23 September 2016
Why everybody should know math
What is the story here?
- 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
Mathematics is not about numbers, equations, computations or algorithms: it’s about understanding
William Paul Thurston (1946 – 2012), American mathematician
The only way to learn mathematics is to do mathematics
Paul Halmos (1916 – 2006) Hungarian-born American mathematician
Math is not Everywhere
- [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
From Big Pyramids …
- 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
… to Big Data
- 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”
How do we get knowledge?
Science: knowledge creation
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
The Scientific Method
Software comes and goes
Math is forever
Software changes every ~5 years
Math last longer
- Computers alone do not solve problems
- Mathematics solves problems
- Then computers do it faster
Models
All models are wrong …
… but some are useful
“But math is hard…”
Well… it depends
3 x 4
3 x 4 + 5
34 x 45
345 x 456
We have two brains
Two systems of thinking
Daniel Kahneman, 2002 Nobel Memorial Prize in Economic Sciences
Two systems of thinking
System 1
Fast
- instinctive
- emotional
- automatic
- cheap
System 2
Slow
- deliberate
- rational
- intentional
- expensive
The priority of our organism is
- 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
Doing math is like running 🏃🏻
- It requires energy and willpower
- Everybody can run 10K … if trained correctly
