## Big Ideas

## Butterfly Biology

Strange Attractor of Health

## Introduction Chaos

Chaos

By having fun we can learn better.

Chaos Theory - Gleick

Zooming on Mandelbrot

Mandelbrot

Magnified by factors of itself

Factor of 1000

People got interested… catchy

Genuine reason for excitement chaos, people sense correctly that there is something revolutionary happening in science.

The erratic side of Nature, the irregular and unpredictable.

Jagged side of Nature, the discontinuous,

Science obsessed with the other side of Nature, the predictable, deterministic, lawful and orderly side especially in

Ecology - unpredicable wild flucuation

Arrthyrias

Turbent sea and atmosphere,

Pathologies monsters…

Geologists

Electronic circuits

chemical reactions

30 years

Strange connections

Heart rate variability, structures reminiscent of the whole.

Rules of chaos turned out to be universe.

Turbulence annoying in science.

We know equations of turbulence, but we still do

Leornardo , swirls within swirls

Laws of chaos intersect all disciplines.

What is Chaos - Paradoxical state , unpredictable, but on the other hand.

Deterministic - future is determined by the present.

Only one possible future.

Double pendulum newtons laws of motion.

Small angles

Large angles unpredictable.

Chaos

1) Breaks a lot of the rules of convential science by asking unusual questions. Everyday scale of normal life, not unusual regimes of small and fast.

2) Chaos takes the focus off the laws of nature and shifts it onto their consequences. Goal of physics - Find the new laws, the fundamental laws.

There is another game… Having found the laws, what the consequences of implications.

3) Way it uses the computer, not just a number cruncher.

An intuition telescope.

4) Emphasizes a different side of nature.

Not reductionism, take a problem that is hard and reduce it by breaking it up into smaller parts, try to analyze each part separately and then that should be easier, then put them back together. (Taylor Series).

Some problems do not permit reductionism, that is if you break them up into parts, you lose something essential. There are some systems that the interaction between the parts creates something that the whole is greater than the sum.

That is where there are cooperative effects taking place or some kind of interference.

In systems like that we have to find a way to do scientific holism to go from the parts to the whole.

Rigorous scientific.

5) Chaos is radically interdisciplinary … Usually walls between disciplines.

Makes a lot of progress by specializing.

Economist and biologists and physicists and mathematician.

Astronomy, zoology, the arts, commerce, humanities, internet, medicine, all of it. Condensed matter physics, population biology.

6) Chaos paints a topsy turvy picture of the world. We thought Simple laws lead to simple consequences. Simple system can show complex behavior.

Very complex things can have simple patterns

7) The change in thinking came suddenly.

Pictures can be much more important then formulas.

Visualizing in pictures.

Chaos is the science of how things change.

Purely mathematical side of chaos.

Isaac Newton gave a view of the universe so regular and so orderly that it seemed to outlaw chaos once and for all.

200 years later a chink in Newtons armor.

Henri Poincare… Horrifying picture.

Forgotten for over 70 years.

Ed Lorenz Butterfly effect .. no effect another 10 years.

Fractals shapes whose structures repeat ad-infinitum like the mandelbrot set.

Tiniest parts look like whole. Fractal structure breaks down in a real system, eventually branches to twigs.

Fractals are the remnants of chaos, the footprints that chaos leaves behind.

Vision - cancer to the mystery of consciousness.

By having fun we can learn better.

Chaos Theory - Gleick

Zooming on Mandelbrot

Mandelbrot

Magnified by factors of itself

Factor of 1000

People got interested… catchy

Genuine reason for excitement chaos, people sense correctly that there is something revolutionary happening in science.

The erratic side of Nature, the irregular and unpredictable.

Jagged side of Nature, the discontinuous,

Science obsessed with the other side of Nature, the predictable, deterministic, lawful and orderly side especially in

Ecology - unpredicable wild flucuation

Arrthyrias

Turbent sea and atmosphere,

Pathologies monsters…

Geologists

Electronic circuits

chemical reactions

30 years

Strange connections

Heart rate variability, structures reminiscent of the whole.

Rules of chaos turned out to be universe.

Turbulence annoying in science.

We know equations of turbulence, but we still do

Leornardo , swirls within swirls

Laws of chaos intersect all disciplines.

What is Chaos - Paradoxical state , unpredictable, but on the other hand.

Deterministic - future is determined by the present.

Only one possible future.

Double pendulum newtons laws of motion.

Small angles

Large angles unpredictable.

Chaos

1) Breaks a lot of the rules of convential science by asking unusual questions. Everyday scale of normal life, not unusual regimes of small and fast.

2) Chaos takes the focus off the laws of nature and shifts it onto their consequences. Goal of physics - Find the new laws, the fundamental laws.

There is another game… Having found the laws, what the consequences of implications.

3) Way it uses the computer, not just a number cruncher.

An intuition telescope.

4) Emphasizes a different side of nature.

Not reductionism, take a problem that is hard and reduce it by breaking it up into smaller parts, try to analyze each part separately and then that should be easier, then put them back together. (Taylor Series).

Some problems do not permit reductionism, that is if you break them up into parts, you lose something essential. There are some systems that the interaction between the parts creates something that the whole is greater than the sum.

That is where there are cooperative effects taking place or some kind of interference.

In systems like that we have to find a way to do scientific holism to go from the parts to the whole.

Rigorous scientific.

5) Chaos is radically interdisciplinary … Usually walls between disciplines.

Makes a lot of progress by specializing.

Economist and biologists and physicists and mathematician.

Astronomy, zoology, the arts, commerce, humanities, internet, medicine, all of it. Condensed matter physics, population biology.

6) Chaos paints a topsy turvy picture of the world. We thought Simple laws lead to simple consequences. Simple system can show complex behavior.

Very complex things can have simple patterns

7) The change in thinking came suddenly.

Pictures can be much more important then formulas.

Visualizing in pictures.

Chaos is the science of how things change.

Purely mathematical side of chaos.

Isaac Newton gave a view of the universe so regular and so orderly that it seemed to outlaw chaos once and for all.

200 years later a chink in Newtons armor.

Henri Poincare… Horrifying picture.

Forgotten for over 70 years.

Ed Lorenz Butterfly effect .. no effect another 10 years.

Fractals shapes whose structures repeat ad-infinitum like the mandelbrot set.

Tiniest parts look like whole. Fractal structure breaks down in a real system, eventually branches to twigs.

Fractals are the remnants of chaos, the footprints that chaos leaves behind.

Vision - cancer to the mystery of consciousness.

## Amazing Mandelbrot Zoom - Comes from a simple equation!

The Equation

The equation of the Mandelbrot Set is really one of the simplest equations that you can write down. In fact, it is even simpler than Einstein’s equation e = mc2 which has three terms (E, M, and C) whereas the equation Z = Z2 + C only has two terms (Z and C).

You will also notice (in the case of the Mandelbrot Set equation)… that Z is on both sides of the equation. What this means is that the output of the EQUATION… is being fed back INTO the EQUATION… thus setting up a positive feedback loop or system. It is this feedback system that gives rise the endless variety of forms and images that I will be presenting to you.

The Mandelbrot Set has been described as the most complex object in mathematics. It has been proven to be the absolute maximum space filling curve possible in 2+ dimensions. It is said that, if its boundary were even one QUANTA more curved inward on itself… … it would HAVE TO overlap thus popping into the third dimension.

The equation of the Mandelbrot Set is really one of the simplest equations that you can write down. In fact, it is even simpler than Einstein’s equation e = mc2 which has three terms (E, M, and C) whereas the equation Z = Z2 + C only has two terms (Z and C).

You will also notice (in the case of the Mandelbrot Set equation)… that Z is on both sides of the equation. What this means is that the output of the EQUATION… is being fed back INTO the EQUATION… thus setting up a positive feedback loop or system. It is this feedback system that gives rise the endless variety of forms and images that I will be presenting to you.

The Mandelbrot Set has been described as the most complex object in mathematics. It has been proven to be the absolute maximum space filling curve possible in 2+ dimensions. It is said that, if its boundary were even one QUANTA more curved inward on itself… … it would HAVE TO overlap thus popping into the third dimension.