots, there is choice of “user total” or “user average” and to me, the two don’t seem to match up. I am led to believe the average is “recent average” rather than a simple (total / days) type. But even so, it seems odd - especially as I have had the software running almost constantly for little or no return in the way of work units.

BOINC - User Total BOINC - User Average

Any feedback or commentary welcome. Given the steady climb shown by the total figures, the mountain-like averages seem somewhat… odd.

Popularity: 23% [?]


Popularity: 23% [?]

Guns and Crime

Posted on 17th January, 2007 by TW

At the risk of turning this into a new topic which is hounded to death on the blog, I found some more interesting comments about carrying guns in public - nothing new, they are just more recent ones on the More Guns, More Homicide post.

Previously I pointed out that, as a Brit, I found it odd that the desire to carry a gun while you go about your daily life is so strong in some Americans and that oddness remains. I still find it strange beyond belief that some one in a civilised western democracy can feel so “unsafe” they need to be armed when ever they are in public.

Now, this self defence argument for “packing heat” makes me wonder a bit more. For example, on the comments “ben” was asked the following question by SG (read original):

let me get this right Ben. Someone walks up to you in the street and sticks a knife in your face, says “gimme your wallet”, and you think you can draw your gun and threaten and/or shoot them before they stab you? Is this how the self-defence argument works? Or does it work by you pulling your gun before they pull the knife, i.e. shooting them if they look threatening?

While this seems like a reasonable method of explaining the self defence argument for carrying a gun the responses it drew included this from MarkP (”I’m an actuary, I own a gun but don’t carry it, and have no particular love for them”) (read original)

No, SG, he thinks if he pulls his gun, the knifewielder will see the gun and will flee. And he is substantially correct. People wield weapons mostly for bluff. If the knifewielder had wanted to just have a fight, he would have stabbed Ben without asking for the wallet.

The only thing funnier than paranoid gun nuts protecting their phallic symbols are gun-phobes revealing that they cannot think logically about guns for one second, and know nothing about the real world. I suggest this be alleviated by talking about “weapons” rather than guns, since guns are only the most effective weapons at killing, but certainly not the only ones. Just ask the people in Rwanda.

While on the surface this seems like a logical line of reasoning, it suffers from a logical fallacy, having said that his attempt to broaden the debate is worthwhile, but I suspect it is futile.

Now as I see it the fallacy is that he is assuming the gun wielder is not bluffing but the robber is. If the statement “people wield weapons mostly for bluff” is true, then it must also apply to the gun owner and therefore drawing the weapon does not carry any reason to assume the robber will run.
When the gun is drawn the situation escalates. The robber will suffer from an adrenaline rush and may well decide that running will result in being shot in the back and attacking the gun owner is the only option. On a purely technical point, if the knife wielder is close enough to be a real threat anyway, the hand gun is probably useless unless it is already drawn.

There is more though. Ben replied to the question with: (read original)

It works like this: If I thought my life was in danger, then I’d draw and shoot if necessary. If not, then he can have my wallet, car and any other inanimate object he likes.

It is an interesting conundrum he presents. Some one is threatening you with a knife and you may not consider your life was in danger? If there is no threat, he will surrender his objects but if there is a threat he will try to fight. Very unusual and difficult to imagine how it can work in practice.

There are a multitude of arguments for, and against, gun ownership. My personal thoughts about the escalation of violence may well suffer from the slippery slope fallacy but I doubt it. When one person is armed and the other isn’t deaths may occur. If both are armed deaths may still occur and may well be more likely. Is the belief the death may not be the victim sufficient grounds for people to carry guns? Would you rather be punched or shot as the result of an argument with another car driver? Would you carry a gun in case the other driver came up to you and started shouting? At what point would you draw the gun?

As soldiers are taught, once the weapon is brought into view the whole situation changes. If your opponent does not back down immediately you pretty much have to kill them. The more people carry guns, the more likely an otherwise heated situation will turn violent. Is this grounds for banning firearms in the US? I don’t think so, but then I don’t live there.

Popularity: 26% [?]


Popularity: 26% [?]

More Content Less Haste!

Posted on 16th January, 2007 by TW

Now, it seems I was a touch hasty with my last post on gun crime and statistics. If I had spent more time reading the comments on the Deltoid post even more comedy bad-statistical goodness would have come to light.

As someone living outside the US, I have no real concept of how this is an issue which creates such a furore. I am dimly aware of the constitutional issues, but as far as I can tell the right to bear arms was there because the founding fathers didn’t believe in a standing army. I don’t think they envisaged a future where both would happen, but who am I to know.

The main pro-gun comments seem to come from a guy called “ben” who proudly proclaims “I pack heat” and while superficially sound, they don’t seem to survive detailed analysis. For example, the numerous studies which have linked gun ownership to homicide are disproven by a the apparent fact that the homicide rate in gun-carrying Seattle is lower than in gun-banned Vancouver. Interesting. I think it is important to highlight that the debate is about “homicide” not “gun crime” which is a mistake I have made in the past.

While it is entirely possible that the apparently obvious more guns = more crime assumption is wrong, this leads to more questions which could have interesting conclusions. If more guns != more crime, then why does the nation with the highest incidence of gun ownership have more crimes per person than other nations? Are God-fearing Americans simply more criminally minded than (say) Canadians?

Popularity: 25% [?]


Popularity: 25% [?]

Numb3rs

Posted on 10th May, 2006 by Heather

Sorry about this, it’s not ground-breakingly brilliant but it’s entertaining. There is something good about having a mathematician and his physicist not-quite girlfriend as the relatively glamourous heros of a cop show. This makes a change from scientists always being portrayed as total geeks.

There is an odd physicist as well - the short guy from Ally McBeal - but there are odd non-scientists - liek the man who used too be the central character in Taxi. The programme doesn’t necessarily assume that having mathematical skills makes you a social outcast, which is nice.

Popularity: 12% [?]


Popularity: 12% [?]