# TOK speech - Does experience with mathematics influence perception of beauty?

Show video: (1:45 - 4:10) http://www.ted.com/talks/michael_pawlyn_using_nature_s_genius_in_architecture.htmlV: So, using mathematics to describe and better understand our perception of beauty in nature is not only an interesting endeavour, but one that can help us create beautiful and sustainable designs based on nature. Imagine a solar panel having the same design as the arrangement of leaves in a Fibonacci sequence. Not only would that be visually awesome, it could provide an answer to using solar panels as a main source of energy. Mathematics and nature is all around us, so putting them together in design would make something incredible.A: Although we have discussed at length about mathematics, and how it is beautiful, our high school education does not teach actual mathematics. Our learning consists of arithmetic and computational math. So what right do we have to talk about mathematics and its beauty? Does experience with mathematics influence perception of beauty?Show picture of nature and picture of mathematical formulaAsk class which is beautiful, and which is easier to perceive as beautiful.V: There is much beauty in nature, and we can all recognize it without any mathematical training. Mathematical beauty, however, may only be appreciated if one is familiar with its language and if one has enough experience and knowledge to identify it.A: There was a time when my uncle challenged me with a math problem. I fumbled through with it but I gave him the correct answer. My uncle being well-versed in math traced through my steps and laughed. He then gave me a much shorter, less complex method to solve the problem. The kind that seems obvious once presented to you. My uncle’s experience enabled him to solve the math problem elegantly, while with less experience in mathematics, I could only stagger through with a correct, but

clumsier solution.V: My experience with mathematics has been limited to the curriculum the provincial government has outlined for our schooling. I’ve only associated mathematics with repeated applications of equations and formulas plus long stuffy lessons, which all adds up to boredom. I can’t find beauty in something I don’t understand that well through my limited education, and not in something I don’t feel much for. My experience with mathematics was hampered by my education in computational math, so finding beauty in pure or applied mathematics comes much harder for me.Does the use of mathematics as a language represented by symbols ...

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clumsier solution.V: My experience with mathematics has been limited to the curriculum the provincial government has outlined for our schooling. I’ve only associated mathematics with repeated applications of equations and formulas plus long stuffy lessons, which all adds up to boredom. I can’t find beauty in something I don’t understand that well through my limited education, and not in something I don’t feel much for. My experience with mathematics was hampered by my education in computational math, so finding beauty in pure or applied mathematics comes much harder for me.Does the use of mathematics as a language represented by symbols affect perception of mathematical beauty?A: When mathematics is represented by symbols, it affects enormously whether we can see it as beautiful. The shorter and more efficient a formula, the better. This makes symbols and signs a much better alternative than verbose words and phrases. They are a mathematician’s best friend. A: However, to the average person, the symbols prove to be more of a headache than a source of joy. Average people are more connected to the images of trees, grass, and animals because they are in physical world. Therefore, when the mathematics of the physical world is presented in the the way of symbols, the average person is out of their depth. However, when the mathematics is presented visually as in nature, the average person is more connected and therefore, can find the beauty more easily.V: Mathematics is a universal language. I think one of its merits is that someone from any country is able to learn this language, proficiently or not, because it relies not on any grammar that is based on lengthy words and grammatical fillers. You won’t find the mathematical equivalent of the article “the” in any equation, because it adds unnecessary baggage. This makes it easier to learn, with universal rules, unlike the English language’s weird exceptions like beige and eight.A: It would probably easier to learn:(x + 1)(x - 1) = x^2 - 1than:The sum of any number plus one multiplied by the difference of the same number minus one equals the difference of the square of the number minus one.V: Even so, these statements are both correct. But as you can see, one is more easy on the eyes, so to say, and more easy to understand. I think of the two statements, the former is more beautiful because it is visually more appealing, and represents the concept more accessibly.A: Now we have to think, is beauty represented by truth in mathematics? Does mathematics have truth when it corresponds to phenomena that we perceive in nature? Or does mathematics have truth when it coheres to a designed structure of definitions and axioms?A: With natural sciences, we use perception to see, hear, or touch something in the physical world, and use those observations to provide evidence and get closer to the truth. Mathematics, in contrast, does not need physical perception to provide evidence for truth. Natural sciences rely on observation and we always have a degree of uncertainty in these observations. Mathematical modelling, however, in itself is undeniable in its certainty. The main issue is how accurate the application of an internally perfect model is in the natural world. If it correctly describes a pattern inherent in nature, we can assume the theory to be true.A: As well, to the average Joe, mathematics has some sort of undeniable truth because it is thought to use numbers and complicated formulas. We readily believe in phi because it has to do with math, which we relate to numbers and their cold clear-cut quality of truth. We may confuse priori knowledge, such as 1+1=2, with new knowledge generated by mathematics and see them as equally valid and sound.V: But, with logical reasoning, a mathematical proof can be valid, but still untrue. Remember our practices with logical syllogisms? Say you have the premise that all IB students BS and that BSing gets you good grades. Therefore, all IB students get good grades. This conclusion has an internal truth within itself since the conclusion follows the premises. But, it does not actually apply to real life and is not consistently true in the physical world, since sadly an IB student will not succeed just by BSing. To me, this incoherence with the physical world has a sort of dissonance that rings badly with me. Even though it is internally correct, because it is not true in the physical world, this syllogism seems ugly to me.A: I think that a true mathematical conclusion, whether in the real world or in the imaginary mathematical world, has a sort of beauty to it. With my uncle, his solution was more beautiful to me because it was elegant, but on top of that, it was correct as well.V: On a different note, beauty compels us to investigate natural phenomenon. The same way how a botanist may be fascinated with flora in nature because of their beauty, a mathematician would be intrigued by the chance to create a beautiful theorem or proof. The difference here is that a natural scientist deals with the physical world, and admires physical beauty in objects, while a mathematician works with ideas in an imaginary world. I argue that even though the beauty in mathematics may be less tangible because it is in the form of ideas that cannot be touched or seen without symbolic representation, it is no less real than beauty in the physical world.A: It could even be argued that the numbers and symbols in the mathematical world are even more real than the flowers and trees in the physical world. In the physical world, there are no colours, texture, or even solid objects. Everything that we perceive about the physical world is merely our brain’s interpretation of the physical world. However in the mathematical world, the mathematicians make the rules. The numbers are actually players that obey the rules of the “game” per say. Therefore, any form of beauty in the mathematical world is more valid than the perceived beauty in the physical world.V: Now, let’s all take a figurative step back and see where all this discussion has taken us.A: Beauty in mathematics in relationship to beauty in nature has been an inconceivable idea for a long time. How can something as cold and strict as math have and aesthetically pleasing aspects let alone aspects that can be compared with beauty in nature? However, by examining mathematics through the mathematician’s eyes, we can see that there are ways in which a formula can appear beautiful. A: Take a look at the Fibonacci sequence in the same way you would view a flower or a pine cone. Most of the barrier that prevents the two subject areas from being compared is the lack of understanding of math. Mathematics is far more than just numbers and symbols. Rather it is a universal language that is cross-cultural. Mathematics is able to describe its own world in black and white without any uncertainly. This is a quality that even the real world cannot achieve. Therefore, if mathematics is not more beautiful than nature, it is at least at an equal level. V: As well, we can analyze beauty in nature with mathematics, finding patterns and drawing correlations between beautiful physical structures and mathematics. If we describe a natural form in mathematical language, through this transcription, we can also apply the concept behind its beauty to design. Inspired by the Fibonacci sequence and phi ratio found in nature, people can design aesthetically-pleasing objects, compose music based on fractals and phi, and create stunning architecture that is both efficient and sustainable. Mathematics, which can demonstrate beauty in itself, also aids in our understanding of beauty in nature and in design.A: And that concludes our presentation. Thank you!