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