• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

TOk Discussion - Do we impose mathematics upon nature or is it naturally inherent in the physical world? Does mathematics mimic nature or does nature follow the rules of mathematics?

Extracts from this document...


First of all, beauty can be described by mathematics. Do we impose mathematics upon nature or is it naturally inherent in the physical world? Does mathematics mimic nature or does nature follow the rules of mathematics? A: Nature, in a sense, existed before humans applied mathematical knowledge to it. Humans saw patterns in nature and wanted to study them and give them names, so I believe mathematics is inherent in nature. V: In contrast, I think that we impose mathematics upon nature. Nature does not have the plan to conform to mathematical ideas, but we have created mathematical ideas to describe what we see in nature. The ideas themselves are created by us and are only constructs in our mind. Although the basis of mathematics come from the physical world, it has expanded far into the imaginary world and its concepts, although they could be applied to nature and the physical world, exist by themselves as imaginary ideas. The phi ratio is but an irrational constant, and cannot be exactly depicted in the physical world, just as you cannot pin down the square root of two on a number line. A: Also, mathematics does not have to be the sole explanation for why we find something beautiful in nature. It could be a biological aid in understanding the mechanisms of our world. ...read more.


These have contributed a great deal not only to the mathematical community, but to the physical world as well, where many others can benefit from the new knowledge gained. Show Phi efficiency video: (0:00 - 3:03) http://www.youtube.com/watch?v=_w19BTB5ino&feaure=related V: "Nature is governed by efficiency." We can relate this to natural selection. Natural selection picks organisms that are best suited to their environment. What are the best organisms? They are the ones with the best traits relative to their respective environments. What qualities constitute a good trait? In my opinion, a good trait should be something that is both simple and efficient. Let us go back to the sunflowers. We can explain and describe how the distribution of their seeds are based on the optimization of space efficiency using a simple mathematical tool, the Fibonacci sequence. Do we find the structure beautiful because of its efficiency? A: Yes, I believe so. To me, the ability to be efficient is inherently elegant, in that many biological structures have evolved to make the most out of limited resources. Many organisms have evolved to survive using only a minimum amount of nutrients to carry out necessary body functions. A: However, we have to recognize that organisms did not evolve to fit our sense of beauty. They grew in order to be the most efficient at surviving. If it turns out to be beautiful, that is merely a bi-product of its struggle to survive. ...read more.


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. ?? ?? ?? ?? 4 ...read more.

The above preview is unformatted text

This student written piece of work is one of many that can be found in our International Baccalaureate Theory of Knowledge section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Theory of Knowledge essays

  1. TOK Mathematics and Sciences Essay

    irrational numbers were discovered, their belief was disproven and eliminated their certainty. The Pythagoras theorem has a logically-structured proof that it works for a triangle where one angle is a right angle and this has been accepted because no contradictions have been found to this law.

  2. To what extent is truth different in mathematics, the arts, and ethics?

    10 as a solitary number). The same process is with the truth in the ethics. People generally have a set of ethics that can always contain exceptions when they are in a situation that demands that it would be ethical to do so.

  1. How Inner nature and survival of the fittest relate to the relationship of mind ...

    He has never been beaten in his boxing career and he retired after obtaining an astounding record of 40 victories and 0 losses. No other boxer has accomplished what he has been able to accomplish and very few hold records near him.

  2. Chapter 5 Discussion

    Reading further into the chapter, another idea I found to be interesting was the ?egocentric predicament.? This states that often times we think of things too selfishly in the sense that we generally think of things from our perspective. The reality in our world around us can be seen differently

  1. Can Mathematics be reduced to logic?

    Another particular division that involves the use of the zero is: 0/0. The answer could be 1 because any number divided by itself is equal to 1, and it seems to be right because if you do an inverse operation, the answer is still valid (1*0 = 0).

  2. A Discussion of the Understanding of Religion In the Lights of Relativity and Interpretation

    In Christianity, for example, the souls of saved people go to heaven, whereas the souls of the damned go to hell. However in a few religions everyone's soul goes to the same place. 2) Why Do They Sound Different? The Theory of Relativity and Interpretation * Protagoras Protagoras is famous

  1. TOK Essay. The entire accuracies of mathematics and the natural sciences rely on the ...

    language, perception, and reasoning. Language is needed as two mathematicians should be able to converse about an equation or question without having to explain everything due to confusions. The ?math language? should be common between the two conversation holders. Perception is important as you need to understand how an answer is reached and also understand how to solve and use certain equations or formulae.

  2. In your opinion, should an atheist who does not believe in God or the ...

    fear, I cannot hold these codes to the same standards as moral codes devolved in the absence of religion. If Christians follow rules set down by God based on what they believe they can gain by being pious, then the motive cancels the purpose of the action itself.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work