Angelina Jolie has had both breasts removed because of the risk of developing breast cancer.
But did she understand the Maths?
She may be right. This could be the best way for her to avoid breast cancer. And it IS her decision.
But maths isn’t that clear cut. Referenced information about BRCA1 and BRCA2: Cancer Risk and Genetic Testing can be found at The National Cancer Institute here.
in the general population will develop breast cancer sometime during their lives compared with about
60 percent of women (600 out of 1,000)
with gene mutation in BRCA1 or BRCA2. This is FIVE TIMES the risk over a lifetime.
BUT and this is a big but …..
It is important to note, however, according to The National Cancer Institute (USA), most
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research related to BRCA1 and BRCA2 has been done on large families with many individuals affected by cancer and the cancer risk associated with BRCA1 and BRCA2 mutations have been calculated from studies of these families. Because family members
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share a proportion of their genes and, often, their environment, it is possible that the large number of cancer cases seen in these families may be due in part to other genetic or environmental factors.
Factors that could affect these risk factors include food, lifestyle, location, inherited temperament and even the air they breathe.
Statistics are a useful tool. But statistics are based on random selection. This is IMPORTANT. Once you bias the data, your results are corrupted.
Removing cancerous breast tissue makes sense. Removing perfectly healthy breast tissue based on the maths … well … you’d want to think about it.
To put this another way the BRCA genes may be correlated with breast cancer, but this event is not independent of all other events in one family. There may be many, yet to be discovered, links . This is a common error in statistics made not only by journalists, but by experts too. (See below)
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Conviction by Maths Error
On 9 November 1998 at Chester Crown Court Sally Clark, a Cheshire solicitor, was convicted, by 10-2 majority, of smothering her two baby boys.
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Clark’s first son died suddenly within a few weeks of his birth in 1996. In 1998, when her second son died in similar circumstances she was arrested and tried for the murder of both sons.
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The prosecution used paedeatrician Prof Roy Meadows as a expert witness. He had discovered Munchausen Syndrome by Proxy (MSbP). Sally Clark was found guilty and spent 3 years in jail.
Prof Roy Meadows testified that the chance of two children from an affluent family suffering sudden infant death syndrome was 1 in 73 million. He arrived at this number by squaring 1 in 8500 for likelihood of a cot death in similar circumstances.
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He was wrong and was later struck off the medical registrar. He assumed that these were independent events. They were not. Maybe the heater was at fault. Or the cot. Or the house paint. Or, as suggested in The Observer article, faulty genes in the family.
Sally Clark died several years later of alcoholic poisoning. More information.
Today we are going to be Food Scientists; food science needs maths and this food science is important for your health and diet.
Before we do the maths we must understand the science of sugar. Here is a simple explanation.
In the USA corn, which is 100% glucose, undergoes an industrial process that breaks down the long glucose chains and converts some glucose to fructose because fructose delivers a bigger sweetness hit on your tongue and corn is cheap. The resulting HFCS (high fructose corn syrup) is, on average, 60% fructose.
Now we can do the maths.
This important information below comes from the Goran Labs
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Food Science Maths
or
Fast Food Maths
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1. Draw up a bar graph of the weight of sugar(sucrose) and fructose for 8 drinks.
2. Plot the weight of sugar(sucrose) and fructose for 8 drinks on axes.
3. Assuming that 100ml of soft drink weighs 100g – this is realistic- calculate the percentage of sugar(sucrose) and fructose. This exercise is to see if students are paying attention. It is very easy!
4. Drinking too much sugar in any form is not advisable, but fructose in large quantities just adds calories without satisfying your hunger. Which drinks are loaded with fructose?
Food Scientists check to see if the stated sugar content of food equals the actual sugar content. Here is a medium sized Macdonald’s Coke.
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The size of a medium sized coke is:
590ml (Australia) containing 55 g sugar.
621 ml (21 fl oz) USA containing 58 g sugar
400ml (UK) with 42 g sugar.
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You can get nutrition information for Macdonald’s coke for Australia here , the USA here and the UK here.
Food Science Maths
Q 1. Calculate the percentage sugar in Maccas cokes in Australia, the USA and the UK assuming 1 ml coke weighs 1 g.
Ans: 9.3% (Aus), 9.3% (USA) and 10.5% (UK)
Here are some interesting results for the Goran Labs. This table shows you the % variation in sugar content of soft drink samples.
Q2. Calculate the actual amount of sugar for by weight for each medium sized Macdonalds coke if, as shown in the graph above, there was 28% more sugar than stated on the nutrition panel, in the brochure or on the website.
Ans: 70.4 g (Aus), 74.2 g (USA) and 53.7g
Well, chug-a-lug mathspiggies, you can see which country is getting a big sugar hit at Maccas.
This is the most awesome way to introduce probability.
Mentalist Derren Brown devises a foolproof gambling system. He sends a girl , Kadisha, the number of a winning horse in race to be run the next day. It wins. He sends her the winning horse and race number 4 more times. She ends up with winnings close to £ 1000 before the final race. Derren convinces her to borrow money for the last bet. She does. She places £4,000 on a horse. Did it win?????
Watch Part 5 of The System
If you are not convinced Derren Brown can come up with a foolproof system for horse race tipping, let me explain The System. He took 7,776 e-mail addresses, divided them into 6 equal groups and sent each group a different number for a horse in a 6 horse race to be run the next day. Naturally, one group of 1296 had been given the winning horse number. This group was divided into 6 again and given the number of the ‘winning’ in a six horse race the next day and so on.
Race 1: 7776
Race 2: 1296
Race 3: 216
Race 4: 36
Race 5: 6
Out of 7776 punters, only one punter was given in advance five horse race winners in a row. Was it Kadisha. You will have to watch the Youtube above.
You can watch THE SYSTEM in full here. It takes 47 mins.
So you wanna be FAMOUS and fabulous and uber-cool too.
Maybe you wanna be the Chris Rock of maths. Being famous is soooooo cool.
…………….……You get attitude!!!
……………………You Get cool sunglasses!!!
….You get a chauffeur that’s not your mum!
But what are the chances? What is the probability that a kid at your school will become famous one day? Cate Blanchet went to Mathpigs kids’ school. But in Australia we don’t make a fuss. They haven’t put a picture of her on the wall or anything.
So mathspigs let’s work out the probability of you becoming a STAR, BABY!
The first question is how do you measure fame? Do you have to be on TV to be famous? Do you have to be a Hollywood star? Should you be a wax dummy in Madame Tussaud’s? Not as a job. I mean because you are so fabulously famous.
Perhaps, you could use Tom Weller’s humorous Rictus scale (a parody of the Richter Scale) for earthquake intensity using media coverage as a guide to fame. Just replace the persons name for the word ‘scene’.
I’m thinking around ’5′ looks like FAME, but you decide. Now count how many ex-students from your school (and any current ones) who have become famous in the last 20 years and do the maths.
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Rictus
Scale #
Richter Scale
Equivalent
Media Coverage
1
0-3
Small articles in local papers
2
3-5
Lead story on local news; mentioned on network news
3
5-6.5
Lead story on network news; photos in nation newspapers; governor visits scene
4
6.5-7.5
Network correspondents sent to scene; president/PM visits area; commemorative T-shirts appear
5
7.5 up
Covers of weekly news magazines; network specials; “instant books” appear
The Hunger Games is about MATHS. Here are some interesting Hunger Game statistics.
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THE PLOT:
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In Suzanne Collin’s book, The Hunger Games, 12 districts in the land of Panem are suppressed and controlled by a vicious elite, who dress like neon-coloured French courtesans.
Each year the cruel rulers select one teen of each sex between the ages of 12 and 18 from each district to become tributes, who must fight to the death in a televised, sponsor-supported media event called The Hunger Games, set in a staged wilderness.
Only one tribute can survive. Katniss Everdeen and Peeta Mellark from the poor coal-mining District 12 are the local tributes for that year and must play at being star-crossed lovers to gain sponsor support and survive.
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THE MATHS:
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……………………………………………….……..The Reaping…..
Tributes are selected in a process called The Reaping. The names of the, approximately, 2,000 young people in each district are placed in separate barrels for males and females and the names are drawn out of these barrels BUT…
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12 year olds …….. 1 slip
13 year olds …….. 2 slips
14 year olds …….. 3 slips
15 year olds …….. 4 slips
16 year olds …….. 5 slips
17 year olds …….. 6 slips
18 year olds …….. 7 slips
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BUT you can gain extra ‘food’ if you accept for more name slips.
Gale Hawthorne (pictured above), Katnis’ friend from District 12, has 42 slips in the barrel. What are his chances?
We will assume that there are 1,000 teens of each sex in each district and an equal distribution – rounded off – for each age group to 1000/7 = 143
Unlike Kill Bill where Tarantino used, literally, hundreds of litres of fake blood (See Mathspig Post: Don’t Bleed Your Fake Blood on Me), The Hunger Games shows very little blood.
Nevertheless 11 tributes are killed violently in the first few minutes of the game and Peeta is wounded later in the movie(pic with Katniss above).
To calculate how long you would last in The Hunger Games if bleeding we must know your volume of blood and the rate of bleeding.
1. How much blood do you have?
According to the BJA, the British Journal of Anaesthesia, blood volume is 7% of body weight in adults and 8 – 9 % of body weight in children. Doctors are not confusing weight and volume. Blood is very close to the density of water and so 1 litre of blood weighs 1 kg.
(NB: Future Engineers: Blood does not flow like water as the blood platelets affect the viscosity.)
Using blood volume (in litres) as 8% of body weight (in kg) then typical blood volumes for teenagers would be:
Mathspig noticed in the film that Katniss was aiming the arrow directly at the target. This is a problem. Arrows drop under gravity. If Katniss aims directly at the target she will hit it below her aim point. To overcome this she must raise her arrow aim.
What angle should she choose?
Robin Hood used a long bow and in the film Robin Hood archers raised their bows at a very high angle to cover long distances. See the diagrams below from Robin Hood Give Us Your Best Shot
According to The Flaming Arrow the speed of a modern arrow is 100 m/sec with a 65 lb draw weight.
Mathspig believes in using the SIMPLEST maths solution. In this case, very short arrow flight times are involved.
So we will assume the arrow velocity (Va) equals horizontal vector speed (Vx). This is an approximation that makes the maths sweet. Such an approximation might work for the arow flight in the first diagram (above), but not in the second.
First, mathspigs, we’ll calculate the arrow flight time to a target 100m away and then we will calculate the distance the arrow would drop vertically in that time as this will tell us the point in the air where Katniss should aim.
NB: An arrow will drop 4.9m over 100m to the target. In other words, Katniss would miss a human completely if she did not allow for gravity. Experienced archers automatically make this adjustment to their aim.
The estimates of lifetime risk are about
Mentalist Derren Brown devises a foolproof gambling system. He sends a girl , Kadisha, the number of a winning horse in race to be run the next day. It wins. He sends her the winning horse and race number 4 more times. She ends up with winnings close to £ 1000 before the final race. Derren convinces her to borrow money for the last bet. She does. She places £4,000 on a horse. Did it win?????
