Monthly Archives: March 2012

Do bowling balls float?

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.

The base rate fallacy

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.

The man who put his head in a particle accelerator

The U-70 synchrotron control room.

On July 13 1978 Anatoli Bugorski, a physicist working on the U-70 synchrotron at the Institute of High Energy Physics in Protvino, Russia decided to put his head into the particle accelerator whilst it was running. Presumably he did not know it was running at the time, and presumably there were some safety features that should have prevented him from doing so but which had failed.

Nonetheless, Bugorski somehow managed to put his head into a beam of 76 GeV protons (for comparison, the LHC accelerates protons to an energy of 3500 GeV).

The beam caused a flash in Bugorski’s eyes “brighter than a thousand suns” and the left side of his face swelled up beyond recognition. He was later taken to a state hospital that specialised in treating radiation injuries where it was expected he would die. Amazingly, despite the huge dose of radiation, Bugorski survived; probably due to the fact that the radiation was confined to a very small area.

A photograph of Bugorski taken for Pravda in 1998.

With the left side of his face paralysed, with no hearing in his left ear and suffering from seizures, Bugorski still managed to complete his PhD and became the coordinator of experiments at the U-70 accelerator.

(I’d like to point out that the original title of this post was going to be In Soviet Russia, Particles Accelerate You [source] but I resisted.)

Does time go faster as you get older?

Whilst two observers moving relative to each other will experience the other’s time as moving slower or faster (Einstein’s Theory of Special Relativity), the passage of time for any given observer in a single reference frame is constant.

But as you get older, time seems to go faster. This is because each subsequent day is a smaller fraction of your lifetime up to that point: for a one year-old baby, one day represents 0.274% of their lifetime; but for an eighty year-old adult one day is a mere 0.00343%.

The progression is easier to see on a logarithmic scale: