Comments on Methods

^z 21st May 2023 at 6:42am

11 Comments.

potential spectrum of "tools":

binary tools (true-or-false)
set tools (collections of stuff)
rank-ordered tools (priority lists without numbers — maybe "posets" = "partially-ordered sets" to a mathematician?)
numerical rating tools
numerical ratings with error-range tools
continuous variable tools
function tools (mappings aka relationships between entities, possibly continuous)
meta-function tools (tools that manipulate function tools)

– z 2017-04-04 14:12 UTC

xrefs to consider:

OnSharpness - list of "key elements of cleverness"
Category Theory Concepts - five principles of generalization

– z 2017-04-04 14:13 UTC

take-aways from Philosophy Tool Kit:

the best heuristics are at a sweet spot between abstraction and specificity
when you see The examine it and challenge the assumption that there is exactly one of something ... could there be many? could there be none? ... aka "Consider Alternative Hypotheses" to The
examine extreme cases ("edge cases") ... and consider self-reference cases, and infinite regression
assume the opposite and look for a contradiction
treat analogies with skepticism

– z 2017-04-05 13:40 UTC

some random quantitative mental tools ... starter set might include:

N! = how many ways there are to reorder N things
2^N = how many ways there are to pick a subset from among N things (including the empty set {} of course!)
N^1/2 = roughly the amount of variation to be expected among N events

refinement: P*(1-P)*N^1/2 * refinement: N^1/2 is 2 or 3 standard deviations or so, depending

some other quantitative concepts to sketch out:

scaling (how stuff grows or shrinks, like power laws or exponentially or whatever)
dimensional analysis (getting the physical units right)
probability & statistics

discrete and continuous probabilities * Bayes Rule * mean, variance & standard deviation, skew, kurtosis, ... * normal distribution (Gaussian aka bell-shaped curve) * other distributions (Poisson, Binomial, ...)

* moments of a distribution

power series expansions
calculus concepts

functions (and functions of functions) * limits * infinities and infinitesimals * continuity and discontinuity * differentiation (rates of change) and integration (areas under curves)

* ...

– z 2017-04-05 14:08 UTC

EpistemologicalEnginerooms :

Probability & Statistics — discrete & continuous probability distributions, means, standard deviations, dependent & independent variables, conditional probabilities, and error propagation
Combinatorics — permutations, combinations, multivariate experiment design, clustering & similarity metrics, and heuristics for scenario generation
Logic — deduction, induction, syllogisms, fuzzy logic, logic programming, and idea-mapping techniques to assist in structured argumentation
Inverse Methods — reverse-engineering, matrix inversion, back-propagation, etc.; see Bypasses by Z. A. Melzak (enlightening reading on these and related topics at the graduate level ... but anyone should feel free to skip the equations and explore Melzak's ideas of metaphor and transformation in literature and language)
Curve-fitting — data modeling, error estimation, and key variable identification; see Mathematical Methods That [Usually] Work by Forman J. Acton (ideas on numerical methods, readable at the advanced undergraduate level, but with many nonmathematical parables of universal relevance)
Noise & Random Perturbations — power spectra, correlation functions, and pattern discovery in unclean data
Game Theory — from rock-paper-scissors to Mutual Assured Destruction (MAD), two-person zero-sum & beyond, prisoners dilemmas, minimax, etc.; see The Compleat Strategyst by John Williams (highly entertaining, with many stories and funny illustrations; needs only high-school math or less)
Information Theory — bits of data, entropy, & evidence; see The Recursive Universe by William Poundstone (fascinating popular-level exposition, with chapters on cellular automata, self-reproducing systems, and deep concepts of information)
Systems Analysis — sources, sinks, valves, delays, positive & negative feedback loops, attractors & instabilities, critical paths & chokepoints; see The Fifth Discipline by Peter Senge (a self-improvement and applied math short-course disguised as a business book ... powerful and important concepts presented in engaging fashion)

– z 2017-04-11 09:42 UTC

via Google metacog profile, from http://scholar.google.com/scholar_url?url=https://www.nesta.org.uk/sites/default/files/solved-making-case-collaborative-problem-solving.pdf&hl=en&sa=X&scisig=AAGBfm1ncYFo2X_GhDDIVrr7OKOWacPhlQ&nossl=1&oi=scholaralrt :

[PDF] Solved!

R Luckin, MC Baines, W Holmes - 2017

... It is therefore even more important for students to understand what they know and what
they don't know, to have excellent metacognitive awareness as well as subject
knowledge. Problem-based learning and e(i)nquiry-based learning ...

– zimm 2017-04-18 12:16 UTC

via Google metacog profile, from http://scholar.google.com/scholar_url?url=http://conservancy.umn.edu/bitstream/handle/11299/185599/Le_umn_0130E_17892.pdf%3Fsequence%3D1&isAllowed%3Dy&hl=en&sa=X&scisig=AAGBfm1rPfJMfz27j55NRctxe9PwxIpYdg&nossl=1&oi=scholaralrt

[PDF] Assessing the Development of Students' Statistical Thinking: An Exploratory Study

L Le - 2017

... One cognitive process that differs between experts and novices is the metacognitive skills that
they possess (Bransford et al., 2000). Metacognition refers to the ability to monitor and adapt
ones decisions while solving a problem. Experts have developed essential metacognitive. ...

– zimm 2017-04-18 12:17 UTC

some "Moves" to make in metacognition:

Zoom out! (look at things from a distant, large-scale, aggregated perspective)
Zoom in! (examine details, special cases, sub-divisions)
Rotate! (try to take a different viewpoint, turn your head, look at another side of the situation)
Hypothesize! (make up one or more new potential explanations, options, reasons)
Seek a refutation! (look for something that disproves a hypothesis)
...

– zimm 2017-04-21 17:35 UTC

add INFORMATION THEORY to the list!

specifically, the concept of Entropy as the sum over all possible i of the values p[i]*log(p[i]) ... see https://en.wikipedia.org/wiki/Entropy_(information_theory) etc.

– z 2017-04-27 00:38 UTC

Method Cards:

"Generate Futures" (2x2 Scenarios)
"Evaluate Hypotheses" (ACH)
"Map the Argument"
"Brainstorm Ideas"
"Look Back" (What If?)
"Imagine the Unlikely" (Low Probability High Impact)
...

– z 2017-06-25 09:20 UTC