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Transcript of TOK Mathematics
Math and Art create one another.
Both are imprints and descriptions;
How they manifest themselves varies.
They incorporate multitudes of our ideals which are FELT THEN depicted.
Where Body Mass Index (BMI) is Flawed
Imagine you were asked to advise two men on their bodyweight:
The couch potato
He is 1.83 meters tall (6 feet tall), never does any exercise, and weighs 92 kilograms (203 lbs).
His BMI is 27
He is an Olympic champion 100-meter sprinter, 1.83 meters tall (6 feet tall), does an incredible amount of exercise, and weighs 96 kilograms (211 lbs)
His BMI is 28
Does math create beauty or vice versa?
Mathematics & Arts
What is subjectivity? In art?
Is there subjectivity behind math?
Gujri Chadha,Melanie Fuentes, Annie Trang
math reflect our subconscious
What is the nature of art and beauty?
What are ideals?
When beauty creates math:
Golden Ratio and Attraction:
We see the application of math to beautiful things. Were beautiful things the basis for math?
Art is open to interpretation and intertwines opinions and emotions.
Subjectivity about an object which can be evaluated with math does not indicate subjectivity within math but does suggest subjectivity about math.
We merely attach significance, as said before.
Therefore, it is not entirely math which consists our ideals.
Our projection of our ideals are our emotional reactions to the math - logic.
Psychology and BMI
When is math subconscious?
Fractals: Geometrical Art
University College London
"To many of us mathematical formulae appear dry and inaccessible but to a mathematician an equation can embody the quintessence of beauty."
- Professor Semir Zeki, Wellcome Laboratory of Neurobiology at UCL
Rated 60 Math Formulas on scale of -5 (ugly) to +5 (beautiful)
Two weeks later, the Mathematicians were asked to rate the Formulas - brain activity measured with functional magnetic resonance imaging (fMRI)
Medial orbito-frontal cortex activity
Srinivasa Ramanujan's infinite series and Riemann's functional equation as the ugliest.
Consistently rated as beautiful (both before and during the scans) were Leonhard Euler's identity, the Pythagorean identity and the Cauchy-Riemann equations
Originate from our biological attractions and our conscious awareness.
Beauty and perfection consists of subjective elements
Symmetry and geometry : what evokes us?
Trimbos Institute, Netherlands
Institute of Mental Health and Addiction
Completed Achenbach's Youth
1826 eighth grade students
5730 High school students
Asked for their height and weight
Evaluated their body weight
Students overweight and underweight considered themselves to be normal.
Discovered that participants who rated themselves as normal may have perceived differently
Perception of the body induced behavioral problems
Internalization of a problem
Study highlights the association between
BMI and perception - a mold.
But if math exists in art, is it possible to have subjectivity in math?
Our biological response to beauty and phi (relation to the main issue):
"The presence of a specific parameter (the golden ratio) in the stimuli we presented determined brain activations different to those where this parameter was violated. The spark that changed the perception of a sculpture from “ugly” to beautiful appears to be the joint activation of specific populations of cortical neurons responding to the physical properties of the stimuli and of neurons located in the anterior insula."
Tangible and intangible creations which evoke an emotional response
Ideals are subjective; they are opinions.
Squares and Circles
For every individual, there are proportions ranging from the span for height and arm span to palms and fingers (ratios of the body)
Neoplatonism basis and structure
Division of the universe and relation to man
Arts and Beauty
What is the nature of mathematics?
Similar to art, it is a combination of elements which express change and depict our view of the world.
Similar but distinct aspects
Interaction between mathematics and art to reveals the creation and justification of our ideals
Math creates beauty when...
Intermingling of philosophical perspective (ideally) with mathematics
Associated value with mathematics
Ideals and beauty arise from the reliance on mathematics as "absolute depiction."
Cinzia Di Dio (2007)
The Mona Lisa
Beauty as biological.
Fifteen 2-dimentional images of Classical and Renaissance sculptures
Shifts in ratios
Observation , aesthetic judgment, and proportion judgment groups
In this case, mathematics is concrete. Our attached perception provides significance.
Legs of the triangle bisect the width at the top and comes across her head perfectly and meets the triangle
The spiral frames her face, winding from the tip of her nose, touching the bottom of her chin all the way around to her right arm from her elbow to her thumb
+ Emotional Response
"Human Beauty" is based on the Divine Proportion or the golden ratio=1.61803398875
Basis of perception of beauty
Our ears reflect the Fibonacci sequence
The dimensions of our teeth are based on phi
The closer an individual reflects the golden ratio, the more attractive we perceive them to be
subconscious activity in perception
Initial perception-- responsive to patterns
intangible concepts construed inside subconscious showcased in fractals
Creation of concepts--unapparent due to the limited mathematical knowledge
origin that is not visible
What is subconscious?
There is no full awareness of action; nonetheless, an influence still induces the behavior.
When addressing the subconscious, math
and art are intertwined - the separation closes.
Ongoing process which defines further describes our art -
to better understand ourselves and the nature around us.
Subconscious requires conscious revelations to be admired.
Mathematics follows a concrete logic while
art is interpretive, derivative of various
Our knowledge cannot be subconscious because knowledge requires further justification and awareness. Therefore, admiration appeals to the aesthetic surface - not the core math.
Dio, C. D. (n.d.). The Golden Beauty: Brain Response to Classical and Renaissance Sculptures. PLOS ONE. http://dx.doi.org/10.1371/journal.pone.0001201
Nordqvist, C. (2013, January 31). BMI - Is The Body Mass Index Formula Flawed? Retrieved March 17, 2014, from Medical News Today website: http://www.medicalnewstoday.com/articles/255712.php
TED. (2010, February). Benoit Mandelbrot: Fractals and the art of roughness [Video file]. Retrieved from http://www.ted.com/talks/benoit_mandelbrot_fractals_the_art_of_roughness
TED-ed. (2013, July 11). Da Vinci's Vitruvian Man of math - James Earle [Video file]. Retrieved from http://ed.ted.com/lessons/da-vinci-s-vitruvian-man-of-math-james-earle
Trimbos Institute. (2006, July). Body mass index and body weight perception as risk factors for internalizing and externalizing problem behavior among adolescents. Retrieved March 17, 2014, from PubMed website: http://www.ncbi.nlm.nih.gov/pubmed/16781958
He who does not understand the certainty of mathematics is wallowing in confusion
--Leonardo da Vinci
like realism in general, holds that mathematical entities exist independently of the human mind. Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same. In this point of view, there is really one sort of mathematics that can be discovered: triangles, for example, are real entities, not the creations of the human mind.
But it is aesthetic as well with it's philosophy
Since we establish ourselves as a piece of art...