nishio.iconI think there’s symbol-level thinking and vector-level thinking.

gpt.iconIndeed, symbol-level thinking and vector-level thinking are ways of viewing problems in different dimensions, and each has its own particular strengths. Distinguishing between them can provide different approaches to problem abstraction and interpretation.

  1. symbol level thinking

    • Symbol-level thinking is reasoning based on logic and explicit rules. It is useful in dealing with problems with variables and symbols and in defining categories and relationships. This level of thinking is used to separate things into separate views.
    • Feature: At the symbol level, concepts are reduced to clear definitions and reasoning is based on rules. For example, this could take the form of a distinction between men and women, or a category of trans athletes that is demarcated by labels (symbols) such as “male,” “female,” or “trans.
    • Example: The
      • Determination of categories: The gender of the athlete is represented by a symbol and the rules are applied based on the distinction “female” or “male”.
      • Set reference values: set conditions such that if testosterone levels exceed a certain threshold, they will be placed in a specific category.
  2. vector level thinking

    • Vector-level thinking is used when dealing with continuous data and parameters, capturing relationships within a continuous space rather than drawing clear boundaries between things. Here, data is represented within a higher dimensional space, allowing for approximate decisions and reasoning based on similarities.
    • Characteristics: At the vector level, parameters and characteristics are expressed numerically and treated as vectors. Here, the importance is placed on how close the physical abilities of the players are to each other (e.g., vector distance) rather than on the strict division by symbols.
    • Example: The
      • Modeling of physical abilities: Place athletes’ muscular strength, reaction speed, etc. in vector space and continuously evaluate differences between competitors.
      • Evaluation of similarity: The difference in ability between athletes is measured by the distance between vectors, and the fairness of the competition is evaluated based on that similarity.
  3. contrast and integration of the two

    • At the symbol level, things are easier to clearly define and distinguish, which is especially useful when establishing rules and laws. For example, symbolic thinking is useful when strictly demarcating categories such as “boys” and “girls.
    • On the other hand, at the vector level, parameters can be handled more flexibly and individual differences can be smoothly evaluated numerically. Vector thinking is appropriate when there are continuous characteristics and subtle differences, as in the case of trans athletes and gender-related issues.
  4. application example: fairness determination in sports

    • At the symbol level, athletes can be divided into “male” or “female” groups, and rules for participation in competitions within those groups can be determined. However, at the vector level, fairness is determined using a more continuous approach, using multidimensional data such as gender, physique, hormone levels, etc., to evaluate athletes’ abilities among themselves in a vector space. In other words, when classification by symbol is difficult, flexible decisions can be made based on similarities and differences at the vector level.

In conclusion, symbol-level thinking is useful when strict definitions and rules are required, while vector-level thinking is useful when dealing with flexible evaluations and continuous differences. The key is to use and integrate these two approaches according to the characteristics of the problem.


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