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thinking cards #182

Closed ajschumacher closed 3 years ago

ajschumacher commented 4 years ago

(original content moved to a child comment)

ajschumacher commented 4 years ago

Imagine the end

What would a solution look like? How would you know you'd succeeded? (Would you be happy?)

❗️

When stuck I often ask myself, "If I had a solution, what would it look like?" This tends to sharpen up the approach, and may reveal new ways of looking at the problem you had subconsciously ignored but now see should not be excluded. What must the solution involve? Are there conservation laws which must apply? Is there some symmetry? How does each assumption enter into the solution, and is each one really necessary? Have you recognized all the relevant factors?

Hamming, The Art of Doing Science and Engineering, page 327

dimensionality analysis?

Begin with the end in mind? Imagine the end?

Earlier titles: "Understand the solution," "Characterize solutions"

how big (or long) does the final product need to be? https://vasilishynkarenka.com/the-writing-matrix/ what are the artifacts that you'll have at the end? (what are the deliverables?)

not imagining in the sense of The Secret, probably...

ajschumacher commented 4 years ago

Focus

Sometimes you need to work harder, not smarter. Whether it's a 25-minute pomodoro or the next month, stop looking for an easy answer and give the problem the attention it deserves.

...saturate the subconscious with the problem, try to not think seriously about anything else for hours, days, or even weeks, and thus the subconscious ... is left with only the problem to mull over. We simply deprive it of all else as best we can! ... In a way, I am repeating Pasteur, "Luck favors the prepared mind." You prepare your mind for success "by thinking on it constantly" (Newton), and occasionally you are lucky.

Hamming, 328

Earlier title: "Do the work"

"It's not that I'm so smart, it's just that I stay with problems longer." Albert Einstein

https://quoteinvestigator.com/2012/07/21/luck-hard-work/ "I’m a Great Believer in Luck. The Harder I Work, the More Luck I Have"

https://quoteinvestigator.com/2010/07/14/luck/ "The Harder I Practice, the Luckier I Get"

But:

If Edison had a needle to find in a haystack, he would proceed at once with the diligence of the bee to examine straw after straw until he found the object of his search. … I was a sorry witness of such doings, knowing that a little theory and calculation would have saved him ninety per cent of his labor. (Tesla, New York Times (19 October 1931))

https://en.wikiquote.org/wiki/Nikola_Tesla and see also https://vasilishynkarenka.com/the-writing-matrix/ which recommends burning the hay

ajschumacher commented 4 years ago

Relax

Give your brain a chance to surprise you. Take a walk. Daydream. Take a micronap. Let your brain work with what it has, without giving it more inputs or directions.

https://www.coursera.org/learn/learning-how-to-learn/lecture/GVacn/using-the-focused-and-diffuse-modes-or-a-little-dali-will-do-you Dali/Edison sit in chair with key/ball bearings and drift off until dropping, then wake and notice your half-conscious thoughts (focuses/diffuse modes)

Original title: "Don't micromanage"

ajschumacher commented 4 years ago

Guess and go

Consider some next step, even if it's wrong, or just skip the next step. Work forward. What do you do next? Try doing it. What does it teach you about the problem?

❗️→

Earlier titles: "Move something forward," "Explore next steps (after a solution)," "Work next steps," "Work more steps," "Guess"

Earlier text: "Try advancing something, even if it's wrong. Get concrete. Get hands-on. What would the next steps be? When you guess and check, you encounter the path a solution will have to travel."

Pólya's "Let us teach guessing" https://vimeo.com/48768091 - fascinating bit where he stumbles around 40 minutes in... he could have handled it better

ajschumacher commented 4 years ago

Add randomness

Consider something you wouldn't otherwise: a random word, WikiPedia article, or the concept of randomness itself. Go to a museum, or a store. Whatever you find, relate it to your problem. What could it mean?

✱

also: is randomness fooling you? could the "problem" be just a random fluctuation?

ajschumacher commented 4 years ago

Talk to somebody

Have a conversation with someone. Or imagine a conversation with someone. What would you do here, Einstein? Or have a conversation with yourself. Ask questions. Try to answer them.

https://en.wikipedia.org/wiki/Dialectic "more dialectic, less debate" and: https://en.wikipedia.org/wiki/Dialectic#Socratic_method

"conversation" with somebody else (or yourself)

ajschumacher commented 4 years ago

Make a picture

It says picture, but should include any different representation.

Re-state the problem. Draw a picture. Make a diagram. Sketch a plot. Write an equation.

"Changing the representation of a problem often makes it easier to address or inspires new ideas that were not available in an old representation. In physics, switching between Newtonian and Lagrangian mechanics can make problems much easier. In evolutionary biology, switching between inclusive fitness and multilevel selection sheds new light on old models. And in statistics, switching between Bayesian and non-Bayesian representations often teaches us new things about both approaches." (page 50, Richard McElreath, Statistical Rethinking)

"As always, it can be easier to see what's going on with the math if we make the numbers small enough that we can draw pictures." (page 258, Ellenberg)

Old titles: "Make a picture," "Make a new representation," "Make another representation," "Make a representation"

"When Feynman was once asked how he developed his legendary ability to solve problems so quickly, he said that it was because he modeled those problems in a multitude of ways, which is to say he looked at them from different perspectives." (page 125, Bad Choices)

Maybe split this into two: change the physical medium / change the representation

https://en.wikipedia.org/wiki/Mind_map

ajschumacher commented 4 years ago

Understand the problem

Reconsider exactly what you're working on. Is the phrasing of the problem limiting solutions more than is necessary?

❓

https://en.wikipedia.org/wiki/How_to_Solve_It

Pragmatic Programmer 2nd ed, page 91, "Tip 31: Failing Test Before Fixing Code" - hmm actually that relates to understanding the problem, I think...

ajschumacher commented 4 years ago

Work backward

Assume you have a solution. How would it come to be? What would immediately lead to it?

←❗️

Lateral Thinking page 181: working backward from the solution

ajschumacher commented 4 years ago

Break it up

Turn a big problem into multiple small problems. Find an initial step that will make some progress.

❓→→→→→❗️
ajschumacher commented 4 years ago

Find checks

If you had a solution, how would you know that it's a good solution? What would be the "check" in a "guess and check" approach?

❗️✅❓

Old title: "Develop verification"

connect: writing tests, TDD

ajschumacher commented 4 years ago

Find similar problems

Do you know a related problem? What have others done in similar situations? How is a similar problem solved in nature, or in another field?

Old title: "Find a similar problem"

ajschumacher commented 4 years ago

Make a list

What are all the options? Consider more possibilities.

ajschumacher commented 4 years ago

Simplify

"A basic rule of mathematical life: if the universe hands you a hard problem, try to solve an easier one instead, and hope the simple version is close enough to the original problem that the universe doesn't object." (page 35, Ellenberg)

"When you're faced with a math problem you don't know how to do, you've got two basic options. You can make the problem easier, or you can make it harder." (page 218, Ellenberg)

Earlier title: "Simplify the problem"

ajschumacher commented 4 years ago

Consider special cases

Are there some specific forms of the problem that are more tractable or help with understanding? Can you extend a method based on these?

(This is meant to include induction.)

ajschumacher commented 4 years ago

Use analogy

What else is this like?

"We reason mainly by analogy. But it is curious that a valuable analogy need not be close —it need only be suggestive of what to do next. A dream by Kekulé about snakes biting their own tails suggested to him, when he awoke, the ring structure of carbon compounds! Many a poor analogy has proved useful in the hands of experts. This implies the analogy you use is only partial, and you need to be able to abandon it when it is pressed too far; analogies are seldom so perfect that every detail in one situation exactly matches those of the other." (Hamming, 329)

Old title: "Make an analogy," "Make comparisons"

ajschumacher commented 4 years ago

Explore origins

Why does this problem present itself? What are the causes? What led to it? Is it necessary, or could it have been avoided? Do the problem's origins suggest possible solutions?

Old title: "Explore the problem's genesis"

connect: root cause analysis

ajschumacher commented 4 years ago

Generalize

The Inventor's Paradox: A specific problem may be harder to solve than a more general problem that includes the specific problem as a special case.

"The more ambitious plan may have more chances of success … provided it is not based on a mere pretension but on some vision of the things beyond those immediately present." (Polya, https://en.wikipedia.org/wiki/Inventor%27s_paradox)

Earlier title: "Generalize the problem"

ajschumacher commented 4 years ago

Eliminate possibilities

What can you be sure isn't a solution?

ajschumacher commented 4 years ago

Consider extremes

What is something in your problem disappeared, or was huge?

"Here's an old mathematician's trick that makes the picture perfectly clear: set some variables to zero." (Ellenberg, pages 6-7)

ajschumacher commented 4 years ago

Think beyond the solution

If you had a solution, what would you do next? How does this step fit into your ideas for where you want to go?

ajschumacher commented 4 years ago

Flip it

How might you achieve the opposite of your goal? Are there other reversals or inversions that might be illuminating?

Original title: "Reverse"

Inspired by https://planspace.org/20200523-peopleware_productive_projects_and_teams/

ajschumacher commented 4 years ago

Change viewpoints

How does this look from different perspectives? How do different people, pieces, places see the problem?

Inspired by "immersion" in https://planspace.org/20200523-peopleware_productive_projects_and_teams/

Anyone who’s read Kahneman knows about the dangers of the inside view, making decisions from within your own perspective, your own mental models, and your own beliefs. That’s where the cognitive bias lives. The antidote to the inside view is the outside view, what is true of the world independent of your own perspective or the way other people would view the problem you’re considering. (from a Farnam Street email)

refing https://en.wikipedia.org/wiki/Reference_class_forecasting, it's largely about comparing to other similar cases, without thinking that your case is special/different

ajschumacher commented 4 years ago

Check assumptions

"What assumptions are you making? And are they justified?" (page 7, Ellenberg, How Not to Be Wrong)

also about what you assume is the answer. Daniel Kahneman wrote in Thinking, Fast and Slow (quoted in https://fs.blog/2015/05/inside-view-michael-mauboussin/)

A remarkable aspect of your mental life is that you are rarely stumped … The normal state of your mind is that you have intuitive feelings and opinions about almost everything that comes your way. You like or dislike people long before you know much about them; you trust or distrust strangers without knowing why; you feel that an enterprise is bound to succeed without analyzing it.

also include in here: considering new ways of doing things that you already have a way of doing (compare to knowing one way to drive to work, for example)

exploration/exploitation

ajschumacher commented 4 years ago

Extract the essence

Something about turning it into a a simpler structure, like: a sentence diagram, an outline, a syllogism, etc...

Maybe this belongs in "Understand the question" or similar?

Maybe "analyze" the essence?

ajschumacher commented 4 years ago

Stay Positive

Something about growth mindset, not taking it personally when you get stuck, it's a challenge that can be overcome through hard work, problems don't have to be solved quickly, etc.

not a problem (not a bad thing) but an opportunity, etc.

"Being a problem solver isn't just an ability; it's a whole mind-set, one that drives people to bring out the best in themselves and to shape the world in a positive way." (page ix, Watanabe's Problem Solving 101)

"Problem solving isn't a talent limited to the lucky few. It's actually a skill and a habit that you can learn." (page 4, ibid)

ajschumacher commented 4 years ago

drafting cards... cards_v2.docx

ajschumacher commented 3 years ago

Jeannette Wing's "Computational Thinking" https://www.cs.cmu.edu/~15110-s13/Wing06-ct.pdf has some ideas that might be incorporated...

ajschumacher commented 3 years ago

Is guess and check a separate thing? Or "generate and check" (Minsky in Society of Mind)

ajschumacher commented 3 years ago

Do an experiment

Studies like art

without a control group is fine for many "experiments"

if using controls, connect to randomness for RCT (instead of matched groups)

ajschumacher commented 3 years ago

decompose/recompose

Watanabe's logic tree, also some Di Bonno stuff...

ajschumacher commented 3 years ago

Build a Model of the System (Pragmatic Programmer 20th anniversary ed, page 67)

"Model building can be both creative and useful in the long term. Often, the process of building the model leads to discoveries of underlying patterns and processes that weren't apparent on the surface." (page 67)

"During the calculation phase, you get answers that seem strange. Don't be too quick to dismiss them. If your arithmetic is correct, your understanding of the problem or your model is probably wrong. This is valuable information." (page 68)

ajschumacher commented 3 years ago

Try a different tool

Get out of your head: Thinking is good - don’t stop - but the mind alone is less than the mind plus

Don’t stop thinking: not about procrastination; don’t wait to be done before the next idea

ajschumacher commented 3 years ago

really just math stuff, but still: https://artofproblemsolving.com/

ajschumacher commented 3 years ago

check biases...

Diana Fleischman http://nautil.us/blog/the-dark-side-of-smart

Human intelligence is incredibly useful but it doesn’t safeguard you against having false beliefs, because that’s not what intelligence is for. Intelligence is associated with coming up with more convincing bullshit and with being a better liar, but not associated with a better ability to recognize one’s own bias. Unfortunately, intelligence has very little influence on your ability to rationally evaluate your own beliefs, or undermine what’s called “myside bias.”

ajschumacher commented 3 years ago

problem-solving connected to http://www.criticalthinking.org/...

https://www.readingrockets.org/article/critical-thinking-why-it-so-hard-teach

a particular kind of critical thinking that has been studied extensively: problem solving

"surface structure" vs. "deep structure"

two factors are especially relevant for educators: familiarity with a problem's deep structure and the knowledge that one should look for a deep structure

Cognitive scientists refer to these maxims as metacognitive strategies. They are little chunks of knowledge — like "look for a problem's deep structure" or "consider both sides of an issue" — that students can learn and then use to steer their thoughts in more productive directions.

Students learn to avoid biases that most of us are prey to when we think, such as settling on the first conclusion that seems reasonable, only seeking evidence that confirms one's beliefs, ignoring countervailing evidence, overconfidence, and others.

"Teaching content alone is not likely to lead to proficiency in science, nor is engaging in inquiry experiences devoid of meaningful science content."

First, critical thinking (as well as scientific thinking and other domain-based thinking) is not a skill. There is not a set of critical thinking skills that can be acquired and deployed regardless of context. Second, there are metacognitive strategies that, once learned, make critical thinking more likely. Third, the ability to think critically (to actually do what the metacognitive strategies call for) depends on domain knowledge and practice.

maybe in an introduction: cards are like training wheels, or flash cards... you won't need to look at them, after a while - connects to learning content in general: you want it in your head; being able to look it up is not enough

ooh! this could be its own card! "choose the right strategy" hmm they should be named... strategies? techniques? cards?

ajschumacher commented 3 years ago

Learn more

informed by Watanabe's "Problem Solving 101" and other sources that emphasize you can't solve problems without content knowledge, like https://www.readingrockets.org/article/critical-thinking-why-it-so-hard-teach (notes above)

"People often fall into the trap of collecting information and conducting analyses just for the sake of doing them." (page 38, Watanabe's Problem Solving 101)

"If you start collecting and analyzing data without first clarifying the question you are trying to answer, you're probably doing yourself more harm than good." (page 39, ibid)

That Pasteur quote? (included above...)

be curious: https://hbr.org/2018/09/curiosity The Business Case for Curiosity by Francesca Gino

The impulse to seek new information and experiences and explore novel possibilities is a basic human attribute.

When our curiosity is triggered, we think more deeply and rationally about decisions and come up with more-creative solutions.

When we are curious, we view tough situations more creatively.

Reading books unrelated to one’s own field and exploring questions just for the sake of knowing the answers are indications of curiosity.

When we accept that our own knowledge is finite, we are more apt to see that the world is always changing and that the future will diverge from the present.

Writers and directors at Pixar are trained in a technique called “plussing,” which involves building on ideas without using judgmental language.

“It’s better to train and have them leave than not to train and have them stay,” (Gail Jackson)

Toyota’s 5 Whys approach

and (same link):

The Five Dimensions of Curiosity Todd B. KashdanDavid J. DisabatoFallon R. GoodmanCarl Naughton

Building on Berlyne’s insights, in 1994 George Loewenstein, of Carnegie Mellon University, proposed the “information gap” theory. He posited that people become curious upon realizing that they lack desired knowledge; this creates an aversive feeling of uncertainty, which compels them to uncover the missing information.

focus on asking the right question...

old title: Get more information

ajschumacher commented 3 years ago

the winding path (directed walk) image from the front of Hamming's book - could fit in something on taking small steps, or also in the initial section on mindset

also: "yes, and" or Pixar's "plussing" (from https://hbr.org/2018/09/curiosity) could be in mindset, or somewhere else on brainstorming, or reconsidering (maybe not assumptions, but something like that)

ajschumacher commented 3 years ago

No Starch publishes Scratch coding cards: https://nostarch.com/scratchcards3

and they're pretty up-front about writing with them: https://nostarch.com/writeforus

ajschumacher commented 3 years ago

Scratch strategies for getting unstuck: https://gettingunstuck.gse.harvard.edu/strategies

ajschumacher commented 3 years ago

"To know what you’re going to draw, you have to begin drawing" (Picasso)

https://www.brainpickings.org/2014/06/24/picasso-brassai-ideas-creativity/

ajschumacher commented 3 years ago

zoom in

zoom out

find a problem

The word problem has an off-putting connotation

lots of kinds of problems

It's okay to have many problems; nice to find good/interesting problems

nothing in life is humdrum (Bennett)

ajschumacher commented 3 years ago

What Would Somebody Else Do?

"One technique for fighting the feeling that you don't know what you're doing is to simply pretend that some expert out there knows exactly what to do, and that they're simply on vacation and you're temporarily subbing in for them. It's a great way to remove the personal stakes and give yourself permission to fail and learn." (page 116, Software Engineering at Google, written by Ben Collins-Sussman, ediged by Riona MacNamara)

ajschumacher commented 3 years ago

Consider quitting

ajschumacher commented 3 years ago

Original main issue content:

gathering good ideas, say from these:

It's a physical deck of cards, and you draw one and do whatever it says as a way of thinking about a topic/problem.

Some possibilities:

Lateral Thinking page 100: The 'Why' Technique

Lateral Thinking Page 215 label techniques:

Lateral Thinking page 137: Two unit division

Lateral Thinking Page 259: concept reuniting

Lateral Thinking Page 291 alternative functions, not just ways of carrying out a particular function - abstract the function from the design, rephrase the problem

ajschumacher commented 3 years ago

moved to https://github.com/ajschumacher/thinking_cards