Thoughts on Zettelkasten numbering systems

I've seen variations of the beginner Zettelkasten question:

"What happens when you want to add a new note between notes 1/1 and 1/1a?"

asked at least a dozen times in the Reddit fora related to note taking and zettelkasten, on zettelkasten.de, or in other places across the web.

Dense Sets

From a mathematical perspective, these numbering or alpha-numeric systems are, by both intent and design, underpinned by the mathematical idea of dense sets. In the areas of topology and real analysis, one considers a set dense when one can choose a point as close as one likes to any other point. For both library cataloging systems and numbering schemes for ideas in Zettelkasten this means that you can always juxtapose one topic or idea in between any other two.

Part of the beauty of Melvil Dewey's original Dewey Decimal System is that regardless of how many new topics and subtopics one wants to add to their system, one can always fit another new topic between existing ones ad infinitum.

Going back to the motivating question above, the equivalent question mathematically is "what number is between 0.11 and 0.111?" (Here we've converted the artificial "number" "a" to a 1 and removed the punctuation, which doesn't create any issues and may help clarify the orderings a bit.) The answer is that there is an infinite number of numbers between these!

This is much more explicit by writing these numbers as:<br /> 0.110<br /> 0.111

Naturally 0.1101 is between them (along with an infinity of others), so one could start here as a means of inserting ideas this way if they liked. One either needs to count up sequentially (0, 1, 2, 3, ...) or add additional place values.

Decimal numbering systems in practice

The problem most people face is that they're not thinking of these numbers as decimals, but as natural numbers or integers (or broadly numbers without any decimal portions). Though of course in the realm of real numbers, numbers above 0 are dense as well, but require the use of their decimal portions to remain so.

The tough question is: what sorts of semantic meanings one might attach to their adding of additional place values or their alphabetical characters? This meaning can vary from person to person and system to system, so I won't delve into it here.

One may find it useful to logically chunk these numbers into groups of three as is often done using commas, periods, slashes, dashes, spaces, or other punctuation. This doesn't need to mean anything in particular, but may help to make one's numbers more easily readable as well as usable for filing new ideas. Sometimes these indicators can be confusing in discussion, so if ever in doubt, simply remove them and the general principles mentioned here should still hold.

Depending on one's note taking system, however, when putting cards into some semblance of a logical sort-able order (perhaps within a folder for example), the system may choke on additional characters beyond the standard period to designate a decimal number. For example: within Obsidian, if you have a "zettelkasten" folder with lots of numbered and named files within it, you'll want to give each number the maximum number of decimal places so that when doing an alphabetic sort within the folder, all of the numbered ideas are properly sorted. As an example if you give one file the name "0.510 Mathematics", another "0.514 Topology" and a third "0.5141 Dense Sets" they may not sort properly unless you give the first two decimal expansions to the ten-thousands place at a minimum. If you changed them to "0.5100 Mathematics" and "0.5140 Topology, then you're in good shape and the folder will alphabetically sort as you'd expect. Similarly some systems may or may not do well with including alphabetic characters mixed in with numbers.

If using chunked groups of three numbers, one might consider using the number 0.110.001 as the next level of idea between them and then continuing from there. This may help to spread some of the ideas out as surely one may have yet another idea to wedge in between 0.110.000 and 0.110.001?

One can naturally choose almost any any (decimal) number, so long as it it somewhat "near" the original behind which one places it. By going out further in the decimal expansion, one can always place any idea between two others and know that there will be a number that it can be given that will "work".

Generally within numbers as we use them for mathematics, 0.100000001 is technically "closer" by distance measurement to 0.1 than 0.11, (and by quite a bit!) but somehow when using numbers for zettelkasten purposes, we tend to want to not consider them as decimals, as the Dewey Decimal System does. We also have the tendency to want to keep our numbers as short as possible when writing, so it seems more "natural" to follow 0.11 with 0.111, as it seems like we're "counting up" rather than "counting down".

Another subtlety that one sees in numbering systems is the proper or improper use of the whole numbers in front of the decimal portions. For example, in Niklas Luhmann's system, he has a section of cards that start with 3.XXXX which are close to a section numbered 35.YYYY. This may seem a bit confusing, but he's doing a bit of mental gymnastics to artificially keep his numbers smaller. What he really means is 3000.XXX and 3500.YYY respectively, he's just truncating the extra zeros. Alternately in a fully "decimal system" one would write these as 0.3000.XXXX and 0.3500.YYYY, where we've added additional periods to the numbers to make them easier to read. Using our original example in an analog system, the user may have been using foreshortened indicators for their system and by writing 1/1a, they may have really meant something of the form 001.001/00a, but were making the number shorter in a logical manner (at least to them).

The close observer may have seen Scott Scheper adopt the slightly longer numbers in the thousands (like 3500.YYYY) as a means of remedying some of the numbering confusion many have when looking at Luhmann's system.

Those who build their systems on top of existing ones like the Dewey Decimal Classification, or the Universal Decimal Classification may wish to keep those broad categories with three to four decimal places at the start and then add their own idea number underneath those levels.

As an example, we can use the numbering for Finsler geometry from the Dewey Decimal Classification wikipedia page shown as:

``` 500 Natural sciences and mathematics

510 Mathematics

    516 Geometry

        516.3 Analytic geometries

            516.37 Metric differential geometries

                516.375 Finsler geometry

```

So in our zettelkasten, we might add our first card on the topic of Finsler geometry as "516.375.001 Definition of Finsler geometry" and continue from there with some interesting theorems and proofs on those topics.

Of course, while this is something one can do doesn't mean that one should do it. Going too far down the rabbit holes of "official" forms of classification this way can be a massive time wasting exercise as in most private systems, you're never going to be comparing your individual ideas with the private zettelkasten of others and in practice the sort of standardizing work for classification this way is utterly useless. Beyond this, most personal zettelkasten are unique and idiosyncratic to the user, so for example, my math section labeled 510 may have a lot more overlap with history, anthropology, and sociology hiding within it compared with others who may have all of their mathematics hiding amidst their social sciences section starting with the number 300. One of the benefits of Luhmann's numbering scheme, at least for him, is that it allowed his system to be much more interdisciplinary than using a more complicated Dewey Decimal oriented system which may have dictated moving some of his systems theory work out of his politics area where it may have made more sense to him in addition to being more productive on a personal level.

Of course if you're using the older sort of commonplacing zettelkasten system that was widely in use before Luhmann's variation, then perhaps using a Dewey-based system may be helpful to you?

A Touch of History

As both a mathematician working in the early days of real analysis and a librarian, some of these loose ideas may have occurred tangentially to Gottfried Wilhelm Leibniz (1646 - 1716), though I'm currently unaware of any specific instances within his work. One must note, however, that some of the earliest work within library card catalogs as we know and use them today stemmed from 1770s Austria where governmental conscription needs overlapped with card cataloging systems (Krajewski, 2011). It's here that the beginnings of these sorts of numbering systems begin to come into use well before Melvil Dewey's later work which became much more broadly adopted.

The German "file number" (aktenzeichen) is a unique identification of a file, commonly used in their court system and predecessors as well as file numbers in public administration since at least 1934. We know Niklas Luhmann studied law at the University of Freiburg from 1946 to 1949, when he obtained a law degree, before beginning a career in Lüneburg's public administration where he stayed in civil service until 1962. Given this fact, it's very likely that Luhmann had in-depth experience with these sorts of file numbers as location identifiers for files and documents. As a result it's reasonably likely that a simplified version of these were at least part of the inspiration for his own numbering system. † ‡

Your own practice

At the end of the day, the numbering system you choose needs to work for you within the system you're using (analog, digital, other). I would generally recommend against using someone else's numbering system unless it completely makes sense to you and you're able to quickly and simply add cards to your system with out the extra work and cognitive dissonance about what number you should give it. The more you simplify these small things, the easier and happier you'll be with your set up in the end.

References

Krajewski, Markus. Paper Machines: About Cards & Catalogs, 1548-1929. Translated by Peter Krapp. History and Foundations of Information Science. MIT Press, 2011. https://mitpress.mit.edu/books/paper-machines.

Munkres, James R. Topology. 2nd ed. 1975. Reprint, Prentice-Hall, Inc., 1999.

Hello u/sscheper,

Let me start by thanking you for introducing me to Zettelkasten. I have been writing notes for a week now and it's great that I'm able to retain more info and relate pieces of knowledge better through this method.

I recently came to notice that there is redundancy in my index entries.

I have two entries for Number Line. I have two branches in my Math category that deals with arithmetic, and so far I have "Addition" and "Subtraction". In those two branches I talk about visualizing ways of doing that, and both of those make use of and underline the term Number Line. So now the two entries in my index are "Number Line (Under Addition)" and "Number Line (Under Subtraction)". In those notes I elaborate how exactly each operation is done on a number line and the insights that can be derived from it. If this continues, I will have Number Line entries for "Multiplication" and "Division". I will also have to point to these entries if I want to link a main note for "Number Line".

Is this alright? Am I underlining appropriately? When do I not underline keyterms? I know that I do these to increase my chances of relating to those notes when I get to reach the concept of Number Lines as I go through the index but I feel like I'm overdoing it, and it's probably bloating it.

I get "Communication (under Info. Theory): '4212/1'" in the beginning because that is one aspect of Communication itself. But for something like the number line, it's very closely associated with arithmetic operations, and maybe I need to rethink how I populate my index.

Presuming, since you're here, that you're creating a more Luhmann-esque inspired zettelkasten as opposed to the commonplace book (and usually more heavily indexed) inspired version, here are some things to think about:<br /> - Aren't your various versions of number line card behind each other or at least very near each other within your system to begin with? (And if not, why not?) If they are, then you can get away with indexing only one and know that the others will automatically be nearby in the tree. <br /> - Rather than indexing each, why not cross-index the cards themselves (if they happen to be far away from each other) so that the link to Number Line (Subtraction) appears on Number Line (Addition) and vice-versa? As long as you can find one, you'll be able to find them all, if necessary.

If you look at Luhmann's online example index, you'll see that each index term only has one or two cross references, in part because future/new ideas close to the first one will naturally be installed close to the first instance. You won't find thousands of index entries in his system for things like "sociology" or "systems theory" because there would be so many that the index term would be useless. Instead, over time, he built huge blocks of cards on these topics and was thus able to focus more on the narrow/niche topics, which is usually where you're going to be doing most of your direct (and interesting) work.

Your case sounds, and I see it with many, is that your thinking process is going from the bottom up, but that you're attempting to wedge it into a top down process and create an artificial hierarchy based on it. Resist this urge. Approaching things after-the-fact, we might place information theory as a sub-category of mathematics with overlaps in physics, engineering, computer science, and even the humanities in areas like sociology, psychology, and anthropology, but where you put your work on it may depend on your approach. If you're a physicist, you'll center it within your physics work and then branch out from there. You'd then have some of the psychology related parts of information theory and communications branching off of your physics work, but who cares if it's there and not in a dramatically separate section with the top level labeled humanities? It's all interdisciplinary anyway, so don't worry and place things closest in your system to where you think they fit for you and your work. If you had five different people studying information theory who were respectively a physicist, a mathematician, a computer scientist, an engineer, and an anthropologist, they could ostensibly have all the same material on their cards, but the branching structures and locations of them all would be dramatically different and unique, if nothing else based on the time ordered way in which they came across all the distinct pieces. This is fine. You're building this for yourself, not for a mass public that will be using the Dewey Decimal System to track it all down—researchers and librarians can do that on behalf of your estate. (Of course, if you're a musician, it bears noting that you'd be totally fine building your information theory section within the area of "bands" as a subsection on "The Bandwagon". 😁)

If you overthink things and attempt to keep them too separate in their own prefigured categorical bins, you might, for example, have "chocolate" filed historically under the Olmec and might have "peanut butter" filed with Marcellus Gilmore Edson under chemistry or pharmacy. If you're a professional pastry chef this could be devastating as it will be much harder for the true "foodie" in your zettelkasten to creatively and more serendipitously link the two together to make peanut butter cups, something which may have otherwise fallen out much more quickly and easily if you'd taken a multi-disciplinary (bottom up) and certainly more natural approach to begin with. (Apologies for the length and potential overreach on your context here, but my two line response expanded because of other lines of thought I've been working on, and it was just easier for me to continue on writing while I had the "muse". Rather than edit it back down, I'll leave it as it may be of potential use to others coming with no context at all. In other words, consider most of this response a selfish one for me and my own slip box than as responsive to the OP.)

https://thevoroscope.com/2022/06/27/sum-total-human-knowledge-4/

https://udcc.org/index.php/site/page?view=subject_coverage

Subject coverage of the UDC.

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

Morens, D. M., Taubenberger, J. K., & Fauci, A. S. (2021). Universal Coronavirus Vaccines—An Urgent Need. New England Journal of Medicine, 0(0), null. https://doi.org/10.1056/NEJMp2118468

Ball, P. (2022, February 26). Will we get a single, variant-proof vaccine for Covid? The Observer. https://www.theguardian.com/society/2022/feb/26/will-we-get-a-single-variant-proof-vaccine-for-covid

Historical Hypermedia: An Alternative History of the Semantic Web and Web 2.0 and Implications for e-Research. .mp3. Berkeley School of Information Regents’ Lecture. UC Berkeley School of Information, 2010. https://archive.org/details/podcast_uc-berkeley-school-informat_historical-hypermedia-an-alte_1000088371512. archive.org.

https://www.ischool.berkeley.edu/events/2010/historical-hypermedia-alternative-history-semantic-web-and-web-20-and-implications-e.

https://www.ischool.berkeley.edu/sites/default/files/audio/2010-10-20-vandenheuvel_0.mp3

Interface as Thing - book on Paul Otlet (not released, though he said he was working on it)

• W. Boyd Rayward 1994 expert on Otlet
• Otlet on annotation, visualization, of text
• TBL married internet and hypertext (ideas have sex)
• V. Bush As We May Think - crosslinks between microfilms, not in a computer context
• Ted Nelson 1965, hypermedia

t=540

• Michael Buckland book about machine developed by Emanuel Goldberg antecedent to memex
• Emanuel Goldberg and His Knowledge Machine: Information, Invention, and Political Forces (New Directions in Information Management) by Michael Buckland (Libraries Unlimited, (March 31, 2006)
• Otlet and Goldsmith were precursors as well

four figures in his research: - Patrick Gattis - biologist, architect, diagrams of knowledge, metaphorical use of architecture; classification - Paul Otlet, Brussels born - Wilhelm Ostwalt - nobel prize in chemistry - Otto Neurath, philosophher, designer of isotype

Paul Otlet

• wrote bibliography on law
• book: Something on Bibliography #wanttoread
• universal decimal classification system
• mundaneum
• Le Corbusier - architect worked with Otlet for building for Mundaneum; See: https://socks-studio.com/2019/05/05/the-shape-of-knowledge-the-mundaneum-by-paul-otlet-and-henri-la-fontaine/

Otlet was interested in both the physical as well as the intangible aspects of the Mundaneum including as an idea, an institution, method, body of work, building, and as a network.<br /> (#t=1020)

Early iPhone diagram?!?

(roughly) armchair to do the things in the web of life (Nelson quote) (get full quote and source for use) (circa 19:30)

compares Otlet to TBL

Michael Buckland 1991 <s>internet of things</s> coinage - did I hear this correctly? https://en.wikipedia.org/wiki/Internet_of_things lists different coinages

Turns out it was "information as thing"<br /> See: https://hypothes.is/a/kXIjaBaOEe2MEi8Fav6QsA

sugane brierre and otlet<br /> "everything can be in a document"<br /> importance of evidence

The idea of evidence implies a passiveness. For evidence to be useful then, one has to actively do something with it, use it for comparison or analysis with other facts, knowledge, or evidence for it to become useful.

transformation of sound into writing<br /> movement of pieces at will to create a new combination of facts - combinatorial creativity idea here. (circa 27:30 and again at 29:00)<br /> not just efficiency but improvement and purification of humanity

put things on system cards and put them into new orders<br /> breaking things down into smaller pieces, whether books or index cards....

Otlet doesn't use the word interfaces, but makes these with language and annotations that existed at the time. (32:00)

Otlet created diagrams and images to expand his ideas

Otlet used octagonal index cards to create extra edges to connect them together by topic. This created more complex trees of knowledge beyond the four sides of standard index cards. (diagram referenced, but not contained in the lecture)

Otlet is interested in the "materialization of knowledge": how to transfer idea into an object. (How does this related to mnemonic devices for daily use? How does it relate to broader material culture?)

Otlet inspired by work of Herbert Spencer

space an time are forms of thought, I hold myself that they are forms of things. (get full quote and source) from spencer influence of Plato's forms here?

Otlet visualization of information (38:20)

S. R. Ranganathan may have had these ideas about visualization too

atomization of knowledge; atomist approach 19th century examples:S. R. Ranganathan, Wilson, Otlet, Richardson, (atomic notes are NOT new either...) (39:40)

Otlet creates interfaces to the world - time with cyclic representation - space - moving cube along time and space axes as well as levels of detail - comparison to Ted Nelson and zoomable screens even though Ted Nelson didn't have screens, but simulated them in paper - globes

Katie Berner - semantic web; claims that reporting a scholarly result won't be a paper, but a nugget of information that links to other portions of the network of knowledge.<br /> (so not just one's own system, but the global commons system)

Mention of Open Annotation (Consortium) Collaboration:<br /> - Jane Hunter, University of Australia Brisbane & Queensland<br /> - Tim Cole, University of Urbana Champaign<br /> - Herbert Van de Sompel, Los Alamos National Laboratory annotations of various media<br /> see:<br /> - https://www.researchgate.net/publication/311366469_The_Open_Annotation_Collaboration_A_Data_Model_to_Support_Sharing_and_Interoperability_of_Scholarly_Annotations - http://www.openannotation.org/spec/core/20130205/index.html - http://www.openannotation.org/PhaseIII_Team.html

trust must be put into the system for it to work

coloration of the provenance of links goes back to Otlet (~52:00)

Creativity is the friction of the attention space at the moments when the structural blocks are grinding against one another the hardest. —Randall Collins (1998) The sociology of philosophers. Cambridge, MA: Harvard University Press (p.76)

The Outline of Knowledge appears in the Propædia volume of the Encyclopedia Britannica. It is similar to various olther classification systems like the Dewey Decimal system or the Universal Decimal Classification.

!- claim : examples of a good enough world * Universal Basic Income (UBI) * Blockchain * Offer network

!- in other words : enoughness * Universal Basic Income (UBI)

https://niklas-luhmann-archiv.de/bestand/zettelkasten/zettel/ZK_2_SW1_001_V

One may notice that Niklas Luhmann's index within his zettelkasten is fantastically sparce. By this we might look at the index entry for "system" which links to only one card. For someone who spent a large portion of his life researching systems theory, this may seem fantastically bizarre.

However, it's not as as odd as one may think given the structure of his particular zettelkasten. The single reference gives an initial foothold into his slip box where shuffling through cards beyond that idea will reveal a number of cards closely related to the topic which subsequently follow it. Regular use and work with the system would have allowed Luhmann better memory with respect to its contents and the searching through threads of thought would have potentially sparked new ideas and threads. Thus he didn't need to spend the time and effort to highly index each individual card, he just needed a starting place and could follow the links from there. This tends to minimize the indexing work he needed to do regularly, but simultaneously makes it harder for the modern person who may wish to read or consult those notes.

Some of the difference here is the idea of top-down versus bottom-up construction. While thousands of his cards may have been tagged as "systems" or "systems theory", over time and with increased scale they would have become nearly useless as a construct. Instead, one may consider increasing levels of sub-topics, but these too may be generally useless with respect to (manual) search, so the better option is to only look at the smallest level of link (and/or their titles) which is only likely to link to 3-4 other locations outside of the card just before it. This greater specificity scales better over time on the part of the individual user who is broadly familiar with the system.

Alternatively, for those in shared digital spaces who may maintain public facing (potentially shared) notes (zettelkasten), such sparse indices may not be as functional for the readers of such notes. New readers entering such material generally without context, will feel lost or befuddled that they may need to read hundreds of cards to find and explore the sorts of ideas they're actively looking for. In these cases, more extensive indices, digital search, and improved user interfaces may be required to help new readers find their way into the corpus of another's notes.

Another related idea to that of digital, public, shared notes, is shared taxonomies. What sorts of word or words would one want to search for broadly to find the appropriate places? Certainly widely used systems like the Dewey Decimal System or the Universal Decimal Classification may be helpful for broadly crosslinking across systems, but this will take an additional level of work on the individual publishers.

Is or isn't it worthwhile to do this in practice? Is this make-work? Perhaps not in analog spaces, but what about the affordances in digital spaces which are generally more easily searched as a corpus.

As an experiment, attempt to explore Luhmann's Zettelkasten via an entryway into the index. Compare and contrast this with Andy Matuschak's notes which have some clever cross linking UI at the bottoms of the notes, but which are missing simple search functionality and have no tagging/indexing at all. Similarly look at W. Ross Ashby's system (both analog and digitized) and explore the different affordances of these two which are separately designed structures---the analog by Ashby himself, but the digital one by an institution after his death.

https://udcsummary.info/php/index.php?lang=en

Interesting defined vocabulary and concatenation/auxiliary signs for putting ideas into proximity.

Could be useful for note taking. Probably much harder to get people to adopt this sort of thing with shared notes/note taking however.

Somewhat similar to the Dewey Decimal classification system.

Noam Chomsky felt that there was a tendency for people to confuse the ideas of deep structure with the ideas of either generative grammar or universal grammar. He also thought that professional linguists confused what he called "the creative aspect of language use" with the recursive property of generative grammars.

Lois Weber<br /> - First woman accepted to Motion Picture Director's Association, precursor of Director's Guild<br /> - First directors committee of the Academy of Motion Picture Arts and Sciences<br /> - Mayor of Universal City<br /> - One of the highest paid and most influential directors in Hollywood of her day<br /> - one of first directors to form her own production company

See also: - https://en.wikipedia.org/wiki/Lois_Weber

Where are My Children?, Universal's top film of 1916, written and directed by their top director Lois Weber, discussed abortion and birth control. It was added to the National Film Registry in 1993.

See also - Stamp, Shelley. Lois Weber in Early Hollywood. University of California Press, May 2015. ISBN 9780520284463

Watched this last night

https://www.kcet.org/shows/lost-la/episodes/dream-factory

https://udlguidelines.cast.org/

https://www.facultyfocus.com/articles/effective-teaching-strategies/bringing-theories-to-practice-universal-design-principles-and-the-use-of-social-annotation-to-support-neurodivergent-students/

A very brief primer on UDL and how Hypothes.is and social annotation might fit within its framework. There seems to be a stronger familiarity with Hypothes.is as a tool and a bit less familiarity with UDL, or perhaps they just didn't bind the two together as tightly as they might have.

I'm definitely curious to look more closely at the UDL framework to see what we might extract from it.

The title features neurodiversity, but doesn't deliver on the promise.

An interesting reframing would be that of social annotation with the idea of modality shifts, particularly for neurodiverse students.

Universal Design for Learning framework https://udlguidelines.cast.org/

http://expositions.mundaneum.org/fr/mundaneum-petite-histoire-dune-grande-idee

Universal Bibliographical Directory (RBU)

This description of "teach[ing] to all the [learning] styles" seems similar to some descriptions of Universal Design for Learning that I have seen.

Liu, C., Yang, Y., Chen, B., Cui, T., Shang, F., & Li, R. (2022). Revealing spatio-temporal interaction patterns behind complex cities. ArXiv:2201.02117 [Physics]. http://arxiv.org/abs/2201.02117

The exact same could be said of the early web which hasn't been evenly archived or easily searchable, so responses to early blog articles may not be easily found amidst a mountain of noise.

Current practice in UK on UDL- updated references and useful publication linked to HEA accreditation

Scott, Jake, Aaron Richterman, and Muge Cevik. ‘Covid-19 Vaccination: Evidence of Waning Immunity Is Overstated’. BMJ 374 (23 September 2021): n2320. https://doi.org/10.1136/bmj.n2320.

will track mounts and fin boxes work together? Do they share standards?

Skimmed opening paragraphs in physical newspaper. Want to revisit. This sounds like the sort of "pulling oneself up by one's bootstraps" that actually works.

Walker, P., Davis, N., & Grover, N. (2021, September 3). UK vaccines watchdog fails to back Covid jabs for children. The Guardian. http://www.theguardian.com/society/2021/sep/03/uk-rules-out-covid-vaccinations-for-children

Nandi, A., Kumar, S., Shet, A., Bloom, D. E., & Laxminarayan, R. (2020). Childhood vaccinations and adult schooling attainment: Long-term evidence from India’s Universal Immunization Programme. Social Science & Medicine (1982), 250, 112885. https://doi.org/10.1016/j.socscimed.2020.112885

This may be well worth reading with respect to my research on memory, stenography, shorthand, etc.

Interesting that this links the idea of universal languages to his mathematical notation and NOT to the idea of translating numbers into words using and early form of the major system.

Kim, M. J., & Lee, S. (2020). Can Stimulus Checks Boost an Economy under COVID-19? Evidence from South Korea. IZA Discussion Paper, 13567.

Evaluates CLUE, Mastering-SP, and POGIL curricula on universal design for learning checkpoints for making materials accessible for students with disabilities Guidelines for universal design for learning valuable for course design

editor, P. B. S. policy. (2020, December 9). Covid-driven recession likely to push 2m UK families into poverty. The Guardian. https://www.theguardian.com/society/2020/dec/09/covid-driven-recession-likely-to-push-2m-uk-families-into-poverty

Adult Learning often takes place within walls or in front of a computer screen this can lead to health problems. This article offers reasons and methods for getting adults outdoors and using Universal Design. Outdoor learning can be used to complement digital learning.

How many times do we use "accommodations" which dance around the relational issues, instead of dealing directly with them?

Good article about the importance of Universal Design when designing learning opportunities. The authors use plenty of strong sources to back their findings and keep the information concise.

9/10

IZA – Institute of Labor Economics. ‘COVID-19 and the Labor Market’. Accessed 6 October 2020. https://covid-19.iza.org/publications/dp13742/.

Lozano, R., Fullman, N., Mumford, J. E., Knight, M., Barthelemy, C. M., Abbafati, C., Abbastabar, H., Abd-Allah, F., Abdollahi, M., Abedi, A., Abolhassani, H., Abosetugn, A. E., Abreu, L. G., Abrigo, M. R. M., Haimed, A. K. A., Abushouk, A. I., Adabi, M., Adebayo, O. M., Adekanmbi, V., … Murray, C. J. L. (2020). Measuring universal health coverage based on an index of effective coverage of health services in 204 countries and territories, 1990–2019: A systematic analysis for the Global Burden of Disease Study 2019. The Lancet, 0(0). https://doi.org/10.1016/S0140-6736(20)30750-9

Original post is here.

This explanation should be combined with 24 Days of GHC Extensions: Rank N Types (see related hypothes.is note).

This was very neatly put, and forall above is also spot on.

My main issue with this book is that the difficulty is exponentially increasing, and by "keeping it simple" (i.e., trying to use simple terms) it is even harder to do a proper research.

For example:

1. The name of this chapter

This chapter should have been called Explicitly quantified type or Explicit universal quantification as it is too general as is, and doing a search to get to know more when someone has no formal/previous functional programming background, makes very hard.

Most importantly though, even if Haskell not mentioned, the word "explicit" would have been important.

It is also more about generic parameters than about quantification itself, and forall is kind of introduced but it is totally misleading.

2. forall

The post “forall” is the type-level “lambda” (saved) is the best, most succinct explanation of forall that I ever found. Unfortunately not before going down the rabbit hole.. (See links below.) One still needs to know about

• typeclasses
• generic parameters
• constraints
• what pragmas are but after that, it is straightforward.

(Jordan's Reference section on forall also doesn't help much.)

forall is also mandatory in PureScript (which is also not mentioned when introducing it), and I believe a comparison (the way the above post did) with Haskell is important, but at the right time. At least Jordan's Reference tries to put it off until later, but still before explaining concepts required to understand it.

3. The "rabbit hole" links

These are all good resources, but not for uninitiated mortals, and at a lower level (such as where I am now) they raise more questions than answers.

• Explicit forall (r/purescript reddit)]

  (Started here initially, but the single sentence there prompted a search for scoped type variables and rank-n types (or Rank N types).)

Arnold, Carrie. ‘Pandemic Speeds Largest Test yet of Universal Basic Income’. Nature, 10 July 2020. https://doi.org/10.1038/d41586-020-01993-3.

Page Le, M. (2020, June 24). Town in UK takes steps to test entire population for coronavirus. New Scientist. https://www.newscientist.com/article/2246880-town-in-uk-takes-steps-to-test-entire-population-for-coronavirus/

Zhou, B., Lu, X., & Holme, P. (2020). Universal evolution patterns of degree assortativity in social networks. Social Networks, 63, 47–55. https://doi.org/10.1016/j.socnet.2020.04.004

Nettle, D., Johnson, E., Johnson, M., & Saxe, R. (2020). Why has the COVID-19 pandemic increased support for Universal Basic Income? [Preprint]. PsyArXiv. https://doi.org/10.31234/osf.io/csr3u

Peto, J., Alwan, N. A., Godfrey, K. M., Burgess, R. A., Hunter, D. J., Riboli, E., Romer, P., Buchan, I., Colbourn, T., Costelloe, C., Smith, G. D., Elliott, P., Ezzati, M., Gilbert, R., Gilthorpe, M. S., Foy, R., Houlston, R., Inskip, H., Lawlor, D. A., … Yao, G. L. (2020). Universal weekly testing as the UK COVID-19 lockdown exit strategy. The Lancet, 0(0). https://doi.org/10.1016/S0140-6736(20)30936-3

Universal design for learning (UDL) is the topic of focus for this webinar hosted by Digital Promise. Multiple experts discuss UDL for adult learners and strategies for UDL. Rating: 6/10

Really interesting point here about the limit of the "curb cut" metaphor.

Great pull quote.

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three definitive models for Universal Health Care

We welcome public feedback to strengthen our communique and potential calls to action. Thank you!

Bradley Kuhn è d'accordo con me sulla necessità di retribuzioni confortevoli ma non da ricconi quando si tratta di progetti comunitari.

True, but still we are not in right track since 1947 !

UDL guidelines. As I post this, I do not know whether this website will be included in our future course readings or not. This website practices what it preaches and provides the same content in multiple forms. The viewer can select/choose the manner in which items are displayed. This has essential information, such as the need to provide "multiple means" of engagement, representation, action, and expression when teaching. Rating 5/5

Unlike Sheridan's method, which was proposed as a universal system. Enlightenment dudes sure love their universal ideas.

Language shapes the way we think and therefore it has the potential to limit what we are capable of thinking.

The desire for both universality and essence is interesting. Universality is a concept with breadth, applicable on a large scale and encompassing many things. Essence, on the other hand, is extremely narrow, focused and boiled down to a pinpoint. It's a juggling act to attempt both.

I already have a problem.

Is sensation a universal phenomenon? If so, that doesn't mean that human's experience sensations in the same way and therefore the ideas generated from those sensations would naturally vary.

The desire for "universal" anything seems fraught with problem, even for seemingly "simple" ideas.

Following lhm8's Fenollosa comment earlier, this was an idea that survived into the early 20th C., as writers like Fenollos and Ezra Pound looked to the Chinese character as a more "natural" state of language, something closer to a universal meaning.

I hadn't thought about the etymology of university before, but the juxtaposition with "universal grammar" spurred my curiosity about their common roots:

From community, corporation (1214 in Old French; also in Old French as universitei , universiteit , etc.), totality, universality (13th cent.)

http://www.oed.com.ezp.slu.edu/view/Entry/214804?rskey=lzyKTO&result=1&isAdvanced=false#eid

I'm noticing a theme here, with the desire of universal ideals, truths, …people. In a time/place where the world (as people knew it) was still relatively small, there seems a pervading sense of attempted connection, of finding common ground, to unify. In our current time/place with a greatly expanded sense of the world and its variety, have we mostly given up on that desire for uniformity? Do we like to think we have? Recent events indicate that perhaps we haven't given up that desire as much as we had thought, but are those events anomalous outliers or an ugly truth?

Language similar to that of Hume, here and in the "General Orations" remark below (where generalities are more likely to be universally true than particulars)

Belonging to the whole world; universal, general, world-wide.

http://www.oed.com.ezp.slu.edu/view/Entry/59462?redirectedFrom=ecumenical#eid

These are also best practices in teaching and learning, which says something about human cognition and motivation generally and how we think about people who need "accommodations." In other words, maybe we all need "accommodations" that serve our need for autonomy, mastery, and purpose.

If only this was an issue in the USA, where going to a doctor is not a free service for the patient, in most cases. The same level of trust is not there; this is unacceptable/

Voters have been known throughout history, most recently in 2016, to vote against their own interests for reasons that are, frankly, stupid.

Canada gets it. The US does not. This must change and quickly.

Translation: they do not see the audience as a problem to be addressed, but an assumed set of factors. Now I will continue to talk about the problem for a few more pages and only respond with an answer at the very end.

This is a confusing construction. Summary: purely rational argument is trying to appeal to a "universal audience," but the editors want to clarify that Perelman and Olbrechts-Tyteca did not really believe that a true universal audience exists. Rather, a speaker imagines a universal audience (rather than one that already has a set of shared values that must be appealed to in a specific way), and then tries to make rational arguments that could appeal to the "universal audience" of their imagination.

This feels like a direct address to the reader. It feels didactic and adds to the overall sense of a religious sermon or teaching that comes from the section as a whole. It implicates the reader in the poem and asks the reader to address their own mortality.

this line could be referencing these two groups to give a unifying or universal sense of community. Perhaps a sort of collective or mutual bond between the two because of the drastic “whirlpool” referenced just before this line relating or joining people across boundaries.

almost universal belief that all people define the real world of objects, events, and living creatures in pretty much the same way.

Highlight of original quote: https://hypothes.is/a/iKeap_T6TauWGfyf19VW_Q