How to Forget You're a Human Being
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Matteo Wyllyamz (aka @mouselink) presents this Ignite talk on the mathematics of Fibonacci, the Golden Ratio, and their relevance to our lives today.
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How to Forget You're a Human Being
- 1. how to forget you’re a human being
- 2. part 1: you’re not just another number. or maybe you are?
- 7. phi φ
- 12. so is everything patterns?
- 13. the behavior of nature is governed by mathematics
- 14. phi explains the nature of growth
- 15. are humans any different?
- 16. human behavior?
- 17. do these patterns also reflect our personal lives?
- 18. are our personal mathematics set, or can they be changed?
- 19. compassion
Editor's Notes
- what does it mean to forget youre a human being? we’ve all been told that being human means certain things, that we behave in certain ways, that we act in certain ways, and if we don’t adhere to those rigid standards, then we’re bad. or *they* are bad. and then the mocking ensues. or ostracization. or violence. I want to tell you that there are other ways of looking at people that might make more sense, and that might work better for us as individuals or as societies. grand unifying theory of everything mandlebrot set sacred geometry
- one way of classifying people that we all rail against is being a number. age height weight phone back account insurance card DL SSN IQ IP address this is a number on the bottom of this screen that I think defines you and me perfectly, and I want to tell you about it and hopefully give you slightly more information than you might be able to get from the wikipedia article.
- our story begins with this guy, leonardo of pisa. yes, the italian town famous for the leaning tower, pictured so typically here. he was the son of this guy Bonacci, who was a trader, and he travelled with his father extensively. during those travels he learned the arabic numeral system and he brought that back to italy where they were still using roman numerals. fibonacci was born three years after the construction of the leaning tower. five years in, during construction of the third floor, it began shifting. In 1202, at age 32, he published what he had learned in Liber Abaci (Book of Abacus or Book of Calculation), and thereby introduced Hindu-Arabic numerals to Europe.
- he became a famous mathematician and he wrote a book called the Liber Abaci. in that book he proposed a problem for his students: if you had one pair of rabbits, and they started procreating, how many would you have at the end of a year? it takes one month for the rabbit mature sexually, and after that they can produce another pair of bunnies every month, and so on. Liber Abaci also posed, and solved, a problem involving the growth of a population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. The number sequence was known to Indian mathematicians as early as the 6th century, but it was Fibonacci's Liber Abaci that introduced it to the West. He considers the growth of an idealized (biologically unrealistic) rabbit population, assuming that: a newly-born pair of rabbits, one male, one female, are put in a field; rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits; rabbits never die and a mating pair always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was: how many pairs will there be in one year? At the end of the first month, they mate, but there is still one only 1 pair. At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field. At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field. At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs. At the end of the nth month, the number of new pairs of rabbits is equal to the number of pairs in month n-2 plus the number of pairs alive last month. This is the nth Fibonacci number.[8]
- well, who would have known that the solution to this problem would become a now-famous series of numbers with the mystical ability to apparently unravel the mysteries of the universe. every number in the series is derived from adding together the two previous numbers. I know this is a little bit like the da vinci code, and I’m sorry.
- this is sometimes called the divine ratio. The Golden Ratio is roughly 1.62 : 1, or 1 : 0.62 or very roughly 8 : 5. (What they say is that it is “approximately” 1.61803398874989484820458… : 1) if a Fibonacci number is divided by its immediate predecessor in the sequence, the quotient approximates φ; e.g., 987/610 ≈ 1.6180327868852 If we break a straight line into two sections, a and b, according to the golden ratio, the ratio between them will be identical to that between the original line and the longer section. In turn, a and b can form the sides of a golden rectangle, considered to be of ideal proportions. Mathematically, two quantities have the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. If we divide a circle into two arcs in the proportion of the Golden ratio, the central angle of the smaller arc marks off the Golden Angle, is 137.5 degrees.
- well its interesting to not that if you divide any number in the series by one of its neighbors you get this figure of .618 “the fingerprint of god” the number that defines all of existence? The golden ratio is often denoted by theGreek letter phi, usually lower case (φ). approximately 1.618 0339887 the Golden Ratio, approximately 1.618. As the Fibonacci sequence grows to greater values, the ratio of one number to the one before it progressively approaches the Golden Ratio of 1.618. if a Fibonacci number is divided by its immediate predecessor in the sequence, the quotient approximates φ; e.g., 987/610 ≈ 1.6180327868852. These approximations are alternately lower and higher than φ, and converge on φ as the Fibonacci numbers increase phi is a universal number of beauty, since it manifests itself in many aesthetically pleasing things, from patterns in nature to famous artwork and architecture
- well somebody figured out that you could built a rectangle out of these proportionate numbers that would have some very interesting qualities. for instance, if you draw a square inside it, it makes another golden rectangle, and put a square inside that one, and so on, and all the measurements of all the squares will be numbers from the fibonacci series.
- Egyptian pyramids the united nations building breakfast cereal boxes, ipod?both davini’s and dali’s last suppers beethoven's 5th du du du dahhhhh yielding 1.6189 for the ratio of slant height to half-base, again more accurate than the data variability. Le Corbusier, an artist, architect, urban planner, writer and designer, often credited as the father of Modern Architecture, loved the golden rectangle. Le Corbusier (October 6, 1887 – August 27, 1965), was a Swiss-French architect, designer, urbanist, writer and also painter, who is famous for being one of the pioneers of what now is called Modern architecture or the International style. He was born in Switzerland and became a French citizen in his 30s. The secret symbol of Pythagoras and his sect was the pentagram – a five-pointed star made up of five identical isosceles triangles. Like the golden rectangle, the pentagram was also considered of perfect proportions and beauty. Each triangle in the pentagram is golden sectioned: the ratio between each of its side and its base is 1.6.18.
- well you remember that golden rectangle and all those squares inside it? well it turns out that if you make an arc through every square and connect them together, that will create this logarithmic spiral. weirdly enough, this exact spiral in all its proportions can be found throughout all the natural universe. some people have called it “the eye of god.”
- the nautilus shell here is the most famous example, but here are just a few more instances of where the fibonacci spiral or its numbers appear in the natural world. one of my favorites is that in most flowers, their number of petals is generally one of the fibonacci numbers. This pattern allows the organism to grow without changing shape. As the nautilus matures it creates new, larger camerae, and moves its growing body into the larger space, sealing the vacated chamber with a new septum. The individual florets of the sunflower (and of the daisy as well) grow in two spirals extending out from the center in opposite directions. The first spiral has 21 arms, while the other has 34. These are Fibonacci numbers, and have the Golden Ratio Most daisies have 21, 34, 55, or 89 petals - all Fibonacci numbers. Phylotaxis is the study of the ordered position of leaves on a stem The leaves on a stem are positioned over the gaps between the lower leaves as they spiral up the stem. What is most remarkable about this spiral spacing, is that irrespective of species, the rotation angle tends to have only a few values. By far the most common of which is 137.5 o (Goodwin). This is considered an efficient arrangement to allow maximum sunlight to reach each set of leaves. This angle is non other than the Golden Proportion related to the perimeter of a circle as in the adjacent figure.
- in fact there are certain types of patterns that appear again and again almost identically in apparently completely different kinds of systems. is this a tree on a hill, or a river, or a scan of somebody’s lung tissue? these are all types of *flowing* systems and they all have the same structure. this is a satellite image of typical river delta. The theory says that flowing systems – from airways in the lungs to the formation of river deltas – evolve in time so that they flow more easily. Bejan believes that this same theory can be applied to the natural design that connects vision and cognition and thus explains the popularity of the golden ratio. Bejan argues that the world – whether it is a human looking at a painting or a gazelle on the open plain scanning the horizon – is basically oriented on the horizontal. For the gazelle, danger primarily comes from the sides or from behind, not from above or below, so their scope of vision evolved to go side-to-side. As vision developed, he argues, the animals got “smarter” by seeing better and moving faster and more safely.” As animals developed organs for vision, they minimized the danger from ahead and the sides,” Bejan said. “This has made the overall flow of animals on earth safer and more efficient. The flow of animal mass develops for itself flow channels that are efficient and conducive to survival – straighter, with fewer obstacles and predators.” For Bejan, vision
- the conclusion we should draw from this is that the behavior of nature is governed by mathematics. virtually every object in the universe can be explained in terms of its mathematics. even predicted.
- in nature, efficiency is created automatically and growth limits are established at the limits of the energy available for a system to continue reproducing itself. also, we see this pattern of increasing specialization. as bandwidth increases we see an increasing amount of diversification in the kinds of information available. this can also illustrate the way information flows on the internet. fractal: A geometric figure, built up from a simple shape, by generating the same or similar changes on successively smaller scales; it shows self-similarity on all scales
- so, are humans any different? we have a tendency to believe that humans are exempt from the universal laws that govern everything else around us. The ratio of successive phalangeal bones of the digits and the metacarpal bone has been said to approximate the golden ratio. inner ear cochliadna 34 angstroms x 21 angstroms = phi 1/1.618 even the clock cycle of human brain waves is said to be in the proportions of phi. In 2003 Weiss and Weiss came on a background of psychometric data and theoretical considerations to the conclusion that the golden ratio underlies the clock cycle of brain waves.[76]
- so if our bodies are governed by the exact same mathematical patterns, what about our behavior? compression waves flow mathematically through patterns of traffic. the stock market is analyzed according to fibonacci retracements. I believe we get ourselves into trouble when we ignore the laws of nature which govern everything around us. if we used those patterns as a guide we could create more efficient and sustainable systems.
- we tend to think of ourselves as a thing, an object. every cell in your body is replaced every seven years. physically, you are not the same “thing” you were ten years ago. you are more like a pattern, and that pattern is created and controlled by the computer-like programming of your DNA. can you change your patterns? perhaps, but it can be a very hard thing. Spira mirabilis "Eadem mutata resurgo" ("Although changed, I shall arise the same.") “Thus the periodicity of life process can not be reduced to a circling when we come back to the initial point and most likely resembles the spiral motion when as though there is also returning but each time at the new level."
- so these patterns get set when we are conceived and they are further developed when we are young. we are programmed biologically, neurologically, by our parents, society, schools, teachers, religions, friends, and by a certain age, some people are so set in their ways that they stop evolving, stop growing. their pattern is set for the rest of their lives.
- if we are more like patterns than things (or human beings), if our lives are governed by mathematical predispositions, then perhaps we don’t have all that much control over what we become and how we act. perhaps others did not have much choice in what they’ve become. if that is true, and I believe it is, then we need to give ourselves and others a lot of compassion. “forgive them, for they know not what they do”?
- forget that you are a human being. forget all you’ve been told about what you are supposed to be, and about what others are “supposed” to be. we must become aware of the patterns that control and influence our lives before we can ever change them. if we don’t take that first step, then we are doomed to mindlessly carry out that programming in an endlessly looping repeating pattern for the rest of our lives. so maybe you *can* be defined by a number. if so, I’d say it’s the most beautiful number. the one they call divine. the one they call “the fingerprint of god.” I’m matteo wyllyamz, and you can find me online @mouselink. thank you.