What do Y, Yb, Tb, Er, Gd, Tm, Sc, Ho, Dy and Lu have in common?

Posted on 15th May by Mr Reid

What do the fol­lowing ten elements have in common?

  • Yttrium
  • Ytter­bium
  • Terbium
  • Erbium
  • Gad­olinium
  • Thulium
  • Scandium
  • Holmium
  • Dys­prosium
  • Lutetium

The answer (and there is a tiny clue in some of the names) is that all ten elements were isolated from one sample, taken from a mine in the small village of Ytterby in Sweden. All of the elements are rare earth metals which occur in similar loc­a­tions and have similar prop­er­ties. This makes their extrac­tion and isol­a­tion very dif­fi­cult and this is where the “rare” in their name comes from.

In 1787 one of the students of Lieu­tenant Carl Axel Arrhe­nius found a dark-coloured ore that was much too heavy to be coal. Arrhe­nius took this ore, which he named “ytterbite”, and sent samples to various chemists for analysis. One of these chemists, Johan Gadolin, determ­ined that ytter­bite did indeed contain a pre­vi­ously unknown element and called this element yttrium.

In 1843 Carl Gustav Mosander demon­strated that ytter­bite was actually made of three metal oxides, not one as Gadolin had thought. The original name was kept for one of these three parts and the other two elements named terbium and erbium, both after the village of Ytterby where they were found.

Terbium was later demon­strated to be a mixture of terbium and a new element which was named gad­olinium in honour of Gadolin. Erbium was demon­strated to be a mixture of erbium and and a new element which was named ytter­bium, again after the village of Ytterby.

Erbium was then itself demon­strated to a mixture of three elements: erbium; thulium, named after Thule, a term used by early map makers for the far north where Sweden is located; and holmium, named after the Swedish capital Stock­holm. Holmium was then later demon­strated to be a mixture of holmium and dys­prosium, which takes its name from the Greek word dys­prositos meaning “dif­fi­cult to get”, reflecting the dif­fi­culty found in isol­ating it.

Ytter­bium was demon­strated to be composed of ytter­bium and a new element which was named scandium after Scandanavia, and finally ytter­bium was split again to yield ytter­bium and lutetium.

A diagram showing the order in which the ten elements were isolated.

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Why is Quincy, Washington so popular with tech companies?

Posted on 13th May by Mr Reid

Quincy, WA is a small town (pop­u­la­tion 6750) in the north-west of the US. So why have tech­no­logy giants Microsoft, Yahoo!, Dell, Vantage Data Centers, Sabey and Intuit all chosen to build huge data centres there? Quincy is now home to nearly 190 000 square metres (more than two million square feet) of data centre.

The answer is very simple: elec­trical power.

The town of Quincy is close to the Columbia river, the fourth largest (by volume) river in the US. There are fourteen hydro­elec­tric dams on the Columbia river, two of which, the Priest Rapids Dam and Wanapum Dam, provide elec­tri­city to Quincy.

The Priest Rapids Dam

The Wanapum Dam

Hydro­elec­tric power is cheap,* but more import­antly from the point of view of data centre oper­ators, it is very reliable. The reli­ab­ility of the elec­tri­city supply to Quincy is better than 99.99% which is very important for “mission-critical” always-on services like cloud com­puting. Using renew­able non-polluting hydro­elec­tric power also helps service pro­viders demon­strate their green cre­den­tials. Server farms consume a huge amount of elec­tri­city — more for cooling than for pro­cessing — and using hydro­elec­tric power helps to reduce their asso­ci­ated carbon footprints.

* The local utility company, Grant County Public Utility District, offered elec­tri­city at a discount rate to attract users to the area.

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Why putting missiles on roofs in London isn’t as dumb as it sounds.

Posted on 13th May by Mr Reid

The UK gov­ern­ment has recently announced that it will be placing Starstreak HVM surface-to-air missiles on some roofs in London as a security measure during the 2012 Olympics. This has caused a bit of a kerfuffle.

Below are some thoughts on the issue from a physicist’s point of view.

What are Starstreak missiles and how do they work?

The Starstreak is a short-range laser-guided surface-to-air missile. When launched it very quickly accel­er­ates to Mach 3.5 (1200 metres per second) and is then guided onto its target by a pair of laser beams pro­jected from its ground-based aiming unit. Being laser-guided means that unlike heat-seaking or radar-seeking missiles the Starstreak cannot be avoided through the use of chaff or flares; however unlike those missiles it does not have fire-and-forget capabilities.

The Starstreak Light Multiple Launcher showing three Starstreak missiles and the guidance unit.

Once the Starstreak approaches its target it releases three 900 gram tungsten-coated beam-riding sub­muni­tions. Once one of the sub­muni­tions (or all three) impacts the target a short delay fuse is activ­ated and the 450g of explosive inside the sub­muni­tion explodes inside the target, throwing out tungsten alloy shrapnel and tearing it to pieces.

What scenario is the deploy­ment of Starstreak missiles designed to prevent?

My guess is that the gov­ern­ment is trying to defend against suicide bombers using aircraft as weapons. A heavy aircraft moving at high speed has a large amount of kinetic energy and this, coupled with the chemical poten­tial energy in the fuel, makes it a for­mid­able weapon.* The Olympics will con­cen­trate a large number of people in a small space which makes the Olympic sites attractive targets.

If a plane is shot down, won’t it kill people when the wreckage lands?

It depends on the size of the aircraft involved. A light aircraft at high altitude wouldn’t produce much dan­gerous wreckage, a low-flying jumbo jet would. But falling wreckage will kill far fewer people than an aero­plane striking one of the Olympic sites would.

The force of the missile’s explo­sion will tear any aircraft into pieces, and once the struc­tural integ­rity of the aircraft is ruined the force of the wind will tear it into further smaller pieces. Each of those falling pieces will reach terminal velocity rel­at­ively quickly and will there­fore strike the ground at a lower speed than if it were flown into the ground under power. The video that has been going around showing a heli­copter shot down by a Starstreak missile crash into the ground in a fireball is of a guidance test — the missile in the video was not carrying an explosive payload.

What about burning jet fuel hitting the ground?

This is much less of a problem. An explo­sion inside an aircraft, combined with the high-speeds involved would aer­o­solise the fuel, causing it to burn up very quickly in mid air. Again, this is a much lower risk than if a plane full of jet fuel were to crash into one of the Olympic stadia.

Won’t the missile launches damage the build­ings they’re launched from?

No. The Starstreak missile is ejected from its launch tube by a low power first stage rocket motor that is extin­guished before the missile leaves the tube. The powerful second stage motor doesn’t kick in until the missile is safely away from the launcher, meaning that there is almost no recoil at all. The launch of a Starstreak missile produces no sig­ni­ficant over­pres­sure so there is no danger to windows or walls. The missiles have to be launched from roofs or open spaces because the rocket requires a certain amount of space to accel­erate to attack velocity.

* It was the chemical energy in the tens of thou­sands of litres of fuel that were respons­ible for the collapse of the Twin Towers in the 9/11 attacks. Had the planes had no fuel aboard the Towers would have survived.

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The classified Space Shuttle missions

Posted on 6th May by Mr Reid

The Space Shuttle flew a total of 135 missions in its lifetime. Of these 135 missions, seven were clas­si­fied Depart­ment of Defense missions whose purposes were never offi­cially announced.*

  • STS-51-C (15th mission, January 1985) deployed a Magnum satel­lite designed to inter­cept com­mu­nic­a­tions, mainly from the Soviet Union and China.
  • STS-51-J (21st mission, October 1985) deployed two satel­lites that form part of the Defense Satel­lite Com­mu­nic­a­tions System that allows the military to com­mu­nicate with units all across the globe.
  • STS-27 (27th mission, December 1988) deployed the first Lacrosse radar imaging recon­nais­sance satel­lite. It is alleged (on Wiki­pedia) that one of the uses of the Lacrosse system would have been to provide real-time tar­get­ting data to the B-2 Spirit stealth bomber.
  • STS-28 (30th mission, August 1989) deployed one of the satel­lites that forms part of the second gen­er­a­tion of the Satel­lite Data System (SDS2) which relays data from low-orbit recon­nais­sance satellites.
  • STS-33 (32nd mission, November 1989) deployed another Magnum satellite.
  • STS-36 (34th mission, February 1990) deployed a MISTY pho­to­graphic recon­nais­sance satel­lite and the PROWLER satel­lite. MISTY satel­lites are alleged to have both optical and radar stealth cap­ab­il­ities to make them dif­fi­cult to track. The purpose of PROWLER is uncer­tain, but it is probably designed to inspect other satel­lites and inter­cept signals; it has been tracked from Earth approaching close to Russian com­mu­nic­a­tion satellites.
  • STS-38 (37th mission, November 1990) deployed the second of the SDS2 satellites.

There was also one par­tially clas­si­fied mission:

  • STS-53 (52nd mission, December 1992) deployed the third SDS2 satel­lite along with a number of unclas­si­fied experiments.

The National Recon­nais­sance Office, one of the sev­en­teen “elements” of the US Intel­li­gence Com­munity, actually influ­enced the design of the Space Shuttle, having its payload bay size increased so that it could accom­modate the KH-9 HEXAGON spy satel­lite. In the end all of the KH-9 satel­lites were actually launched by third gen­er­a­tion Titan rockets.

* Everything in this post should be heavily prefaced with “allegedly”.

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Where is the best place to launch a rocket from?

Posted on 29th April by Mr Reid

NASA has quite often had to “scrub” (cancel) launches from the Kennedy Space Center (KSC) in Florida because of inclement weather. But why build a Space Centre in Florida in the first place? It’s location makes it par­tic­u­larly vul­ner­able to hur­ricanes and other weather “events” so there must be a sig­ni­ficant advantage to its location.

The paths of the eighty-three Florida hur­ricanes that occurred between 1975 and 1999.

Florida is a good location for rocket launches because it is both on the east coast of the US and because it is close to the equator.

Launching from the east coast of the US means that the rocket can take advantage of the Earth’s west-to-east spin. If a rocket were launched from the west coast it would either have to fly right across the con­tin­ental US, which would be dan­gerous if it mal­func­tioned; or it would have to take off east-to-west, flying against the spin of the Earth.

At the North or South pole the speed at which you are moving, relative to a sta­tionary observer not on Earth, is zero. As you move closer to the equator this speed increases, until at the equator you are trav­el­ling at a speed of 465 metres per second (1040 mph). At KSC, which is at a latitude of 28°N, this speed boost is reduced slightly, to about 410 m/s (916 mph). This is the best possible location in the con­tin­ental USA, pre­sum­ably more suitable (i.e. more southern) loc­a­tions in Hawaii, Puerto Rico or one of the US’s other ter­rit­ories were dis­counted because of their remoteness.

The closer to the equator you can get, the greater the speed boost you receive. This reduces the amount of energy required to get into space and means that less fuel is required. The European Space Agency makes its launches from the Guiana Space Centre in French Guiana which is only 5° north of the equator. The com­mer­cial space launch service Sea Launch uses a mobile launch platform that sails nearly 5000 kilo­metres from Long Beach in Los Angeles where the rockets are assembled, to a location actually on the equator where the launches take place.

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Transporting the Shuttle

Posted on 22nd April by Mr Reid

The Space Shuttle always launched from one of the two launch pads at the Kennedy Space Center’s Launch Complex 39.

But until the tenth mission (STS-41-B) the Shuttle always landed at Edwards Air Force Base in Cali­fornia, more than 3500 kilo­metres away on the opposite coast of the US.

So how did the Shuttle get back from Edwards to Kennedy? It cannot fly like an aero­plane because it has no con­ven­tional engines, only rocket engines powered by fuel con­tained in the giant orange external tank and two reusable solid rocket boosters. Whenever the Shuttle came into land it was not in powered flight like an aero­plane, but rather gliding, without any engine power at all — it relied on a large drag chute to come to a halt after touching down.

In order to get from Edwards to Kennedy the Space Shuttle was attached to a modified 747 known as the Shuttle Carrier Aircraft (SCA) and flown right across the US.

The Shuttle Atlantis mounted to the SCA. Note the aero­dy­namic cover placed over the main engines.

During the testing phase the Shuttle pro­to­type Enter­prise was delib­er­ately released from one of the SCAs in mid-air and glided to a landing at NASA’s Dryden Flight Research Center.

The Shuttle Enter­prise glides over the Cali­fornia desert after being released from the SCA.

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Clockwise

Posted on 21st April by Mr Reid

Because the Earth rotates west to east, no matter where on Earth you are, the Sun rises in the east and sets in the west. In the northern hemi­sphere it passes through the south as it travels across the sky*, and in the southern hemi­sphere it passes through the north.

The first clocks that dis­played the time (rather than meas­uring inter­vals of time) were simply sticks inserted ver­tic­ally into the ground (gnomon). As the Sun moved across the sky the shadow cast by the stick would move across the ground; at midday the Sun would be at the south and the shadow would point north, to the “twelve o’clock” position.

An inter­esting con­sequence of this relates to the con­ven­tion of “clock­wise”:
If the devel­op­ment of the first clocks taken place in the southern hemi­sphere rather than in the northern hemi­sphere, clock­wise and anti­clock­wise would be in opposite directions.

* Hence why, in the northern hemi­sphere, a south-facing garden is an attractive selling point for a house.

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Why kettles boil slowly in the US

Posted on 16th April by Mr Reid

I saw a tweet recently that intrigued me:

London beats San Fran­cisco at:1) Oyster card2) CHOCOLATE3) Boiling kettles quickly. Won­dering if I can sneak some volts home in my case
15th April 09:37 via Tweetbot for iOSReplyRetweetFavorite
@yoz
Yoz

The voltage of mains elec­tri­city varies from country to country: the majority of coun­tries use between 200 and 240 volts, but a small minority (most notably the US, Canada and Japan) use between 100 and 127 volts.

Coun­tries using 100 – 127 volts are shown in red; coun­tries using 200 – 240 volts are shown in blue. Coun­tries with a mixture of the two systems are shown in purple.

The voltage* of an elec­trical supply is what pushes elec­trons around in a circuit. The higher the voltage, the faster the elec­trons move and thus the higher the current (one amp is equi­valent to about six billion billion elec­trons flowing past a point per second). With a low voltage the rate of transfer of elec­trical energy is there­fore much slower. In the UK, with a mains voltage of 230 V and a limit of 13 A per socket the maximum possible power to one appli­ance is 2990 watts (2990 joules per second). In the USA, with a mains voltage of 120 V and a limit of 15 A per outlet the maximum possible power is reduced to only 1800 watts, which is why in the US many large appli­ances (e.g. washing machines, tumble dryers) have to be con­nected to a separate high-voltage circuit.

To raise the tem­per­ature of one litre of water from 15°C to boiling at 100°C requires a little bit over 355 kilo­joules of energy. An “average” kettle in the UK runs at about 2800 W and in the US at about 1500 W; if we assume that both kettles are 100% effi­cient† then a UK kettle sup­plying 2800 joules per second will take 127 seconds to boil and a US kettle sup­plying 1500 J/s will take 237 seconds, more than a minute and a half longer. This is such a problem that many house­holds in the US still use an old-fashioned stove-top kettle.

* As a phys­i­cist I would normally use the term “poten­tial dif­fer­ence” in place of “voltage” but voltage is better under­stood by the general public. Looks like the engin­eers (who prefer “voltage”) won that battle.

† As electric kettles actually use the joule heating effect that is respons­ible for most of the energy wasted in other elec­trical devices this isn’t a terribly unfair assumption.

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Poverty and the wind

Posted on 15th April by Mr Reid

A map of poverty* in London clearly shows a clus­tering of poorer areas to the north-east of the city.

There is a very simple reason for this, and it’s the same reason that poorer areas are found towards the north and east of most large and old towns in the UK: the pre­vailing wind.

Because of its position to the north-east of the Atlantic Ocean, the pre­vailing wind in the UK is from the south-west (i.e. blowing north-east). Any atmo­spheric pol­lu­tion produced in London — and in the 1800s and 1900s that was be a lot of pol­lu­tion — would be blown to the north-east, making that area less attractive and there­fore cheaper to live in.

You can explore poverty in the UK using the inter­active Google Map below, which I found via a story in The Grauniad:

* The data used is the 2007 Index of Multiple Depriva­tion, and the mapping is by London Profiler.

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Why you can’t open aeroplane doors in flight

Posted on 11th April by Mr Reid

There have been many stories of people trying to open aero­plane doors whilst the aero­plane is in flight. Below is an explan­a­tion of why you shouldn’t worry if this happens during your flight.

The cruising altitude of most trans­port aero­planes is about 38 000 feet (11 600 metres). At this altitude there is less air above the aero­plane pushing down upon it and thus the air pressure is lower. At 38 000 feet the air pressure is about 21 kilo­pas­cals (21 000 newtons per square metre) compared with 100 kilo­pas­cals (100 kPa) at ground level.

At this altitude there wouldn’t be enough oxygen present in the cabin air for people to breathe (this is why aero­planes carry oxygen masks, in case the cabin depres­sur­ises for some reason). Therefore the cabin has to be kept pres­sur­ised to a greater level, usually to the equi­valent of about 8000 feet (2440 metres). At 8000 feet the air pressure inside the cabin is about 75 kPa, more than three times the exterior pressure at cruising altitude. There is there­fore a dif­fer­ence in pressure between the interior and exterior of the aero­plane of 54 kPa, or 54 000 newtons per square metre.

The pas­senger doors on a 747 (for example) are 1.19 metres wide by 1.93 metres tall, giving the door an area of 2.3 square metres. This means that there is a force of 124 000 newtons (54000 N/m2 × 2.3 m2) pushing the door closed. To put this in per­spective, a force of 124 000 newtons is equi­valent to the weight of 12.6 tonnes; so unless a pas­senger is some sort of Superman, capable of exerting a force bigger than this, the door will remain closed.

Aero­plane doors are wedge-shaped so that the fuselage bears this force, relying on the pressure dif­fer­en­tial rather than on some sort of internal locking mech­anism to keep the door closed and maintain a good seal. The same is also true for space­craft doors.

Thanks to JU for asking the question that prompted this post.

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What are contrails?

Posted on 9th April by Mr Reid

Con­trails are arti­fi­cial clouds that form behind aircraft flying at high altitude.

Jet fuel (also known as AVTUR for AViation TURbine fuel) is made up of long-chain hydro­car­bons, from nonane (C9H20) to hexa­decane (C16H34). When these long-chain hydro­car­bons are burnt they combine with oxygen to form carbon dioxide and water. The water vapour in the plane’s exhaust con­denses out (some­times as ice) to form trailing arti­fi­cial clouds known as contrails.

Military aircraft often have to be careful to avoid leaving con­trails as it makes them very easy to spot. This can be done by adding chloro­sul­phuric acid to the exhaust, as the chloro­sul­phuric acid reacts with water to form sul­phuric and hydro­chloric acid which doesn’t condense out in the same way as water. However, it is usually easier for the pilot of the aircraft to simply decrease altitude until con­trails cease forming.

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Three different types of magnetism

Posted on 4th April by Mr Reid

When you think of mag­netism the chances are that you’re only thinking of one type of mag­netism: fer­ro­mag­netism. But there are two other types of mag­netism: para­mag­netism and dia­mag­netism, that are less well known.

Fer­ro­mag­netism is the only type of mag­netism that produces forces large enough to be easily felt, and fer­ro­mag­netic mater­ials are the only ones that demon­strate spon­tan­eous mag­netism — mag­netism outside of an applied magnetic field. The most common fer­ro­mag­netic mater­ials are those that contain iron, cobalt and nickel but other elements such as dys­prosium and gad­olinium and com­pounds such as chromium oxide and man­ganese bismide also demon­strate fer­ro­mag­netic properties.

Para­mag­netic and dia­mag­netic effects only exist in the presence of an applied magnetic field: para­mag­netic mater­ials such as tungsten and alu­minium create an attractive force when exposed to magnetic fields and dia­mag­netic mater­ials such as pyro­lytic carbon and mercury create a repulsive one.

A small sheet of pyro­lytic carbon lev­it­ates above an array of neodymium-iron-boron magnets.

Water is weakly dia­mag­netic, about forty times less dia­mag­netic than the pyro­lytic carbon shown above, but this is enough that light objects which contain a large amount of water can be lev­it­ated if placed in a very strong magnetic field.

This frog was lev­it­ated using a 16 tesla Bitter elec­tro­magnet at the High Field Magnetic Labor­atory at the Radboud Uni­ver­sity Nijmegen in the Netherlands.

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Consanguinity and the coefficient of relationship

Posted on 29th March by Mr Reid

Or What per­centage of your genetic code do you share with your second cousin?

Two people who share some of their genetic code (their DNA) are said to be con­san­guin­eous (“co” meaning shared and “sanguis” being Latin for blood) and the extent to which their DNA overlaps is known as the coef­fi­cient of rela­tion­ship and is measured as a percentage.

Bearing in mind that you get 50% of your genes from each of your parents, it’s rel­at­ively easy to cal­cu­late the per­centage of your DNA that you share with any relative you choose.

The closer to white a relation is, the lower the amount of DNA shared with that person.

To explain where these figures come from let’s take an example: How much of my DNA do I share with my sister Caroline?

Every one of your genes is split into two parts called alleles; you get one of these two alleles from each of your parents to make up each of your genes. If we take as an example a random gene, OCA2 (a gene that controls for eye colour) it will make it easier to under­stand the cal­cu­la­tion process.

I got half of my OCA2 gene from half of my Dad’s OCA2 gene and the other half of my OCA2 gene from my Mum’s OCA2 gene; the same is true for my sister. I’ll call my Dad’s OCA2 alleles ED1 and ED2 and my Mum’s OCA2 alleles EM1 and EM2. There are there­fore four pos­sib­il­ities for my and my sister’s OCA2 genes:

  • ED1EM1
  • ED1EM2
  • ED2EM1
  • ED2EM2

With four possible choices for the OCA2 gene there is a 25% chance of us sharing 100% of our DNA, a 50% chance (25%+25%) of sharing 50% of our DNA and a 25% chance of us sharing 0%. If you sum these per­cent­ages across all of our genes you get:
(25% × 100%) + (50% × 50%) + (25% × 0%) = 50%.

To quickly cal­cu­late the per­centage of DNA you share with a relative simply count the number of (vertical) steps you have to take to get to them, and raise one-half to that power. For example, to find the per­centage of DNA shared with a second cousin once removed you have to go three steps up and three steps down (the step between grand­par­ents and great-grandparents is not counted twice) giving six steps in total. One half to the power of six is 0.015625 or 1.5625%; this is shown on the diagram below.

All of these cal­cu­la­tions assume that none of your distant ancestors inter­bred with each other: i.e. that you have four unique grand­par­ents, eight unique great-grandparents, sixteen unique great-great-grandparents and so on. Any half-relationships (e.g. half-brother, step-mother) cannot be included and of course I’m ignoring the fact that we are all related if you go back far enough.

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Magnetic coins

Posted on 28th March by Mr Reid

In case you missed the previous post on the subject, the UK’s new “silver” coins are magnetic.

Four five pence pieces sus­pended from a neodymium-iron-boron magnet.

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A rectangular galaxy

Posted on 26th March by Mr Reid

Most galaxies are either spiral or ellipt­ical (“len­ticular” galaxies fall some­where inbetween).

A typical spiral galaxy, the Pinwheel Galaxy (M101, NGC 5457).

A dwarf ellipt­ical galaxy, M110 (NGC 205).

A new arXiv preprint describes the dis­covery of LEDA 074886, which has a unique rect­an­gular shape.

LEDA 074886 is thought to have formed as a result of a col­li­sion between two disc-shaped ellipt­ical galxies that met “face-on”. The galaxy, 21 mega­par­secs (68 million lightyears) away from Earth, is described by the authors of the paper as being “Emerald Cut”, which I think it pretty accurate.

Source: Alister W. Graham et al, “LEDA 074886: A remark­able rectangular-looking galaxy”, arXiv:1203.3608v1.

 

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Smiths

Posted on 21st March by Mr Reid

Most people are familiar with the term “black­smith” and think that it refers to someone who works with metal, but this isn’t entirely correct. The term “black­smith” only refers to someone who works with the “black” metals such as iron and steel.

Red­smiths* work with copper, white­smiths work with light-coloured metals such as pewter or tin and bright­s­miths work with silver. Many smiths are known by the type of object they produce, for example a gunsmith makes guns and and a blade­smith makes knives and swords; others are known by the metal they work with: gold­smiths and zinc­smiths work with gold and zinc respectively.

* Red­smiths are also known as brownsmiths.

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Water in Bermuda

Posted on 20th March by Mr Reid

Fresh water is very hard to come by on the Islands of Bermuda. There are no lakes, and only a small number of water-collecting “lenses” under­ground. Rain­water is not salty, as the salt from seawater does not evap­orate with the water, so by law every home in Bermuda must collect 80% of the rain that falls on its roof.

Bermudan rooves are made of local lime­stone and channel rain­water into large under­ground tanks where the water is treated so that it can be used in homes. On average each Bermudan home can store about 50000 litres of water per bedroom.

Because Bermuda does not have a cent­ral­ised water dis­tri­bu­tion system it also does not have a cent­ral­ised sewage system and there­fore has the highest density of private cesspits per square kilo­metre of anywhere in the world.

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Do bowling balls float?

Posted on 15th March by Mr Reid

The largest bowling ball allowed by USBC or FIQ has a cir­cum­fer­ence of 27 inches, equi­valent to a diameter of 21.9 cen­ti­metres and a volume of 5447 cubic cen­ti­metres. Whilst the size of a bowling ball is fixed, its weight can vary, typ­ic­ally between six and sixteen pounds (2.7 to 7.3 kilograms).

With a fixed volume and a changing mass the density (mass per unit volume) of a bowling ball will change, and as a result some bowling balls float, and some sink.

The low weight balls (including the 12 lb ball at a density of 999.6 kg/m3) all float. Only the 14 lb and 16 lb balls will sink.

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The base rate fallacy

Posted on 10th March by Mr Reid

Imagine that there is a rare genetic disease that affects 1 in every 100 people at random. There is a test for this disease that has a 99% accuracy rate: of every 100 people tested it will give the correct answer to 99 of those people.

If you have the test, and the result of the test is positive, what is the chance that you have the disease?

If you think the answer is 99% then you are incor­rect; this is because of the base rate fallacy — you have failed to take the base rate (of the disease) into account.

In this situ­ation there are four possible outcomes:

Affected by disease Not affected by disease
Test correct Affected by disease, and test gives correct result. (DC) Not affected by disease, and test gives correct result. (NC)
Test incor­rect Affected by disease, and test gives incor­rect result. (DI) Not affected by disease, and test gives incor­rect result. (NI)

This is easier to under­stand if we map the contents of the prob­ab­ility space using a tree diagram, as shown below.

In two of these cases the result of the test is positive, but in only one of them do you have the disease.

P(DC) = P(Affected) × P(Test correct)
P(DC) = 0.01 × 0.99
P(DC) = 0.0099 = 1 in 101

The other case that results in a positive result, when you don’t have the disease and the test in incor­rect has the same 1 in 101 prob­ab­ility: P(NI) = 0.0099.

Of the two remaining cases, not having the disease and getting a correct negative test result takes up the vast majority of the remaining prob­ab­ility space: P(NC) = 0.9801 or 1 in 1.02. The chance of having the disease and getting an incor­rect test result is extremely small: P(DI) = 0.0001 or 1 in 10000.

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Recent solar flare

Posted on 9th March by Mr Reid

After the jump are two animated GIFs of the recent X5 class solar flare that I made from imagery from NASA’s SOHO satellite’s LASCO instru­ment. They’re quite large images, so you’ll need to wait a while for them to load.

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