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    #31
    Re: Math 7

    What interesting conversations you all are having here! I got through (barely!) high school AP Calculus and remember a direct corollary between two things: homework and skill. When I did my homework, I did fine in math. When I stopped doing my homework, I crashed and burned. Most of Calculus was crash and burn, but I did not fail! Sometimes that is a win in my book.

    Back to the questions though--Martin is always pointing out that the questions you ask will determine the answers you get (I'm probably paraphrasing him embarrassingly here, sorry!). One of the main points of classical Christian education is that we have jettisoned the merely utilitarian questions of, "Why do I need this? What am I going to use the for? If I'll never use it, why learn it?" etc. These are the type questions that are thrown at us regarding studies like Latin, Classical Studies, and cursive every day. Our answers are usually along the lines of "this is what you need to know to be a well educated human being, prepared for any calling that is placed on your life." Instead, we could ask: "What should you study to become a well educated human being, exhibiting wisdom and virtue, and guided by charity." Or similar...You can start from what do we include?

    Now I don't hear anyone saying they want to scrap math (although I am sure you could find some student volunteers!). What I do hear being discussed is how much math, and for how long? Ultimately, we'll be making these decisions for our children because we are homeschoolers and have assumed the responsibility to direct their learning year by year. Our states have varying requirements as well that guide us. Some of us have careers that will influence our children's perception and knowledge of certain fields.

    Another way to think of it is this: what are you good at--what do you love? When you explain to someone else why they should be curious what you love, how do you describe your field? Do you wish more people knew about the thing you love and could see it with your eyes? Cindy Davis is one of our chief math-lovers around here and I love the way she responded. I think a love of _fill in the blank__ is "caught" by being around people who love it. Anita, to your rhetorical question about "what if you'd had the other teacher" for the classes in which you did so poorly--we'll never know. What we do know from your story was the ability of a teacher to bring something alive to you, to teach it well, and to teach you to the point of understanding and appreciation.

    We were listening the other day to book 3 in the Peter and the Starcatchers series, The Secret of Rundoon. There's a point when two young men who are obviously after the heart of one girl come to a place of ally-ship (a word?). They are not friends. They are competitors. The author comments on their farewell--shaking hands like two men who respect each other a lot more than they like each other. I think we miss the mark when we allow being favorably disposed to something to be the indicator of whether or not it gets a place of importance. No one enjoys discipline at the time... Even if math isn't liked, there is a certain mystery, beauty, and majesty than can be appreciated, even if it's your nemesis. I'm thinking of Anne and Euclid.

    As Martin detailed in this article, the foundation must be solid. That is primary. Getting through all the levels for the sake of getting through is not a good goal all by itself. However, the attitude we adopt towards a subject will rub off on our students. If we see the three years of high school math as an unfortunate derailment of time then they will likely reflect that back to us.

    In summary, I would say that there are some things you can only learn through long perseverance. Latin, Math, and Music are some of the best fields of play you can find for "wisdom and virtue" formation. And yes, that window of school years is the time for putting tools in the tool box. Just my two cents to add to the conversation. I appreciate the question and the ensuing discussion.

    ETA: I picked up the book Here's Looking at Euclid and have on my to-buy list his follow-up The Grapes of Math. I really enjoy books like this that get me thinking about math in new ways!
    Last edited by pickandgrin; 02-05-2018, 02:12 PM.
    Festina lentē,
    Jessica P

    2020-2021
    11th year HSing · 9th year MP
    @ Home, HLN, & Latin online
    11th, 9th, 6th, 3rd

    Highlands Latin Nashville Cottage School

    Comment


      #32
      Re: Math 7

      I had a math teacher, who used to say that women couldn't do math because of the way their brains were formed. Yes, I am not making this stuff up. When I told my mom, she came to school to tell him what she thought of his theory. I always wondered what happened to him. Maybe he went on to program those talking Barbies. Maybe you remember them? It is was the ones that said, "I hate math!"
      Catherine

      Dd - 13 - 8A
      Dd - 11 - 6A

      Comment


        #33
        Re: Math 7

        Originally posted by Aquila View Post
        I had a math teacher, who used to say that women couldn't do math because of the way their brains were formed. Yes, I am not making this stuff up. When I told my mom, she came to school to tell him what she thought of his theory. I always wondered what happened to him. Maybe he went on to program those talking Barbies. Maybe you remember them? It is was the ones that said, "I hate math!"
        There is fairly solid data to back up the fact that females are roughly as adept in STEM as their male counterparts. (Roughly. Men tend to catch on faster. But women tend to catch up faster, if that makes sense.) There is also a ton of data reflecting that most female students have not historically achieved higher careers in STEM because of teachers like Mr “I Hate Math” Barbie.

        But, controversially, there is also a substantial mound of study which indicates that women, classically and post-modern(ly?) do not tend to go as far in STEM because they do not stick with it as long and as consistently. The reason for this has been primarily: “children”. No one has said you *can’t* do both, they’ve just said that — the data has said that — more women aren’t PhD-chairs at MIT because they dropped out to have or rear their children.


        (Don’t shoot the messenger.)
        Boy Wonder: 12, Seton and MP Electives (Special Needs)
        Joy Bubble: 10, Seton and MP Electives (Special Needs)
        Snuggly Cowboy: 8, Seton and MP Electives
        The Comedian: 4, Seton/MP Pre-K, though she’ll probably zoom through that in a week.

        “Have no fear of moving into the unknown. Simply step out fearlessly knowing that I am with you, therefore no harm can befall you; all is very, very well. Do this in complete faith and confidence.”
        ~Pope St John Paul II

        Comment


          #34
          Re: Math 7

          Originally posted by pickandgrin View Post
          What interesting conversations you all are having here! I got through (barely!) high school AP Calculus and remember a direct corollary between two things: homework and skill. When I did my homework, I did fine in math. When I stopped doing my homework, I crashed and burned. Most of Calculus was crash and burn, but I did not fail! Sometimes that is a win in my book.

          Back to the questions though--Martin is always pointing out that the questions you ask will determine the answers you get (I'm probably paraphrasing him embarrassingly here, sorry!). One of the main points of classical Christian education is that we have jettisoned the merely utilitarian questions of, "Why do I need this? What am I going to use the for? If I'll never use it, why learn it?" etc. These are the type questions that are thrown at us regarding studies like Latin, Classical Studies, and cursive every day. Our answers are usually along the lines of "this is what you need to know to be a well educated human being, prepared for any calling that is placed on your life." Instead, we could ask: "What should you study to become a well educated human being, exhibiting wisdom and virtue, and guided by charity." Or similar...You can start from what do we include?

          Now I don't hear anyone saying they want to scrap math (although I am sure you could find some student volunteers!). What I do hear being discussed is how much math, and for how long? Ultimately, we'll be making these decisions for our children because we are homeschoolers and have assumed the responsibility to direct their learning year by year. Our states have varying requirements as well that guide us. Some of us have careers that will influence our children's perception and knowledge of certain fields.

          Another way to think of it is this: what are you good at--what do you love? When you explain to someone else why they should be curious what you love, how do you describe your field? Do you wish more people knew about the thing you love and could see it with your eyes? Cindy Davis is one of our chief math-lovers around here and I love the way she responded. I think a love of _fill in the blank__ is "caught" by being around people who love it. Anita, to your rhetorical question about "what if you'd had the other teacher" for the classes in which you did so poorly--we'll never know. What we do know from your story was the ability of a teacher to bring something alive to you, to teach it well, and to teach you to the point of understanding and appreciation.

          We were listening the other day to book 3 in the Peter and the Starcatchers series, The Secret of Rundoon. There's a point when two young men who are obviously after the heart of one girl come to a place of ally-ship (a word?). They are not friends. They are competitors. The author comments on their farewell--shaking hands like two men who respect each other a lot more than they like each other. I think we miss the mark when we allow being favorably disposed to something to be the indicator of whether or not it gets a place of importance. No one enjoys discipline at the time... Even if math isn't liked, there is a certain mystery, beauty, and majesty than can be appreciated, even if it's your nemesis. I'm thinking of Anne and Euclid.

          As Martin detailed in this article, the foundation must be solid. That is primary. Getting through all the levels for the sake of getting through is not a good goal all by itself. However, the attitude we adopt towards a subject will rub off on our students. If we see the three years of high school math as an unfortunate derailment of time then they will likely reflect that back to us.

          In summary, I would say that there are some things you can only learn through long perseverance. Latin, Math, and Music are some of the best fields of play you can find for "wisdom and virtue" formation. And yes, that window of school years is the time for putting tools in the tool box. Just my two cents to add to the conversation. I appreciate the question and the ensuing discussion.

          ETA: I picked up the book Here's Looking at Euclid and have on my to-buy list his follow-up The Grapes of Math. I really enjoy books like this that get me thinking about math in new ways!
          Einstein loved Math because he said it brought him closer to the mind of God. There is order to the universe. That, to me, is almost as high as mysticism gets. If Math can bring you to eternity’s threshhold, then you do yourself a disservice if you do not at least try to go.
          Boy Wonder: 12, Seton and MP Electives (Special Needs)
          Joy Bubble: 10, Seton and MP Electives (Special Needs)
          Snuggly Cowboy: 8, Seton and MP Electives
          The Comedian: 4, Seton/MP Pre-K, though she’ll probably zoom through that in a week.

          “Have no fear of moving into the unknown. Simply step out fearlessly knowing that I am with you, therefore no harm can befall you; all is very, very well. Do this in complete faith and confidence.”
          ~Pope St John Paul II

          Comment


            #35
            Re: Math 7

            Originally posted by Anita View Post
            Einstein loved Math because he said it brought him closer to the mind of God. There is order to the universe. That, to me, is almost as high as mysticism gets. If Math can bring you to eternity’s threshhold, then you do yourself a disservice if you do not at least try to go.
            Truly! I remember the day we found the surface area of a bead in calculus. It's one of my only memories of that entire year of math. Since that year, I have never found (nor needed to find) the surface area of a bead, but wow--I remember that moment. I was like C. S. Lewis with his brother's little make-shift garden on a tin lid. It awoke something of the numinous in me.

            ***chill bumps***
            Last edited by pickandgrin; 02-05-2018, 07:57 PM.
            Festina lentē,
            Jessica P

            2020-2021
            11th year HSing · 9th year MP
            @ Home, HLN, & Latin online
            11th, 9th, 6th, 3rd

            Highlands Latin Nashville Cottage School

            Comment


              #36
              Re: Math 7

              I think there are many many things that we learn or aspire to learn that aren't at all useful. They might just be beautifully useless, and all the more valuable for all of that. What "use" is music, after all? But I think that you absolutely need subject matter to learn with- and math seems like the ideal thing to hone in on when it comes to training the brain to think. Sometimes I have a crazy thought and I wonder if it really matters at all, *what* you learn- as long as you are learning, and in the process, learning how to learn, and being challenged to go ever higher?
              But I still think higher math is crucial. I ended up studying music, an area where I thought, higher math would not be needed- I had a terrible time with advanced theory and harmony. And there are "glitches" in my music ability to this day that I suspect have to do with the area of the brain that never learned how to think "that way." I always suspected that if I had studied high school math, it would have been easier because I bet I would have known how to learn that material. But it gets real hard to change the way you are wired when you are my age, lol!

              Comment


                #37
                Re: Math 7

                Originally posted by Maria2 View Post
                Sometimes I have a crazy thought and I wonder if it really matters at all, *what* you learn- as long as you are learning, and in the process, learning how to learn, and being challenged to go ever higher?
                I would draw a distinction between learning/studying cumulative subjects versus non-cumulative subjects. But yes, the 'ever higher' is a good call. It's like "further up and further in."

                Perhaps you music people will enjoy this--it's quoted in Beauty for Truth's Sake:

                Music is the pleasure the human mind experiences from counting without being aware that it is counting. Gottfried Leibniz

                If you want to look into "number" more, I heartily recommend Stratford Caldecott's book on the quadrivium, Beauty for Truth's Sake. Wow. What a book.
                Festina lentē,
                Jessica P

                2020-2021
                11th year HSing · 9th year MP
                @ Home, HLN, & Latin online
                11th, 9th, 6th, 3rd

                Highlands Latin Nashville Cottage School

                Comment


                  #38
                  Re: Math 7

                  Originally posted by Maria2 View Post
                  I think there are many many things that we learn or aspire to learn that aren't at all useful. They might just be beautifully useless, and all the more valuable for all of that. What "use" is music, after all? But I think that you absolutely need subject matter to learn with- and math seems like the ideal thing to hone in on when it comes to training the brain to think. Sometimes I have a crazy thought and I wonder if it really matters at all, *what* you learn- as long as you are learning, and in the process, learning how to learn, and being challenged to go ever higher?
                  But I still think higher math is crucial. I ended up studying music, an area where I thought, higher math would not be needed- I had a terrible time with advanced theory and harmony. And there are "glitches" in my music ability to this day that I suspect have to do with the area of the brain that never learned how to think "that way." I always suspected that if I had studied high school math, it would have been easier because I bet I would have known how to learn that material. But it gets real hard to change the way you are wired when you are my age, lol!
                  Painting. Singing. Performing arts. Climbing mountains. Are these things “useful”? They’re not utilitarian at all. At worst, they’re a waste of time. At best, they elevate the soul higher. “Useful” is animal. Truth and Beauty are Human.

                  I got a good education in this though educating my own children. We had a chapter study in catechism that discussed how people and animals are different precisely because we have souls and animals do not. The distinctions are some of what I listed above as well as things like laughter. Laughter isn’t utilitarian. But life without it? Purgatory.
                  Boy Wonder: 12, Seton and MP Electives (Special Needs)
                  Joy Bubble: 10, Seton and MP Electives (Special Needs)
                  Snuggly Cowboy: 8, Seton and MP Electives
                  The Comedian: 4, Seton/MP Pre-K, though she’ll probably zoom through that in a week.

                  “Have no fear of moving into the unknown. Simply step out fearlessly knowing that I am with you, therefore no harm can befall you; all is very, very well. Do this in complete faith and confidence.”
                  ~Pope St John Paul II

                  Comment


                    #39
                    Re: Math 7

                    Originally posted by Anita View Post
                    Painting. Singing. Performing arts. Climbing mountains. Are these things “useful”? They’re not utilitarian at all. At worst, they’re a waste of time. At best, they elevate the soul higher. “Useful” is animal. Truth and Beauty are Human.

                    I got a good education in this though educating my own children. We had a chapter study in catechism that discussed how people and animals are different precisely because we have souls and animals do not. The distinctions are some of what I listed above as well as things like laughter. Laughter isn’t utilitarian. But life without it? Purgatory.
                    I've long been intrigued with the idea of mathematics as something very beautiful. It's an idea I've heard expressed in many places. I want to be able to see that. And I hope so much my kids will get to the point that they can see that, because I know it is true and I know I'm missing something... the world is so full of a number of things...

                    Catherine was there really a Barbie that said "I hate math?"
                    Last edited by Girlnumber20; 02-05-2018, 04:38 PM.

                    Comment


                      #40
                      Re: Math 7

                      Maria, I think the Barbie said something like, "Math is tough." It was pulled from the shelves because there was such a backlash. Come over one day and we will rework the talking Barbie so she speaks in the affirmative for math. Then we can play it over and over again during those tough math school days. What else are we going to do when it is this cold here? It is relentless this winter.

                      I'll race you to the library to see if the book, "Beauty for truths sake" is available! That is a beautiful quote by Leibniz. I may write it out and place it above the piano.

                      As for my math 'instructor' he will be added to the 'why I chose to homeschool' list. As a teenager it is hard to hear these things because you aren't given the tools to question properly. And so Anita, I agree with your reasoning as to why more women aren't in mathematics.

                      There are so many good tidbits of information on this thread and a lot of great insight. It is inspiring. I haven't heard someone speak of mathematics and the mind of God in a long time.
                      Catherine

                      Dd - 13 - 8A
                      Dd - 11 - 6A

                      Comment


                        #41
                        Re: Math 7

                        The idea that math involves discipline and rigor and should be pursued because those are good for you (discipline and rigor are good for you, I wish either had been required of me in school), might be where I am disconnected with this. High school math was not an issue of rigor and discipline for me. I enjoyed them because they were so easy that I could finish the homework during the lesson and then read novels the rest of the class. The teacher would change up the standard assignments sometimes because I would do a week's worth to give me more goof off time. So for me I see an easy class I took not at all seriously with near perfect grades that didn't get used again.

                        Which is actually a part of why I homeschool. I was bored out of my mind in school, but they wouldn't let me advance. It was a tiny rural school that didn't have a single program for advanced students other than detention for boredom induced behaviors. Memoria's program is so different from that in quality and content, but I had mostly been focused on what the Latin, literature, classical and Christian studies were bringing to the table as so different that I wasn't seeing the math as the same value. It's something to think about even if my kids seem to take after me in math.
                        Miah - married to Warcabbage, 3 boys, BS in social work, AS in Electrical Engineering Technology

                        Evulcarrot - 18, freshman in college, Medical Technology , mild autism
                        Battlebroccoli - 17, lives with grandma, attends a special high school program part time
                        Doomsprout - 10, highly verbal moderate autism, anxiety, motor delays, sensory processing issues - SC 4 with R&S 4

                        Comment


                          #42
                          Re: Math 7

                          Originally posted by Colomama View Post
                          Waving! We're park rangers too.
                          Sorry, he is not a park ranger. He wanted to be, at the state level, in Arkansas. He never got through all the math (though he did finish college algebra eventually) and ended up with nothing to show for it but debt. He's a nuclear security guard now, which is a good living that doesn't require algebra. He had plenty of discipline. His last two years in high school he boxed, did marching band, and worked full time. Some people are just apt for a different type of discipline.

                          Sometimes I feel like we leave too many people behind. I've always told my kids that college isn't for everyone and there is no shame in trade schools, military service, etc. That if they ever change their minds when they are older it'll still exist and if they have to work harder at that point at least they'll know it's what they really want.
                          Miah - married to Warcabbage, 3 boys, BS in social work, AS in Electrical Engineering Technology

                          Evulcarrot - 18, freshman in college, Medical Technology , mild autism
                          Battlebroccoli - 17, lives with grandma, attends a special high school program part time
                          Doomsprout - 10, highly verbal moderate autism, anxiety, motor delays, sensory processing issues - SC 4 with R&S 4

                          Comment


                            #43
                            Re: Math 7

                            Originally posted by Enigma View Post

                            I plan to use dvd instruction when we get there. Yep, I'm a wimp!
                            Sheesh. No wimp word allowed. The math woes around here were sucking the life out of me. When I saw that MPOA was offering exactly what we needed this fall, I did a happy dance.

                            Sending up THREE CHEERS for the MPOA 6th grade Math class. I owe Mr Piland and Mrs Hutchins chocolate, at the very least.
                            Plans for 2020-21

                            Year 10 of homeschooling with MP

                            DD1 - 25 - Small Business owner with a STOREFRONT
                            DD2 - 14 - 9th grade - HLS Cottage School/MPOA - equestrian
                            DS3 - 12 - 5A Cottage School - soccer
                            DS4 - 12 - 5A Cottage School -soccer
                            DD5 - 8 - 3A, Cottage School -equestrian and Irish dance
                            DS6 - 6 - MP K - home with Momma

                            Comment


                              #44
                              Re: Math 7

                              Originally posted by Maria2 View Post
                              I will be your test case. I never learned mathematics beyond basic arithmetic, say, up to about 5th-6th grade math. I can state positively that not learning algebra and higher math has very adversely affected me in my life. My college choices were very severely limited. Science classes were impossible, although I had developed a strong interest. It was a problem I constantly ran up against, over and over again, and that haunts me to this day as I struggle to teach my children, who are very interested in science and technology. Not learning higher math has placed so many unnecessary obstacles in my path, both practically and even psychologically speaking. I have gone through my life with the belief that my brain is incapable of higher level reasoning skills. I would never in a million years sentence my children to not learn algebra and higher math -to the best of their ability- to at least go through the sequence- because I know with a certainty that not learning it has affected the development of my own brain in such adverse ways, and has severely limited my own potential in life. All I can really say is that it is like having a giant hole in your brain where you absolutely know something is supposed to be. That is my two cents on the issue, for what it is worth. Not very evidence-based, I realize, it's just my own experience...

                              ETA: You can't really know what you are missing unless you don't have it. If you didn't have math ability and the knowledge that comes only from "knowing" if that makes any sense- you might very well miss it, and even become an advocate for it. I'm willing to bet that you use the higher math you breezed through in ways that you may not be even aware of. To me it just seems like a beautiful gift.
                              Wow! There has certainly been some deep conversation going on today.
                              Why do we study any of these subjects? They teach us more about ourselves, our world, and God. Latin and Greek knowledge allows our children the chance to study many of the world's greatest thinkers, pagan and Christian, in their native tongue. Each language gives insight into the culture that developed it if one cares to look. Arithmetic is sort of analogous to the alphabet, you can't learn the language without it, while mathematics as I have long contended is a language all its own. It is worth study on its own merits...the patterns and order are amazing if you slow down to analyze and study, but it really is a tool to explain so much of how the world works. I have always had a hard time believing that those who were good at languages couldn't master algebra. Calculus gets very visual...I sometimes have a hard time believing that many artistic types wouldnt be better at math than they give themselves credit for. So much of what has been shared here confirms my belief that attitude and confidence and desire are so very important to success in mathematics. You won't get very far if you set yourself up for failure by telling yourself you aren't good at it or if you don't have someone along the way to inspire or encourage you in your study. Our kids have a goal for Latin, but sometimes the point of math gets a bit murky when you are in the beginning stages. My father very much believed that his girls were every bit as capable as boys in math and even tried to get my mother to major in engineering in 1959. She didn't bite (her best friend was told - really, threatened- that she wouldn't succeed if she actually enrolled in engineering at Michigan State that same year), mostly because she didn't intend to go away to Michigan for more than the year that he made her before getting married. Still, she always knew she could. Kids have great powers of observation and can tell if you are afraid or unsure about anything. My father was never a great fan of the fact that many of our elementary school teachers were ones who lacked confidence in math themselves, yet found themselves forced to teach it. At least by middle school and high school it was their chosen profession.

                              Why continue beyond algebra 2 if there is time left to do it? Like Cindy said, you don't know what your child will be inspired to study later on down the road. Those classes don't have to be pre-Calc or calculus, but could be statistics or discrete math. Like many subjects, if you stop math it is hard to ramp back up to level where you used to be. From a purely practical view even a business major is going to be required to take some basic calculus. As an engineer, I studied through partial differential equations. That was as far as I had to go and a bit farther than I cared to dedicate brain power to really understand. Some of that may be due to everything else that was going on in my life. Math is challenging (no, I am not trying to be Barbie, but saying it is easy isn't really true for everyone) and requires time to really wrap your head around what it is trying to accomplish. To this day I am not really quite sure what we were trying to accomplish in that class, but my math major roommate seemed to which was probably why she kept going. I couldn't get past the professor writing every word uttered from his mouth on the board and always wearing the same shirt and jeans to every class. My job really never required me to integrate anything, but it didn't make calculus worthless. All those classes filled my toolbox, taught me how approach and solve a problem put before me, and to appreciate the work of those who continued on further than I did. It also inspires me to keep learning. By the time college rolls around most of our kids will need to decide what they want to do with their life. Maybe their passion and job coincide, maybe it just provides the living to let them pursue their passion. I hope to allow mine to spend their time mastering and enjoying what they do cover in high school, and prepare them to have choices when they get to college.

                              Hope that makes some sense.
                              Dorinda

                              For 2020-2021
                              DD 17-12th with MPOA(Classical Studies 3), CLRC (Latin 6, Greek 5), Thinkwell (Calculus and Chemistry), Vita Beata (Divine Comedy), American History
                              DS 15-9th with Lukeion(Latin 1 and Greek 1), Vita Beata (9th Literature)
                              DS 12-7th with Right Start Level H online class, Vita Beata (6th Literature)
                              DS 6 - 2nd blazing our own trail with Right Start D and a mix of MP materials

                              Comment


                                #45
                                Re: Math 7

                                Originally posted by Aquila View Post
                                Maria, I think the Barbie said something like, "Math is tough." It was pulled from the shelves because there was such a backlash. Come over one day and we will rework the talking Barbie so she speaks in the affirmative for math. Then we can play it over and over again during those tough math school days. What else are we going to do when it is this cold here? It is relentless this winter.

                                I'll race you to the library to see if the book, "Beauty for truths sake" is available! That is a beautiful quote by Leibniz. I may write it out and place it above the piano.

                                As for my math 'instructor' he will be added to the 'why I chose to homeschool' list. As a teenager it is hard to hear these things because you aren't given the tools to question properly. And so Anita, I agree with your reasoning as to why more women aren't in mathematics.

                                There are so many good tidbits of information on this thread and a lot of great insight. It is inspiring. I haven't heard someone speak of mathematics and the mind of God in a long time.
                                Ha- reworking a talking Barbie to say something like "My brain froze when it got to 40 below, I now fully understand the philosophical implications of negative numbers!" - I'm in.

                                As for Jessica's Leibnitz quote, I love it. But I was always puzzled at it, too, because I always had to count like a madwoman to get things to come out right, and it was far from pleasurable...

                                I fear that if God is a mathematician I am doomed.

                                Comment

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