23 September 2016

- 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 big companies have immense power because they have
*models*of people’s behavior - New technology reduced the price of experiments. It is cheap to have Big Data in Science
- “Knowledge is Power”

We combine observations and reasoning

- We find
*patterns*in observations - We describe patterns and relationships with a
*model* - We use the model to make
*predictions* - We test the predictions with
*experiments* - We
*interpret*the model back into biology

Software changes every ~5 years

Math last longer

- Computers alone do not solve problems
- Mathematics solves problems
- Then computers do it faster

… 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