Mathematics, intro session

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.

History

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?

Historical materialism

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.