This week we began to explore mathematics as an Area of Knowledge (AOK) and the presentation used can be found on Edline. It was interesting watching and listening to your definitions of mathematics and the certainty with which the truths of mathematics are held. Notably the reaction generated when it was demonstrated that NOT all angles of a triangle add up to 180 degrees. This demo and the problem with finding a flat plane to create real parallel lines should have secured for you the importance of using Axioms in Mathematics. Interesting that we need assumptions before we can do the sums!?!
The Thursday group featured a really good presentation by Kuba based on decision making. We then fell into one of those discussion rabbit holes for over 30 minutes contemplating how to make winning decisions in Chess based on more than just pure logic. Dias and I now need to play chess to settle our difference of views! If he plays like a robot I will let you know with my easy victory. mMaybe though I am making an emotional statement there or maybe I planned such an opening statement? - the mind games begin... Well done Kuba.
So Friday we did our maths in the park and not in the dark. Groups reported back on the defining language for mathematics: Axioms Theorum Conjecture Theorum
With Dashaably helping the randomly selected speakers we ended up with the following explanations:
Axiom: (Paula) We need a starting point., basic assumptions for our theorums. By creating assumptions such as Euclids original 5 we can create a hypothesis based upon our observations (sounds like Science's methodology ). Axioms are independent assumptions and give us that starting point.
Theorum: (Boris) Using Axioms and deductive reasoning we can design a proof proposal (a theoretical conclusion - Karl)
Conjecture: (Sergei)When you are not completely sure - right or wrong - a hypothesis that feels to work but so far is not shown to be true.
Proof: (Celine) Theorum shown to be made of relevant axioms. The process of proving is within the proof.
Feel free to add to these and question the language, otherwise a good attempt by tyhe Friday group to clarify.
Finally we had the second run of the History sessions with Chris this week. This means we are (both classes) back in synch and I can blog again! Once again many thanks are due to Chris and also to those of you in the Tursday group who made very perceptive comments, contributions and also importantly raised good questions. i would like to summarize a few of the things Chris' presentations raised. History as you know is an important Area of Knowledge (AOK) in TOK and these ideas will give some of you scope for answering one of the TOK set essays using History and its aims and methodologies. History and everyday life Can you ever know the past?
"We are creatures that rely on experience more than instinct". Do you agree with Chris' view in this regard?
History provides us with a shared fabric of society. Is this important?
Who could have predicted the current levels of global interdependence during the cold war?
Why do people crave personal histories, why do so many people search and research family trees and additionally witness national histories being celebrated. History has a certain materialism to it - however:
Leopold van Ranke gives us the Rankian view that a historians (one who writes history) job is purely to show "what happened".
Marxism provides a contrasting view - all past events are explainable and all futures are predictable.
History and progress
Have we progressed? History is often reported as a march forwards - a march to progress. If so why are we slaughtering ourselves in continued wars in ever more sophisticated ways?
History and cause and effect
WW2 seemingly was a response to the failures of settlement of WW1
Regarding the history of thought, we have shown that paradigm shifts in thought occur every so often and so if history tells us anything it is that most things we know hold as true will turn out to be false. This is a big idea in TOK. What can we know from history if this is the case?
So to summarize History:
Do we study it because we have to? People just want pegs back in time - could we live in a world where a sense of history did not exist?
Is History a Science? Yes in the sense their are methods to follow. No in the sense Science employs facts. History cant say anything is a fact other than dates of events, people who existed BUT peoples motivations are subject to the retrospective reporting of biased historians
In History it may be more difficult "to know" than in say Science. Consider how the cold war is recorded in USA, Russian and British history books. Howwver in both History and Science (due to falsification) you can never achieve the goal of knowing for certain the truths you are searching for.
Other issues with history may include: A time limit - who cares after say 50 years? Governments often only release official documents after 50 years - by which time the truth of events and those affected have or are passng into memory.
The Societal perceptions of history - are there conformity pressures to celebrate historical accounts. e.g celebrating the dambusters is a part of the British culture, D Day etc. No accounts of the numbers of germans dying is wrapped in the history, the Dresden Bombings are not discussed. Why? The British invented the concept of concentration camps in the Boer war - how well know and studied is this by British School children?
History as an AOK raises many good TOK ideas for discussion. The above should support your own notes. Please reflect upon Chris' class on your own blogs.
Assumptions- making personal judgements containing guesses and biases, can be accurate but lead to errors being made
Fallacy - a mis calculation in thinking, an error in the making..
The incident in the store exercise we looked at was demonstrating that when it comes to recalling incidents, with our memories we tend to tell a story. This is problematic in Law courts and for us in TOK it highlights one issue with Reason as a source of knowing. Different storytellers see different things in the same incident, so who to believe? This is the narrative fallacy. This is a problem in History/ historical record.
The list of argument or inductive fallacies is lomg, I like this clip here. It aims to demonstrae some key fallacy terms using the debate as to whether God exists. Always a good TOK topic!
Can you give your own examples of Straw man, Red herring and circular reasoning? Slippery slope or ad hominem arguments? Any other?
As we looked at sample essays this week you should attempt to craft the opening sentence for one of the TOK essays, then build up the first paragraph. Plan the rest. This is the process we will follow so get on with this when you havve the confidence to begin. We are only two terms in but I believe a number of you can attempt this now.
I have posted on edline an article from New Scientist (one of the best respectable resources for TOK ideas). It is from May 2008 and the title of the article is "Some swans are Grey". Incredibly (perhaps?) I found the article in a chance glance at the front cover of the journal as I returned the projector to Bryans room today, straight from TOK. Serendipity!! Well, true serendipity required some action. We talked Thurs and today about the current paradigm of thought being science based and science more than any disipline is defined by its methodology. I mentioned tipping points in both classes and speculated where the new shift of ideas might come from. Well the article in new scientist claims that "Poppers definition of science is being sorely tested by the emergence of scientific ideas which seem to fail it" "it " being, of course, falsification. The article then goes on to cite Colin Howson of LSE in London promoting "an alternative view of science based not on simplistic true/false logic, but on the far more subtle concept of degrees of belief" Essentially a mix of mathematical probability and the" subjective concept of belief". If you want to research this its called the Bayensian view of science, after Thomas Bayes the mathematician (18th c). Its pretty interesting and gives us now 4 views about how science methodologies exist. I hope you can remember the other 3?
Reasoning creates knowledge issues - I believe there were plenty of debatable syllogisms in class, the powerpoint is on edline if you wish to check out the premises/ argument/ conclusions presented again. As always thank you for the engaging, intelligent contributions. Special note to Kuba for introducing a new "freedom of thinking" model - Check it on his blog!
Please remember syllogisms are arguments set up to show deductive reasoning but demonstrate issues/problems that illustrate the occurence of inductive fallacies. Therefore exposing the two types of logic we examined this week.
Check out the wave on Siljes blog. If you doubt what these two clips show then have a quick gander (look ) at the "Stanford Prison experiment" Or check it out anyhow - the power of role play is incredible. Ta ra ra Boom dee ay!!
Also once you watch "the wave" have a look at my post "brown eyes, blue eyes" it also demonstrates role play power - this time a teacher demonstrating how children can become racist.
I am beginning to notice those who are not reflecting....it only takes 2 minutes..
The clip this week from youtube came from the movie "Dead Poets Society" well worth watching some time.
I showed this clip as it demonstrates the problem with methodologies for finding knowledge in the arts. If you can compare this with the three methodologies we discussed for science then you should be able to plan an essay for question 5 on the prescribed set essay list. You will see notes on the blog in November regarding the science methodologies.