DCSZ TOK Class Blog

Mapping the Brain

Mr. MacKnight — Sat, 11 May 2013 17:36:13 +0000

Fascinating conversation; just keeps getting better.

http://www.wnyc.org/shows/lopate/2013/apr/16/mapping-brain/

Wine-tasting “experts” seem to have no expertise

Mr. MacKnight — Fri, 10 May 2013 10:46:31 +0000

This blog post about wine-tasting is filled with ‘earthy’ language (in other words, obscenity and profanity) but it does suggest some interesting TOK questions.

http://io9.com/wine-tasting-is-bullshit-heres-why-496098276

How to put together a successful TOK oral presentation

Mr. MacKnight — Thu, 25 Apr 2013 15:29:29 +0000

Most of what you need to know, right here:

http://prezi.com/7nugodcso5zd/tok-presentation-tips/

Is maths an invention or a discovery?

Katie — Wed, 24 Apr 2013 00:19:13 +0000

I’m not really sure whether it is an invention or a discovery. I believe that perhaps there were things that didn’t make sense and when you look at it in a mathematical way everything starts to come together and it provides answers that were unknown. Without humans though would maths still be there? If there was no humans maths wouldn’t be solved so therefore maths waiting to be solved and has always existed! I guess it’s more of a discovery as living in a world without maths is almost unimaginable.

Is Mathematics invented or discovered?

Sung Jin Kim — Tue, 23 Apr 2013 16:28:32 +0000

In my point of view, like science and other subject related with statistics and probability math is discovered by human.

First, math somehow underlies the physical world, generates it. Or second, math is a human description of how we describe certain regularities in nature, and because there is so much possible mathematics, some equations are bound to fit.
As for the essence of mathematics, there are four possibilities. Only one is really true.

Nobel laurea said that mathematics is both invented and discovered,” but he thinks “it’s mostly discovered.” Mathematics, he says, “is the process of taking axioms, definite sets of assumptions, and drawing out the consequences. So, devising axioms is invention, and drawing out the consequences is discovery.”
He explains that, “Occasionally, you have to introduce new sets of axioms like the passage from Euclidean geometry to non-Euclidean geometry. These are epical events in mathematics, which, in a sense, are inventions.”
But isn’t the world constructed with non-Euclidean geometry, such as Einstein’s theory of relativity, so that it was somehow always there?

What is math?

Jay Kim — Tue, 23 Apr 2013 15:29:47 +0000

Nowadays, there are a lot of area using math and last week we discussed about how math invented or discovered by humans. i think math is discovered and developed by the human just like a gemstone. We never say that human invented gemstone but human can change it’s shape or uses by processing. So we can say that people discovered math and invented the way of using math.

Is Mathematics invented or discovered?

Peter Byun — Tue, 23 Apr 2013 13:42:45 +0000

Science, History and other areas of kowledge are related to the real world. They are the studies that draw off some rules or theories from observation on real world, therefore meaning that they have been discovered.

However, Mathematics is quite different from those areas of knowledge. As we all have come across with imaginery number, we are able to find most of the stuffs and knowledge in Mathematics just exist in concepts but not in a real world. Well, some of us may argue that there are lots of circular-shaped or triangular-shaped objects around us and that Mathematicians have simplified those objects into Mathematic shapes. However can you determine there is a perfect triangle or a circle in the real world? If Mathematics is discovered shouldn’t there be at least one example that satisfies the terms of Mathematics perfectly?Even the term that we call a straight line doesn’t exist in real world since the line that you have drawn with a ruler is just a wobbling line when you magnify it with a microscope.

What’s more, Mathematicians develop their axioms and definitions of the terms into new theories and equations. For instance, there is a term “addition”. Mathematicians developed this term into a new term called “multipication” since adding up same numbers again and again was an onerous work. They have also developed “multiplication” into “index” as well. Not only that, the term, index, has also lead to the term “log” so that it would be easier to find the value for index. This indicates that Mathematic terms derives from each others and that they have been created by Mathematicians who are just too lazy to do some calculatings.

Furthermore, have you seen Mathematicians wandering around streets to see if there is a shape that has not yet been discovered? Well, obviously Mathmaticians do not look for new equations or theories through observations. They use their logics to reach new theories. For example, an area of a triangle is 1/2 x bc sinA. That’s because the area of an triangle is 1/2 height (a) x the base (b) and since sin A is a/c you can get the value for a, the height, when you multiply c to sin A. Thus, I once more stress that Mathematic theories are invented by Mathematicians through their logics.

In conclusion, Mathematics is invented though there are some overlaps with the real world. However, what is important is that they are concepts only existing in our mind, not in tangible forms since its knowledge has been acquired through circulation of logic and mathematic prooves.

Is mathematics discovered or invented?

michaelc — Tue, 23 Apr 2013 13:20:22 +0000

In my view, I believe mathematics is invented.The definition of Mathematics is a subject that use symbolic language to investage concepts such as volume, structure, change and space. I think maths is a method that human created to solve the questions in the world. People found some special phenomenon or questions in their normal life, then, they want to solve these question and think and use lots of ways to solve, after long time ponder and lots of people investigate, people find a way to solve these question, they created maths and better understand about the world. After a long period of development, posterity develop new and different methods to solve same kind of questions and develop symbolic language to solve questions more efficiency, then, mathematical theory become more and more completely. We can have a example to support my idea, π. At the past, ancients want to find the perimeter of a circle, and they use methods like cyclotomic method, then they find the number is a irrational numbers, almost 3.14, then they decide this is π and work out the formula to calculate the permeter and area of circle, then, maths method of circule formula was been created. So, I think mathemathic is invented.

Is mathematics discovered or invented?

Karen — Tue, 23 Apr 2013 13:19:39 +0000

Mathematics is both discovered and invented. It is discovered because the basic mathematical concepts are and have always been there, in the universe. We discover the basic concepts of math from observations. And we give names to the discoveries that are made. So the language that we use to present these mathematical concepts and the application of these concepts are invented.

For example, if we say that math is purely invented, then before math was invented, if an apple fell from the tree and another apple fell from the tree onto the ground, does math have to be invented first in order for there to be two apples on the ground? We only invent the language to describe the mathematical concepts that already exist.

On the other hand, we can’t say that math is purely discovered either because there are also things that we cannot observe or find in nature, like imaginary numbers, which we invented because they can be useful for us to solve problems. Therefore, mathematics is both discovered and invented.

The weakness of history

michaelc — Tue, 23 Apr 2013 12:02:19 +0000

At last Friday TOK lesson , our group read and discuss the article called “Texas Conservatives Win Curriculum Change”. The article said Conservatives win the vote and decided to change the contents in the history textbooks, they want to stress the superiority of American capitalism, question the Founding Fathers’ commitment to a purely secular government and present Republican political philosophies in a more positive light. Some group of people disagree and criticize them, these group of people think Conservatives can’t change the history, they need to show and respect truth,but Conservative said they are adding banlance, the history has changed too far to the left already, they need to change back and balance it.

Different groups of people’s point made us confusing, we don’t konw which group of point is right, however, there is one information we can get from the text, that is the history can be changed for any reasons like government politicy, education. People can change the history for what they want. This is the weakness of history. History is just a story and written by person, so, people will put their views into the history and make the truth confusing, even through ecognized history, there are still some doubts that historians can not work out. History can be changed just like Texa Conservatives did, change the textbook, change the truth to show some fake things to build up false confidence. So, we can not believe it, it will misleading people to the wrong side.