If the universe was infinite, everything in it would repeat after a certain point.
50% of grade are open-ended questions
50% exercises
about 125-150 hours of study for this course.
No questions unanswered by week 12 in the work sheet.
Mechanics: a part of physics.
Core: Newtonian mechanics
To do: practice, exercises and online simulations to get a feel for what students in the sciences tend to get.
Also: history of the philosophy related to the development of newtonian mechanics: Newton’s mechanics (not the same as newtonian)
Kinematics and Dynamics.
Kinematics: looking at how things move.
Dynamics: Explaining why motion happens.
Dilthey: Erklaren vs. Verstehen
Windelband: Sciences study Patterns and Humanities study Exceptions
The term liberal arts come from late roman times.
The Trivium and the Quadtrivium.
The Trivium:
Grammar
Dialectics (Logic)
Rhetoric
Quadtrivium:
Arithmetic (Numbers)
Geometry (Numbers in space)
Astronomy (Numbers in motion)
Harmonics (Numbers in time)
→ Studia humanitatis in 14:th century
Explicit distinction between humanities and natural sciences in 17:th century
”Two proper cultures” The Two cultures by Snow 20:th century.
The sciences seem to work according to the Hypothetico-deductive method (Cyclical method of science.
It mixes theoretical data with experimental data, and in the end the experimental data always overpowers the theory.
This can be traced back to Plato and the Middle Ages.
In modern science 17:th c.: Christiaan Huygens standardised
Whewell and J.S. Mill standardised further.
Jean Nicod (1924)
It looks quite similar to the Hermeneutic circle, however, this seems to deal with meaning rather than purely empirical phenomena.
Mathematics is the science of patterns which humans care for
Patterns in the natural world: the natural sciences
There seems to be a kind of proto-mathematical abilities in many animals that are needed for survival; there seems to be a kind of culture of mathematics in some of them, but not as clearly outlined as in humans.
Similarly so in human infants: before they are verbal, if something is more surprising, children will look at that longer, especially in regards to shapes.
This research was summarised by Stanislas Dehaene in The Number Sense.
There seems to be a greater appreciation for mathematical reserach, differently from the rote memorisation of school of math.
Mathematics is about exploration, and furthermore a collective endeavour. It is common work against ignorance and what we do not yet know.
Mathematics for Human Flourishing by Francis Su. Mathematics as awy to let people develop their virtues.
Mathematics is needed in society for people to live well.
The book includes a correspondence with the writer and a man in prison, beautiful.
”Just as humans are endowed with an ability to dance and play music (even if education too often crushes this out of us), so we have innate form-making and pattern-playing proclivities- Sea slugs, sound waves and falcons do mathematics; islamic mosaicists and african architects do it too. So can you.” (That last part kinda weird ngl, of course they do lol)
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Margaret Wertheim.
”Math is hard on the ego because, until you solve a problem, you feel profoundly ignorant and slow. Then, you get like 30 econds of the very austere pleasure of insight before everything looks obvious in retrospect and you are humbled again by the thought that you are foolish for not having seen it all along. To make progress, you have to find a way to embrace those 30 seconds and not worry about the countless painful moments when it all feels impossible and inscrutable.”