The Science of Santa

We all know Father Christmas is one of the most wonderful and magical parts of Christmas, so we thought we’d use our scientific knowledge to work out how the fastest man in the universe delivers all those presents in one night!

There are approximately 2 billion children in the world. Of those, about 700,000,000 celebrate Christmas (and make the nice list!). With an average of three children per house, that’s a whopping 233,000,000 stops that Saint Nick has to make! Now bear with us…

If those stops are distributed evenly around the world, with a total surface area of 317,000,000 miles, each stop is 0.91 miles apart, making a total of 212,030,000 miles that Santa has to travel.

Because of the time differences across the globe, Santa has approximately 32 hours to complete his trip, maximising the night time (and sleeping children) available. Using speed = distance ÷ time, we can then work out that he has to travel at 6,650,807.72 mph! That’s about 1,800 miles per second.

So, remember to leave out a mince pie or two to help him along on this, his busiest of nights!

Competitive Edge at Christmas – the mathematical way to beat the family

Toilet Trouble is the must-have family game this festive season. Determined not to be flushed away by their families, our Mathematics lecturers, Dr Andrew Baggaley and Dr Nick Parker got ahead of the game to analyse the seemingly random sequence of flushes and squirts.

On Christmas morning many families will wake up to a rather unexpected gift from Santa Claus: “Toilet Trouble”.  This does not involve an emergency call to your local plumber or your GP, but is rather a family game devised by Santa’s most mischievous elves.

Each player nervously awaits their fate as they place their face over the toilet bowl and flush the handle.  If they are lucky, they breathe a sigh of relief at staying dry and the suspense moves to the next player; if they are unlucky, a jet of toilet water comes to greet them.  Is this squirting truly random or is there some hidden order?  Can the occurrence of the next tinkle be predicted?  And can you beat the odds to stay dry, while soaking your nearest and dearest?  Here we self-proclaimed wizz kids combine scientific experimentation and mathematical analysis to give you the edge in this festive problem.

We put the game to the test by flushing the toilet over 1000 times and noting whether the jet squirted or not.   The data was conveniently recorded in binary format as a series of zeros ( = no squirt, dry) or ones (= squirt, wet).  The dataset, shown below, appears random with no evident pattern.  However, just because it looks random, is it random?  A large area of mathematics is devoted to analysing such patterns, seeking out hidden order and the information that this may carry, from identifying the trends in stock markets to deciphering information embodied in secret communications.  On the flip side of this latter example is the branch of mathematics which creates the codes in the first place; cryptography designs tricks to hide information in a jumble of numbers.  Central to this are the “pseudo-random-number generators”, mathematical functions which produce a seemingly random series of numbers but which are nonetheless orderly mathematical functions – if we start the function from the same number we will always get the same random-looking series of numbers being produced.  In this sense, the numbers only appear random.  An everyday example of pseudo-random-number generation is when we play our music tracks on shuffle.  Interestingly, however, a good generator would mean that there was a chance that the same number (music track) would be produced twice in a row, or within a short interval. For example if you create a random playlist from a 10 track album, there is a 10% chance that you would have to listen to the same track twice in a row. To avoid this unwanted effect, the original number generators used for shuffling had to be tweaked to prevent the same track arising in close succession.

We return to the matter at hand – the “random” squirting of the toilet.  As is typical of scientific analyses, we begin our analysis at the most basic level, before drilling down to increasing detail until we reach a required level of understanding of the problem.  From the data (see image) it is evident that the squirts (ones) are relatively spaced out.  In other words, at each flush there is not an equal 50:50 chance between squirt or no squirt – the chance is biased towards not being squirted, which is some good news for the players.  Our 1000 flushes produce 196 squirts, informing us that, on average, there are 5.1 flushes between squirts.  This doesn’t help us to identify whether or not there is a pattern to the squirts, and so next we look at the number of flushes between squirts, shown below.  Several important features now become evident.  There is not an equal chance of a squirt for all number of flushes, and this allows us to ascribe a confidence/concern scale. If it is your turn to flush immediately after a squirt has taken place, you can give your most cocky grin at the toilet bowl and your fellow players – no squirts arise on this turn.  If you flush on the second, sixth or eighth flush after the previous squirt, you can smile with a confidence at the bowl – these turns have less than 5% chance of squirting.  If you take the fourth flush, then have your towel handy – this leads to the highest chance of squirting, over 30%.  Finally, if you are about the take the tenth flush then brace yourself for a guaranteed soaking since all squirts happen within ten flushes.

If the squirting were entirely random, then the distribution in the histogram would be flat; the fact that it varies indicates that there is some hidden order which, for example, favours the fourth flush and suppresses the first, second, sixth and eighth flushes.  Closer examination of the squirting reveals a pattern in which the squirting fires around the 10th, 3rd, 4th, 8th, 4th, 4th and 5th flushes.  This pattern then repeats.  So the squirting is orderly after all, it is just the irregularity of this pattern that creates an illusion of randomness.

So how random is our game? In order to understand this we can compute the entropy of the squirt signal, a single number which will quantify this.  If you have met the idea of entropy before then it was probably in the context of disorder.  Indeed one of the most important laws of physics tells us that the natural tendency of any isolated system is to become more disordered. Leave a young child in a tidy bedroom and they will soon provide a definitive proof of this.

However we can also apply this idea to a random signal. Imagine flipping a fair coin lots of times and noting down a 1 if it is heads and 0 if it is tails. This would build up a signal of 1’s and 0’s which is completely random. If we computed the entropy of this signal we would find it is one. On the other hand imagine a coin which is completely biased, it always landed showing the head. This signal would be completely predictable, it would always be a 1, and the entropy would be zero. From our data we expect a squirt roughly with a probability of around 1 in 5, a truly random signal of 1s and 0s with this probability has an entropy of 0.72. What about our game? We find the entropy of our signal is a little lower, almost exactly 0.7, expressing the fact that our data has some intrinsic pattern.

Will this understanding allow us to stay dry on Christmas morning?  Well no.  The number of flushes that a player must make is random, decided by spinning a wheel numbered from 1 to 3.  This serves to ensure that each player has no control over their own destiny.  You can predict when the squirts will fire but you can’t control whether they will fire on you!

#TryThisTuesday Crystal Christmas Decorations!

Crystal Christmas Decorations

It’s the most wonderful time of the year… and for this #TryThisTuesday Christmas Special, we’re making beautiful decorations for your Christmas tree using science!

Step 1

Mould your pipe cleaners into the desired shape, we chose to make a Christmas tree out of green pipe-cleaners, and a snowflake out of white pipe-cleaners

Step 2

Carefully fill a large container with boiling water then add the salt bit by bit, stirring continuously, until the water is saturated.

This means that the salt stops dissolving and instead sits at the bottom of the water, as the water can no longer hold any more salt crystals.

Step 3

Tie one long piece of string around your decorations in a row

Step 4

Dip the decorations in the water, and suspend over the container (as shown in the picture)

Step 5

This next part will take some patience!

Over the next 24 to 48 hours, watch as the crystals develop around the fibres of the pipe-cleaners, and see your beautifully festive decorations develop!

Step 6

Tie a piece of string around the top of your decoration and hang on your tree!

The Science

Salt crystals are formed due to ionic bonding, meaning they form a specific pattern which is always a square shape. When salt is dissolved into water, the water molecules separate the salt molecules. This means that even when it looks like the salt has disappeared in the water, it is actually there all along.  This happens especially well in hot water, as the heat means the water can hold many more salt molecules than cold water. As the water cools and evaporates, the salt crystals bond again as the water can no longer hold all the salt. The crystals stick to the pipe-cleaners because as the water evaporates, it takes some of the salt with it which clings to our suspended decorations, leaving beautiful crystal ornaments!

Our top STEM jokes!

It’s nearly Christmas and that means it’s time for awful Christmas cracker jokes. Hopefully our favourite STEM jokes will be a bit more funny! Scientific explanations are underneath each one.

Neutrons make up the middle (nucleus) of atoms and don’t have any electric charge, unlike protons (positively charged) and electrons (negatively charged).

Light is made up of small particles, these are called photons. Therefore, a photon is travelling light.

The chemical symbol for oxygen is O and potassium is K.

H2O is water, but H202 is hydrogen peroxide. Hydrogen peroxide would cause chemical burns and choking if it was drunk.

Atoms are very small and make up everything, including us.

Schrodinger’s Cat is a thought experiment in physics, where a cat is kept in a box with a radioactive source and poison. Until the box is opened, the cat can be assumed to be both dead and alive.

Helium is a noble gas, this means it is doesn’t react with other elements so is inert.

Extrapolation is when you estimate what the result may be beyond what you measured. The joke is that some people can’t extrapolate from data so can’t work out the end of the joke

Binary is a way of using two different symbols, 0 and 1, to represent any number, this is often used to create code for computers. 10 in binary is the same as writing 2. Therefore, there are two types of people, those who understand binary and those who don’t.

If an atom loses an electron (a negatively charged particle) it will become positively charged.

If time travel is ever invented, it doesn’t matter when as you can just travel back in time with the time machine.

Anti gravity is a place or object that is free from the force of gravity, so would float around.

This is a play on words, as the atmosphere in a restaurant is how you feel when you are there, but in science terms the atmosphere is a mixture of gases that surrounds the Earth. The moon has a much thinner atmosphere than the Earth and was originally thought not to have one.

Why Perfumes are not the Perfect Christmas Present…

Many animals rely heavily on their sense of smell for finding food, getting a whiff of the competition and even sniffing potential mates. You might not often see humans checking the scent of their partners, but scientists have found it does play a subtle role in helping us chose mates – as do perfumes.

All animals are made up of a collection of genes that are inherited from parents, these code for all sorts of things like eye colour and taste buds. All mammals, including us, have a section of genes called the major histocompatibility complex (MHC) which affects how well your immune system fights diseases. It is also linked to your natural scent.

There have been experiments on mice, mandrills, meerkats and many other animals showing that females tend to mate with males that have a different MHC to their own. This ensures that their offspring have a more varied set of genes and so will likely have a better immune system and survive for longer – which is what every parent wants for their child.

When tested in humans, the usual method is to get a group of men to wear a t-shirt for several days to get it nice and sweaty and smelly. Women will then smell each of the t-shirts and rate the odours in order of which they find the most pleasant. These experiments have consistently found that women tend to prefer the scent of men with MHC genes different to their own.

So what happens when you wear perfume and cover up that lovely natural odour of yours? Two researchers, Wedekind and Milinski wanted to find out. They asked over 100 people to rate a selection of perfumes based on whether they would like to smell like that. They found a correlation between the type of MHC and the scents selected, suggesting that we choose perfumes for ourselves that will enhance our natural odour. However, when asked to rate perfumes based on whether they would like their partner to smell like that, they found no significant link.

It appears that we are great a picking out odours for ourselves, but not so much at selecting the perfect perfume for others. Maybe a gift card would be better this year…

#TryThisTuesday: Making Snow

We’re feeling very festive this Tuesday so we thought it was the perfect time to make snow with science. All you need for this one is some shaving foam and bicarbonate of soda.

Simply mix the bicarbonate of soda and shaving foam together in a bowl until you get a powdery consistency.

Pick it up and have a play – you might notice that your fake snow actually feels cold too. This is due to the reaction between the bicarbonate of soda and the shaving foam. The reaction is endothermic meaning that it requires heat to occur, it takes this from the environment and so decreases the temperature around it.

The Science of Shaving Foam

Do you think shaving foam is a liquid or a solid? It’s actually a colloid. A colloid is a substance which has droplets of one state surrounded by another state. There are lots of different types of colloids with different combinations of states making up the droplets and the surrounding. In the case of shaving foam, the droplets are gas and the surrounding is liquid making it a foam colloid.