- Why math?
- Descriptive statistics: simple models
- Linear models
- Introduction to
*Probabilities* - Statistical inference

23 September 2016

- Why math?
- Descriptive statistics: simple models
- Linear models
- Introduction to
*Probabilities* - Statistical inference

- To understand the story we need to know the language
- Without the language we only see the pictures and try to guess the meaning
- “The laws of Nature are written in the language of mathematics”

The universe […] cannot be understood unless one first learns […] the language and interpret the characters in which it is written. It is written in the language of mathematics, […] without these, one is wandering around in a dark labyrinth.

*Galileo Galilei (1564 – 1642),* *Italian astronomer, physicist, engineer, philosopher, and mathematician*

Mathematicsis not about numbers, equations, computations or algorithms: it’s aboutunderstanding

*William Paul Thurston (1946 – 2012),* *American mathematician*

The only way to

is tolearnmathematicsdomathematics

*Paul Halmos (1916 – 2006)* *Hungarian-born American mathematician*

- [Historically] mathematics that makes the most difference to society has been the province of […] few
- Societies have valued and cultivated math not because it is everywhere and for everyone but because it is difficult and exclusive
- […] elite mathematics today […] remains a discipline that vests special authority in those who […] are already among our society’s most powerful

- Political power in ancient Egypt was based on the “god” status of the pharaoh
- He showed his power by
*ordering*the Nile to grow - It worked because he had a
*model*of the seasons - Today CEOs have immense power because they have
*models*of people’s behavior - “Knowledge is Power”

- Optical illusions: which blue circle is bigger?
- Dreams
- Incomplete information: the Earth is flat

We cannot trust 100% our senses

- Poster child: Aristotle
- We are bad at generalizations

We combine observations and reasoning

- We find
*patterns*in observations - We describe patterns and relationships with a
*model* - Many models are possible
- Discard models that do not match evidence
- Prefer simpler models
*Occam’s razor*

- We
*abstract*the question - We
*model*the relationships - We
*solve*the model (using computers) - We
*interpret*the solution back into biology

Software changes every ~5 years

Models last longer

… but some are useful

Well… it depends

3 x 4

3 x 4 + 5

34 x 45

345 x 456

Daniel Kahneman, 2002 Nobel Memorial Prize in Economic Sciences

**Fast**

- instinctive
- emotional
- automatic
*cheap*

**Slow**

- deliberate
- rational
- intentional
*expensive*

- Survival
- Save energy

So *System 1* is the default mode

Most of the time we use the *cheap* intuitive system

*Rational thinking (i.e. math) is not spontaneous*

- It requires energy and willpower
- Everybody can run 10K … if trained correctly