Comments

• ZettelDistraction

  May 27 edited May 27

  You will probably dislike the writing: I have been adding dreams to my ZK. I won't comment on my mathematics notes. Here is the first dream.

  ---
  title: Dream2024052701 Authoritarian Party
  reference-section-title: References
  ---
  

  Dream2024052701 Authoritarian Party

  My cat Wilf and I wandered into a strange apartment. M came in and inadvertently let a dog out.

  RFK Jr. appeared and urged me to join his group despite objections from my former acquaintances, one of whom accused him and his "interventions" of sowing chaos, which he denied.

  Later, I saw the Democrats seated in a gallery, believing they were the chosen. Their seats became restraints; they had no future. I left them for the Authoritarian Party. Wilf fled the apartment.

  The Authoritarians set to work dividing the apartment building, isolating themselves and the Democrats in separate sections. The Authoritarians declared in a radio broadcast that they were restricting movement in the city. I had to see for myself.

  Outside, I searched for Wilf, staying close to the building. The Authoritarians had gouged deep rectangular depressions at 45-degree angles into the asphalt streets. An escape vehicle hit one of them; it flipped over with its axles snapped. There were no survivors.

  I rode the elevator back to the apartment. I couldn't quite remember the floor. The elevator headed for the roof, then reversed course. It would have transformed past the roof into a cable car and descended to street level. It somehow knew my floor.

  Back in the apartment, I focused, tensed my muscles, and found my footing on one of the invisible planes encircling the earth. It took effort, but I could walk above the floor with large sections removed, where the apartment below was visible. My acquaintances thought I was deceiving them but soon fell silent. 

  The Authoritarian Party continued renovating by removing the floors and ceilings to install a surveillance system.

  A group of Authoritarians were staging a play in one of the adjacent rooms. I floated in, treading on the invisible plane above the floor, and saluted three uniformed women who momentarily broke character. 

  I sat on the hardwood floor with M. I was wearing only my shirt. M spoke in a trailing Brooklyn monotone while lifting herself partially off the floor to remove her underwear. "We should get married." Her brown eyes were unreadable. Her breath stank of cigarettes.

  Outside, a recruiter handed me the lapel pin of the Authoritarian Party. I was to wear the stylized hawk outline, silver against a black background, on my jacket from now on. He was wearing one; they all were. I took the pin and asked where on the lapel it should go. The recruiter hesitated.

  SEE ALSO

  [[Dream.5b.0.23.0313]] Mutant son
  [[0000.0000.0ABC]] A-B-C

  #dream #authoritarianism #nightmare #wilf

  "Authoritarian Party" links to the next dream.

  ---
  title: Dream.5b.0.23.0313 Mutant son
  reference-section-title: References
  ---
  

  Dream.5b.0.23.0313 Mutant son

  I dreamed last night that I had a baby boy in my dresser drawer for several years. I hadn't noticed him–how could I have been so self-absorbed? He was wrapped in a blue blanket in the second drawer from the top on the left. I took him out, and he aged instantly. He was now nine years old and had developed an independent history, a distinctive personality, and friends waiting to play with him outside.

  He asked me who I was. "I'm your father." He accepted this without comment. His nose was unusually prominent and hawklike, with numerous protruding red nodules and a network of veins and arteries connecting them. Was his condition operable? I cursed my genetics: why couldn't I have an ordinary boy instead of a mutant?

  "I have hundreds of books on mathematics and physics here–do you like mathematics?" He knew them by heart. He used a word I didn't recognize–his vocabulary was more developed than mine. "I'm going to have to look up the meaning of that word." He looked away.

  My apartment became a house. My son's friends outside were affable, older, undemonstrative, and capable of violence–they had guns. He left to join them. I drove the house out of range of the guns onto the highway.

  SEE ALSO

  [[Dream.5a.0.23.0214]] The professor who faked his death

  #dreams #mind

  Post edited by ZettelDistraction on May 27

  GitHub. Erdős #2. Problems worthy of attack / prove their worth by hitting back. -- Piet Hein. Alter ego: Erel Dogg (not the first). CC BY-SA 4.0.
• GeoEng51

  May 27

  @ZettelDistraction The clarity of your dream recall is astounding! I rarely do better than remembering feelings and some vague images.
• ZettelDistraction

  May 27 edited May 27

  Refresh the page, lest the prior revisions remain in your browser. Here is another one, though there is no reason that anyone should find it interesting.

  ---
  title: Dream2024052713 French class at Harvard
  reference-section-title: References
  ---
  

  Dream2024052713 French class at Harvard

  I found myself in a classroom at Harvard. The class was studying French. The instructor asked me to pronounce a few basic phrases and words, such as "j-ième," "Je suis francophone," "ou," and "Je ne suis pas Japonais." The instructor eyed me suspiciously as I spoke. A woman from work stood at the head of the class and selected someone to read an extended passage in French. She selected me.

  I scanned the text and realized I had no idea how to pronounce it. I sat in my seat, silently mouthing a few words. The class erupted in mocking applause.

  My coworker read the passage aloud—I could not have reproduced her flawless élision. Afterward, she discreetly handed me a cassette wrapped in class notes with basic instruction in French pronunciation.

  I sat across from her during lunch. "I was the worst possible choice," I said. "Humiliation in class was necessary for progress," she replied. I was never a Harvard student.

  Although much of French is unfamiliar, I have picked up a few French words and phrases here and there. My prior impression of French in College was off-putting. The air on the second floor of the building above the Mathematics department office was breathable, unlike the suffocating atmosphere of the library. I could study in the second-floor hallway unless the French teachers and their students traipsed in to speak French at the loudest possible volume, making it unmistakably clear to anyone within earshot that they were speaking French. I disliked French for years afterward. Those older memories no longer inhibit my curiosity, and I find myself interested, at least in "mathematical French."

  SEE ALSO

  [[Dream2024052701]] Authoritarian Party
  [[0000.0000.0DEF]] D-E-F

  #dreams #French

  Post edited by ZettelDistraction on May 27

  GitHub. Erdős #2. Problems worthy of attack / prove their worth by hitting back. -- Piet Hein. Alter ego: Erel Dogg (not the first). CC BY-SA 4.0.
• ZettelDistraction

  May 28 edited May 28

  Perhaps that was uninteresting. von Neumann had clever method to compute the lengths of bounded intervals. The proof of the estimate below was one of those omitted details from which I sometimes create exercises.

  ---
  title: Math2024052510 von Neumann on the length of a bounded interval
  reference-section-title: References
  ---
  

  Math2024052510 von Neumann on the length of a bounded interval

  John von Neumann calculates the length of an interval first by establishing an inequality. Let $(|[a,b]\cap\mathbb{Z}|)$ denote the number of integer points in the interval $([a,b]\subseteq\mathbb{R})$. The integer count is a translation-invariant, finitely-additive measure.

  Estimate

  Let $(I\subset\mathbb{R})$ be a bounded interval with endpoints $(a, b\in\mathbb{R})$ where $(a\le b)$.

  $$(b-a-1\le\lceil{b-a}\rceil-1\le|I\cap\mathbb{Z}|\le\lfloor{b-a}\rfloor+1\le b-a+1.)$$

  Proof

  We may assume $(a=0)$ and proceed by induction on $(n)$, where $(0\le{n}\le{b}<n+1)$.
  The second and third inequalities become $(n\le|I\cap\mathbb{Z}|\le n+1)$. The case of $(n=0)$ is immediate. Make the induction hypothesis for $(n>0)$. If $(n+1\le{b}< n+2)$, the induction hypothesis holds for bounded intervals with left endpoint $(0)$ and right endpoint $(b-1)$. Increasing the right endpoint from $(b-1)$ by $(1)$ to $(b)$ adds one more integer to the count $(|I\cap\mathbb{Z}|)$. This completes the induction step. The case of arbitrary left endpoint $(a)$ with $(a\le b)$ follows from the translation invariance of the integer counting measure.

  Remark

  The strict inequality in $(0\le{n}\le{b}<n+1)$ is needed for the induction to go through.

  Dilation

  This is von Neumann's clever construction.

  Let $(\varepsilon>0)$. Define the dilation $(T_\varepsilon:\mathbb{R}\rightarrow\mathbb{R})$ by $(x\mapsto\varepsilon\cdot x)$. By previous estimates,

  $$(\varepsilon\cdot (b -a) -1\le|T_\varepsilon(I)\cap\mathbb{Z}|\le \varepsilon\cdot (b -a) +1)$$

  Dividing by $(\varepsilon)$ and taking the limit as $(\varepsilon\rightarrow\infty)$,

  $$(
  b-a=\lim_{\varepsilon\rightarrow\infty}\left((b -a) -\frac{1}{\varepsilon}\right)\le\lim_{\varepsilon\rightarrow\infty}\frac{|T_\varepsilon(I)\cap\mathbb{Z}|}{\varepsilon}\le\lim_{\varepsilon\rightarrow\infty} \left((b -a) +\frac{1}{\varepsilon}\right)=b-a
  )$$

  John von Neumann's lemma

  $$(
  \lim_{\varepsilon\rightarrow\infty}\frac{|T_\varepsilon(I)\cap\mathbb{Z}|}{\varepsilon}=\ell(I)
  )$$

  Proposition

  If the bounded interval $(I)$ is covered by a finite collection of bounded intervals $(\lbrace{I_k}\rbrace^n_{k=1})$, then

  $$(
  \ell(I)\le\sum_{k=1}^n \ell(I_k)
  )$$

  Proof

  Take $(\varepsilon>0)$. The interval $(T_\varepsilon(I))$ is covered by the finite collection of bounded intervals $(\lbrace{T_\varepsilon(I_k)}\rbrace^n_{k=1})$. The integer count is finitely additive, so

  $$(
  |T_\varepsilon(I)\cap\mathbb{Z}|\le\sum_{k=1}^n |T_\varepsilon(I_k)\cap\mathbb{Z}|
  )$$

  Divide both sides by $(\varepsilon)$ and take the limit as $(\varepsilon\rightarrow\infty)$. The result follows from von Neumann's lemma.

  SEE ALSO

  [[Math.8.1.0.24.0504]] Floors, Ceilings, Rational Approximation
  [[Math2024051110]] Translation as a set map
  [[Math2024051115]] Translation invariance of outer and Lebesgue measure
  [[Proj.0.24.0404]] Top-down math review
  [[0000.0000.0JKL]] J-K-L

  #length #measure-theory #john-von-neumann #floor #ceiling

  Reference

  Fitzpatrick, P. (2023). Real analysis (Fifth edition). Pearson Education, Inc.

  Post edited by ZettelDistraction on May 28

  GitHub. Erdős #2. Problems worthy of attack / prove their worth by hitting back. -- Piet Hein. Alter ego: Erel Dogg (not the first). CC BY-SA 4.0.
• ZettelDistraction

  May 28 edited May 28

  @GeoEng51 said:
  @ZettelDistraction The clarity of your dream recall is astounding! I rarely do better than remembering feelings and some vague images.

  @GeoEng51 My apologies for missing your generous comment earlier. Thank you. Some elements appear in recurring dreams, such as the elevator that goes past the roof, becomes a cable car that descends to the street, or goes below the basement and tunnels underground between buildings. In the Authoritarian Party dream, the elevator stopped before reaching the roof and then found its way to the apartment floor. Recurring elements are relatively easy to recall.

  I didn't include all the details I remember, such as the recruiter's black jacket, my previous encounter with him in the dream, and his 1970s hairstyle, parted in the middle as if to broadcast his poor judgment.

  None of this would have been written if I had set out to write stories. I lack the imagination and eye for detail.

  Post edited by ZettelDistraction on May 28

  GitHub. Erdős #2. Problems worthy of attack / prove their worth by hitting back. -- Piet Hein. Alter ego: Erel Dogg (not the first). CC BY-SA 4.0.
• hiragi

  May 28

  Hi, I'm new here.

  I have tried an index card system in the past but didn't like the top down categorisation, so I'm trying it a different way.

  This week I'm mainly trying to get into a rhythm of capturing information that I stumble across daily into the ZK. Next week I will probably work on adding from my notebooks, but last week I tried writing a poem using the cards directly. (Excuse my rather loose and woolly explanation of a ZK in the body of the post, I'm currently dealing with significant brain fog, and I don't have many cards yet to pull from to help in writing.) I'm hoping to try this experiment again when I have more cards as I had around 50 when I made that.

  Poem is here: https://hiragi.substack.com/p/can-you-use-a-zettelkasten-to-write
• hiragi

  May 28

  @ZettelDistraction

  This is an interesting idea. It would be awesome to explore what recurs in dreams. Do you note down what you ate/sleep duration/events of the day elsewhere? I used to do that, and it was enlightening to see correlations, even if one could not always isolate a causation.
• Loni

  May 28

  French class was quite a nightmare for french students themselves, no need for the Harvard location. They probably would relate. It is interesting to add a dream journal into the Zettelkasten. I put them into my journal, when I remember them. I don't know if there is a pattern there, excepting thaht taking transports seem to really scare me.

  My ZK is a little bite calmer this week. I have a examen in two weeks. I add some articles about plants - they seem to react to the buzz of pollenizers, producing more sugar in their nectar, they seem to have prioception and memory of previous stressful experiences. I have finished American Gods of Neil Gaiman and some articles were added to my ZK.

  Thank you @Will for the discovery of Felix Rösch
• ZettelDistraction

  May 28 edited May 28

  @Loni said:
  French class was quite a nightmare for french students themselves, no need for the Harvard location. They probably would relate.

  So that's where it comes from! I nearly lost faith in language instruction. I was never a Harvard student.

  It is interesting to add a dream journal into the Zettelkasten. I put them into my journal, when I remember them.

  I don't keep a separate journal; my Zettelkasten is an amorphous, undifferentiated blob.

  GitHub. Erdős #2. Problems worthy of attack / prove their worth by hitting back. -- Piet Hein. Alter ego: Erel Dogg (not the first). CC BY-SA 4.0.
• ZettelDistraction

  May 28

  @hiragi said:
  @ZettelDistraction

  This is an interesting idea. It would be awesome to explore what recurs in dreams. Do you note down what you ate/sleep duration/events of the day elsewhere?

  Hardly any time for that. I have to continually remind myself to take notes with pen and paper. I chose the wrong parents.

  GitHub. Erdős #2. Problems worthy of attack / prove their worth by hitting back. -- Piet Hein. Alter ego: Erel Dogg (not the first). CC BY-SA 4.0.
• hiragi

  May 29

  @ZettelDistraction said:
  Hardly any time for that. I have to continually remind myself to take notes with pen and paper. I chose the wrong parents.

  That's exactly why I stopped after a while - I barely remember to write a to-do list. I got the initial benefit out of it of noticing that whatever biochemical nonsense preceded night terrors/paralysis began in the early evening. Although I do wish I recorded dreams themselves more often.
• hiragi

  May 29

  @Loni said:
  I put them into my journal, when I remember them. I don't know if there is a pattern there, excepting thaht taking transports seem to really scare me.

  I get transport-related nightmares when I feel a lack of control. For me it was aeroplanes (never really go on them) and other people's cars (I can't drive). If it's a lack of options or a forceful personality I'm dealing with, somebody else will drive. If I feel I can't cope with the task ahead, I'm forced to either drive the car or fly the plane. I haven't yet noticed the pattern as to whether it's a car or a plane. Maybe the larger the task, the larger the dream vehicle?
• jregan

  May 29

  Very interesting dream discussion. I have been keeping a dream log/journal since 2013 in Bear. Theses dreams are not part of my Zettelkasten. Some of the dreams I capture occur over and over again. And there are others that happen only once and I have often found them to be more symbolic and profound. I also find that I capture more detail if I record them as soon as possible. It can be early morning or the middle of night. If I convince myself to capture them later, I often lose a lot of detail that I had hoped to record. Sometimes I forget the dream entirely. One of the recurring dreams that I have is walking across a university campus. Often with another person beside me who makes comments as we walk together.
• Edmund

  May 30 edited May 31

  

  My main take-aways this week when playing around with Zettelkasten principles and a quadrant chart [1][2]:

  • Start here: Implement these principles for quick, significant improvements in productivity with minimal effort.

  • Quick Wins: Simple to adopt and contribute to incremental improvements and overall enjoyment.

  • Rewarding Engagements: Require more effort but lead to substantial productivity gains.

  • Long-Term Investments: These principles require significant effort and provide more gradual improvements. Invest in these for future payoffs.

  References
  [1] “Quadrant Chart | Mermaid.” Accessed May 30, 2024. https://mermaid.js.org/syntax/quadrantChart.html.
  [2] Krogerus, Mikael, and Roman Tschäppeler. The Change Book: How Things Happen. First American edition. New York: W.W. Norton & Company, 2015.

  Post edited by Edmund on May 31

  Edmund Gröpl
  Writing is your voice. Make it easy to listen.