Author Archives: jhanschoo

To start from 0 or 1? Heuristics for ordinals.

Computing is famous for having many languages begin their enumerations from 0. Many humans, on the other hand, begin enumerating from 1. Arguments for whether 0 and 1 is better often pick up examples from the real world and claim that either is more natural. There are, I suppose, qualities that differentiate natural arguments for 0-based and natural arguments for 1-based.

1-based indexing seems natural for counting. When we count apples, we go 1 apple, 2 apples, 3 apples; it makes sense to assign the first apple we point to to 1. I like to think of this as the discrete cardinality heuristic, because the number assigned to the element is the size of the entire set.

0-based indexing is what I like to think of as the distance heuristic. We can define ordinals as the number of units from a base element we call the first element. When we go to large numbers, and think in terms of orders of magnitude, we tend to think in terms of distance from a center, rather than in terms of counting every discrete unit from the center, picturing in our mind the real number line.

When we started counting the years, we began from year 1. As we started to think of time as a measurable, continuous commodity, our perception of time shifted from discrete years to years as containers for 12 months, like how tens are like containers for ten ones. We have the unfortunate convention today that there is no year 0; hence there are only 12 months between 1 BCE and 1 CE. We, too, have the unfortunate convention that 20xx refers to the 21st century, not the 20th century. We should rightly be celebrating the commencement of the 21st century in 2001, not 2000; else one of the centuries counted will have been missing one year. If we enumerated from 0 and not 1, I would not have struggled with century numbers as a boy.

TL;DR because Arabic digits.


Unsubstantiated Hypotheses

  • Concept resolution: when we hear a complex sentence, several distinct faculties/cognitive processes come into play.
  • One faculty/cognitive process is the verbal modeling faculty. This faculty is not used very much.It is used when we hear a very vague sentence and do not have an immediate concept and/or context to attach that sentence to. We attempt to search for concepts we have in our experience, and failing which, attempt to build permutations of concepts from existing ones based on relationships implied by the grammar, tone and context in which we encounter the sentence.
  • The other faculty is the analogous faculty. When this faculty is exercised, we have in our minds a strong, specific concept that we attach to the sentence. C.f. Saussure’s semiotics. When we exercise this faculty without conscious restraint, which is most of the time, since it is easy and intuitive and normal especially among friends, we tend to think of the sentence’s expression in terms of what we have experienced, attaching the sentence’s expression to a highly personal context. For people whose lives are extremely parallel, the implied context behind the sentence and the personal context of the listener are highly parallel and little further elaboration is required. For highly different lives, the listener will require a lot of elaboration in order to construct a sufficiently accurate model-concept of what the speaker is trying to express. Note that I use the word construct here. This means that the listener will have to exercise the aforementioned permutation faculty. Even so, the constructed concept lacks a lot of unexpressed context and is probably very different from what the speaker is trying to convey.
  • These two faculties are the foundation on which indirect learning is formed. Indirect learning is taken to mean the formation or modification of personal ideas and concepts that is performed not through direct, personal observation (with or without the employment of instruments or conceptual frameworks), but through received information, for example through speech or text.
  • When we read or speak, we perform simultaneously direct learning about the medium and the source of the message, and indirect learning about the message itself.
  • Individuals who are intimate with one another tend to have good, elaborate and accurate models of the contexts in each others’ minds. People who have such high-quality models tend to communicate efficiently, that is, when the speaker speaks little, often the listener is well aware of the meaning of the words, and when the speaker performs elaboration, often elaboration is required for the listener to understand the context. This can be contrasted with a speaker-listener relationship where the speaker knows little about what the listener does and does not know; the speaker will tend to provide unnecessary context and fail to provide necessary context if needed. In media where communication is asymmetric in effort, that is, where it is easy for a speaker to communicate to a listener but difficult for a listener to reply, or asymmetric in scale, that is, when the speaker is communicating to a plural audience, the good speaker will err on the side of unnecessary elaboration, providing as much context as is needed for a less-than-average Joe to construct sufficiently accurate models.
  • Highly specialized knowledge workers and trades often deal frequently with concepts with a highly complex, yet specialized context. By complex I mean that the context is sufficiently departed from regular everyday experience that to construct this context from regular experience will require a lot of experience, potentially months and years. By specialized I mean that the utility if this concept is very limited outside this trade/profession. Because of this, such people, when communicating to others of the same trade, often employ jargon in order to make communication sustainably efficient.

The Streets of Japan

One huge departure from other countries that Japan’s cities make is that it is structured around walking. There are streets that are open only to pedestrians. There are retail stores and malls and restaurants that you can get to only by walking a fair distance from either mass transit or the carpark.

This one defining characteristic is what makes me love Japan. Whereas in, say, American suburbs and cities the middle class would commute from their safe private apartment to the safe shopping district or the safe workplace enclosed within the safety of their car, and in between the commute might venture through several bad neighborhoods, in Japan the middle class is invested in the upkeep of their streets and alleys and their public infrastructure.

The streets of Japan are decent and clean and hospitable, and one does not need to be in a car to feel safe. Families throng through promenades, as do unsupervised children and men and women of all ages. Groups of elderly congregate in the many public parks adjacent to the roads.

Roads are narrow, and often single-lane. Multi-level buildings huddle up close to each other, giving the pedestrian a sense of coziness; you do not know what’s around the corner past the next street, you do not know where the side alley will lead, but you know that it will be safe. Vending machines outside every other establishment give the pedestrian decent refreshment. This is simply heaven for the flâneur.

In the heart of cities people may dress in bright, whimsical colors. No need to worry standing out, many others do too. No need to appear strong and powerful. No need to appear street-smart. No need for that extra caution. Enjoy the freedom you have as a pedestrian. Feel free to feel at home in the public spaces of Japan.

Literary Analysis: A Mathematical Formulation


There exists world states W, which refer to precise states/static configurations empirical physical universe.

There exists ideas I, which are idealized concepts. We represent ideas with the notation I(<word>), where <word> is an English approximation; we call this I-notation.We can impose a distance measure on ideas. For example, I(village) is closer to I(hamlet) than I(sea).

In using a model of ideas, we formalize the notion that whereas communication in literary analysis benefits from having common notions and definitions in academic writing, the diction and devices a writer uses might differ from the standard usage/reading, but instead contain delightful nuance, and the full force of diction and other nuances can be explicated using I-notation.

Words w are words in the traditional sense, but might also include poetic visual space, poetic enjambment, etc.

We have the reading function r(W, o) = I; where r is the reading function, W is the world state, o is the literary work, i is a set of ideas.

A text consists of words.


Activity Domains

Assume that income is exponentially distributed.

Assume that given a real-world function x, goods and services g that achieves that function are log-normally distributed.

Consider an activity domain. An activity domain is a set of functions such that the execution by an agent are highly correlated with each other; the purchase of goods and services that achieve this execution by that agent are then highly correlated with each other as well. Consider a median expenditure m which is the median amount spent on goods in an activity domain by one individual.

Consider an agent that participates in multiple activity domains. We can presume that there exists a number m, such that for most activity domains, the agent spends lower than median if the median expenditure for that good is greater than m, and the agent spends greater than median if the median expenditure for that good is smaller than m.

Agents with lower incomes are excluded from activity domains with high media expenditure.

Discourse of Mathematics

  • Mathematical subfields come and go over the centuries
  • What is “mathematical maturity
    • Pre-rigorous
    • Rigorous
    • Post-rigorous
  • Model of the discipline of mathematics, (knowing what is known, knowing where lies opportunities for discovery)
  • Definition-theorem structure (c.f. ProofWiki)
  • Formalizing intuition gives insights; opportunities in model of discipline of mathematics result in new intuitions to formalize
  • We can shoehorn this conversation of discipline and formalization into Hegelian synthesis
  • Relationship between mathematics and other fields
  • Explored mathematical subfields occasionally map to generalizable patterns in life (c.f. electrodynamic waves, epidemic propagation)
  • Explored theorems in mathematics converse with observations
  • Models are contextualized instances of the definiton-theorem structure
  • Definition-theorem structure as a language to express objectives in the discipline and in real-world motivations; consider the definition-theorem structure and models a more expressive form of logical structure and syllogistic arguments.