We like to think that when faced with an important decision, that intuition or the so called ‘gut feeling’ will help aid us in making the right decision. Research into decision making and statistical reasoning by Kahneman and Tversky has suggested that decisions made by individuals are predictable and often misguided.

Consider this scenario:

You are the head of a pharmaceutical company which has recently found treatment for HIV. 600 people have volunteered to take part in trials. As a company you must choose which one to trial.

• The first pill will save 200 people
• The second pill has a 1/3 chance of saving all 600, and 2/3 chance of saving none.

Which one would you choose?

Most will choose option one to guarantee the survival of 200 people, without gambling the loss of all 600.

Let’s rephrase the situation:

• The first pill will kill 400 people
• The second has a 1/3 chance that none will die, and 2/3 chance that 600 will die.

Do you still choose pill one?

Turns out, the majority will actually choose pill two, as rather than settling for 400 deaths, there is a chance all will survive.

But if you look closely, both situations are identical. This paradox has been addressed by Kahneman and Tversky as the influence of question framing; scenario one being positive, and scenario two being negative. Humans tend to prioritise the pain from loss above the pleasure from gain.

Applying this theory to a difference scenario;

A bank teller provides you with two funding options;

1. $1000
2. $2000 or zero depending on the toss of a coin

What option do you take?

Most people want to maximise the gain and choose option 2 on the chance that you win the $2000.

Now, what happens if the bank says they are taking;

1. $1000
2. $2000 or zero depending on the toss of the coin

This time it would be assumed that you take the $1000 in order to prevent losing $2000.

These are just two of the scenarios where personal evaluation of risk lead you astray.

A study conducted in Hawaii has found that drinking more coffee could reduce middle aged Japanese men’s risk of developing Parkinson’s Disease. This came following increasing Parkinson’s prevalence in the United States, and the lack of treatment to help prevent it’s onset.

Researcher G. Webster Ross from the Veterans Affairs Pacific Island Health Care system in Honolulu was the lead author of the study which was published in the Journal of the American Medical Association (JAMA) and found a link between caffeine intake and the incidence of Parkinson’s Disease in middle-aged Japanese men during a 30 year study period.

Over the period of 30 years, age of Parkinson’s diagnosis’ were recorded along with daily coffee and total caffeine intake. Parkinson’s was diagnosed by two neurologists based on proven criteria; Parkinsonism, a progressive disorder, signs of asymmetry at onset, and absences of any aetiology known to have similar symptoms. Caffeine intake included coffee consumption, and total caffeine from dietary recall. Coffee intake was categorised by; Non Drinkers, 4 – 8 oz/d, 12 -16 oz/d, 20 – 24 oz/d, >28 oz/d, while total caffeine was calculated to be; None, <8oz/d, 8 – 16oz/d, 16-24oz/d, and >24oz/d.

Of the 8006 men who were involved in the study, 2 were excluded due to already possessing symptoms characteristic of Parkinson’s. Over the 30 year follow up period, 102 were diagnosed with Parkinson’s Disease. The research found that on average Japanese middle aged men who did not drink coffee were between 1.8 and 14.4 times as likely to develop Parkinson’s Disease than those who drank more than 28oz of coffee per day. This statement can be made with 95% confidence. This was a statistically significant result with a p value of <0.01. This is an increase from approximately 2 per 10000 person/years to 10 per 10000 person/years. As well as this, it can be said with 95% confidence, that on average those who consumed less than 2.8mg/d of caffeine from non-coffee sources had a risk of Parkinson’s Disease between 1.4 and 5.4 times higher than those who consumed more than 106.8mg/d after the results were adjusted for smoking and age (p=0.03).

Caffeine has been known to stimulate the central nervous system, and is suspected to be an inhibitor to the adenosine receptor which produces agonists that inhibit dopamine neurotransmission, that has a role in decreasing locomotor activity. If this is the case, caffeine may act to decrease Parkinson’s Disease incidence though the increasing dopamine concentrations leading to decrease in parkinsonism.

It is important to recognize that the sample was only comprised of middle aged Japanese men in Hawaii. This means the results can only be representative of this specific population. It should also be acknowledged that as this was an observational study, no claim can be made that high caffeine intake causes a lower incidence of Parkinson’s, only that a link may exist. There is also the issue that as caffeine intake was not randomly assigned, some confounding factors may not have been addressed. This could include; individuals who have a physiological intolerance to caffeine also being susceptible to the development of Parkinson’s. Another issue which was mentioned by G. Webster Ross was the decline in the study cohort through follow-up examinations. This could lead to a disproportionate reduction in those who are heavy coffee drinkers and developed Parkinson’s within the 30 year period that are not recorded, compared to those who are light coffee drinkers and did attend follow-up sessions with Parkinson’s. Recall bias and behavioral considerations would also have to be recognized as a potential issue when documenting an individual’s total caffeine intake based on dietary recall. Therefore, excessive caffeine intake for the purpose of decreasing the chance of getting Parkinson’s is not encouraged without further research.

The humble grape. This fruit has so many positive qualities including:

• Easy to eat 
• Can be made into wine
• Contains melatonin (helpful for sleep)
• Great sharing fruit
• Comes in a variety of colours, shapes and sizes
• Creates plasma

Yes… you read that last one right! Grapes really do form plasma. Plasma is said to be the fourth state of matter. It is essentially a gas cloud of ions and electrons. 

Grapes are the ideal fruit to create a little ball of plasma. They are the right size to trap electromagnetic waves within the fruit and these go back and forth when heated. The point at which the grapes touch is where the electromagnetic waves accumulate. And boom! You will see a glowing light in the middle of the two halves of the grape.

Steps to Creating Plasma from Grapes

1. Cut the grape in half but leave part of the skin connected at one end. 
2. Put the grape in a microwave for 5-10 seconds

It is pretty simple! There should be mini plasma ball which bursts in the centre. But personally, I would not try this at home. Plasma can be dangerous especially due to the condensed energy in the grape. I am pretty sure your parents/flatmates/halls friends will not appreciate a broken microwave! But, if anyone ever asks you about why grapes are an elite fruit, I hope you can add this cool phenomenon to the list!

You probably saw this kind of video online. A person put Mentos into a bottle full of coke. Then a huge amount of bubble form and push the all coke out of the bottle. It is really fun and could be a good prank on your friend ;). But how does it work?? Is there some chemical reaction happening? Or is it a physical reaction. I thought is a chemical reaction between the mint and the CO2 in the coke. But after some research (like watching video on YouTube for 10 mins xD) I realized I was wrong. It is in fact a physical reaction.

As you probably know there are lots of CO2 (carbon dioxide) in coke. Whenever those molecules touch objects with tiny dents, scratches, and bumps on them, the CO2 will quickly change into CO2 gas (the bubble). This is why you can see a bubble forming on the surface of the bottle. Also when you put a straw into the bottle. Bubbles will form on the straw and push it up. Mentos may look like it has a smooth surface. But if you have a strong microscope, then you can see it has lots of tiny dents, scratches on its surface.

In the picture above the red and black things are the CO2 molecules. When it touches the dents on the Mentos surface bubble will form. The more dents the more bubble. If you want to test this theory out. Buy a bottle of coke and put some object with a not very smooth surface (like sand etc.). You will see the same reaction :D. This is the science be hide Mentos and coke reaction 🙂 I hope you like it.

This blog is mostly based on the video below, which is about a mathematicians vision to formalise modern mathematics. If you’re interested at all in mathematics I’d recommend giving it a watch, but if not, the speaker’s deadpan and sarcasm make it interesting to listen to alone.

If you have taken a mathematics course this year, you’ve probably encountered, to your dismay or delight, the notion of a proof. It is a rigorous argument with the purpose to convince the reader of the truth of a statement, the theorem. It uses a mixture of formulae and natural language (what we speak/write). Most proofs assume a certain level of background knowledge and logical steps are often skipped for brevity and/or left as an exercise to the reader. This format is the standard convention for the mathematics in textbooks, journals, presentations and conferences.

In contrast to this is the notion of formal proof (you might then call the other informal). Written in a formal language, a formal proof does not omit steps (no matter how small), nor rely on any reader intuition. A proof assistant (sometimes called an interactive theorem prover) is a type of software that verifies formal proofs, and can help prove new ones.

An informal proof can be converted into a formal proof, however this is a practice rarely done in research mathematics. Instead of using infallible software for proof verification, the mathematical community verifies proofs with what Kevin Buzzard (the speaker in the video) calls ‘the committee of elders’.

The committee of elders are essentially those at the very top of the mathematical pecking order. If the committee of elders deems a proof to be correct then the formal correctness of the proof is not important. And for the most part this system works extremely well because mathematicians are good at what they do and most of the time errors are ‘smelled out’. There is a non-zero chance that important areas in mathematics are built on fallacious foundations, but this is very unlikely. The current belief system works just fine, so there isn’t really a perceived need in research mathematics for results to be verified.

This is not to say that no mathematics has been formally verified. The irrationality of √2 (500 BC), Taylor’s Theorem (1712) and more have all been done in various languages. More recently in 2012 was the verification of the Odd Order Theorem, which was first proved in 1962. As you can see, this is a fifty year lag time. The area of mathematics the theorem is involved with has been dead since the 1980’s so when computer scientists came out with the formal verification in 2012, there was ‘nobody left who’s interested’. Essentially, the work done with proof software is far behind that of the state of current research mathematics. Mathematicians, much like consumers, are interested in the latest and greatest thing. Proving old theorems is of no interest.

So how do you market proof assistant software to mathematicians? Well, any work done on formalisation must be on high level mathematics that is currently an active area of research and discussion. Buzzard chose to work on an area of mathematics called perfectoid spaces (developed in 2012) because he knew ‘mathematicians found it sexy’. It took eight months working with two other mathematicians to formalise the definition of this object from the axioms. He says, ‘Mathematicians love it. They don’t understand it, but they know it’s different’.

Definitions are the building blocks in which theorems are built up from, so the formalisation of a perfectoid space is a proof of concept which shows that we can actually formalise definitions of high level mathematics. Buzzard recently wrote out a grant proposal to the EU for two millions euros to acquire a group of postdocs who will spend their time formalising definitions and famous mathematical conjecture and theorem statements.

With enough time it will be possible to make a database of definitions and theorem statements that maps out the beliefs of the elders. Each theorem will have an attachment saying who proved it and in what journal, creating a way to search for mathematics never available before. Something that appeals to me about proof checkers is that they provide instant feedback to the validity of your proof. This is something I like from my computer science courses, in where the compiler instantly tells me whether I am right or wrong. From a pedagogical standpoint, instant marking would greatly reduce the strain on lecturers and markers, meaning resources can be allocated elsewhere.

Buzzard wants to create a culture where mathematics research and learning, and proof assistants, are intertwined. From what little I know, I understand that learning how to write in these proof assistants doesn’t quite have the same learning curve as MATLAB (to put it lightly), but my interest has been piqued enough by the video to start having a look around.

The removal of caffeine is something most coffee drinkers would scoff at, however for someone that likes to drink the beverage for the taste, and not the caffeine, finding a good decaf is a never-ending journey.

But before I answer how come it’s so hard to find a good decaf, how does the coffee become decaffeinated in the first place?

It starts with dissolving the caffeine out by some solvent, or other compound.

This can be done is range of ways and is designed to minimise the amount of flavour compounds that are dissolved with the caffeine.

Firstly, this can be done by chemical solvents that selectively dissolve caffeine. The original solvent being Benzene, a known carcinogen, which we have gladly moved on from to methylene chloride, approved by the FDA, and ethyl acetate, which occurs naturally in trace amounts in ripening fruit. Even if some of these solvents remain in the beans, they are very volatile and so when the beans are exposed to heat in the roasting process and finally the brewing, it is very unlikely these solvents will still be in the beans and therefore in your cup of coffee.

Indirectly-dissolved

The beans are soaked in hot water, and then is water is added to the solvent which bonds to the caffeine, before the mixture is heated, and the solvent and caffeine is evaporated. The remaining water is then added back to the beans and so the oils and flavouring compounds are reabsorbed the beans.

Directly-dissolved

The beans are first steamed, to open their pores for better absorption of the solvent. Then they are rinsed repeatedly for 10 hours with the solvent to remove the caffeine, before being steamed again to evaporate the remaining solvent.

The beans can also be treated by other substances that act to dissolve the caffeine that aren’t classified as “chemicals”.

Swiss-Water Process:

First the beans are soaked in hot water to dissolve the caffeine, and this water in then passed through an activated charcoal filter, which allow smaller molecules like oils and flavour compounds to pass through and blocks larger caffeine molecules.

This first batch of beans is entirely caffeine free, but also flavourless, but you are left with the water that is saturated with dissolved flavour compounds.

Another batch of coffee beans is then able to be dissolved with the previous water. Since this water is saturated with flavouring compounds, no more can dissolve, but the caffeine in the new batch of beans is able to be dissolved, and then removed via the activated carbon filter.

Supercritical Carbon Dioxide Method:

This method is the mostly recently developed and utilises carbon dioxide to selectively dissolve the caffeine in the coffee beans.

Water soaked beans are placed into an extraction vessel, which is pressurised and sealed, to create the conditions for Co2 to be in its liquid phase and dissolve the caffeine. The CO2 is then transferred to the absorption chamber where the pressure is released, and CO2 returns to its gaseous state, and the caffeine is left behind. This allows the CO2 to be recycled and decaffeinate another batch of coffee beans.

Many problems that arise from these methods is the use of heat and loss in moisture content.

 As we know that heat can denature proteins and break bonds in compounds, so heat treating the coffee beans, in addition to roasting and making the coffee, can compromises the flavour compounds in the coffee.

Decaffeinating the coffee beans also reduces their moisture content, and browns them, which means they roast faster, but also lack the visual indicator of how roasted the bean is as compared to caffeinated beans which are green before the roasting process.

These factors mean it is more likely your cup of decaf is over-roasted and has that burnt flavour that we all hate, as well as less favourable than your regular cup.

Referenced from https://coffeeconfidential.org/health/decaffeination/ and Chem 120 Section One Content: application of CO2 as a supercritical fluid.

Although superheroes have always been popular, in recent years their cinematic interpretations have broken through into the mainstream. 
But sometimes the mystical powers these heroes possess truly exploit the suspension of disbelief and this blog trilogy will explore whether we could one day have costumed vigilantes swooping from the sky, or if comic book writers need to spend a semester taking Physics 120.

We’ll take a look at two characters in each blog – one DC and one Marvel for the sake of equity.

First up is the fastest man alive, the scarlet speedster of the DC universe: Barry Allen, or as the citizens of Central City know him, The Flash. He posseses a connection to something known as ‘the Speed Force’ which protects him from all kinds of harm – and if we’re being honest more specifically from the basic laws of physics.

Three incarnations of The Flash. The two live action versions, one from a film and the other from a TV show, are played by Ezra Miller and Grant Gustin.

This is probably one of the easiest cases – almost everything about the Flash, scientifically, is terribly wrong. He consistently violates Einstein’s theory of relativity by running faster than light and his speed based powers are oddly connected to electricity generation. Even if The Flash was to run at above light speeds, the electricity he generates wouldn’t be able to do the same meaning he would probably just be electrocuting literally everything he runs past…

Verdict: It’s a good thing the ‘Speed Force’ exists otherwise The Flash would be even more ridiculous than he already is.

From the other side of the comic book world, we have someone else who also has similarly… interesting powers. With the ability to shrink himself to absolutely ridiculous sizes, Antman from Marvel comics is another superhero who violates just… pretty much everything.

• 

• 

Paul Rudd portrays Antman in the films – he plays a second version of the character, Scott Lang. On the left is the original Antman from the comics who invents the shrinking particles, Hank Pym.

While DC chose to decide everything about relativity is useless, Marvel took a similar sledghammer to quantum mechanics with this character. Antman uses particles that supposedly shrink him by reducing the space between his particles, however this quickly runs into some problems. He frequently makes himself smaller than atoms themselves which makes no sense in terms of the explanation given for his powers – if Antman is made of the particles he is smaller than how can he exist?

We also see a rather acute case of ‘slap-on-the-word-quantum-and-pray’ syndrome with the ‘quantum realm’, a world Antman enters when he shrinks even smaller than subatomic. According to the Heisenberg uncertainty principle, speed and position can’t be known simultaneously – this isn’t really seen in the scale of the real world, but on this scale it definitely would be important. Meaning Antman would probably dissolve into a probability cloud and exist everywhere and nowhere or something weirdly quantum like that. Not to mention there is actually a smallest possible length – The Planck length – so technically it shouldn’t be possible for Antman to indefinitely shrink anyway…

Verdict: Physicists need to copyright the word quantum.

Since I’m reducing my meat consumption for the planet, on those rare times where I get to bite into a juicy steak, I want my steak to be top quality.

Firstly, it starts with your choice of meat chosen:

• Tenderness of the Steak:
• This is controlled through what area of the cow is selected, avoiding muscles that have been very active during the life of the cow which will be tougher and better suited for a slow cooking, stewing process to further break down the meat.
• Amount of Marbling present:
• This is a measure of the proportion of connective tissue, which is primarily fatty to muscle fibre. A higher proportion of connective tissue, and as fat compounds are the flavouring compounds of most meats.

Treatment of the meat:

• Dry Aging: a very expensive and something I don’t not imagine eating anytime in my student life.
• A process in which the large cuts of meat is kept in low humidity conditions in cold temperatures for a minimum of 30 days. The hard rind that forms on the outside is then cut off before the meat can be further cooked and served. This is done to intensify the flavours in the beef but done in such a way that discourages the growth of harmful bacteria that would ordinarily cause rotting.
• Marinating:
• Using components like acids in the forms of vinegars can chemically tenderise the meat by breaking down the meat fibres.
• An opportunity to add additional flavours to the meat. This technique can be enhanced by putting the meat under vacuum, which opens up the pores for the flavour to penetrate deeper into the meat.
• However, if you are dealing with a high-quality piece of meat with high marbling content, masking the natural flavours of the meat would be a shame here.

Cooking techniques:

• Browning is the product of the Milliard reaction, is the reaction between simple sugars that act as reductants and amino acids in proteins that are susceptible to the reaction.
• This reaction occurs in three stages and produces hundreds of products that contribute to the flavour profile and aroma of browned food.

• This is reaction occurs optimally between 141-165 C at the surface of the meat. Using a BBQ or Stovetop method to achieve this is recommended.

• You also must balance cooking of the inside of the meat with the external sear. The internal temperature of the meat can range from Rare at 40 to Well Done at , and it is up to personal preference and cut of meat for what to aim for.

For more food inspiration check out Bon Appetit 🙂

Look around. Do you see any people? If you answered yes, then please proceed. If not, then go find some friends. Found some? Good. Do they all have birthdays? Great, we’ll need those. There’s an interesting “paradox” in probability theory called the “Birthday Problem”, and I’m going to tell you about it. If you go ask your friends what their birthdays are, intuition usually says that the chance for any two of them to have the same birthday is small. After all, there are roughly 365 days in a year, and assuming we’re equally likely to be born on any given day, that means we have quite a lot of “choice”. However, if you now record all your friends’ birthdays, you’ll be surprised to see that two of them will probably share birthdays (depending on the number of friends, of course). In fact, if you have about 23 friends, there’s roughly a fifty-fifty chance that at least two of them will share birthdays, which is totally counterintuitive. What’s wrong then? Could it be that we don’t have that much “choice” after all? Well, not quite. The problem here lies in our intuition, which turned out to be wrong. If we think of how likely it is for two people (at least) in a group to share a birthday, we’re very likely to do something wrong, and then get the wrong answer. However, luckily for us, there’s an easier way to think about it: instead of how likely it is to happen, let’s think of how unlikely it is to happen. Imagine the following situation: a person enters a room, and they have a birthday (let’s not include leap years for now). What’s the chance they won’t share a birthday with anyone in the room? Well, it’s impossible, since they share a birthday with themselves. A second person enters the room. In order for them to not share a birthday with anyone else in the room (i.e. the one other person), they need to “choose” from 364 days. So the chance for two people to not share a birthday is 364/365. Now a third person enters the room, and they now need to choose from 363 days. You can probably guess where this is going, so I’ll leave the rest as an exercise. The formula you end up getting is , where N is the number of people in your group. Now, all you have left to do is convert this result into the thing you want: the probability of people sharing birthdays. That’s easy though, since you just found the formula of its complementary probability, so you just subtract the formula from 1. And voilà, you get what you wanted, neatly expressed as . Graphing this yields the following:

I’m only showing you a small chunk of the function here, since it gets quite boring after 80 people; at about 70 people, the probability becomes 99.9%, and it doesn’t change much from that point onwards. 

Hopefully you learned something new from this little thought exercise: either that our intuition is not always right, or that you need to go find some new friends.