267 Matching Annotations
  1. Feb 2024
    1. When writing ranges of numbers, most style guides agree on the use of an en dash (although the AP style guide prefers a hyphen). Do not use an em dash.

      Use en dash for number ranges and no space either side

  2. Jan 2024
    1. Lenstra’s elliptic curve algorithm for fac-toring large integers. This is one of the recent applications of elliptic curvesto the “real world,” to wit, the attempt to break certain widely used public keyciphers.
    2. the emphasis of this book is on number theoretic aspects ofelliptic curves, so we feel that an informal approach to the underlying geom-etry is permissible, since it allows us more rapid access to the number theory.

      The approach of the book is underpinned more by number theory rather than geometry, though the geometry is used for some basic motivations.

  3. Dec 2023
    1. ociocratic Neighbourhood Circles (SoNeC) ideally consist of between 20-40 households (with 1 adultrepresentative per household) in the same local neighbourhood. The neighbourhood should be mappedso that the total population of the neighbourhood will fall within “Dunbar’s number” of residents, or 150people, the number with whom most humans can easily maintain personal relations.
      • for: SONEC - Dunbar number

      • comment

        • SONECs are based on Dunbar number of 150 people to maintain group intimacy
    1. How to fold and cut a Christmas star<br /> Christian Lawson-Perfect https://www.youtube.com/watch?v=S90WPkgxvas

      What a great simple example with some interesting complexity.

      For teachers trying this with students, when one is done making some five pointed stars, the next questions a curious mathematician might ask are: how might I generalize this new knowledge to make a 6 pointed star? A 7 pointed star? a 1,729 pointed star? Is there a maximum number of points possible? Is there a minimum? Can any star be made without a cut? What happens if we make more than one cut? Are there certain numbers for which a star can't be made? Is there a relationship between the number of folds made and the number of points? What does all this have to do with our basic definition of what a paper star might look like? What other questions might we ask to extend this little idea of cutting paper stars?

      Recalling some results from my third grade origami days, based on the thickness of most standard office paper, a typical sheet of paper can only be folded in half at most 7 times. This number can go up a bit if the thickness of the paper is reduced, but having a maximum number of potential folds suggests there is an upper bound for how many points a star might have using this method of construction.

  4. May 2023
    1. was digested with PstI (TaKaRa, Japan) to prevent the copy number from being underestimated (66).

      Why does digestion improve the estimation of plasmid vs the chromosome? I would assume the chromosome is more tightly supercoiled and inaccessible unless digested right?

  5. Apr 2023
    1. The first major insight on God’s Number was by Dr. Morwen Thistlethwaite in 1981, who proved it was at most 52. That means he proved every scrambled cube can be solved in 52 moves or less.Progress continued through the 1990s and 2000s. Finally, in June 2010, a team of four scientists proved that God’s number is 20.

      With respect to the Rubic's Cube, God's number is defined as the minimum number of turns to solve a randomly scrambled cube. Morwen Thistlethwaite proved that it was at most 52 moves in 1981. By June 2010 a group of four had a proof that God's number is 20.

    1. the overarching paradigm that underlies the global system, however useful it might have been, is not only obsolete, but actively pushing us toward self-annihilation. This paradigm reduces human existence to competition between disconnected, materially-defined units whose primary imperative is individual material self-maximisation and accumulation. Yet it is precisely this way of being that is eroding our mental health and destroying planetary life-support systems. Our inherently relational nature, the fact that our well-being is tied up with our connections to others – that we are fundamentally interconnected – is obfuscated.Moving through the global phase-shift, then, requires us to completely reorient ourselves into a new way of being in the world, rooted in new ways of understanding our relationship with the world that actually connect with reality.

      In Other Words The human INTERbeing - our relational nature - our Dunbar number past - is denied by modernity

  6. Mar 2023
    1. Unlike the other apps listed here, Authy requires your phone number when you first set it up. We're not fans of this requirement, since we’d rather have the app consider our phones to be anonymous pieces of hardware; and some have suggested that requiring a phone number opens the app up to SIM-card-swap fraud.
    2. 2FAS doesn't need your phone number or even require you to create an online account, so it's not susceptible to SIM-swapping fraud.
    1. But 150 alone doesn’t tell the whole story. Other numbers are nested within the social brain hypothesis too. According to the theory, the tightest circle has just five people – loved ones. That’s followed by successive layers of 15 (good friends), 50 (friends), 150 (meaningful contacts), 500 (acquaintances) and 1500 (people you can recognise). People migrate in and out of these layers, but the idea is that space has to be carved out for any new entrants.
      • Paraphrase
      • 150 alone doesn’t tell the whole story.
      • Other range numbers are nested within the social brain hypothesis.
      • curiously, Dunbar recognized they were all multiples of 5.

        • the tightest circle has just 5 people (loved ones).
        • 15 (good friends),
        • 50 (friends),
        • 150 (meaningful contacts),
        • 500 (acquaintances) and
        • 1500 (people you can recognise).
      • People migrate in and out of these layers,

      • but that space has to be carved out for any new entrants.
    2. to avoid alienation or tensions, city residents should find quasi-villages within their cities.
      • Applying Dunbar's number to urban planning gives us the idea of the = "quasi-village"
      • Comment
        • this could be quite useful for creating more = citizen social capital within cities,
      • and from that, more impactful, bottom-up civic engagement
      • for climate change action, this could be a Very key strategy
      • Claim
        • alienation is rife in many large cities and "communities" are:
      • no longer communities in the traditional anthropological sense in which social capital was high.
      • hence, there is an urgent need for:
      • Quotable phrase
        • communities need to relearn how to be communities once again.
  7. Feb 2023
  8. Jan 2023
  9. Oct 2022
    1. The question often asked: "What happens when you want to add a new note between notes 1/1 and 1/1a?"

      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.


      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.

    1. https://en.wikipedia.org/wiki/Stephanus_pagination

      Stephanus pagination is a system of reference numbers used in editions of Plato based on the three volume 1578 edition of Plato's complete works published by Henricus Stephanus (Henri Estienne) and translated by Joannes Serranus (Jean de Serres).

      See also: - Bekker numbering (for Aristotle) - Diels-Kranz numbering (for early pre-Socratics)

    1. https://youtu.be/ILuSxUYYjMs

      Luhmann zettelkasten origin myth at 165 second mark

      A short outline of several numbering schemes (essentially all decimal in nature) for zettelkasten including: - Luhmann's numbering - Bob Doto - Scott Scheper - Dan Allosso - Forrest Perry

      A little light on the "why", though it does get location as a primary focus. Misses the idea of density and branching. Touches on but broadly misses the arbitrariness of using the comma, period, or slash which functions primarily for readability.

  10. Sep 2022
  11. Aug 2022
  12. Jul 2022
  13. Jun 2022
    1. can someone explain to me the relationship between Luhmann's numbering and the "categories" of Wikipedia (1000-6000)? I can't find the video where Scott explains that the first number used by Luhmann for the entry note is of the order of thousands and that it indicated a general category?

      Since I just happen to have an antinet laying around 🗃️😜🔎 I can do a quick cross referenced search for antinet, youtube, and numbering systems to come up with this: https://www.youtube.com/watch?v=MrjUg4toZqw.

      Hopefully it's the one (or very similar) to what you're looking for.

      Since it was also hiding in there in a linked card, an added bonus for you:

      "Here I am on the floor showing you freaking note cards, which really means that I have made it in life." —Scott P. Scheper

  14. May 2022
  15. Apr 2022
  16. Feb 2022
    1. Yamasoba, D., Kimura, I., Nasser, H., Morioka, Y., Nao, N., Ito, J., Uriu, K., Tsuda, M., Zahradnik, J., Shirakawa, K., Suzuki, R., Kishimoto, M., Kosugi, Y., Kobiyama, K., Hara, T., Toyoda, M., Tanaka, Y. L., Butlertanaka, E. P., Shimizu, R., … Sato, K. (2022). Virological characteristics of SARS-CoV-2 BA.2 variant (p. 2022.02.14.480335). bioRxiv. https://doi.org/10.1101/2022.02.14.480335

  17. Jan 2022
    1. Also, researchers have disputed the empirical observation of mean human group sizes approximately averaging around 150 persons, presenting empirical observations of group sizes indicating a wide variety of other numbers [46–53]. Thus, ecological research on primate sociality, the uniqueness of human thinking and empirical observations all indicate that there is no hard cognitive limit on human sociality. Our reanalysis provides the last piece of evidence needed to disregard Dunbar's number.

      Even if Dunbar's number is disproved, the range of social network sizes seem to all be less than some upper bound, such as 1,000. This is aligned to common sense - we simply cannot invest meaningful time to maintain more than a group size of even 1,000.

  18. Dec 2021
    1. Possibility of linking (Verweisungsmöglichkeiten). Since all papers have fixed numbers, you can add as many references to them as you may want. Central concepts can have many links which show on which other contexts we can find materials relevant for them.

      Continuing on the analogy between addresses for zettels/index cards and for people, the differing contexts for cards and ideas is similar to the multiple different publics in which people operate (home, work, school, church, etc.)

      Having these multiple publics creates a variety of cross links within various networks for people which makes their internal knowledge and relationships more valuable.

      As societies grow the number of potential interconnections grows as well. Compounding things the society doesn't grow as a homogeneous whole but smaller sub-groups appear creating new and different publics for each member of the society. This is sure to create a much larger and much more complex system. Perhaps it's part of the beneficial piece of the human limit of memory of inter-personal connections (the Dunbar number) means that instead of spending time linearly with those physically closest to us, we travel further out into other spheres and by doing so, we dramatically increase the complexity of our societies.

      Does this level of complexity change for oral societies in pre-agrarian contexts?

      What would this look like mathematically and combinatorially? How does this effect the size and complexity of the system?

      How can we connect this to Stuart Kauffman's ideas on complexity? (Picking up a single thread creates a network by itself...)

  19. Nov 2021
    1. there are over 1,300 cryptocurrencies in existence

      According to Statista, there are 7557 cryptocurrencies as at November 2021.

  20. Oct 2021
  21. Sep 2021
    1. The main idea comes at the beginning, the bodyparagraphs support the main idea, and the conclusion wraps up the whole thing

      This is good to know and remember so you know what to look for when reading something. i have to make sure to have these 3 components when writing any kind of essay.

  22. Aug 2021
  23. Jul 2021
  24. Jun 2021
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  27. Mar 2021
  28. Feb 2021
    1. Any time a change is needed, rather than creating new ads and groups, business data can be updated seamlessly, trickling the change to ad copy without triggering an ad Quality Score review.

      Not creating new ad groups or campaigns is mentioned frequently, what is the average number of campaigns recommended to use per vertical?

  29. Jan 2021
    1. RSF1010 is maintained at a copy-number of about 10-12 per chromosome in E coli, P. aeruginosa and S. enterica sv.Typhimurium (Frey and Bagdasarian, 1989)
  30. Dec 2020
  31. Nov 2020
    1. Copy numbers of the oriV region and gfp gene on the plasmid relative to a chromosomal gene were determined by qPCR. The chromosomal gene dapA was set up as the reference gene
    1. Designed probes were modified at the 5′ end with the fluorophore FAM for the reference gene cysG and HEX for the plasmid marker oriT, and furthermore modified at the 3′ end with the quencher BHQ-1

      plasmid copy number qPCR assay.

      Why cysG: Siroheme synthase gene?

  32. Oct 2020