Guest Lc-is-a-loser Posted July 27, 2007 Report Share Posted July 27, 2007 Hey,I'm doing question 9 for May 2008 TOK. I'm quite unsure how I'm supposed to start the essay and the format it's supposed to take?Any help?The title: Mathematicians have the concept of rigorous proof, which leads to knowing something with complete certainty. Consider the extent to which complete certainty might be achievable in mathematics and at least one other area of knowledge. Reply Link to post Share on other sites More sharing options...
~Lc~ Posted July 30, 2007 Report Share Posted July 30, 2007 Hey,I'm doing question 9 for May 2008 TOK. I'm quite unsure how I'm supposed to start the essay and the format it's supposed to take? Any help? Lc: Mod edit- don't piss off LC I also hope the answer to my question is on the sticky threads already, it will then totally irradicate the use of this particular topic...you'll delete at least half of this post in the next few minutes anyway... you're very welcome, and thx for letting me have my first mod edit ... nice username btw haha ok title 9 seems like a good choice for a maths dude (which I am far from, but given as you are then woohoo go on). as you asked about how to start the essay I take it you want to know how to shape your intro. This is my favorite part of the essay [/geek]. firstly you have to define what other AOK you want to discuss with math. After that explain generally how you think you reach "complete certainty" in math and how you might or might not reach it in the other AOK you wish to discuss. for your thesis say something along the lines of Spoiler - Click me! if you agree with what I'm about to say, you might not if you don't don't use it[Close] "because we get definite answers when solving mathematical equations, it is safe to assume that maths is more likely to reach “complete certainty” in that given equation” then discuss how likely it is to reach “complete certainty” in the other AOK. Plus discuss the idea that the “certainty” that the solution you have for a math problem given to you is only determined after you’ve proven that it is correct. What made me think of this is that I usually go out of a maths exam thinking I would get 100% on it and end up messing up a few points because I misread the question or put + instead of -. So this could be discussed as a POK created by emotion (nervousness) or perception (you produce an incorrect answer because you answer what you think you saw). Reply Link to post Share on other sites More sharing options...
Guest Lc-is-a-loser Posted July 30, 2007 Report Share Posted July 30, 2007 you're very welcome, and thx for letting me have my first mod edit ...nice username btw haha ok title 9 seems like a good choice for a maths dude (which I am far from, but given as you are then woohoo go on). as you asked about how to start the essay I take it you want to know how to shape your intro. This is my favorite part of the essay [/geek]. firstly you have to define what other AOK you want to discuss with math. After that explain generally how you think you reach "complete certainty" in math and how you might or might not reach it in the other AOK you wish to discuss. for your thesis say something along the lines of Spoiler - Click me! if you agree with what I'm about to say, you might not if you don't don't use it[Close] "because we get definite answers when solving mathematical equations, it is safe to assume that maths is more likely to reach “complete certainty” in that given equation” then discuss how likely it is to reach “complete certainty” in the other AOK. Plus discuss the idea that the “certainty” that the solution you have for a math problem given to you is only determined after you’ve proven that it is correct. What made me think of this is that I usually go out of a maths exam thinking I would get 100% on it and end up messing up a few points because I misread the question or put + instead of -. So this could be discussed as a POK created by emotion (nervousness) or perception (you produce an incorrect answer because you answer what you think you saw). Wow, you're good at this...fancy writing the rest Lc? Please... Reply Link to post Share on other sites More sharing options...
~Lc~ Posted July 30, 2007 Report Share Posted July 30, 2007 Wow, you're good at this...fancy writing the rest Lc? Please... haha trust me I would love to but given you just called me a loser, and that I got a B in my own essay.. I wouldn't want to be the reason you get a B as well I think you're better off writing it yourself Reply Link to post Share on other sites More sharing options...
Guest Lc-is-a-loser Posted July 30, 2007 Report Share Posted July 30, 2007 haha trust me I would love to but given you just called me a loser, and that I got a B in my own essay.. I wouldn't want to be the reason you get a B as well I think you're better off writing it yourself Nah, you might get an A this time round, you never know! haha!! Besides I'm sure I'll get an A for my FM EE so...its fine if you get a B.. Reply Link to post Share on other sites More sharing options...
~Lc~ Posted July 30, 2007 Report Share Posted July 30, 2007 haha! nice try dude read the Alchin book he's a genius! you'll def get a B if you portrayed most of the ideas he has in there in your essay Reply Link to post Share on other sites More sharing options...
Bandev Posted July 31, 2007 Report Share Posted July 31, 2007 I think that book is good as guide in direction for your ideas but you need to go into to more depth the what is in there or at least that is what I have found from reading essays which received an A. Also in my opimion the style in which you write the essay has alot to do with how well you will do, it isn't supposed to be in the style of the EE or group 3 IAs, it is meant to be about you in relation to the title you choose, showing *cringe* your journey. Reply Link to post Share on other sites More sharing options...
~Lc~ Posted August 1, 2007 Report Share Posted August 1, 2007 Just a thought...You could counter-argue that even maths doesn't always give "complete certainty" as mathematical proofs are dependent on axioms. I can't remember off the top of my head but I swear there's a proof where 1+1=1. But..you don't have to this in as it might lead you off track. actually presenting both sides of an argument is a good thing so would've lead him off track, but he'll have to know how to present it so that it won't show that he's contradicting himself offtopic: I keep clicking the edit button instead of the quote one Reply Link to post Share on other sites More sharing options...
winter Posted September 6, 2007 Report Share Posted September 6, 2007 and that 0.999999' = 1.(9/9 = 1)Have a look at trigonometry, for example, and where THE HELL they came up with it. You might be interested in some of the axioms.Not to mention that everything we do is with the base-10 number system.... imagine if it were a base-12!Logic may be able to provide complete certainty. Or, you may be CERTAIN as to what you are perceiving. You cannot, however, be certain as to what anyone else is perceiving. Reply Link to post Share on other sites More sharing options...
Afterglow Posted September 6, 2007 Report Share Posted September 6, 2007 Ah this is one of my fave titles of the list (don't like them very much sadly) and I MIGHT be doing it on this even though I am not a mathematical person It's just that since our ToK teacher is also the Math HL teacher, we spent a great deal in ToK, discussing math. and that 0.999999' = 1.(9/9 = 1) Have a look at trigonometry, for example, and where THE HELL they came up with it. You might be interested in some of the axioms. Not to mention that everything we do is with the base-10 number system.... imagine if it were a base-12! Logic may be able to provide complete certainty. Or, you may be CERTAIN as to what you are perceiving. You cannot, however, be certain as to what anyone else is perceiving. Oh or one of my favourite ; 1/3 = 0,333... BUT 0,333 x 3 = 0,999 Reply Link to post Share on other sites More sharing options...
Ruan Chun Xian Posted September 25, 2007 Report Share Posted September 25, 2007 Ah! A good thing to look at if you're really going to do this problem and considering the 1+1 = 1 argument...which is indeed a fallacy.HereWhere this helps you any with the "certainty" of maths...I don't know. Depends on the way you're approaching the question, I suppose. Reply Link to post Share on other sites More sharing options...
Lil Posted October 21, 2007 Report Share Posted October 21, 2007 Ah this is one of my fave titles of the list (don't like them very much sadly) and I MIGHT be doing it on this even though I am not a mathematical person It's just that since our ToK teacher is also the Math HL teacher, we spent a great deal in ToK, discussing math. Oh or one of my favourite ; 1/3 = 0,333... BUT 0,333 x 3 = 0,999 yeax, that's cool topic but in my opinion it is really hard too good luck with this topic and try to find a lot of examples Reply Link to post Share on other sites More sharing options...
icecoldstar Posted October 28, 2007 Report Share Posted October 28, 2007 i wrote this one as well because we had to write 3 of of the 9 essays and choose one of them..just for the record, I completely BSed this stuff... wrote it in less than 1 and half hours.. Reply Link to post Share on other sites More sharing options...
snowday Posted November 10, 2007 Report Share Posted November 10, 2007 Hey, I wrote my TOK essay on this topic last year. I just wanted to give you a heads-up about using things such as the 1+1=1 fallacy or things such as 0.9999 = 1. These examples are pretty weak, as either they are proven false in the realm of mathematics (in the case of 1+1 = 1) or the boundaries of mathematics encompass certain things as truth (i.e. 0.99999 = 1) I think that the key to writing a strong essay for this title is really looking at the structure of mathematics as a whole, looking at the foundations of the subject itself. Take a look at the evolution of the subject; mathematics has evolved quite a bit, and some of what was considered mathematics hundreds of years ago would no longer be considered mathematics today. Granted, many mathematical concepts have endured thousands of years; nonetheless, much of the foundation has been altered. Having said this, there may very well be many other brilliant ways to approaching the title that I simply can't see, and I would love to hear any other ways of looking at the question (I handed in my paper last year, so it's purely for the sake of curiosity). Also, I realize that my answer may have been rather vague; I simply don't want to influence you with the specific ideas presented in my paper, so I tried to keep it general.Hope it helps. Reply Link to post Share on other sites More sharing options...
Guest sour_rous Posted November 24, 2007 Report Share Posted November 24, 2007 Would it be right to talk about the Gödel theorem? We had a look at it last year, and that's what i came up with when I looked at this title, but maybe it's too complex to make an argument on what he said... I also think that the IBO want us to think, not to talk about what the philosophers say. I'm a bit confused about that, because I think Gödel's theorem might be the answer, but I don't want to just expose in my essay what that guy said. Should I just make a short explanation about him or base my essay on him? PD: One more thing, the only AOK able to reach certainty is logic. Can I just talk about this AOK, or can I choose another AOK such as Science and talk about the cause-effect logic problem? Thanks a lot!! Reply Link to post Share on other sites More sharing options...
snowday Posted December 8, 2007 Report Share Posted December 8, 2007 Would it be right to talk about the Gödel theorem? We had a look at it last year, and that's what i came up with when I looked at this title, but maybe it's too complex to make an argument on what he said... I also think that the IBO want us to think, not to talk about what the philosophers say. I'm a bit confused about that, because I think Gödel's theorem might be the answer, but I don't want to just expose in my essay what that guy said. Should I just make a short explanation about him or base my essay on him? PD: One more thing, the only AOK able to reach certainty is logic. Can I just talk about this AOK, or can I choose another AOK such as Science and talk about the cause-effect logic problem? Thanks a lot!! Hi there, I think Godel's incompleteness theorem is a valid way of demonstrating that math is perhaps not as "certain" as one thinks, since there is always a mathematical truth that cannot be proven given a reasonably complex mathematical system. I wouldnt worry about going in-depth into his theorem (i.e. talking about Godel numbers), because I think that would be taking it too far. Also, I would not use the Godel theorem as the foundation for your essay, I think it works better as a supporting argument. Hope it helps. Reply Link to post Share on other sites More sharing options...
Guest baxterity Posted February 28, 2008 Report Share Posted February 28, 2008 Hi there, I think Godel's incompleteness theorem is a valid way of demonstrating that math is perhaps not as "certain" as one thinks, since there is always a mathematical truth that cannot be proven given a reasonably complex mathematical system. I wouldnt worry about going in-depth into his theorem (i.e. talking about Godel numbers), because I think that would be taking it too far. Also, I would not use the Godel theorem as the foundation for your essay, I think it works better as a supporting argument.Hope it helps.So I'm trying to finish my essay up right now. I put about 750 words into analysing mathematical certainty, and am curious what to do for my other AOK. I was going to do religion, but I don't think that it's an AOK. Reply Link to post Share on other sites More sharing options...
Bandev Posted March 27, 2008 Report Share Posted March 27, 2008 My friend did this one and she got an A, and according to her, what she wrote was utter crap...so good luck! Lol. Reply Link to post Share on other sites More sharing options...
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