Notes on Resource Convertibility

  • See Resource Convertibility by Tobias Fritz
  • Tiny point but isn’t the whole point of the inequality
  • $latex \text{timber} + \text{nails} \geq  \text{table}
  • missed by “given timber and nails, we can make a table?”  You need “given enough timber and nails, we can make a table.”  Otherwise our words do not stress the constraints on resource allocation.
    • An thus, for example: a cup of sand > Intel i7 CPU
  • Wow. I was reading this backwards “I like to write it as an inequality like this, which I think of as stating that having timber and nails is at least as good as having a table, because the timber and nails can always be turned into a table whenever one needs a table.” 
    • Pending further reading: I do not like this.  Timber and nails is not better than a table without additional information: skill, hammer, time, workshop, plans, purpose for the end product, …
  • This thought is sort of addressed later, but I am still not comfortable with applying this abstraction to real world problems without clarifying the meaning of the ordering: does x \gt y mean
    • “x is sufficient for y”
    • “x is necessary for y”
    • something else
  • In his example, neither is true: you need more than just wood and nails to build a table and you could build a table with a sheet of steel and a welder.
  • Fascinating:
    1. John Baez is active in yet another application of category theory
    2. Azimuth
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