Problem:

• The number of possible values for any parameter is always finite, and we know them with a certain precision and confidence—this was already discussed in the section 1+1 ≠ 2.

• It is critical to understand that analytical formulas, which are “correct” and “precise”, and account for events with a probability of 0.00001%, are not only useless but harmful—especially when our input data is only 80% reliable or has a precision of 0.15%.

  • It is important to clearly recognize this harm.

  • The logic of “since our input data is uncertain, let’s at least calculate everything else with absolute precision” is fundamentally flawed because:

    • It wastes resources at every level:
      • Instead of 1 byte per variable → 4 bytes.
      • Instead of a simple loop → a complex module.
      • Instead of 100 bytes per program → 10 kB.
      • As a result, instead of 0.1 seconds per computation (imperceptible to a human) → it becomes 1 second, making the system unusable.

• This is a classic trap of quantity turning into quality.

  • This transition is not just abstract philosophy, something “nice in theory but hard to apply to code.”
  • It is a fundamental law that must guide both code and system design—from the very foundation.
  • When applied correctly from the lowest level, everything becomes simpler and more natural.

Key Takeaways and Practical Steps

• Granularity should initially be chosen randomly, just like anything else without prior history.

  • It can start with some buffer and shrink if unnecessary.
  • Or it can start coarse and refine itself until reaching the point where “the effort is not worth the gain.”

• Avoid excessive literalism.

  • If we previously measured current in kA, but later discovered it operates in microamperes, we should not suddenly switch to kV.
  • Yes, randomness plays a role, and we could start from either extreme, but we almost always have some prior experience.
  • The system should extract common sense patterns:
    • Amperes are associated with volts.
    • Microamperes are (probably) associated with microvolts.
  • However, the system can never be certain—as proven earlier, absolute certainty is only ever an accident.

• “The effort is not worth the gain” is a balance of cost vs. benefit.

  • The system should automatically assign cost to everything and minimize it whenever possible.
  • If increased precision still yields more benefit than cost, granularity should increase—more digits, finer time resolution, etc.
  • However, saturation must be a core principle of system design—beyond a certain point, more precision stops being useful.