Instructions for 27/4
April 27, 2009 by ithinkthereforeib
1) Get into groups of 2-3 people. Each group should include students from different math courses (Math Studies, Math Standard and Math High).
2) Go to this website: Distok Math
3) Click through the slideshow – but do so slowly, discussing points that your interesting, responding to questions asked, accessing links giving (e.g. The Monty Hall problem). Explain terms and concepts to each other as needed (I am counting on those of you who are stronger in math to help those who are weaker.)
4) Respond to the final question of the slideshow. Discuss it verbally first, but then prepare a well-considered written response and post it below this blog. (In addition, you may also post on the link provided in the slideshow. Do check that link and peruse the comments there for inspiration.)
P.S. I am aware this might take longer than a 50-minute period. If you don’t finish in time, we’ll complete the activity on Tuesday.
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Post on Mathematics, MARIO ADRIO AND ANA VIC
In our opinion, math is a safe as far as we have experienced. It is very safe, but not entirley, just highly likley. Axiosomes are a perfect example of the degree of “safeness”in math. Although there are certain patterns and results that are repated more often ,(and thus make it safer than other Aok’S) we will never be able to classify it as completley safe beacuse we have not experimented with every single variable that exsists. Still, in the limited spectrum of human knowledge math is as safe as an area of knowledge can get. This is to some extente exemplified by the fact that math is much more universal than, lets say, culture; because math is safer and thus more objective. Because of its safeness and the perfecteness of it make it harder to debate, resulting in more objective and less subjective claims, which, in turn, make it even safer.
Does mathematics provide the ultimate truth? If yes, how do you justify this? If no, is there any other WOK similar to mathematics?
First of all, concerning our society, mathematics is commonly percieved as an absolute truth. This arguments does not arrive without reason, given that if used correctly, mathematics is extremeley accurate. This relates back to the example used previously on axioms. We are almos certain numbers can keep adding up infinitely. Yet, we cannot know given that we haven’t (and can’t) keep adding numbers infinitly. Math is thus based on observation, trial and experimentation. In this way math is not absolute. It is very very likely numbers can keep adding infinitly yet we cannot know. However, math does provide a great quantity of evidence. Evidence that is very likely to be accurate and precise and, by applying to the reason WOK, it aquires a very high reputation of certainty.
It is a common belief that mathematics is purely logical and has no room for creativity. How would you respond to this?
This statement is completely false, as math is one of the fields where creativity is vital. It is true that logic is one of the, if not the most, important characteristic of math. Logical steps are crucial, yet one needs creativity to come up with these steps. We must remember that there are many ways to come up with one solution in math and the way through which we find these answers is creativity. The greatest mathematicians and physicists have usen an awesome amount of creativity to find how math explains several phenomena of our universe.
Is mathematics “safe”? Is there one definitive answer for every question?
- Mathematics is not safe because it was created by human beings. It makes us believe that we can explain the world, when in fact this is impossible. Most of the time there is one definite answer for every question, but since it was man made it cannot be fully trusted.
Does mathematics provide the ultimate truth? If yes, how do you justify this? If no, is there any other way of knowing that is similar to mathematics in this respect?
- Mathematics does not provide the ultimate truth because postulates might be false or wrong and therefore, the entire concepts that arise from this postulate will be wrong. Therefore, it does not always provide the ultimate truth. EX: an electron wouldn’t say that the shortest distance between two points is a straight line since electrons tend to skips dimensions (Andy Fletcher). Mathematics, however, can be considered the less biased approach because it is accepted world wide while the other areas of knowledge are very subjective.
It is a common belief that mathematics is purely logical and has no room for creativity. How would you respond to this?
-Mathematics has a lot to do with creativity because when you are trying to solve problems you have to be creative in order to come up with a solution. Even though logic is involved always, creativity is needed in order to come up with new “logical” steps. People are always constantly learning in the field of mathematics and there are several ways to solve different problems, you just have to be creative and choose the one you prefer the most.
The article/slide show presentation is very interesting, although it changes the way one sees the Areas of Knowledge. This leads to question the Mathematics area that many individuals believe to be the “surest”, or the “most certain”.
However, if mathematics is based on axioms, and axioms are based on our own observation, then these axioms pass inevitably through the different filters of the individuals. The filters make these observations subjective, therefore that would mean that mathematics looses some of its “certainty”. This also weakens the perspectives and the “absolute” of math as an Area of Knowledge.
Furthermore, postulates that do not agree with an older postulate, hypothesis or theorem (or axiom), does not mean that it is incorrect. It does not prove or disprove anything, as even though they might refer to the same point, they present different observations.
Axioms or postulates that are both coherent and complete, but are not useful might seem pointless to some persons. However, this does not mean that they are wrong, they just dont have a clear point. Furthermore, since the usefulness of things is objective and depends from person to person, the point of a certain axiom will differ.
Theorems, postulates and axioms can be used to solve real-life situations, but the “certainty” of these will vary. Since these are based on observations, then the solution of the real-life situation will be solved on observation and will therefore be subjective, different for each person.
Is mathematics “safe”? Is there one definitive answer for every question?
If we approach mathematics based on axioms then it cannot not be safe since these are based on observations. Axioms are the foundations of a mathematical system. A good system is built on good axioms. These cannot be proven to be true. They are claimed to be “self-evident” although sometimes they are not always. Axioms are based on observations in the world or they are based on observations about relationships within axiomatic systems. Hence all if not most of maths is subjective. The beginning of; the foundation of maths is based on what humans observe, what we are able to “see” through our senses. Since our sense perception cannot be completely exact, our mathematical equations and formulas cannot be either.
For the second part to this question I believe that there is in fact only one definitive answer for every question. This does not go against what I first stated, rather it expands on it. As I said, I don’t think Maths is safe but that is only at the beginning, the foundation of the equations and so on. After that point, once you accept the things as givens all of the mathematical questions have definitive answers. For example, an answer may include two answers or have no answers; these are none the less an answer in itself.
Does mathematics provide the ultimate truth? If yes, how do you justify this? If no, is there any other way of knowing that is similar to mathematics in this respect?
Does anything provide the ultimate truth? What is the ultimate truth? Just because maths is quite precise and has definite answers, doesn’t mean that it can give us the ultimate truth (if there even is an ultimate truth, which after the Inter-TOK presentation has made me think NO). As previously stated, it is based on our observations which are in themselves only a small part of the whole picture. Another way of knowing that is similar to mathematics in this respect would probably be sense perception. This is because like mathematics, sense perception is only able to observe a small part of the “whole”; a part of everything that is around us and everything that isn’t around us.
It is a common belief that mathematics is purely logical and has no room for creativity. How would you respond to this?
No, as this common belief can be shattered in a matter of seconds upon entering a Maths High class. In some of the more complicated equations in mathematics, such as complex imaginary numbers as well as trigonometric formulas, you have to be really quite creative to actually be able to get to the solution. There are so many ways that you can manipulate numbers that in order to find the right transformation for the specific equation, the whole process needs a lot of imagination and creativity. Also, it’s interesting to mention what Mr. Andy Fletcher said today, Science is also looking for beautiful equations. This in itself needs room for creativity in order to be.
2.so basically after todays conference with the “IB GOD” ajaja… umm our idea of math changed and for that reason we come to believe that math does not provide the ultimate truth. this is because, like perception, math is based on observations that can vary upon every person, what makes math as reliable we see it to be is the fact that we all share a common idea of math and (once again referring to what was said in the conference) if we all have a common idea amongst a large group of people for that group what is being said is true. math can only provide evidence for a theory that might not even be true making the ultimate truth impossible to reach, math is only a key to getting closer to prove a possible theory.
Cata / Juan / Dani V (which one?) – like your re-reflection (-: Always good to reconsider!
Pierre – you say that “Science is also looking for beautiful equations.” But what about math purely (no science involved)? Any other level creativity that it involves?
Clement & Joaquin – I rather like your (flying) spaghetti monster!
Catalina Juan Daniela Viteri
Part 1. Like Andy Fletcher said, there are no absolutes (even in math). Math can never be considered completely safe or completly unreliable. It has different degrees of reliability, which of course depends on the persons perspectives. Perhaps the perspective which undermines maths reliability is the fact that math is based on things we cannot prove, rather we assume to be true. Consequently math cannot be safe, there is a chance that everything about it is false- that our entire perspective of the universe is false. This does not make math complelty unreliable though, because there is still some chance that it is true. To answer the question directly, no math is not safe (mainly because one can never know for sure if math is correct or not) but neither is it completly unreliable
Daniela, Catalina, Juan
# 3
It is a common belief that mathematics is purely logical and has no room for creativity. How would you respond to this?
This question can only be answered if we reconsider what creativity is. Math can be creative not in the sense of “artsy” creative or ingenious. Instead we can consider math completely creative, because mathemeticians are able to create mathematic equations that make sense and work, however assuming everything every step of the way. BY this we mean, like Andy fletcher had said, a plane nor a point can be defined, however logical math is made out of something that does not exist. If this is not out of the box thinking than i really do not know what is. Mathemeticians imagine and predict things out of ideas, and from there create a whole study. In this case a mathemetician has to be creative, and from there forth use logic. Indeed, math is a mix of both. If math had no room for creativity, then the logic that follows it would have never been discovered.
Steffan B., Jaime G., Gloriana G., Paola S.,
1. One can say that math is “safer” if the word safe is determined as the given set of rules or procedures society has used in a certain “problem” in order to “solve” it with their own determined answers. Nothing is actually safe. There isn’t an answer for every question except if you see the questions and answers as a creation from human beings. Having human beings create a question one can then state that the answer is that there is no answer; there might be an answer or state a given element as the answer. Since human beings state what the question asks and they reply, that is already an answer stated in human beings way of thinking
2. There’s no ultimate truth, so math would not be able to provide the ultimate truth. The definition varies; a definition can cause a huge change in what is the interpretation of the data. It can be considered as a collective agreement between individuals since there isn’t a correct answer, it can be said that it is in the present but the present is instantaneously so it is left in the past when it is said so new ultimate truths can come in hand. With mathematics, the ultimate truth would once again be a collective agreement by society that agrees on a certain procedure that gives a certain answer.
3. Mathematics is mostly logical; nevertheless, there is room for creativity to a certain extent. For example, when studying certain theories or procedures in mathematics one applies there logical reasoning. But, when you can’t find a logical answer, some creativity may be used along with the logic. It can present a new development of the procedure using logic but it appeared there creatively.
Kristel and Constanza:
Is mathematics “safe”? Is there one definitive answer for every question?
-There are many ways to look at the systems created for the world of mathematics and other areas of knowledge in the world. The term “safe”, also meaning “based on good reasons or evidence and not likely to be proven wrong” is not a term that describes the world of mathematics to its greatest extent. Mathematics is based on observations and these observations become axioms. These axioms later become theorems and corollaries. It is because of this that some consider the term “safe” to be inaccurate for describing math. When one thinks of mathematics, one normally looks at the fact that the angles of a triangle add up to less than two right angles. Normally one would jump to their feet and be in complete disagreement with this statement, but the truth is that there is more than one system to use when looking at geometry and different mathematical areas. Seeing that there can be more than one answer for many questions in mathematics, some might say it is not “safe”, but by reading the definition, if one cannot have the evidence to “disprove” the statement and one can see that there is good reasoning behind the thought, their is no statement to provide evidence that mathematics is not “safe” even though there are more answers than what one thinks there is.
Does mathematics provide the ultimate truth? If yes, how do you justify this? If no, is there any other way of knowing that is similar to mathematics in this respect?
-Mathematics does not provide the ultimate truth because it is impossible to “prove” something. Although many other areas of knowledge support their claims with mathematical evidence that seems to be correct because it cannot be proven wrong, there is no right to claim that mathematics is the “ultimate truth”. It becomes evident that these evidences become truths to oneself, but it clearly does not mean that there is an ultimate truth because there is no such way of neither “proving” something nor making sure it is 100% correct. A way of knowing that has some characteristics from the same math reasoning is sense perception and also reasoning. In sense perception, one can perceive many things the way one wants. Many people believe because they see something or touch something… as Andy Fletcher said, were are mostly composed of NOTHING, but we feel a lot of “something” when we touch other things. This is somewhat misleading but we feel something so we believe it is there. This can be compared to math because one makes these axioms because one makes observations that cannot be proven wrong. Reasoning is also another way of knowing that can be compared to mathematics because it has a lot of things that come through logic and is a way that one can “know” something. It is kind of difficult to disprove assumptions made by logic as well as observations made in math.
CONSTANZA & KRISTEL – QUESTION 3
It is a common belief that mathematics is purely logical and has no room for creativity. How would you respond to this?
Mathematics is not always purely logical, there must be room for creativity. As it is a common belief it is most likely to be wrong, or at least not a completely accurate statement. Logic and creativity go together. A mathematical problem cannot be solved if one does not combine logic and creativity. The first person to understand, or at least solve a mathematical problem must have been creative enough to be logical when solving it. Also, when solving imaginary number equations one must use their imagination and creativity to reach an answer. Logic does not come from nothing, it must come from something and that something can be creativity. Logic must come in a certain order A leads to B that gives C. Creativity can be deriving A from C from B. Working the problem in different ways in order to achieve the same outcome is considered creativity. Logic and creativity can be combined in order to solve mathematical equations, they are compatible.
I believe that math cannot be considered completely safe, even though there is such thing as mathematical proof, due to the fact that the bases of math are constituted of observations. This means that in the same way that we cannot be sure our observations in the other areas of knowledge are true, we cannot be sure that math is true either simply because it foundations could be cracked. Nevertheless, I don’t think that you can totally discard safety in math because ironically enough math is itself the foundations of our reality. The nature of the events that occur in the world are explained mathematically, the nature of our responses as well… This means that for the practical purposes of life, to live life as it is, you cannot discard the level of certainty math has because through it we have structured our world to the point that if there is something we can consider to be truth it is math. This does not mean it is necessarily true for as any other knowledge it is acquired through the Wok’s which are patterned according to other factors. I don’t think math provides the ultimate truth, I think it provides the collective truth, one that is accepted and irrefutable by everyone. I think that other ways of knowing that work in the same way is history because it does provides collective truth, simply not for the totality of the people. The reason why no one from the collective math comprises refutes it is because math is the roots of their thinking, roots from which apparent proof has grown which causes one to consider that the knowledge is proof as well. I don’t think mathematics is the ultimate truth simply because of the fact that it is knowledge, and as knowledge one can never be sure 100% of its certainty. However, I think it is trustworthy knowledge because it is not easily disprovable. I don’t think there is any other way of knowing that is similar to mathematics in this respect simply because of the fact that these are subject to factors to which mathematics is not, like the weather, the context… I believe that is a common belief that mathematics is purely logical and has no room for creativity due to the fact that the world logic carries a connotation of robotic and mechanical, while creativity has a connotation of impulsive and irrational which collides with the image we have of math. I actually think that despite whatever the perception we might have mathematics does have a creative part, and I think evidence of that is that mathematicians even say they are creative solving problems, like Gloriana who says she moves thinks around and plays with them to find the answer. I think math is actually material for creativity since there is an answer but there are infinite ways of getting to it, math only gives the bricks with which one must build the path towards the answer, a path that can have various forms, colors… Math is like play-do for kids, they can do anything with it.
Sorry for the delay, I decided to post the entire thing and then I forgot completely, sorry