If you find something hard to understand, BLAME YOUR OWN LACK OF KNOWLEDGE! since you were first born knowing nothing, then you've learned. There’s so much you still don’t know. things that confuse you now, but later, you may see them clearly and understand. — Nahj al-Balagha, (Letters 31-35), by Imam Ali
the turning point was when in a class, the teacher classified a question with answer of about 2 pages long as "very simple", it got me thinking that "what is the real measurement of simplicity?"
I did some Mind Map and it really could not help me to solve end of chapter problems. I've noticed that every problem has unique GoT and relates different ideas, hence there is no sparse GoK (i.e. mind-map) that can help us.
In order to mitigate the above problem, one might suggest adding lots of edges between nodes (cross referencing), but nobody can understand a super dense GoK, by looking at it! Another solution would be to create different versions of GoK based on different aspects e.g. centeric nodes be people, centrric nodes be time periods, etc
That is why tools like GoK of Obisidian software would not help much and they are rather a fancy feature to make people say WOW!. I've tried implmenting a GoK app similar to Kumu and not only it was time-consuming, it would not help me understant better. sure the remembering got easier but it was mostly becuase of documenting stuff; and I even want to say that, it was very shallow kind of remembering.
I've asked DeepSeek AI to give opinion about mind maps if he were Richard Feyman. the result is actually impressive (some of them are rather funny):
"Nature doesn’t organize itself into pretty radial diagrams. If your understanding can’t handle a little chaos, it’s not understanding—it’s interior decorating."
"Mind maps are like tour buses: you see all the sights, but you never step into the street. Real thinking means getting lost sometimes."
"Drawing a line between two ideas doesn’t mean you’ve connected them—any more than tying a string between two lampposts means you’ve invented the telegraph."
"The best mind map is the one you crumple up and throw away—because you don’t need it anymore."
"Drawing a mind map to understand physics is like painting a sailboat to learn the wind."
"Knowledge isn’t a dot you can connect—it’s the fire that burns between them."
"Understanding isn’t a tree. It’s a wildfire—and you’re supposed to be the arsonist."
The talk "simple made easy" by Rich Hickey made me thinking that, there are for sure better and more deterministic ways to find out difficulty of a problem ...
it is recommended to read Demystifying Chains, Trees, and Graphs of Thoughts before reading this chapter.
Typical mind-maps are just GoT based on "contents list" of the book. GoK is a lot more dense than you might think.
GoT (Graph of Thought) is a DAG (Directed Acyclic Graph), that is specific (but no unique) to question. GoK on the other hand is more general and it is intended to be able to answer various questions.
pattern matching (i.e. making particular neural connection between or in other words, "shortcuts"), ability to do basic pattern matching i.e. repeating tasks in predicted order. unable to reason new situations (problems)
ability to relate what you know and what you learnt, not useful without K since causes false conclusions.(Misunderstandings due to faulty connections).
can solve problems and from new thoughts but requires time
A person learns patterns (L) intuitively (e.g., native speakers picking up grammar rules without being taught) And develops some level of understanding (U) from those patterns, Even without explicit knowledge (K)
highest level of understanding. enabling combining and creation.
Learning (L) refine Knowledge (K) through practice, Understanding (U) feed back into improving Learning (L) e.g. learning strategies
A student studying physics might start by memorizing formulas (K), practice solving problems (L), then grasp why those formulas work (U). KLU would let them invent a novel experiment or critique flawed theories.
here's the steps that are being taken by almost everyone:
the first step to every thing in life is to focus and pay attention period.
Thinking is sinking and growing ideas in the brain ...
there are concepts that are obviously related to each other, you know how to solve it when you see it. but some of them are meant to consider and dig deeper to find (or mine) related ones. thinking is exactly that.
Asking a question is shouting into cave of mind. you get an echo of your own words, bent by the shape of the cave ... what you get might not be the answer, but fragmented clues and ideas needs to be processed
...
make connection
here what I mean by the word "create" is that makeing/producing something that the creator/author has not seen like it before.
to create something new, the person need to connect sometimes even unrelated nodes in his GoK in a way that makes sense. the feature of connecting no so obvious unrelated nodes in brain requires some level of forgetting since he or she must not consider all of the details about it and sometimes has to misremember or misinterpret the details about it. I didn't know that forgetting can be blessing.
I've read somewhere that creative people tend to forgot more, as their brain gets good at losing connection between nodes in KoG and even creating false connections between them.
by the definition, you might've guessed that creative work is not straight-forward.
conclude or process
repeat the process until you're done.
explore the possibilities of other answers by assuming you're answer is wrong or you've missed something
the step (5) is too abstract, I felt that all of nodes are not the same, they seem different in nature and their purpose. so I categortized them as:
- ⚫ black: problem or sub-problem or goal
- 🟣 purple: recall ( please read What Good Is Learning If You Don’t Remember It? 📃 )
- 🟢 green: reason
- 🟠 orange: calculate or compute
- 🟡 yellow: Think-aloud protocols? [overlay]
- Edges : Show connections (i.e., "Relates to" or "Builds on")
the image below is the summary of terms that I've introduced. each of these terms will be explained:
to know why I places terms in a circle like this, please watch Arthur M. Young: Geomtery of Meaning.
If a solution to a problem resembels the direction of edges between nodes similar to what the learner's mind, we say that the solution is straight-forward, on the other hand if the direction of edges between nodes for an solution to a does not exist between nodes or does not exists directly between the nodes in the learner's mind, then we say that the solution is not straight-forward (SF) or it is Explorative (Ex).
Thus the term straight-forward is subjective according to the learning material and the learner.
Note that just connecting 2 nodes are not important, the direction of the edge also matters. for example a language learner first looks at the word e.g. "camera", then translates it to his mother tongue e.g. Persian ("دوربین") and then translating, he imagines the real camera in his mind. but he may have trouble to do it vice verse i.e. seeing a camera and then finding its English word. it is true that the person probably can find the word after some time but it is not obvious i.e. it's not present directly in his GoK.
In the above case we say that the person "knows" that word, but he must think more and accordingly takes more time for him compared to another learner that the image of every word is associated along with the word in his mind.
in above example, the height of the node English "Camera" from Persian "دوربین" is high but not vice versa.
think of GoT as Valley, and nodes as hills and Mountains. The more unconventional to get from a neighbours of a node to it, the more the height of it.
hints are trying to lower the height of the next node; it is the ability of a teacher to make everything obvious for his/her students
nodes that have more more than 1 in-edges. these nodes are mostly conclusion nodes which are created by combining different ideas.
nodes that have more more than 1 out-edges. these nodes usually are in direct relation with other concepts.
Graph of Thoughts: Solving Elaborate Problems with Large Language Models: https://hub.baai.ac.cn/view/29222
the complexity of a GoT is determined by number of its collector nodes and number of their in-edges. the more in-edges, the more you have to consider ideas and reason based-on them.
In simple terms, a more complex GoT means more ideas are involved.
https://www.sfu.ca/complex-systems-frameworks/frameworks/complex-vs-complicated.html
https://www.sfu.ca/complex-systems-frameworks.html
The more the width of the GoT more ideas involved or more options have to be considered, we use the term heavy for such GoT.
The energy takes to build the GoT is the measurement of difficulty of a problem. the coefficients may vary for each person. the formula is as following:
The scientists of today think deeply instead of clearly.One must be sane to think clearly, but one can think deeply and be quite insane -- Tesla
most people in social media want quick and easy conclusions, i.e. shallow GoT and straight-forward edges which takes them least amount of energy and most of the times appears to be incorrect. this behaviour is exactly opposite of what Quran want from us: افلا تعقلون i.e. why don't you think [more]?
I've developed an app to evaluate my theory.
TODO
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theory of syntax: chomsky
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7 FAST Chinese and Japanese SECRETS for students to EASILY become TOPPERS
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Thanks to Eric Demaine for his SRTBOT method for formulating dynamic programming solution. see "introduction to algorithms" in MIT open course ware.
- Eureka effect
- Cowan’s 4±1 Chunks
- Cognitive Load Theory
- De-cluttering science doesn't dumb it down | Advanced cognitive load theory
- When Thinking Aloud Fails
- think aloud protocol: https://www.slideserve.com/JasminFlorian/reading-comprehension-strategies-for-english-language-learners
- tests are magic
- Learning Beyond Facts | Conceptual Knowledge, Procedural Knowledge, and More