**Math. In Real Life.**

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.

Thanks.

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%.

Wenli Dickinson

ToK Presentation

Objectivity?

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

Perception

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?

Human Sciences

No laws, only trends

But, patterns in social data

Other Applications

international events—the collapse of the USSR...future relations with the Middle East?

Known Unknowns: Zombie Apocalypse!

Natural Sciences?

Objectivity

Relationship with math

less room for error

underlying laws

less affected by things like Cassandra Paradox

Unanswered Questions

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!

Other Influences

Reputation of the statistician

example: credit-raters

Political Climate

example: Laplace

Personal Motives: Entertainment

Money

Ignorance: tests vs. probability

Emotion: Level of Confidence

Language: wording of prediction

To what extent are mathematical models effective in predicting outcomes?

Natural Sciences

More objectivity-

Discovery of laws

Quantitative data: discrete or continuous

Bibliography

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)

Examples

regressions of data points

algorithms

Bayes theorem

Applications:

Human Sciences

Natural Sciences

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)

sample size

sources of data: empirical or a priori?

the illusion of patterns

Advantage: manipulative

Can you quantify everything? How do you assign variables?

Probability issues:risks versus uncertainty

Magnitude of error

Emotion-intuition

no data overload or complexity

personal motives skewing gut reaction

History

past isn't always indicative of future

More qualitative data

Politics: political predictions are about as accurate as guessing randomly (Silver 50)

Economy

trends = quantifiable

collective human behavior = ?

Cassandra Paradox

Natural vs. Artificial Trends

Chaos Theory and the Butterfly Effect

dynamic system = (errors)!

seismology = statistical

Counter

Arguments

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.)**