by Mr. MacKnight, on May 17th, 2015
The Golden Ratio is a staple of mathematics classes, art classes, and TOK textbooks. In this article by John Brownlee, however, he makes that case that the Golden Ratio is a load of rubbish.
. . . the idea that the golden ratio has any relationship to aesthetics at all comes primarily from two people, […]
by zPrevious Student, on March 5th, 2014
When Edison was in school, he claimed that 1+1=1 with following statement; if one chunk of clay is added to another chunk of clay, it is still one chunk of clay. Therefore, 1+1=1 However, Edison was wrong. Actually, his way of saying is wrong. First, the clay that is on his left hand […]
by zPrevious Student, on April 24th, 2013
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 […]
by zPrevious Student, on April 23rd, 2013
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 […]
by zPrevious Student, on April 23rd, 2013
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 […]
by zPrevious Student, on April 23rd, 2013
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, […]
by zPrevious Student, on April 23rd, 2013
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 […]
by zPrevious Student, on April 23rd, 2013
Contrary to the viewpoints of many of my peers, I believe mathematics is invented rather than discovered. The cause of this confusion is a matter of definition. Maths can be described as a universal code that dictates omnipotently (Platonistic maths). It can also describe the way we try to define our universe and its […]
by zPrevious Student, on April 22nd, 2013
I believe mathematics is discovered, but it always have been there. Many famous mathematicians like Pythagoras, Euclid, Fibonacci, and Newton left us with lots of maths concepts, but they discovered these.
Long before human existence, maths has existed. So we are discovering maths that was already there. We can also see maths applied in […]
by zPrevious Student, on April 22nd, 2013
Math has been invented not discovered. We invented the concept of maths and have learned to apply it to understand the world around us. We as a society now have become so comfortable with using math to explain everything that it is hard to imagine that math wasn’t always there. Some people argue that […]
by zPrevious Student, on April 22nd, 2013
I believe that math is discovered. Of course, math symbols such as +,,/,* etc. are invented so as to understand math easier; Math symbols and numbers are language in math. However, basic concepts of math are not created by human. Pythagora’s theorem is defined as ” In any rightangled triangle, the area of the square […]
by zPrevious Student, on April 22nd, 2013
I believe that the concept of maths in our lives is discovered. However, though we do not invent the concepts of math, we do invent the ways to communicate the concepts in an understandable fashion to others; we’ve invented the mathematical language.
Finding a mathematical explanation for a certain circumstance is a discovery, because […]
by zPrevious Student, on April 20th, 2013
I believe that math is discovered. What I mean my math are the rules, like the rule of gravity or Pythagoras, these are things that already existed before us. It existed when humans lived in caves and t will still exist in 2000 years (I think..). Therefore I believe that math id discovered. It […]
by zPrevious Student, on April 19th, 2013
In my opinion, math is definitely invented by people but not discovered. I am so sure to say that because we cannot touch math, it doesn’t naturally exist. Be more specific, math is only and idea that formed in our minds.
Take the example of number; we cannot say number exists by itself. […]
by zPrevious Student, on April 19th, 2013
I think that math may be discovered and invented, but it depends on the area of math, since we can invent math as an engineer and we discover in physics. This can be argued by a ton of mathematicians.
If we would take the opinion of a Platonism we would only discover math and […]
by zPrevious Student, on April 18th, 2013
In TOK, IB students learn many different areas of knowledge. Mathematic is one of them. Some people say that mathematics is invented while other say that it is discoverd. The definition of invent is ‘to originate or create as a product of one’s own ingenuity, experimentation, or contrivance’ and the definition of discover is ‘to see, get […]
by zPrevious Student, on April 18th, 2013
Personally, I think that mathematics is discovered. Discovered means find something unexpectedly or in the course of a search. Whereas, invent implies create or design something that has never existed before. Hence, mathematics is discovered, since math has always existed. In the TED video, the hyperbolic shape has always existed on earth. Since it […]
by zPrevious Student, on April 18th, 2013
Look at nature and all the species that reign in it, and you will see that math is all around you. Its been around since before our grandparents, since before Jesus, before the Romans, the Greeks, before we even knew what the answer to two plus two. It has always been there, humans have […]
by zPrevious Student, on April 18th, 2013
In my opinion maths is discovered because we are using laws and formulas to things that already exist in the world around us. Inventing to me is when you come up with a whole new concept from scratch and it comes from one inventor. We’ve always used maths. Ever since the beginning of time. […]
by zPrevious Student, on April 17th, 2013
Is maths invented or discovered?
Invented: create or design (something that has not existed before); be the originator of
Discovered: 1)find (something or someone) unexpectedly or in the course of a search 2)become aware of (a fact or situation) and 3) be the first to find or observe (a place, substance, or scientific phenomenon)
Maths has […]
by Mr. MacKnight, on September 30th, 2012
The Heisenberg Uncertainty Principle has crossed over from physics to become a sort of ‘common knowledge’ like Darwin’s ‘survival of the fittest’ or Freud’s ideas about neurosis or the ‘Oedipal complex’. This article from ars technica, however—“Demolishing Heisenberg with clever math and experiments”—makes the Uncertainty Principle seem much less than certain.
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by zPrevious Student, on September 19th, 2012
To avoid confusion, I shall define the following terms first (These definitions may differ from how you might define it):
Justification – In order for a statement/conclusion/principle to be justified, it must involve valid reasoning. This may include deductive reasoning and inductive reasoning
Ethics – A system of moral principles
Well Supported – I […]
by zPrevious Student, on September 19th, 2012
Through different methods of justification, we can reach conclusions in ethics that are as wellsupported as those provided in mathematics.’
To what extent would you agree?
(May 2012)
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by zPrevious Student, on June 10th, 2012
Around the last TOK – day we discussed how the scientists are looking for simple equations to solve everything. That’s what’s happening in maths. Maths is beautiful when converted into art and when it is drawing from nature. People want to make order from the chaos and they cannot appreciate the chaos. While we […]
by zPrevious Student, on June 10th, 2012
What does it mean for maths to be beautiful?
This question is a interesting question, as it stands out from the rest of the group. Whilst the other questions strive for truth and answers, this one seems to endeavor to receive opinion and subjective ideas. This question is a mix of what many of […]
by zPrevious Student, on June 10th, 2012
Why does math work in real world?
(This has always been the question that intrigues me since we started learning about mathematics.) Human mind is part of the real/natural world; so mathematic is technically part of the “real world” as well. Since it is already part of the real world, it is not a […]
by zPrevious Student, on June 10th, 2012
Okay, so we were supposed to discuss some questions realated to math last ToK lesson. And after that, we had a kind of discussion as a class. I have to admit that I was confused 99% of the time. Maybe it’s true that I just dont think enough about what things are.
So is […]
by zPrevious Student, on June 9th, 2012
How is math beautiful? In my perspective, math is most beautiful when the answer is simple or the formula to find the answer is very simple. For example a simple formula can capture a whole idea or concept in just a few symbols because it shows how even though we think elements in nature […]
by zPrevious Student, on June 8th, 2012
If maths is discovered not invented do we ever really have new mathematical knowledge?
First, we must define what we mean by Maths. The term used in the question could mean 2 very different things:
Mathematical Principles that define the universe and are therefore universal and are there all the time Mathematical Languages, which […]
by zPrevious Student, on June 5th, 2012
I know i’m a bit behind on blog posts, so here i am catching up, just messing up how organized the posts seem 😛
Anyway, maths as a language.I thoroughly believe that maths is a language of sorts. The basis of mathematics most of the population of the world know, much like nonverbal signals […]
by zPrevious Student, on June 4th, 2012
One of the implicit messages in the movie we watched about 2D shapes is that those in authority love to supress knowledge in order to stay in power. In the movie, the circles supress knowledge on 3D shapes so the other shapes will continue to follow the “perfection” of the circles. I think we […]
by zPrevious Student, on June 4th, 2012
We discussed if math is a language or not. Arguments arouse from the point if ‘anything’ can be a language or not. Frankly, this is just a trick of words. It really depends on how, to your own extent, a language is.
If language is generously defined, such as as long as it has […]
by zPrevious Student, on June 3rd, 2012
When talking about languages, about verbal and non verbal. But no one ever discussed sign language. I think that this can help trying to understand maths as a language.
There are many different types of sign language just as there are many types of mathematics. But if we understand one type of the language […]
by zPrevious Student, on June 3rd, 2012
I think a language is anything which enables coherent expression and communication; languages also exist for this sole reason and achieve this sole aim. So while Maths is precise and allows ideas to be conveyed, I do not believe it is a language. A rhyme, to take the example proffered, does not constitute a […]
by zPrevious Student, on June 2nd, 2012
We are taught that in order to answer a question, we’ve got to first understand the key terms. So what is math and what is language. I think we spent the entire lesson talking about defining math and language, and ended up being completely confused. Math cannot exist, and language is just funny. After […]
by zPrevious Student, on June 1st, 2012
When we are discussing Mathematics in terms of communication, there are 3 things that we should take into account:
The difference between Mathematical Principles and Mathematical Language The purpose of language Whether the laws for mathematics are universal.
1. When we were discussing whether extraterrestrial sentient lifeforms would understand the Mathematics that we are speaking to […]
by zPrevious Student, on June 1st, 2012
Today in TOK we talked about language and what constitutes a language. We decided that language is a kind of notational system. People discussed different kinds of language and how they are different. I thought what was more important was the common purpose of language to communicate or represent things, concepts and ideas. When […]
by zPrevious Student, on June 1st, 2012
Who says there’s no poetry in Mathematics? Consider this equation:
This equation translates to:
Integral zsquared dz From 1 to the cube root of 3
Times the cosine
Of three pi over 9 Equals log of the cube root of e.
Or this one
Translation:
A dozen a gross and a […]


Bertrand Russell on Skepticism 
But if philosophy is to serve a positive purpose, it must not teach mere skepticism, for, while the dogmatist is harmful, the skeptic is useless. Dogmatism and skepticism are both, in a sense, absolute philosophies; one is certain of knowing, the other of not knowing. What philosophy should dissipate is certainty, whether of knowledge or of ignorance. Knowledge is not so precise a concept as is commonly thought. Instead of saying "I know this," we ought to say "I more or less know something more or less like this."
—Unpopular Essays (1950)

"The less people know, the more stubbornly they know it."
—Werner Vogels
Your Daily Chinese Character
Comments . . . . . . are open only to students of the class, but if you are a nonstudent and would like to comment you can email Mr. MacKnight at ericmacknight AT mac DOT com.
Is TOK a Philosophy Course? YES, in the sense that the name of the course itself is in any dictionary effectively synonymous with "epistemology."
NO, in the sense that IBspecific ToK has many philosophical elements, but is not just philosophy. ToK is at root an interdiscipinary course that allows students to become aware of how the six subjectgroups on the corners on the Diploma hexagon overlap and integrate. The interdisciplinary aspect is the crucial thing . . . .
—Bruce Bartlett
Le Collège français
Toronto, Canada

"A conclusion is the place where you got tired of thinking."
—Steven Wright

Webs & Chains Natura in reticulum sua genera connexit,
non in catenam: homines non possunt nisi
catenam sequi, cum non plura simul
possint sermone exponere.
Nature knits up her kinds in a network, not
in a chain; but men can follow only by
chains because their language can’t handle
several things at once.
—Albrecht von Haller (tr. Howard Nemerov)
[Epigraph to Nemerov's poem, "The Dependencies"]
About This Blog This TOK blog features work by IB Theory of Knowledge students at Dulwich College Suzhou and at Suzhou Singapore International School, in Suzhou, China, from 2009 to 2015.

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