Understanding the topology of a space can disproportionally increase understanding

• Matt argues that trying to map out a problem onto a topological different map promotes asking useful questions:
  • https://interconnected.org/home/2024/01/05/triangles

  • Triangles share the 2x2’s legibility and ease of rapid whiteboard sketchability. The memetic power.

    But 2x2s tend towards binaries and division.
    Even Venn diagrams, another typical diagram, as combinatorial as they are, have underlying binary assumptions: something possesses a quality or it is outside the circle.
    Whereas the triangle describes a landscape.
    Who will invent the BCG Growth Share Matrix of triangles?
    There are gradients and spectrums and magnitude.
    Ternary plots seem to promote asking: well what if we could move slightly over there? Where are the tipping points, what’s the terrain? How would we explore this unmapped region?

• Examples

  • Decentralisation is a mutli-dimensional continuum: A system can not be described as either fully centralised or fully decentralised but has multiple aspects each of which it can be more or less centralised
  • Herzberg’s Motivation-Hygiene Theory: More and more money will not lead to more and more happiness. There are other inputs of the happiness function that
  • In pragmatists guide to sexuality the authors argue that while the “straight-gay continuum” is a commonly applied model for understanding sexuality, but a more useful model is viewing the domain of human’s arousal function as a disconnected set.
    • Arousal domain: A list of stimuli (disconnected set). An arousal impulse (visual, auditory, …) can trigger multiple stimuli.
    • Arousal function: Arousal per stimuli is assigned a volume and sign.
    • Arousal codomain: The codomain is a continuum from Disgust to Arousal.
    • From the book:
      • The brain creates an “arousal impulse” when exposed to certain stimuli, the strength of which is modulated by environmental and hormonal factors. Our sexuality should be defined as a list of the stimuli that cause us to become aroused and the relative “volumes” of those arousal outputs to each stimuli type—with a caveat.
      • Arousal pathways should be thought of as existing in one of three states: positive, neutral, and negative. Negative arousal is experienced as a “gross” sensation. One person may find the idea of sleeping with an elderly individual arousing, another may find this concept deeply “gross,” and yet another may be completely indifferent to the concept. Regardless of the ethics of such an involuntary impulse, all of these are different and equally valid expressions of a person’s sexuality.
      • In other words, arousal is a sensation that our brains evolved to draw us toward something. Arousal makes us want to look at something longer; it dilates our pupils so that we can take in more of that thing, it compels us to move closer to the target and inhale deeply. Disgust is a sensation that our brains evolved to get us away from something. It makes us want to leave the room, look away from the thing, linger as shortly as possible, and hold our noses. Disgust is not just another emotion; disgust is the manifestation of arousal with a negative modifier attached (we go into the evidence for this in detail later).