good math

[ajschumacher]

pulled from Mindstorms notes:

thought: what do we expect to "make sense"? what are ways of making sense? spelling: broken but maybe historical? vs. math? etc.?

models "vs." abstract systems (make an abstract system and it's hard to avoid finding or thinking about something it maps onto)

idea: name things (useful for thinking; reason for notation)

idea: reasoning about quantification (universal, existence, etc.) (multiple choice rules is a toy application) (intro notation here) (people who speak in universals may not be concerned with the truth (see: On Bullshit))

what "method" is "play turtle"? p. 59

"experiment"? (when valuable? how to describe?)

components to favor modularity

and

state

p. 60

hierarchy, planning, debugging

p. 60

"The programmer is encouraged to study the bug rather than forget the error." p. 61

angle, controlled repetition, state-change operator p. 63

mathetic vs. mathematical p. 63

mathetic principle "Make sense of what you want to learn."

syntonic (Freud-y)

http://www.amazon.com/Mathematics-Plausible-Reasoning-Volume-Induction/dp/0691025096#productDescription_secondary_view_div_1451236901224

subproblems and averaging averages

idea: relative levels of trust; implicit assumptions (if what he said is true, then...) (related to quantification?)

"deductive principles such as transitivity, the conservations, the intuitive logic of classifications, and so on" p. 66

idea: debugging syllogisms (if conclusion is wrong, then what of the assumptions and rule?)

idea: those "sufficient" questions?

idea: re: combinatorial thinking: knowing all the possible states? "is, isn't , or some assumption is wrong"?

Recursion quote bottom p. 71

idea: googling/research as a kind of debugging

quote middle p. 74

quote bottom p. 76 yesss

Why do constructivists write books?

Important component quote mid p. 96

child as epistemologist (throughout)

formalism match bottom p. 99

programming as choosing formalisms

programming as science (choosing hypotheses)

"experimental programming"

"written his program " quote top p. 102

structured programming

cool juggling instructions around p. 111

quote end first paragraph p. 113

same place on p. 115

quote bridging from 116

p. 120 relate to known, make own

"explorable and manipulator environment " p. 129

bridge from 139

2-body/1-body p. 142

keep intuition, don't go all equations (dissociated) p. 144

procedural thinking p. 155

studying learning 2nd para 158

bike quote p. 159 end first paragraph

mother structures bourbaki p. 160

"transitional objects"

ps qs quote 2nd paragraph p. 172

[ajschumacher]

that card-flipping experiment about what you check could be interesting here

[ajschumacher]

numbers as interface - miles per gallon vs. gallons per mile

miles per gallon - gallons for 100 miles 10 - 10 20 - 5 50 - 2 etc.

easier to see some things some ways

[ajschumacher]

Mindstorms write-up is largely here: https://planspace.org/20160327-mindstorms/

other ideas noted in vis_book/