On Tuesday 5th June, the Williams project welcomed Chigwell School’s very own Mr Ennis. Mr Ennis spoke to us on the subject of ‘The Wisdom of Crowds- are the many really smarter than the few?’. The audience was captivated by the mélange of statistics and psychology that was on offer.
The talk started off with Mr Ennis educating us about various economic crises such as the Sub-Prime crisis which affected the mortgage industry due to borrowers being approved for loans they could not afford and as a result leading to the collapse of leading institutions and big hedge funds globally.
Then, we were shown various quotes on the subject of crowds which were very interesting to read such as “Madness is the exception in individuals but the rule in groups” (Nietzsche) and “I do not believe in the collective wisdom of individual ignorance” (Carlyle).
Mr Ennis organised an intriguing experiment which allowed us to understand whether the many really were smarter than the few. First, we individually filled out a question sheet of a selection of random questions, then, we were put into groups to come up with an answer to the same questions. Some very interesting discussions arose whilst we were trying to figure out suitable answers for questions such as ‘What age are you most likely to die?’.
Whilst we were in our groups, Mr Ennis was working very hard in order to calculate various statistics from our individual questionnaires to then compare with our group questionnaires. And so, after some very quick calculations, on this occasion, it seemed as though the few were smarter than the many!
On behalf of all who attended, we would like to thank Mr Ennis for all of his great efforts. The talk was enthralling and certainly brought our attention to the wisdom of crowds- a key principle underlying modern day democracy and economics. Thank you Mr Ennis!
Jonathan Burn (OC) works in merchant bank IT and marketing. He is, in addition, a funk musician and mathematician, was a primary school teacher, and did a degree in Economics at the LSE in his own time for fun. He also has a masters in Artificial Intelligence from Imperial.
With an engaging and clear set of slides, Jon took us carefully through what sound is, how computers store the information contained in sounds, and how they can be set up to learn the best ways of identifying new sounds. This is done mainly through the ‘random forest’ technique: a way of generating questions to ask about a new sound which most accurately and efficiently put it into the right group (e.g. robin or blackbird).
On Tuesday 7th November, Dr Nils Kürbis, a philosophy lecturer from King’s College London, visited Chigwell to give a talk on ‘What the Tortoise said to Achilles’ by Lewis Carroll. Two Chigwell students read the dialogue. The opening part eluded to one of Zeno’s most famous paradoxes – the race between Achilles and the tortoise. Even though we know Achilles will overtake the tortoise (given the Tortoise had a head start), when broken down into small intervals it seems that the gap between Achilles and the tortoise gets smaller but never diminishes, hence Achilles can never overtake the tortoise. This is why this is a paradox. I helped to explain this using a simple diagram.
However Nils’ main focus was on what the text went on to describe. The tortoise was using the example of Euclid’s first proposition, which states that things that are equal to the same thing are equal to each other. This is a proposition. The problem began when we had to go from the proposition to the conclusion. To do this you need a middle step to reach the conclusion. Since the middle step contains the proposition you need another step to convince the very stubborn tortoise (in this example). This creates an infinite number of middle steps creating a sequence infinitely increasing (the opposite to the infinitely decreasing sequence in Zeno’s paradox).
As a philosophy professor he was able to really engage us into this problem which had a lot of people scratching their heads as they were being asked to think in what seemed to be a very illogical way.
Nils Kürbis on triangles
On Tuesday the 6th of June, Mr Chaudhary, one of Chigwell’s maths teachers, gave a talk on “God – the ultimate reality”. First, he took measurements of a student in “good proportion” and pointed out similarities. Then he started with the human embryo and how the embryo develops, then showed a sentence in the Quran that also explains the human embryo and how accurate it was. He showed us another quote in the Quran which tells us that two seas never meet, and then showed us a video of two seas that don’t mix. He then shows some more believable facts that God exists. Finally Mr Chaudhary was asked questions with the hope of proving him wrong, but he stood his ground and answered them in detail.
Dr. Florian Steinberger, philosopher and lecturer at Birkbeck College, University of London, spoke to both branches of the Williams Project. He spoke to us about two very different philosophical topics, beginning with “animal rights”: what are they? Do animals really have them and should we respect them? There were multiple discussions, questions and debates on whether animals could really have preferences and feelings to be deserving of rights as humans do. We also covered the issue of why we are willing to protect them to a certain extent, nonetheless, also willing to consume them. We outlined the religious, moral and health aspects linked to the matter to delve deeper into if we could and should give animals rights. The discussion was thoroughly enjoyed by all of us of all age groups, being a very controversial and interactive talking point.
He continued with second session on the topic of “infinity” – a more mathematical approach towards philosophy and the possibility and impossibility of infinity, the contradictions and the proof – in particular whether some kinds of infinity can be greater than others (for example the infinity of real numbers can be shown to be larger than the infinity of integers). Although complex for a few of us(!), many were able to grasp the concept of how infinity could be perceived; it was an engaging and stimulating lecture on a rather unfamiliar topic.
We are grateful for the discussions led by Dr. Steinberger, and thank him for enlightening us on two of the many contemporary philosophical issues we face today.
Our Head of Maths, Mr Chaudhary, gave us a vastly wide-ranging and heartfelt exposition of the centrality of the ratio φ (“phi”) in the universe and the human body, and what that centrality meant.
He showed that the ratio (see above, equivalent to 1:1.618…, which is, uniquely, the same as 0.618…:1) lies behind the Fibonacci sequence, which we see in so many growth patterns in animals and plants, as well as in the relationship between a myriad of measurements of the human body. It’s also one of the commonest principles in the way we perceive beauty: painters place horizons at it.
Mr Chaudhary argued that the odds of this one ratio being at the centre of so much were virtually nil, and so it is convincing evidence of divine design behind creation. He showed us verses from the Quran which point out that God has designed the universe in a way whereby we can detect, even deduce, his hand.
Universal Laws and the Golden Ratio
15 Uncanny examples in nature
Disputed observations (Wikipedia)
James Grime, from the University of Cambridge, introduced a large WP audience to codes and their history (from shaving a slave’s head to sending credit card details across the internet), and then demonstrated an original Enigma machine (see right). It was an engaging and fun session, and led to an interesting discussion on the use of codes in the Second World War, and finally to a code-breaking workshop where our students broke, or attempted to break, various encoded messages. A great start to the WP year.
Ace VIth-form mathematicians (Wojciech, Egor and Yunlin) taught (or attempted to teach) our Remove-UV guinea pigs about complex numbers and other delights.