Private

Projects

Projects for the next two months:

Linear algebra: integrating it into the knowledge network.
Probability and statistics: learning and problem solving.
IOQM: problem solving and recording solutions here.
Sri Aurobindo and the Mother on education.
Music: consolidate existing songs and learn new songs.
Gita: learning Sanskrit through the Gita.

Approach to Projects

For projects that involve the humanities and the study of Sri Aurobindo and the Mother, maintain a set of questions that you want to answer. These questions at once act as guides and evaluators. They perform the role of guides because they direct your study in a particular direction and give a starting point for your exploration. They act as evaluators because your success in the project is determined by your ability to answer the questions.

Need for Projects

Sri Aurobindo holds that the vicious practice of teaching by snippets has to be relegated to the lumber room of dead sorrows. It follows that the concomitant habit of learning by snippets should suffer a similar fate.
One can’t learn a hundred different things at the same time. The need for concentrating it into well defined projects with a proper timeline becomes ncessary.
Six projects at a given time seems to be a good number. Three of them that are right-brain heavy and three that are left-brain heavy.

External memory and Spaced repetition

One of the aims of this website is to act as an external memory for all the ideas that I wish to embed into my long-term memory. However, this external memory is only a temporary device whose services are needed until I assimilate the ideas and integrate them into my network of existing ideas. Once this process is complete, that part of the external memory which houses these ideas no longer plays an active part in my life. It shall continue to remain as a physical manifestation of this internal representation, a passive presence.
This external memory is therefore to be treated as a digital notebook with a finite utility period, an expiry period, so to speak. It is not to be treated as a permanent crutch or as a second brain, as it is sometimes refered to in certain discussions. Also, it is not to be treated as a reference. Such a use disincentivies the memory from performing its natural function.
For any set of ideas which are yet to be assimilated and integrated into the long-term, permament memory network, the external memory serves as a useful temporary reference. For the process of firmly embedding an idea into long-term memory, I turn to spaced repetition and the testing effect. The use of apps such as Anki is a common practice. But I am going to dispense with them. A simple mechanism such as a reminder on a calendar to engate with a particular set of ideas should be sufficient.
The problem with tools such as Anki is the loss of context when it comes to their approach of flashcards. Reviewing flashcards in isolation, stripped of their context becomes boring beyond a certain point. Besides, there is no simple way of integrating all flashcards associated with a certain context. Therefore, my review sessions will not be on isolated ideas, but will be on clear sub-areas that I wish to focus on. For example, I might decide to spend one afternoon reviewing orthonormal vector spaces and the key results associated with them. Or I might spend a morning reviewing all that I know about Napolean Boneparte.

Presentation workflow

The following workflow has been finalised for hosting content related to mathematics.

Be as succinct as possible. Use mathematical symbols and connectors like arrows instead of words.
To faciliate this, use slides for both notes and problems. Use articles only if necessary.
Use Mathcha desktop app to generate SVG. The template for a slide template can be found below.
Add SVG images as slides. Save the SVG images in the folder where they are needed. Follow the naming img-x.svg.
Save the raw Mathcha content as text files. Follow the naming img-x.txt.

Mathcha Slide Template

Slide dimensions:

width = 1300px
height = 700px
font-size = 24px for both text and math

/*!)-*&~n/{"isRoot":true,"isTextMode":true,"isTabularCellsSelected":false,"isPureText":false,"insideInlineMath":false,"lines":[{"blocks":[{"text":"\\diagram","type":"composite","elements":{"de5001702766228076":{"id":"de5001702766228076","lines":[{"blocks":[{"text":"Sample Slide Deck"}]}],"shape":{"data":{"p":{"x":398,"y":217}},"anchor":"left-top","settings":{"fontSize":"\\Huge"}},"isTextMode":true},"de8111197690855165":{"id":"de8111197690855165","lines":[{"blocks":[{"text":"Karthik Thiagarajan"}]}],"shape":{"data":{"p":{"x":534,"y":411}},"anchor":"left-top","settings":{"fontSize":"\\normalsize"}},"isTextMode":true}},"connections":[],"intersections":{"id":"di34837459085638445","items":[],"style":{}},"shapes":[],"settings":{"grid":false,"diagramHeight":656.0625}}]},{"blocks":[{"text":"\\page-break","type":"composite","elements":{}}],"style":null},{"blocks":[{"text":"\\diagram","type":"composite","elements":{"de5349582672091666":{"id":"de5349582672091666","lines":[{"blocks":[{"text":"Slide-1"}]}],"shape":{"data":{"p":{"x":11,"y":10}},"anchor":"left-top","settings":{"fontSize":"\\Huge"}},"isTextMode":true},"de15282884539246622":{"id":"de15282884539246622","lines":[{"blocks":[{"type":"composite","text":"\\aligned","elements":{"0_0":{"lines":[{"blocks":[{"text":"x"},{"text":"\\power","type":"composite","elements":{"powerValue":{"lines":[{"blocks":[{"text":"2"}]}]}}},{"text":"-y"},{"text":"\\power","type":"composite","elements":{"powerValue":{"lines":[{"blocks":[{"text":"2"}]}]}}}]}]},"0_1":{"lines":[{"blocks":[{"text":"=x"},{"text":"\\power","type":"composite","elements":{"powerValue":{"lines":[{"blocks":[{"text":"2"}]}]}}},{"text":"-xy+xy-y"},{"text":"\\power","type":"composite","elements":{"powerValue":{"lines":[{"blocks":[{"text":"2"}]}]}}}]}]},"1_0":{"lines":[{"blocks":[]}]},"1_1":{"lines":[{"blocks":[]}]},"2_0":{"lines":[{"blocks":[]}]},"2_1":{"lines":[{"blocks":[{"text":"=x"},{"type":"single","text":"("},{"text":"x-y"},{"type":"single","text":")"},{"text":"+y"},{"type":"single","text":"("},{"text":"x-y"},{"type":"single","text":")"}]}]},"3_0":{"lines":[{"blocks":[]}]},"3_1":{"lines":[{"blocks":[]}]},"4_0":{"lines":[{"blocks":[]}]},"4_1":{"lines":[{"blocks":[{"text":"="},{"type":"single","text":"("},{"text":"x-y"},{"type":"single","text":")"},{"type":"single","text":"("},{"text":"x+y"},{"type":"single","text":")"}]}]}},"row":5,"column":2}]}],"shape":{"data":{"p":{"x":356,"y":191}},"anchor":"left-top","settings":{"fontSize":"\\LARGE"}},"isMathDisplayMode":true}},"connections":[],"intersections":{"id":"di34837459085638445","items":[],"style":{}},"shapes":[],"settings":{"grid":false,"diagramHeight":656.0625}}]},{"blocks":[{"text":"\\page-break","type":"composite","elements":{}}],"style":null}],"rootEditorId":"321241621323","inlineMathDisplayStyle":null}

Sample Slide Template

YAML file for a sample slide template. This has been discontinued in favour of Mathcha HTML. For legacy reasons, this template’s YAML is being maintained here.

---
title: "IOQM-2024"
subtitle: "Problems and Solutions"
author: "Karthik Thiagarajan"
format:
  revealjs:
    progress: true
    fontsize: 30px
    history: false
    width: 100%
    height: 100%
    theme: default
    incremental: true
    navigation-mode: vertical
    html-math-method: katex
    preview-links: true
---