Modern Models in the Social and Biological Sciences Dan Teague NC School of Science and Mathematics teague@ncssm.edu.
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Modern Models in the Social and Biological
Sciences
Dan TeagueNC School of Science and Mathematics
teague@ncssm.edu
New Models/New Mathematics1985 – 2015 – 2045
• Why is the content (and intent) of the mathematics curriculum what it is?
• If the mathematics curriculum is designed to focus on the methods and techniques for the current models of our world, will the curriculum change when those models change?
New Models/New Mathematics1985 – 2015 – 2045
Why are Latin and Mathematics the
only subjects which appear to have
been unaffected by developments
in the 20th century?
Which good mathematics students
are being left out of the math
pipeline, and why do they leave?
What was Hot in 1985?
What Happened to Fractals?
Mandelbrot’s Goal“In the whole of science, the whole of mathematics, smoothness was everything. What I did was to open up roughness for investigation.”
Fractal Geometry is the true
geometry of the natural world.
Air view of Nördlingen, an old walled city on the "Romantische Strasse" (Romantic Road) in Southern
Germany.
Alpo Dog Food
• An organism’s metabolic rate is the rate at which its cells convert nutrients to energy.
• The organism gives off heat at the same rate as a by product.
Max Rubner’s Suface Hypothesis (1880’s)
In order to safely radiate the heat that is generated in the metabolic process through the boundary (skin), the metabolic rate should scale with body mass in the same way as volume and surface area.
So, the metabolic rate should scale with body mass to the 2/3 power. Hence, the Alpo bag.
Kleiber’s Law (1937)
Space Filling Curve
Brown, Enquist, WestMetabolic Scaling Theory
Life? Hunting the Hidden Dimension
Game of Life
Cellular Automata led to Mathematica…
then what?
Cellular AutomataPeer Pressure
Each agent (cell) looks at their neighbors and decides what to do based on what their neighbors have decided to do.
This simple idea has led to a new and important area of mathematical modeling known as agent based models.
2-Dimensional Cellular Automata
“Standard” Neighborhoods
Schelling Segregation Model
David Batten, Discovering Artificial Economies, Westview Press, 2000.
The Cascade Begins
Thomas Schelling (2005 Nobel in Economics)
Phase Transition
I will if you will cascades…
Requires diversity of threshold values in the individual agents.
Imagine if everyone has a threshold of 4, what would happen.
You need at least one person with a threshold of 1, another with a threshold of 2, and several with a threshold of 3.
I will if you will…
• Revolutions - Moral Mondays• Acceptance of Innovations (Smart Phones, Electric Autos) (advantages of owning the first fax machine)
• Local Influence in TI vs Casio
Local Decisions Create Emergent Behavior
• Traffic
• Economy
• Immune System
• Consciousness
• Ant Colony Behavior
More is Different
Classical DE Models
dSS I
dtdI
S I Idt
dRR R F
dtdF
F R Fdt
Theoretical vs Actual
?
dSS I
dtdI
S I Idt
Agent-Based Predator-
Prey Model
Network as Cellular Automata
Network Model
If every vertex
connects to
every other vertex,
then we have the
classical Mass
Action or Mean Field model.
Fundamental Fact of Life in a Social Network
Your friends
have more friends
than you do.
Theoretical Results (YFHMFTYD)
Actual Results
Network Disease Models
Network MedicineNetwork of all known human diseases
Network Dynamics
Network Structure
Dynamics on Networks
Dynamics of Networks
If the Models Change, Does the Curriculum
Follow?
Wrong Optimization Model
• Teach as much as you can of subject A because this may be the last math course they take.
• Teach subject A in such a way that it is followed by B and C.
Modern Models in the Social and Biological
Sciences
Dan TeagueNC School of Science and Mathematics
teague@ncssm.edu
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