Or. perhaps, it's just rampant civic ignorance. I think there's a significant portion of the population who just don't care to be informed about the demographics of their own countries.

https://xtiles.app/en

Map of Content Vizualized (VMOC)

a start of thinking on the space of converging written and visual thinking, but not as advanced as even Raymond Llull or indigenous ways of knowing which more naturally merge these modes of thinking.

Western though is just missing so much... sigh

quote is from Highsmith's Plotting and Writing Suspense Fiction

I love the concept of "slender ideas" as small, fleeting notes which might accumulate into something if written down. In saying "Close the notebook and think about it for a few days" Patricia Highsmith seems to be suggesting that one engage in diffuse thinking, passive digesting, or mulling rather than active or proactive thinking.

She also invokes the magic word "presto!" (which she exclaims) as if to indicate that magically the difficult work of writing is somehow no longer difficult. Many writers seem to indicate that this is a phenomenon, but never seem to put their finger on the mechanism of why it happens. Some seems to stem from the passive digestion over days with diffuse thinking, with portions may also stem from not starting from a blank page and having some material to work against instead of a vacuum.

From Patricia Highsmith: Her Diaries and Notebooks: 1941-1995 (Swiss Literary Archives)

"[What] I like about the [zettlekasten] system is that it's a constant reminder to to make up your mind and to specify what you what you're thinking."<br /> —Sönke Ahrens, [Tinderbox Meetup - May 7, 2023 00:30:36]

depends on how you look at it: "normal"

Where are the tools for graphing inter-dependencies of areas of study? When entering a new area it would be interesting to have visual mappings of ideas and thoughts.

If ideas in an area were chunked into atomic ideas, then perhaps either a Markov monkey or a similar actor could find the shortest learning path from a basic idea to more complex ideas.

Example: what is the shortest distance from an understanding of linear algebra to learn and master Lie algebras?

Link to Garden of Forking Paths

Link to tools like Research Rabbit, Open Knowledge Maps and Connected Papers, but for ideas instead of papers, authors, and subject headings.

It has long been useful for us to simplify our thought models for topics like economics to get rid of extraneous ideas to come to basic understandings within such a space. But over time, we need to branch out into related and even distant subjects like mathematics, psychology, engineering, sociology, anthropology, politics, physics, computer science, etc. to be able to delve deeper and come up with more complex and realistic models of thought.Our early ideas like the rational actor within economics are fine and lovely, but we now know from the overlap of psychology and sociology which have given birth to behavioral economics that those mythical rational actors are quaint and never truly existed. To some extent, to move forward as a culture and a society we need to rid ourselves of these quaint ideas to move on to more complex and sophisticated ones.

For the intellectual worker, an Antinet can be used to keep track of such questions and the thought-lines corresponding to these questions.

As an educator, be courageous, lead by example. Start by asking questions out loud, not only those you wish students to answer, but also those you genuinely don't know, and wish to research together with your students.

Asking questions is how we learn. Do not avoid it for the sake of not looking stupid. That is stupid. Inquiry-Based Learning.

As Confucius said: "The one who asks a question is a fool for a minute, the one who doesn't ask is a fool for life."

‘who seldom reason at all, but do and think according to the example of others, whether parents, neighbours, ministers...for the saving of themselves the pains and trouble of thinking and examining for themselves’ (p. 169).

Interleaving

Perhaps of interest here, would not be a specific OER text, but an OER zettelkasten or card index that indexes a variety of potential public domain or open resources, articles, pieces, primary documents, or other short readings which could then be aggregated and tagged to allow for a teacher or student to create their own personalized OER text for a particular area of work.

If done well, a professor might then pick and choose from a wide variety of resources to build their own reader to highlight or supplement the material they're teaching. This could allow a wider variety of thinking and interlinking of ideas. With such a regiment, teachers are less likely to become bored with their material and might help to actively create new ideas and research lines as they teach.

Students could then be tasked with and guided to creating a level of cohesiveness to their readings as they progress rather than being served up a pre-prepared meal with a layer of preconceived notions and frameworks imposed upon the text by a single voice.

This could encourage students to develop their own voices as well as to look at materials more critically as they proceed rather than being spoon fed calcified ideas.

We need more scholarship which leaves open thinking spaces for future scholars.

Google translation:

The sheer quantity exceeds the possibilities of book publication, the complex, multidimensional structure of a networked information base cannot be reproduced in print, and finally the dynamic of a constantly growing and constantly correcting material does not fit into the rigid rhythm of book production, in which each expanded and corrected new edition is associated with an incalculable amount of effort. A book publication could only offer a snapshot of such a database, reduced to a specific perspective. This too can be very useful from time to time, but it does not solve the problem of publishing the entire material.

While the writing criticism of "dumping out one's zettelkasten" into a paper, journal article, chapter, book, etc. has been reasonably frequent in the 20th century, often as a means of attempting to create a linear book-bound context in a local neighborhood of ideas, are there other more complex networks of ideas which we're not communicating because they don't neatly fit into linear narrative forms? Is it possible that there is a non-linear form(s) based on network theory in which more complex ideas ought to better be embedded for understanding?

Some of Niklas Luhmann's writing may show some of this complexity and local or even regional circularity, but perhaps it's a necessary means of communication to get these ideas across as they can't be placed into linear forms.

One can analogize this to Lie groups and algebras in which our reading and thinking experiences are limited only to local regions which appear on smaller scales to be Euclidean, when, in fact, looking at larger portions of the region become dramatically non-Euclidean. How are we to appropriately relate these more complex ideas?

What are the second and third order effects of this phenomenon?

An example of this sort of non-linear examination can be seen in attempting to translate the complexity inherent in the Wb (Wörterbuch der ägyptischen Sprache) into a simple, linear dictionary of the Egyptian language. While the simplicity can be handy on one level, the complexity of transforming the entirety of the complexity of the network of potential meanings is tremendously difficult.

Is language acquisition a very complex method of pattern recognition?

Consider how rhetorical analysis applies to alt-right political arguments. Alt-right arguments fail miserably under rhetorical analysis. Rhetorical analysis is a tool of academia. Therefore academia is inimical to the alt-right. Therefore, the alt-right will seek to weaken and impune academia. And this is in fact what they do.

the phrase "intellectual furniture" is sort of painful here...

There's a danger to using digital tools to help with Higher Order Thinking; namely, it offloads precious cognitive load, optimized intrinsic load, which is used to build schemas and structural knowledge which is essential for mastery. Another danger is that digital tools often make falling for the collector's fallacy easier, meaning that you horde and horde information, which makes you think you have knowledge, while in fact, you simply have (maybe related) information, not mastery. The analog way prevents this, as it forces you to carefully evaluate the value of an idea and decide whether or not it's worth it to spend time on writing it and integrating it into a line of thought. Evaluation/Analysis is forced in an analog networked thinking tool, which is a form of Higher Order Learning/Thinking, as they are in the higher orders of Bloom's Taxonomy/Hierarchy.

This is also true for AI. Always carefully evaluate whether or not a tool is worth using, like a farmer. (Deep Work, Cal Newport).

Instead, use a tool like mindmapping, the GRINDE way, which is digital, for learning... Or the Antinet Zettelkasten by Scott Scheper, which is analog, for research.

The power of an Antinet Zettelkasten. Use this principle both in research and learning.

Seems similar to Communicating with an Antinet Zettelkasten.

An article about contemporary philosopher Agnes Callard

Stop Procrastinating With Note-Taking Apps Like Obsidian, Roam, Logseq https://www.youtube.com/watch?v=baKCC2uTbRc by Sam Matla

sophisticated procrastination - tweaking one's system(s) or workflow with the anticipation it will help them in the long run when it is generally almost always make-work which helps them feel smart and/or productive. Having measurable results which can be used against specific goals will help weed this problem out.

Example of someone who says most of their best flashes of thought or creativity come when they're out walking or doing something else #

Sam Matla talks about the collector's fallacy in a negative light, and for many/most, he might be right. But for some, collecting examples and evidence of particular things is crucially important. The key is to have some idea of what you're collecting and why.

Historians collecting small facts over time may seem this way, but out of their collection can emerge patterns which otherwise would never have been seen.

cf: Keith Thomas article

concrete examples of this to show the opposite?

Relationship to the idea of AI coming up with black box solutions via their own method of diffuse thinking

Way to get new ideas

Bruno Latour showed us how to think with the things of the world | Aeon Essays<br /> by Stephen Muecke

Stephen Johnson's "slow hunch" is built up of information acquisition over time and mixed with diffuse thinking.

#

vs intuition?

In addition to "critical thinking, resourcefulness, creativity, attention to detail, and academic pride and humility", the ability to use a note card-based research system like Umberto Eco's is the key to overcoming information overload.

This is, in part, why the tools for thought space should be looking at intellectual history to see how people have worked in the past.

Rather than looking at how writers have previously worked and building something specific that supports those methods, they've taken a tool designed for something else and just thrown it into the mix. Perhaps useful creativity stems from it in a new and unique way, but most likely writers are going to continue their old methods.

The interface of Wordcraft sounds like some of that interface that note takers and thinkers in the tools for thought space would appreciate in their

Rather than pairing it with artificial intelligence and prompts for specific writing tasks, one might pair tools for though interfaces with specific thinking tasks related to elaboration and continuation. Examples of these might be gleaned from lists like Project Zero's thinking routines: https://pz.harvard.edu/thinking-routines

https://en.m.wikipedia.org/wiki/Incremental_reading

Incremental reading is spaced parallel reading of multiple sources with note taking and spaced repetition.

It's not far from how I read and take notes myself, though I place less emphasis on the spaced repetition piece as I tend to run across things naturally within my note collection anyway.

One of the major potential benefits of incremental reading (not mentioned in the Wikipedia article; is it in Wozniak's work?) is the increase of combinatorial creativity created by mixing a variety of topics simultaneously.

There is also likely a useful diffuse thinking effect happening between reading sessions.

This site is a cesspool of authoritarian, fascist-apologist, conspiracist mind-mangling content. It's a good place to find out what kinds of bizarre notions people (particularly Catholics of an authoritarian bent) are being fed, and consuming — ridiculous fabrications and warped interpretations of the sort contributing (with giddy joy) to the suffocation of democratic inclinations and institutions.

The site does have some interesting images. I think this will be an inspiration for some dystopian and horror fiction ideas.

Sascha Fast juxtaposes his new notes with his own favorite problems to see if they have any connections with respect to improving on or solving them.

This practice is somewhat similar to Marshall Kirkpatrick's conceptualization of triangle thinking, but rather than being randomly generated with respect to each other, the new things are always generated toward important questions he's actively working on or toward.

This helps to increase the changes of forward progress in specific areas rather than undirected random progress.

Gian-Carlo Rota (1997): Ten Lessons I Wish I Had Been Taught, Notices of the American Mathematical Society 1, 1997, Vol. 44, pp. 22-25.

Richard Carter uses his writing journal practice to "think out loud" to himself. Often, laying out extended arguments helps people to refine and reshape their thinking as they're better able to see potential holes or missing pieces of arguments. It's the same sort of mechanism which is at work in rubber duck debugging of computer code: by explaining a process one is more easily able to see the missing pieces, errors, or problems with the process at hand.

Carter's separate note taking and writing journal practice being used as a thought space or writing workshop of sorts is very similar to the process seen in my preliminary studies of Henry David Thoreau's work in which he kept commonplace books and separate (writing) journals which show evidence of his trying ideas on for size and working them before committing them to his published works.

As humans we're good at separating things based on categories. The Dewey Decimal System systematically separates mathematics and history into disparate locations, but your zettelkasten shouldn't force this by overthinking categories. Perhaps the overlap of math and history is exactly the interdisciplinary topic you're working toward? If this is the case, just put cards into the slip box closest to their nearest related intellectual neighbor—and by this I mean nearest related to you, not to Melvil Dewey or anyone else. Over time, through growth and branching, ideas will fill in the interstitial spaces and neighboring ideas will slowly percolate and intermix. Your interests will slowly emerge into various bunches of cards in your box. Things you may have thought were important can separate away and end up on sparse branches while other areas flourish.

If you make the (false) choice to separate math and history into different "sections" it will be much harder for them to grow and intertwine in an organic and truly disciplinary way. Universities have done this sort of separation for hundreds of years and as a result, their engineering faculty can be buildings or even entire campuses away from their medical faculty who now want to work together in new interdisciplinary ways. This creates a physical barrier to more efficient and productive innovation and creativity. It's your zettelkasten, so put those ideas right next to each other from the start so they can do the work of serendipity and surprise for you. Do not artificially separate your favorite ideas. Let them mix and mingle and see what comes out of them.

If you feel the need to categorize and separate them in such a surgical fashion, then let your index be the place where this happens. This is what indices are for! Put the locations into the index to create the semantic separation. Math related material gets indexed under "M" and history under "H". Now those ideas can be mixed up in your box, but they're still findable. DO NOT USE OR CONSIDER YOUR NUMBERS AS TOPICAL HEADINGS!!! Don't make the fatal mistake of thinking this. The numbers are just that, numbers. They are there solely for you to be able to easily find the geographic location of individual cards quickly or perhaps recreate an order if you remove and mix a bunch for fun or (heaven forfend) accidentally tip your box out onto the floor. Each part has of the system has its job: the numbers allow you to find things where you expect them to be and the index does the work of tracking and separating topics if you need that.

The broader zettelkasten, tools for thought, and creativity community does a terrible job of explaining the "why" portion of what is going on here with respect to Luhmann's set up. Your zettelkasten is a crucible of ideas placed in juxtaposition with each other. Traversing through them and allowing them to collide in interesting and random ways is part of what will create a pre-programmed serendipity, surprise, and combinatorial creativity for your ideas. They help you to become more fruitful, inventive, and creative.

Broadly the same thing is happening with respect to the structure of commonplace books. There one needs to do more work of randomly reading through and revisiting portions to cause the work or serendipity and admixture, but the end results are roughly the same. With the zettelkasten, it's a bit easier for your favorite ideas to accumulate into one place (or neighborhood) for easier growth because you can move them around and juxtapose them as you add them rather than traversing from page 57 in one notebook to page 532 in another.

If you use your numbers as topical or category headings you'll artificially create dreadful neighborhoods for your ideas to live in. You want a diversity of ideas mixing together to create new ideas. To get a sense of this visually, play the game Parable of the Polygons in which one categorizes and separates (or doesn't) triangles and squares. The game created by Vi Hart and Nicky Case based on the research of Thomas Schelling provides a solid example of the sort of statistical mechanics going on with ideas in your zettelkasten when they're categorized rigidly. If you rigidly categorize ideas and separate them, you'll drastically minimize the chance of creating the sort of useful serendipity of intermixed and innovative ideas.

It's much harder to know what happens when you mix anthropology with complexity theory if they're in separate parts of your mental library, but if those are the things that get you going, then definitely put them right next to each other in your slip box. See what happens. If they're interesting and useful, they've got explicit numerical locators and are cross referenced in your index, so they're unlikely to get lost. Be experimental occasionally. Don't put that card on Henry David Thoreau in the section on writers, nature, or Concord, Massachusetts if those aren't interesting to you. Besides everyone has already done that. Instead put him next to your work on innovation and pencils because it's much easier to become a writer, philosopher, and intellectual when your family's successful pencil manufacturing business can pay for you to attend Harvard and your house is always full of writing instruments from a young age. Now you've got something interesting and creative. (And if you must, you can always link the card numerically to the other transcendentalists across the way.)

In case they didn't hear it in the back, I'll shout it again: ACTIVELY WORK AGAINST YOUR NATURAL URGE TO USE YOUR ZETTELKASTEN NUMBERS AS TOPICAL HEADINGS!!!

!!!!

Henry David Thoreau from 1852

https://wiki.rel8.dev/rethinking_the_tools_for_thinking_podcast

https://app.thebrain.com/brains/3d80058c-14d8-5361-0b61-a061f89baf87/thoughts/b73d9af9-c054-4c46-86ed-a255e52e8099/attachments/f6b66f7f-b268-4d4b-9ee1-c2d5d7c93d23

https://wiki.rel8.dev/tools_for_thinking_podcast

see also: https://www.betaworks.com/media

!- claim : we live in a corrupted and minimalist democracy with the consequence that we lack generational thinking - privilege individiual, special-interesting thinking - only ask citizens to express their private preferences - confound opinion and knowledge - we even deny expert science, believing it is tantamout to democratic thinking !- claim : within this minimalist, corrupted version of democracy, present thinking trumps future thinking - we do not apply generational thinking aka Edmund Burke - Burke's idea of generational thinking conceptualizes an ideal democracy that encompasses past, present and future generations - generational thinking requires a space of prudent deliberation rather than present-mind thinking only

The idea of expressing the worst possible idea first in brainstorming can often often be helpful.

Example: when brainstorming restaurant suggestions for a group, suggest McDonalds first to subtly pressure people to create better ideas to prevent the lowest common denominator from winning.

Melechi, Antonio (11 June 2020). Weintraub, Pam (ed.). "Lateral thinking is classic pseudoscience, derivative and untested". Aeon Essays. Aeon.co.

A good list of tactics to communicate about innovation. For example,

• publish blogs, guides, videos with concrete tips,
• create a pool of champions
• basic education programs that help solve problems on the job

One could also think about a "virtual innovation" lab approach ...

• Government policy innovation
• Public services innovation (including service design and digital)
• Science and technology — governments employ thousands of scientists, engineers and researchers. Labs can think of ways for them to become more effective.
• Management systems innovation — “innovate” how government innovates to build skills, capacity and culture.

The article speaks about that "Management systems innovation" -- the way howe we build skills, capacity and culture -- is a key element for successful attempts for governments to innovation.

Concentrating on these aspects -- howe we work together, how we develop skills and capacity -- might be the key ingredients for a future for the OpenLab -- and the future of the innovation activities.

Maybe we could start offering "services" from the "OpenLab" to managers and teams ...?

This seems to be the key element here: systems-thinking approach and thinking about our role within our departments.

!- Futures Thinking: The value of Coal, Oil and Gas in our current industrial society - If we do away with coal, we cannot manufacture - How do we find a solution to this? - Efficacy - can we get rid of / redesign infrastructure so that we can eliminate unnecessary use of coal / oil / gas? - ie. relocalize to eliminate need for energy intensive transportation, locally produced bio-fertiilzed food production to get rid of fossil fuel fertilizers, replace 24/7 refrigerators in every home with fruit and veg underground cold cellars and only very small fridge or freezer with ultra insulation for very low energy consumption

!- Futures Thinking : summary - our generation has the most wisdom to deal with the problem, even though it is an unprecedented problem - We need diversity of opinions and perspectives. Like in evolution, that diversity will emerge an optimal solution - To consciously culturally evolve, we need to put all ideas on the table and discuss openly - An open, interpersonal, people-centered knowledge ecosystem such as Indyweb is suitable for such a process

I love that he points this out explicitly.

Some don't see the underlying processes of complexity within note taking methods and as a result ascribe magical properties to what are emergent properties or combinatorial creativity.

See also: The Ghost in the Machine zettel from Luhmann

Somehow there's an odd dichotomy between the boredom of such a simple method and people seeing magic within it at the same time. This is very similar to those who feel that life must be divinely created despite the evidence brought by evolutionary and complexity theory. In this arena, there is a lot more evolved complexity which makes the system harder to see compared to the simpler zettelkasten process.

Cathy Marshall was an early digital gardener!

https://readwriterespond.com/2022/11/commonplace-book-a-verb-or-a-noun/

Sometimes the root question is "what to I want to do this for?" Having an underlying reason can be hugely motivating.

Are you collecting examples of things for students? (seeing examples can be incredibly powerful, especially for defining spaces) for yourself? Are you using them for exploring a particular space? To clarify your thinking/thought process? To think more critically? To write an article, blog, or book? To make videos or other content?

Your own website is a version of many of these things in itself. You read, you collect, you write, you interlink ideas and expand on them. You're doing it much more naturally than you think.

I find that having an idea of the broader space, what various practices look like, and use cases for them provides me a lot more flexibility for what may work or not work for my particular use case. I can then pick and choose for what suits me best, knowing that I don't have to spend as much time and effort experimenting to invent a system from scratch but can evolve something pre-existing to suit my current needs best.

It's like learning to cook. There are thousands of methods (not even counting cuisine specific portions) for cooking a variety of meals. Knowing what these are and their outcomes can be incredibly helpful for creatively coming up with new meals. By analogy students are often only learning to heat water to boil an egg, but with some additional techniques they can bake complicated French pâtissier. Often if you know a handful of cooking methods you can go much further and farther using combinations of techniques and ingredients.

What I'm looking for in the reading, note taking, and creation space is a baseline version of Peter Hertzmann's 50 Ways to Cook a Carrot combined with Michael Ruhlman's Ratio: The Simple Codes Behind the Craft of Everyday Cooking. Generally cooking is seen as an overly complex and difficult topic, something that is emphasized on most aspirational cooking shows. But cooking schools break the material down into small pieces which makes the processes much easier and more broadly applicable. Once you've got these building blocks mastered, you can be much more creative with what you can create.

How can we combine these small building blocks of reading and note taking practices for students in the 4th - 8th grades so that they can begin to leverage them in high school and certainly by college? Is there a way to frame them within teaching rhetoric and critical thinking to improve not only learning outcomes, but to improve lifelong learning and thinking?

https://untools.co/

Tools for better thinking Collection of thinking tools and frameworks to help you solve problems, make decisions and understand systems.

<small><cite class='h-cite via'>ᔥ <span class='p-author h-card'>Howard Rheingold</span> in Howard Rheingold: "Y'all know about "Tools for …" - Mastodon (<time class='dt-published'>11/13/2022 17:33:07</time>)</cite></small>

Looks similar to Project Zero https://pz.harvard.edu/thinking-routines

A Systems Thinking approach to understand culture.

5 Core Principles Of Design Thinking Process

Design thinking is a process that starts with empathy, curiosity and imagination to create solutions. By following the core principles and steps of design thinking, you can learn how to think like a designer and develop creative solutions to the challenges you face in your life. In this blog we have shared 5 Core Principles Of Design Thinking Process. https://bit.ly/3E8zyx5

This definition can be used to demonstrate why the following function is continuous:

\(f: [0,2\pi) \to S^1\) where \(f(\phi)= (\cos\phi, \sin\phi)\) and \(S^1\) is the unit circle in the cartesian coordinate plane \(\mathbb{R}^2\).

Intuition

The preimage of open (in codomain) is open (in domain). Roughly, anything "close" in the codomain must have come from something "close" in the domain. Otherwise, stuff got split apart (think gaps, holes, jumps) on the way from our domain to our codomain.

Formalism

For some \(f: X \to Y\), for any open set \(V \in \tau_Y\), there exists some open set \(U \in \tau_X\) so that it's image under \(f\) is \(V\). In math, \(\forall V \in \tau_Y, \exists U \in \tau_X \text{ s.t. } f(U) = V\)

Demonstration

So for \(f: [0,2\pi) \to S^1\), we can see that \([0,2\pi)\) is open under the subspace topology. Why? Let's start with a different example.

Claim 1: \(U_S=[0,1) \cup (2,2\pi)\) is open in \(S = [0,2\pi)\)

We need to show that \(U_S = S \cap U_X\) for some \(U_X \in \mathbb{R}\). So we can take whatever open set that overlaps with our subspace to generate \(U_S\text{.}\)

proof 1

Consider \(U_X = (-1,1) \cup (2, 2\pi)\) and its intersection with \(S = [0, 2\pi)\). The overlap of \(U_X\) with \(S\) is precisely \(U_S\). That is,

$$ \begin{align} S \cap U_X &= [0, 2\pi) \cap U_X \ &= [0, 2\pi) \cap \bigl( (-1,1) \cup (2,2\pi) \bigr) \ &= \bigl( [0, 2\pi) \cap (-1,1) \bigr) \cup \bigl( [0,2\pi) \cap (2,2\pi)\bigr) \ &= [0, 1) \cup (2, 2\pi) \ &= U_S \end{align} $$

Seemingly both rubber duck debugging and casual conversations with acquaintances would seem to be soft forms of diffuse thinking which may help one come to a heuristic-based decision or realization.

These may be useful, but should also be used in combination with more logical, system two forms of decision making. (At least not in the quick, notice the problem sort of issues in which one may be debugging.)

Notation of a random process that has outcomes

The "universal set" aka "sample space" of all possible outcomes is sometimes denoted by \(U\), \(S\), or \(\Omega\): https://en.wikipedia.org/wiki/Sample_space

Probability theory & measure theory

From what I recall, the notation, \(\Omega\), was mainly used in higher-level grad courses on probability theory. ie, when trying to frame things in probability theory as a special case of measure theory things/ideas/processes. eg, a probability space, \((\cal{F}, \Omega, P)\) where \(\cal{F}\) is a \(\sigma\text{-field}\) aka \(\sigma\text{-algebra}\) and \(P\) is a probability density function on any element of \(\cal{F}\) and \(P(\Omega)=1.\)

Somehow, the definition of a sigma-field captures the notion of what we want out of something that's measurable, but it's unclear to me why so let's see where writing through this takes me.

Working through why a sigma-algebra yields a coherent notion of measureable

A sigma-algebra \(\cal{F}\) on a set \(\Omega\) is defined somewhat close to the definition of a topology \(\tau\) on some space \(X\). They're both collections of sub-collections of the set/space of reference (ie, \(\tau \sub 2^X\) and \(\cal{F} \sub 2^\Omega\)). Also, they're both defined to contain their underlying set/space (ie, \(X \in \tau\) and \(\Omega \in \cal{F}\)).

Additionally, they both contain the empty set but for (maybe) different reasons, definitionally. For a topology, it's simply defined to contain both the whole space and the empty set (ie, \(X \in \tau\) and \(\empty \in \tau\)). In a sigma-algebra's case, it's defined to be closed under complements, so since \(\Omega \in \cal{F}\) the complement must also be in \(\cal{F}\)... but the complement of the universal set \(\Omega\) is the empty set, so \(\empty \in \cal{F}\).

I think this might be where the similarity ends, since a topology need not be closed under complements (but probably has a special property when it is, although I'm not sure what; oh wait, the complement of open is closed in topology, so it'd be clopen! Not sure what this would really entail though 🤷‍♀️). Moreover, a topology is closed under arbitrary unions (which includes uncountable), but a sigma-algebra is closed under countable unions. Hmm... Maybe this restriction to countable unions is what gives a coherent notion of being measurable? I suspect it also has to do with Banach-Tarski paradox. ie, cutting a sphere into 5 pieces and rearranging in a clever way so that you get 2 sphere's that each have the volume of the original sphere; I mean, WTF, if 1 sphere's volume equals the volume of 2 sphere's, then we're definitely not able to measure stuff any more.

And now I'm starting to vaguely recall that this what sigma-fields essentially outlaw/ban from being possible. It's also related to something important in measure theory called a Lebeque measure, although I'm not really sure what that is (something about doing a Riemann integral but picking the partition on the y-axis/codomain instead of on the x-axis/domain, maybe?)

And with that, I think I've got some intuition about how fundamental sigma-algebras are to letting us handle probability and uncertainty.

Back to probability theory

So then events like \(E_1\) and \(E_2\) that are elements of the set of sub-collections, \(\cal{F}\), of the possibility space \(\Omega\). Like, maybe \(\Omega\) is the set of all possible outcomes of rolling 2 dice, but \(E_1\) could be a simple event (ie, just one outcome like rolling a 2) while \(E_2\) could be a compound(?) event (ie, more than one, like rolling an even number). Notably, \(E_1\) & \(E_2\) are NOT elements of the sample space \(\Omega\); they're elements of the powerset of our possibility space (ie, the set of all possible subsets of \(\Omega\) denoted by \(2^\Omega\)). So maybe this explains why the "closed under complements" is needed; if you roll a 2, you should also be able to NOT roll a 2. And the property that a sigma-algebra must "contain the whole space" might be what's needed to give rise to a notion of a complete measure (conjecture about complete measures: everything in the measurable space can be assigned a value where that part of the measurable space does, in fact, represent some constitutive part of the whole).

But what about these "random events"?

Ah, so that's where random variables come into play (and probably why in probability theory they prefer to use \(\Omega\) for the sample space instead of \(X\) like a base space in topology). There's a function, that is, a mapping from outcomes of this "random event" (eg, a role of 2 dice) to a space in which we can associate (ie, assign) a sense of distance (ie, our sigma-algebra). What confuses me is that we see things like "\(P(X=x)\)" which we interpret as "probability that our random variable, \(X\), ends up being some particular outcome \(x\)." But it's also said that \(X\) is a real-valued function, ie, takes some arbitrary elements (eg, events like rolling an even number) and assigns them a real number (ie, some \(x \in \mathbb{R}\)).

Aha! I think I recall the missing link: the notation "\(X=x\)" is really a shorthand for "\(X(\omega)=x\)" where \(\omega \in \cal{F}\). But something that still feels unreconciled is that our probability metric, \(P\), is just taking some real value to another real value... So which one is our sigma-algebra, the inputs of \(P\) or the inputs of \(X\)? 🤔 Hmm... Well, I guess it has the be the set of elements that \(X\) is mapping into \(\mathbb{R}\) since \(X\text{'s}\) input is a small omega \(\omega\) (which is probably an element of big omega \(\Omega\) based on the conventions of small notation being elements of big notation), so \(X\text{'s}\) domain much be the sigma-algrebra?

Let's try to generate a plausible example of this in action... Maybe something with an inequality like "\(X\ge 1\)". Okay, yeah, how about \(X\) is a random variable for the random process of how long it takes a customer to get through a grocery line. So \(X\) is mapping the elements of our sigma-algebra (ie, what customers actually end up experiencing in the real world) into a subset of the reals, namely \([0,\infty)\) because their time in line could be 0 minutes or infinite minutes (geesh, 😬 what a life that would be, huh?). Okay, so then I can ask a question like "What's the probability that \(X\) takes on a value greater than or equal to 1 minute?" which I think translates to "\(P\left(X(\omega)\ge 1\right)\)" which is really attempting to model this whole "random event" of "What's gonna happen to a particular person on average?"

So this makes me wonder... Is this fact that \(X\) can model this "random event" (at all) what people mean when they say something is a stochastic model? That there's a probability distribution it generates which affords us some way of dealing with navigating the uncertainty of the "random event"? If so, then sigma-algebras seem to serve as a kind of gateway and/or foundation into specific cognitive practices (ie, learning to think & reason probabilistically) that affords us a way out of being overwhelmed by our anxiety or fear and can help us reclaim some agency and autonomy in situations with uncertainty.

By waiting some amount of time (days/weeks/a few months) between originally reading something and processing one's notes on it allows them to slowly distill into one's consciousness. It also allows one to operate on their diffuse thinking which may also help to link ideas to others in their memory.

Robert Green's definition of creativity sounds like it's related to diffuse thinking processes. read: https://billyoppenheimer.com/august-14-2022/

Often note taking, and reviewing over those notes is more explicit in form for creating new ideas.

Come back to explore these.

I love this framing! In my experience companies don't generally acknowledge that metrics can be in tension, which usually means they're only tracking a subset of the metrics they ought to be if they want to have a more complete/realistic understanding of the state of things.

https://lu.ma/NickMilo?past=1

List of past videos Nick Milo has made with regard to note taking, thinking, Obsidian, etc.

Perhaps that should be addressed, rather than treating it as bedrock upon which to build.

If you're thinking without writing, you only think you're thinking. —Leslie Lamport.“Thinking Above the Code.” Lecture presented at the Microsoft Research Faculty Summit, Microsoft Research, July 15, 2014. https://www.microsoft.com/en-us/research/video/leslie-lamport-thinking-code/. Timestamp: 03:26

Link to:<br /> https://hypothes.is/a/rvisgFDXEe2s-SuJJGw3cA<br /> https://hypothes.is/a/yEFMHoCkEeyl34fItJe__w

Note that the spoken quote is different from the written quote.

https://www.wired.com/2013/01/code-bugs-programming-why-we-need-specs/

apparently quoted from Guindon: Michigan So Far<br /> see: https://www.goodreads.com/work/quotes/3403680-guindon-michigan-so-far#:~:text=%E2%80%9CWriting%20is%20nature's%20way%20of,how%20sloppy%20your%20thinking%20is.%E2%80%9D

Link to: https://hypothes.is/a/yEFMHoCkEeyl34fItJe__w along with the commentary there. This quote is another example of this fallacy.

Natto https://natto.dev<br /> built by Paul Shen https://twitter.com/_paulshen

https://www.loom.com/share/a05f636661cb41628b9cb7061bd749ae

Synopsis: Maggie Delano looks at some of the affordances supplied by Tana (compared to Roam Research) in terms of providing better block-based user interface for note type creation, search, and filtering.

These sorts of tools and programmable note implementations remind me of Beatrice Webb's idea of scientific note taking or using her note cards like a database to sort and search for data to analyze it and create new results and insight.

It would seem that many of these note taking tools like Roam and Tana are using blocks and sub blocks as a means of defining atomic notes or database-like data in a way in which sub-blocks are linked to or "filed underneath" their parent blocks. In reality it would seem that they're still using a broadly defined index card type system as used in the late 1800s/early 1900s to implement a set up that otherwise would be a traditional database in the Microsoft Excel or MySQL sort of fashion, the major difference being that the user interface is cognitively easier to understand for most people.

These allow people to take a form of structured textual notes to which might be attached other smaller data or meta data chunks that can be easily searched, sorted, and filtered to allow for quicker or easier use.

Ostensibly from a mathematical (or set theoretic and even topological) point of view there should be a variety of one-to-one and onto relationships (some might even extend these to "links") between these sorts of notes and database representations such that one should be able to implement their note taking system in Excel or MySQL and do all of these sorts of things.

Cascading Idea Sheets or Cascading Idea Relationships

One might analogize these sorts of note taking interfaces to Cascading Style Sheets (CSS). While there is the perennial question about whether or not CSS is a programming language, if we presume that it is (and it is), then we can apply the same sorts of class, id, and inheritance structures to our notes and their meta data. Thus one could have an incredibly atomic word, phrase, or even number(s) which inherits a set of semantic relationships to those ideas which it sits below. These links and relationships then more clearly define and contextualize them with respect to other similar ideas that may be situated outside of or adjacent to them. Once one has done this then there is a variety of Boolean operations which might be applied to various similar sets and classes of ideas.

If one wanted to go an additional level of abstraction further, then one could apply the ideas of category theory to one's notes to generate new ideas and structures. This may allow using abstractions in one field of academic research to others much further afield.

The user interface then becomes the key differentiator when bringing these ideas to the masses. Developers and designers should be endeavoring to allow the power of complex searches, sorts, and filtering while minimizing the sorts of advanced search queries that an average person would be expected to execute for themselves while also allowing some reasonable flexibility in the sorts of ways that users might (most easily for them) add data and meta data to their ideas.

Jupyter programmable notebooks are of this sort, but do they have the same sort of hierarchical "card" type (or atomic note type) implementation?

Goutor defines self-help notes as notes which one would use to refresh their memory about what remains to be done or researched, problems that remain to be solved, or information which is needed to be researched or found. (p26) These are akin in some sense to what I call "open questions". He also indicates that these notes might be triggered by one's daily activities or occasional musings which relate to one's project but occur outside of its active pursuit. In this sense, they have a similar feel to the idea of Ahrens' fleeting notes, but in Goutor's practice they aren't defined as occurring while one is doing active reading or research.

He suggests that one keeps these notes in a separate area so that they might be systematically and regularly visited for review, further research, or answering as the opportunities to do so present themselves. Once the questions have been answered and appropriate notes updated or added, these self-help notes can be discarded.

C. Wright Mills delineates a rough definition of "sociological imagination" which could be thought of as a framework within tools for thought: 1. Combinatorial creativity<br /> 2. Diffuse thinking, flâneur<br /> 3. Changing perspective (how would x see this?) Writing dialogues is a useful method to accomplish this. (He doesn't state it, but acting as a devil's advocate is a useful technique here as well.)<br /> 4. Collecting and lay out all the multiple viewpoints and arguments on a topic. (This might presume the method of devil's advocate I mentioned above 😀)<br /> 5. Play and exploration with words and terms<br /> 6. Watching levels of generality and breaking things down into smaller constituent parts or building blocks. (This also might benefit of abstracting ideas from one space to another.)<br /> 7. Categorization or casting ideas into types 8. Cross-tabulating and creation of charts, tables, and diagrams or other visualizations 9. Comparative cases and examples - finding examples of an idea in other contexts and time settings for comparison and contrast 10. Extreme types and opposites (or polar types) - coming up with the most extreme examples of comparative cases or opposites of one's idea. (cross reference: Compass Points https://hypothes.is/a/Di4hzvftEeyY9EOsxaOg7w and thinking routines). This includes creating dimensions of study on an object - what axes define it? What indices can one find data or statistics on? 11. Create historical depth - examples may be limited in number, so what might exist in the historical record to provide depth.

"Relaxed browsing and allowing the mind to wander" as a method of thinking and work is stated differently, but is highly related to the idea of diffuse thinking or working as a flâneur.

https://www.youtube.com/watch?v=wRssjvU2d-s

Starts out with some of the personal histories of how both got into the note making space.

This got more interesting for me around the 1:30 hour mark, but I was waiting for the material that would have shown up at the 3 hour mark (which doesn't exist...).

Scott spoke about the myths of zettelkasten. See https://www.reddit.com/r/Zettelkasten/comments/urawkd/the_myths_of_zettelkasten/

He also mentions maintenance rehearsal versus elaborative rehearsal. These are both part of spaced repetition. The creation of one's own cards helps play into both forms.

An explicit reference in 1931 in a section on note taking to cross links between entries in accounting ledgers. This linking process is a a precursor to larger database processes seen in digital computing.

Were there other earlier references that are this explicit within either note making or accounting contexts? Surely... (See also: Beatrice Webb's scientific note taking)

Just the word "digital" computing defines that there must have been an "analog' computing which preceded it. However we think of digital computing in much broader terms than we may have of the analog process.

Human thinking is heavily influenced by associative links, so it's only natural that we should want to link our notes together on paper as we've done for tens of thousands of years (at least.)

Es verdad que tiene bastante mala prensa pensar. Por ejemplo: falta de acción, pasivo. poco práctico. aislado de los verdaderos problemas, etc..

https://www.youtube.com/watch?v=P2HegcwDRnU

Makes the argument that note taking is an information system, and if it is, then we can use the research from the corpus of information system (IS) theory to examine how to take better notes.

He looks at the Wang and Wang 2006 research and applies their framework of "complete, meaningful, unambiguous, and correct" dimensions of data quality to example note areas of study notes, project management notes (or to do lists) and recipes.

Looks at dimensions of data quality from Mahanti, 2019.

What is the difference between notes and annotations?

Wrong. Here, I'll show you:

Forget about AGI for a moment. Instead, pretend we're talking about pecan pie. Most people probably can't answer the question, "What would I recognize as a pecan pie?" (or a sandwich). And yet thousands of people are able to make (and thousands more people are able to enjoy) pecan pie all the time—probably every day.

Den analogizes their note taking system to computing on 2010-11-11 8:43 PM.

Here's some justification for the prior statement on equity, but it comes after instead of before. (see: https://hypothes.is/a/SHEFJjM6Ee2Gru-y0d_1lg)

While there is some foundation to the claim given, it would need more support. The sage on the stage may be becoming outmoded with other potential models, but removing it altogether does remove some pieces which may help to support neurodiverse learners who work better via oral transmission rather than using literate modes (eg. dyslexia).

Who is to say that it's "just" sage on the stage lecturing and regurgitation? Why couldn't these same analytical practices be aimed at lectures, interviews, or other oral modes of presentation which will occur during thesis research? (Think anthropology and sociology research which may have much more significant oral aspects.)

Certainly some of these methods can create new levels of agency on the part of the learner/researcher. Has anyone designed experiments to measure this sort of agency growth?

Are some of the critical reading methods they're framing here similar to or some of the type found at Project Zero (https://pz.harvard.edu/thinking-routines)?

https://forum.zettelkasten.de/discussion/2373/zettelkasten-for-architecture-or-visual-output-in-general#latest

I am not sure if I agree with this statement, since for every discipline, the details of manipulating the data, refining, and creatively thinking may be vastly different. Can one really confidently declare that after the selection of data, the manner of thinking and manipulation of specific data can be generalized?

What is the size of a single thought?

500 words is about the size of a typical blog post. It's also about the size of a minimum recommended post for SEO purposes.

Nice to see his link to Steven Johnson here as I think this is where I've seen similar thoughts recently myself.

https://lu.ma/az338ptc

Joey Cofone: Are there laws to creativity?

Joey Cofone, author of the upcoming book The Laws of Creativity, is selling the idea of "float" (in comparison to Mihaly Csikzentmihaly's "flow"), which is ostensibly similar to Barbara Oakley's diffuse thinking framework, Nassim Nicholas Taleb's flâneur framing, and a dose of the Zeigarnik effect.

I'm concerned that this book will be broadly prescriptive without any founding on any of the extant research, literature, or science of the past. I'll think more highly of it if it were to quote/reference something like Merton and Barber's The Travels and Adventures of Serendipity: A Study in Sociological Semantics and the Sociology of Science.

Following on the above:

David Allen (of GTD fame) indicates that one should close all open loops to free up working memory, but leaving some open for active thought, follow up, and potential future insight creation can be a useful pattern too. (2022-09-09 9:05 AM)

https://lu.ma/e1jca29m

Priya Mohan: Design Thinking Strategies to solve complex problems in STEM

DICE Discover Ideate Create Evaluate

Mostly this was a tour through the DICE framing while using Obsidian for STEM.

Harford, T. (2021, May 6). What magic teaches us about misinformation. https://www.ft.com/content/5cea69f0-7d44-424e-a121-78a21564ca35

Second-order thinking

Ward in the context of Rare Earth hypothesis says this. An intriguing notion seeing thinking as a form of (deliberate) movement. How is this meant / to be understood? Chemically, in terms of what it requires in an animal (ie us)? The remark is made in the context of the need for oxygen for complex life to be possible. (based on David Catling Univ of Washington) after all. Or environmentally/contextually, as both deliberate physical movement and brain activity are response to outside impulses?