
The Science of Problem Solving - adbge
http://rs.io/2014/02/21/problem-solving.html
======
superflit
It seems a lot like what the Russian Scientist Altshuller [1] did and modeled
as TRIZ [2]

There is another one very useful scientist take on problem solving (more math
related) : Mr. Polya [3]

[1]
[http://www.amazon.com/s/?_encoding=UTF8&camp=1789&creative=3...](http://www.amazon.com/s/?_encoding=UTF8&camp=1789&creative=390957&field-
keywords=Altshuller&linkCode=ur2&tag=cid10-20&url=search-
alias%3Dstripbooks&linkId=HVGC6C2SAAGRO5NQ")

[2] [http://en.wikipedia.org/wiki/TRIZ](http://en.wikipedia.org/wiki/TRIZ)

[3]
[http://www.amazon.com/s/?_encoding=UTF8&camp=1789&creative=3...](http://www.amazon.com/s/?_encoding=UTF8&camp=1789&creative=390957&field-
keywords=polya&linkCode=ur2&tag=cid10-20&url=search-
alias%3Daps&linkId=RB5HW7HUQ4RARLOA)

~~~
yankoff
Altshuller is amazing, I'm surprised he is known outside of Russia though.

~~~
tomaskazemekas
Open Source TRIZ site has a collecion of freely available resourses on the
methodology of inventive problem solving.
[http://www.opensourcetriz.com/main/page_ebooks.html](http://www.opensourcetriz.com/main/page_ebooks.html)

------
b_emery
There is something haunting about Feynman's blackboard at the time of his
death. The text mentions one of the quotes, the other is "What I cannot
create, I do not understand" which I assume refers to his ability to create
the solution to a problem from scratch. His list of problems (and solutions?)
to learn is also there (non-linear chemical hydro!?). I wonder what he would
have accomplished given more time.

~~~
JadeNB
> The text mentions one of the quotes, the other is "What I cannot create, I
> do not understand" which I assume refers to his ability to create the
> solution to a problem from scratch.

Although I cannot speak to Feynman's mind, it is also possible that he was
referring to creating the _problem_. When someone poses you a problem, he is
asking you to think of it as _he_ does; but you might have more success by
figuring out why _you_ might be interested in the problem—a trick of which
Feynman was a master.

~~~
jimhefferon
In Gleick's book he mentions that, for instance, Feynman talked about
inventing his own notation for various mathematical operations when he was
young, and that the habit of thinking things through on his own, without
reference to other people's approaches, persisted throughout his career. You
see that in his famous _Lectures_ : he expressed disappointment that his
approach in the third book is the standard one, that he was not able to come
up with his own, because he must not understand it well enough.

------
scottndecker
Great article. Love that the author put some time into the research and links.

Bit on Practice also dovetails nicely with a post I wrote (much less
scientific in nature):

[http://scottndecker.com/blog/2014/04/25/Never-Solve-the-
Same...](http://scottndecker.com/blog/2014/04/25/Never-Solve-the-Same-Problem-
from-Scratch-Twice/)

------
henryw

      The very last line:
    

To improve problem solving, one should study solved problems, attack the
problem while in different moods, and try explaining the problem to others

    
    
      As recapped in bold at the end by the author:
    

Problem solving can be thought of as search on a graph.

Insight is distinguished by a change in problem representation.

Insight can be facilitated by active seeking of new problem representations
[ie drawwing, analogies]

Incubation [taking breaks during working] enhances problem solving ability.

A night’s sleep improves problem solving ability to a considerable degree.

Mind-wandering [ie low effort tasks] facilitates creativity.

[One] should study solved problems, attack the problem while in different
moods, and try explaining the problem to others

------
gumby
I am sorry to rain on one minor side point in a good essay. The divorce
complaint from Feynman's ex wife's was quite funny and made a great point in
the essay, but actually I don't think was interpreted correctly.

In the USA in the 1950s you couldn't have a no fault or non-acrimonious
divorce; one party had to be cruel or otherwise violate the contract (e.g.
have an affair), else marriage was for life.

So it was clear that they were making a fig leaf "complaint", and in the style
of Feynman (and I presume anyone who would marry him!) they made a joke of it.

~~~
oldbuzzard
I see this less as a joke and more of a sign of mutual respect...

Feynmann's womanizing was legendary[1]. The fact his wife chose to sue for
emotional estrangement instead of explicit acts is interesting. It suggests a
residual level of respect or at least a cynical quid pro quo...

[1] See
[http://tech.mit.edu/V119/N10/col10lipman.10c.html](http://tech.mit.edu/V119/N10/col10lipman.10c.html)
for a somewhat nuanced take on the issue... This was the first link I
googled... presumably there are other/better sources...

------
mathattack
Great article overall. I like the last line in the summation.

 _To improve problem solving, one should study solved problems, attack the
problem while in different moods, and try explaining the problem to others._

------
tothetop
Great insight in to problem solving. One thing I'm curious about is how
environment plays a role whether in a high or low stress work place or social
environment, etc.

~~~
duncanawoods
My response to this is that environment is a little like what the author
describes as mood. Different environments help frame problems in different
ways.

A high pressure environment might drive aggressive simplification, skipping
steps and question assumptions in order to side-step entire issues. It might
also accelerate the time taken to exhaust solutions and put the issue to one
side for background incubation.

A more relaxed environment might foster more creativity, more connection
making and a more playful approach bending and transforming concepts and
risking absurdity.

IMHO if you are really stuck on a problem then changing environments is one of
the tools to try to help unstick it.

------
shailesh
Well-thought and a fine read.

Re: sleep and moods, though a plausible idea, suffers from a tight binding
problem. This is _very_ costly in terms of time invested for reaping the
"aha!" moment.

I sat down to elaborate the reason and a possible solution, but the word count
went over 1100. So, here it is in all its glory:

[https://medium.com/@vidagdha/qualitative-improvement-for-
pro...](https://medium.com/@vidagdha/qualitative-improvement-for-problem-
solving-b9872fa2b07b)

Basically. Decouple. Please read through and feel free to comment.

~~~
shailesh
My earlier comment might seem off-putting, so here is the text of the article
linked in it, to provide a context for the discussion.

Robb Seaton has written an excellent, must read article on the “The Science of
Problem Solving.”

In the quest to optimize the process wherein the solver is happier most of the
time and is able to do it more quickly, I observed that the approach could be
further refined. We can and we should develop a better strategy.

So, here we go.

Key challenge \-------------

The article proposes two ideas: Leverage the sleep time for the incubation,
and Think about the problem in different moods

These ideas are plausible. However, they suffer from a steep cost in terms of
the time invested for reaping the “aha!” moment.

To discuss the reason and a possible solution, let us introduce a variable
called “protag,” short for the protagonist, so that we say that the “Protag
wants to solve the problem,” rather than, “We want to solve the problem of
improving the problem solving.”

Let’s begin analyzing the terrain. What are the minimum, always available
tools for the protag? The triplet: the body, the mind and the intellect.

A few definitions \----------------- What is sleep? A tight binding of the
body and the mind. What is a mood (happy or unhappy etc.)? A tight binding of
the mind and the intellect. We can get rid of a minor lemma: the necessity of
the sleep. We agree it to be a necessity for obvious reasons. We acknowledge
it and leave it because we want to explore another interesting dimension of
this “problem solving” hypergraph.

Formulating the conjecture \-------------------------- Could there be a more
effective approach, in which, lesser cost in terms of time and physical energy
is spent, to improve the problem solving ability?

Search for an answer \-------------------- Let’s model the problem in terms of
protag’s mind’s quest to walk out of the maze. The darker the maze, the
scarier the problem.

For the mind trying to navigate through the dark maze, the intellect is the
torch that illuminates. The brighter the torch, the easier to avoid obstacles
and hence, the faster the solution. The candela of this torch depends on the
mind’s ability to recall a specific pattern.

Since the mind can travel faster than light, the protag can optimize the
effort required to boost the candela simply by a continual build-up of the
pattern library. In other words, the protag need not worry about the mind
facing the heavy burden of carrying the library in one hand and the torch in
the other.

Why do the bindings matter? \--------------------------- During the
navigation, the protag’s mind has reached a door it wants to unlock. It has
summoned every single pattern to be applied for unlocking it. In the process,
the mind (as algorithm) has exhausted the problem space. How does it react?

It does not know how to react!

In practice, the mind slips into the library of dark patterns and picks up the
thing that is on the top of the stack.

It can be a feeling of fatigue, or it can be a tantrum.

The mind yells and throws an egg into an electric fan. Meanwhile, the poor
protag, suffering from a tight coupling of the mind and the intellect as well
as that of the body and the mind, might actually: throw an egg into an
electric fan, take a drink, sleep, take a shower, or take a stroll in the park
— we all get the idea.

Clearly, to bring in a qualitative improvement, the protag ought to work on
actively decoupling the body, mind and the intellect, before and during
problem solving.

It can start with a realization, that “I am not my mind!” just as “I am not my
pen!” Once this realization is internalized, the protag can liberate negative
feelings (like “I am exhausted,” “I am angry”) from the stable of dark
patterns; treating them more as blinking LEDs indicating exhaustion of the
pattern library, rather than “dark walls.”

The protag can then say, “Oh, this LED says that I need to add more patterns
in the library, so how about applying the intellect for synthesis of existing
patterns. But, exactly how am I supposed to compose them?”

Good question.

By now, must have noticed that, instead of the mind leading the protag to a
solution, what is happening is quite the other way? On a happiness scale, this
approach looks better. May be, even wiser. Enriching the library of patterns

We might say that the process for understanding is akin to parsing a new
program. During parsing, the type information is generated and most of it is
strongly typed as in Haskell. Now that the pattern is parsed, and does not
exist in the pattern library, how to store in the library in terms of existing
patterns in the library. Summon the Common Lisp and defmacro to the rescue.
But, this defmacro must obey one rule:

Never violate type safety, i.e. 2 + “Hello I am an A” is a a big no-no.

Consequently, it should be no surprise that a well-chosen set of primitives,
together with a good set of macros is especially valuable. In that sense, we
can say that the acquiring knowledge is constant re-factoring of this
“language of thoughts.”

Let P be the no. of primitive types and M be the no. of macros.

Then, the size of the library, denoted by L is:

L = P + O(M), in big-O notation.

Intuitively, P < M. But, M “grows”, for each defmacro.

To shrink “M,” the protag must re-factor the existing macros in the library by
leveraging macro writing macros.

Essentially, this illustrates the difference between the smart and the
smarter,

M(smart) > M(smarter) in numbers, but,

M(smart) < M(smarter) in enrichment due to re-factoring.

As L grows, P should grow O(N), while the growth of M must be tamed from
O(N^x) to O(N^y.logN) for some N, x and y, such that x > y.

Building this all important library is more akin to growing a plant from the
seeds. How does the protag water this plant?

In other words, how does the protag know that a new macro needs to be
introduced?

Thinking about thinking will surely help, but only so much.

The protag can know that for a new macro must be introduced, only when its
mind is faced with an unlocked door. Hence, building the library is a constant
struggle: the protag must improve the candella by attempting radically new
problems. It is going to take time, but lesser, compared to depending on the
bolt from the blue.

However, as every seasoned Lisper knows: growing a library of macros, where
many of them are macro writing macros, is hard. So, the protag must wander in
different disciplines for inspiration: like Physics, Cognitive Psychology,
Literature, Music, Maths, Poetry, Sculpture, Sports, and so many different
pursuits.

Inspiration \-----------

Let’s simplify the definition of an inspiration. An inspiration is an external
force that upsets the equilibrium in the protag’s universe, mandating a re-
assessment of the library and the eventual struggle to re-factor the macros
and in the rare case, the addition of a new primitive.

Wrapping up, let’s look at the pros and cons of this approach. The pros
Greater accuracy a.k.a. qualitative improvement Faster As a nice side effect,
finer control over emotions i.e. to be phenomenally happy even during the
oddest of the odds

The cons Conscious and systematic effort is required to develop the skill.
Where is the roadmap? How does one assess the progress? Where does one even
begin?

Closing remarks \---------------

This merits further thought. But, since we now understand the problem better,
we can work towards a better solution.

Thanks \------ I wish to convey a sense of deep gratitude towards the author
of the article. The article left with interesting questions and the pursuit of
the answers was both, a profitable and a pleasant outcome.

Comments welcome.

