## The maths of hallucinations ๐ง ๐

Have you ever seen something briefly that you then realise wasnโt actually there? Or rubbed your eyes and seen patterns dancing on your eyelids?๐These are called visual hallucinations and they happen when your brain is trying to make sense of the information it receives from your eyes.ย  Your brain uses this information but also fills in the gaps based on what you have seen before.ย  What we think we see, therefore, may actually be slightly different to what is actually there.๐ค Mathematical equations can be used to look at the changes in activity of neurons (brain cells) across the part of the brain that first gets the information from the eyes.ย  By comparing these patterns of activity with the patterns of the hallucinations that are seen, we can better understand how hallucinations happen and predict other hallucinations that may occur. Maths can also help us to learn more about hallucination causing illnesses such as schizophrenia, Parkinsonโs or epilepsy.๐๐ป Using maths takes us one step closer to understanding the most complex structure in the universe.๐ง ๐ค What do you see when looking at the image above?๐๐ This research is being undertaken by Abigail Cocks at the University of Nottingham.๐๐ปย #appliedmathematicsย #neuroscienceย #brainย #hallucinationsย #mathsinlifeย #mathsinnatureย #mathsinmedicineย #stemย #womeninmathematicsย #scicommย #keeplearning

## Using maths to find the culprit!๐ง The statistics of text ๐ ๐ ๐๐

Did you know that maths can be used to find patterns in text in order to help police find out who wrote a ransom note?? ๐ง๐ฎ๐ผโโ๏ธ Text can be represented as mathematical structures called networks. Networks are made up of things called nodes and edges, we can think of nodes as houses ๐  that may or may not be connected by paths ๐ or edges. For a piece of text, each word is a node of the network and these are joined to each other by edges when words appear near each other in the text. By comparing patterns in networks like these, it is possible to determine the gender, education level and even personality traits of the writer of the ransom note! This information can then narrow down the search for the culprit! ๐ต๐ปโโ๏ธ – –
Using statistics on text actually makes a lot of sense since this would take far too long for us to do ourselves. For example, to decide if an email is spam, the computer must have looked at thousands of emails and found a pattern in what makes a โspam emailโ. A person wouldnโt have time to sit and go through every email to decide what is spam, so we need to train a machine to do this for us automatically using statistics ๐ป

Other examples of uses of this technique include in plagiarism detection and in comparing novels written by different authors. This work is being undertaken by Katie Severn at the University of Nottingham ๐๐ป – –
#appliedmathematics#mathsandliterature#mathsinlife#statistics#whodoneit#findingtheculprit#networks#womeninmaths#girlsinstem#scicomms#communicatingscience#maths#keeplearning

## Breakfast maths ๐ฅฃ๐

Why are the large nuts always at the top of the cereal packet and not mixed in?! ๐ฉ๐ฅor even at the bottom?!๐ค It can be super annoying when you want a breakfast of properly mixed cereal and get a bowl full of one ingredient. It also seems very strange that the larger things are at the top and haven’t sunk to the bottom๐คจ. But anyway, this can be solved by just shaking the box right?! โ Well actually the shaking of the cereal box on its travels into your food cupboard is probably what has caused this annoyance in the first place! When the cereal shakes, the larger nuts move and jump around forming gaps underneath them and the smaller muesli grains drop into these spaces. This means that the nuts eventually rise to the top of the pack and the muesli grains fall to the bottom. We call this the Brazil nut effect ๐ฅ. Cereals are granular materials (this means they are made up of grains!) and the Brazil nut effect can be seen with other granular materials too. Other examples of granular materials are sand, sugar, dessert sprinkles, coffee grains and snow. These materials have unusual properties – while one grain of sand is clearly a solid material, a group of loads of grains of sand can flow like a liquid through your fingers! If the change from being solid like to liquid like happens when you don’t want it to however, then it could cause big problems – like avalanches! ๐ป๐จ Once again maths comes to the rescue ๐. Maths can be used to find safe ways of handling these granular materials by modelling how forces pass through each grain and the changes in flow when there are objects in the way. This maths has been used in the design of avalanche barriers to protect people.๐ โญ๏ธTry at Home activity๐๐ป: Add sugar and dessert sprinkles to a container and try to mix these together through shaking the container in different ways. What happens?!๐ย #appliedmathematicsย #physicsย #everydaymathย #mathsinlifeย #stemย #scienceeducationย #didyouknowย #materialsย #avalancheย #sandย #granularmaterialsย #womeninstemย #breakfastmathsย #scicomm

## How maths can be used to give me a dog face ๐ถ Snapchat filter algorithms!๐ฆธ๐ฝโโ๏ธ๐ฐ๐ป๐ธ๐ฝ๐งโโ๏ธ๐ฉ๐ปโ๐๐ฉ๐ผโ๐ฌ

How does snapchat know where to put the filters so that they are on the right part of your face and even stay on your face when youโre moving around?!๐ค First your phone needs to decide which part of the image is your face! Pixels (or picture elements) are tiny squares of colour that make up the image. Snapchat uses a mathematical algorithm to repeat many searches through all the pixels of the image looking for regions of contrast between light and dark pixels. This is because there are common regions of every face that are lighter or darker than others (e.g. the middle of your forehead is lighter than the outside). Using this snapchat has found your face! But how does it know where your nose is so that it can replace it with a dog nose๐ ? Or where your lips are so they can be puckered up ๐ ?!…Well this is where statistics comes in. To do this, many people have manually told a computer where the outlines of their different facial features are – so many faces in fact that the average of this is used as a template on snapchat. This template is put over the image of your face and adjusted to your specific features through scalings, rotations and movements based on contrast in light and on where other features have been detected. The coordinates of your face and facial features are then remembered as a mask and tracked as you move your face to create the best pose ๐บ๐ปย #appliedmathematicsย #mathsinlifeย #scienceiscoolย #mathsisfunย #keeplearningย #stemeducationย #womeninmathematicsย #snapchat๐ปย #filtersย #faceย #dogfaceย #scicommย #spreadingtheword

## Why do ambulance sirens sound different as they are driving away? ๐

Sound travels in a wave starting from something that is vibrating and ending up in your ear๐๐ป. When the sound wave travels through the air it makes pockets of different air densities (how packed together the air molecules are in a given space). This corresponds to alternating regions of high and low air pressure (you might have heard these terms when listening to a weather forecast โ ). The faster the air molecules vibrate, the faster each wave reaches your ear (higher frequency) and the higher the pitch we hear ๐ถ

So back to the ambulance sirens ๐… When an ambulance is driving away from you, there is a longer distance between the air molecules that are close to the ambulance meaning that the vibration is slower between these molecules. Each wave will therefore take slightly longer to reach your ear and so you hear a progressively lower pitch. This is called the Doppler effect. We can use a simple mathematical equation to calculate the speed of the vibrations (frequency) we hear if we know the speed an ambulance is travelling away from us as well as the speed of the vibrations leaving the siren.๐๐ป This principle can also be used to detect speeding vehicles using radio waves fired from a police radar gun! ๐จ โญ๏ธ Try at home sound waves activity: attach two pieces of string to one end of a slinky and tie the other ends of each string around one finger on each hand. Now listen to the difference in sound when dropping the slinky with those fingers in and out of your ears! Why does it sound different? ๐ง
(Hint: think about how densely packed molecules are in solids compared to in the air)
#appliedmathematics#scienceisforeveryone#mathseducation#stem#mathsinlife#ambulance#sirens#sounds#waves#tryathome#howthingswork#scicomm#mathscommunication

## Weird& Wonderful random maths fact ๐

Penguin eggs donโt hatch unless they have been rotated and maths can help us understand why! ๐ง ๐๐ป As we all know, eggs contain a round yellow yolk surrounded by a fluid egg white (called the albumen)๐ณ The albumen contains important nutrients that the baby penguin needs to grow!
When a penguin lays an egg, the embryo develops at the top of the yolk. The density of the embryo compared to the yolk means that it always returns to the top of the yolk (since it is buoyant like a float in a swimming pool) . As well as this, the density of the yolk compared to the albumen means that the yolk (and therefore the embryo) always return to the very top of the egg! ๐ฅ
When a penguin rotates their egg, the yolk and embryo slowly move back to the top of the egg. This creates a flow which mixes the nutrients in the albumen so that the embryo gets everything it needs to grow ๐

This mixing can be mathematically modelled using fluid dynamics!
It is important to know why penguins turn their eggs so that artificial incubators can be made to turn the eggs in the best way!
#appliedmathematics#stem#mathematicalbiology#scienceeducation#keeplearning#peguins#eggs#fluiddynamics#scicomm#mathcommunication

## Weird& Wonderful random maths fact ๐

There is an angle above which an airplane will stall and fall ๐ณ
But okay no need to panic, pilots correct this in most situations because they know their maths!
This important angle (called the angle of attack) is the angle between the imaginary line following the horizontal direction that the plane is flying in (or the direction that air is blowing against the front of the plane) and the imaginary line through the centre of the plane going from its tail to its nose. If this angle is too large, there will not be enough air flowing over the wings to keep the plane lifted causing a stall. Note that this stall is not to do with the engine like it is with cars!
But how come airplanes can do a loop the loop?! โ๏ธ Well this angle of attack is never reached in a loop since the direction of both(!) of the imaginary lines mentioned above will change throughout the loop.
#appliedmathematicsย #mathsphysicsย #engineeringmathsย #stemย #scienceeducationย #scicommย #learnscienceย #mathsfunย #didyouknowย #aerodynamicsย #flightย #planeย #designย #funfactย #womeninscienceย #maths

## Tortoise Turns ๐ข

The shape of some tortoise shells means that if they fall on their back, they can turn back over all by themselves. These shells look a lot like the shape called a Gรถmbรถc, which is unique because it only has two resting places and one of these is nearly impossible to achieve (so that it always turns back to the same position). The mathematics behind this shape and itโs properties can be used in a range of ways including in designing the shape of drones which often collide and get turned over!
#mathsinnatureย #appliedmathematicsย #whyweneedmathย #stemย #scicommย #learnscienceย #scienceeducationย #mathsisfunย #animalsย #shapesย #interestingfactsย #mathsinlife

## Weird& Wonderful random maths fact ๐

In a room of 23 people there is a 50% chance that 2 people have the same birthday! ๐คWhatโs more is that in a room of 70 people this chance is 99.9%! ๐ค๐ค This might seem strange since there are only 23 people and 365 possible days to have a birthday. However if we think about pairs of people, 23 people gives 23*(23-1)/2 = 253 pairs which is more than half of 365. Using this and some basic probability we can calculate the percentage chance given any number of people๐ฅณ

The understanding of this โbirthday problemโ has been used in computer hacking ๐ป

## How does a zebra get its stripes and why should we care? ๐ฆ

We can see lots of patterns in nature: leopard spots, butterfly wing eyes and zebra stripes to name a few. While these all look pretty different, it turns out that there is a simple set of mathematical rules that can produce all these patterns. Alan Turing (the guy who created these rules) thought of cells as producing 2 chemicals that act very differently to each other. The rules show us that one of these chemicals spreads out faster than the other, leading to the slower chemicals all getting trapped in clumps. These clumps can be in different shapes like spots and stripes.

Knowing how these patterns are made is important for something called tissue engineering. This is because we can get cells outside of the body to organise themselves in the way they do naturally. These are then used to create tissues to replace damaged tissue eg. artificial skin for people with bad burns.