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Transcript of TOK Presentation:
Background on Mathematical Models
Definition: an abstract model used to describe the behavior of a system (different from statistics)
Underlying Knowledge Issues
Keep Calm and ToK on.
Real Life Situation:
The Great Recession that began in 2008: Three major credit-rating agencies failed to accurately predict the likelihood of American debt going into default, estimating the risk being a mere 0.12% when it was actually closer to 28%.
Math mainly employs the use of REASON as a way of knowing = objective.
Adequacy of math?
Models by definition aren't reality
Pros and Cons of Using Other Wok & AoK
more concrete than abstract mathematical concepts
but not a lot of foresight
First, what is "effective?"
Calculating PROBABILITY vs. predicting actual OUTCOMES
When are mathematical models most effective, then?
No laws, only trends
But, patterns in social data
international events—the collapse of the USSR...future relations with the Middle East?
Known Unknowns: Zombie Apocalypse!
Relationship with math
less room for error
less affected by things like Cassandra Paradox
How do mathematical models relate to the arts? to ethics?
Our models become more accurate as we obtain more data over time. Will they ever be PERFECT since there is always more data we haven't accounted for—because it hasn't happened yet!
Reputation of the statistician
Personal Motives: Entertainment
Ignorance: tests vs. probability
Emotion: Level of Confidence
Language: wording of prediction
To what extent are mathematical models effective in predicting outcomes?
Discovery of laws
Quantitative data: discrete or continuous
Kaznatcheev, Artem. "Three Types of
Mathematical Models." Web log post. Theory Evolution and Games Group. Wordpress.com, 8 Sept. 2013. Web. 19 Nov. 2013.
Mlodinow, Leonard. The Drunkard's Walk: How
Randomness Rules Our Lives. New York: Pantheon, 2008. Print.
Munz, P., I. Hudea, J. Imad, and R.J. Smith."When
Zombies Attack! Mathematical Modelling of An Outbreak of Zombie Infection." Infections Disease Modelling Research Progress. Ed. Jean Michel. Tchuenche and Christinah Chiyaka. New York: Nova Science, 2009. 139. Print. Public Health in the 21st Century.
Silver, Nate. The Signal and the Noise: Why So Many
Predictions Fail—but Some Don't. New York: Penguin, 2012. Print.
Graph: population over time
blue = susceptables
red = zombies
("When Zombies Attack! 139)
regressions of data points
Probability-if situation is approximately ideal
Bernoulli's Golden Theorem
Outcomes-to learn more about our understanding of the issue
Flaws with the use of math/reason:
overfitting and underfitting data (Silver 163)
sources of data: empirical or a priori?
the illusion of patterns
Can you quantify everything? How do you assign variables?
Probability issues:risks versus uncertainty
Magnitude of error
no data overload or complexity
personal motives skewing gut reaction
past isn't always indicative of future
More qualitative data
Politics: political predictions are about as accurate as guessing randomly (Silver 50)
trends = quantifiable
collective human behavior = ?
Natural vs. Artificial Trends
Chaos Theory and the Butterfly Effect
dynamic system = (errors)!
seismology = statistical
Is it still a PREDICTION if there are underlying predetermining laws?
Accuracy—weather forecasting or economic predictions?
weather forecasting = combo of math and human judgment
Chaos Theory in human science(Mlodinow 194) = underlying laws?
(You'd better believe it.)