The dynamically changing model of exchange as interaction between cone-relation and equivalent-relation

Y. Nakajima*, Y. P. Gunji

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Marx's argument on 'the form of value' is based on state-oriented physics (SOP) and has 'the problem of transitivity.' This problem is inevitably led by an assumption of SOP that observer is able to identify a rule of exchange, so we cannot solve this problem directly. If we hold a standpoint of measurement-oriented physics (MOP), this problem is not a pardox but can be treated as the possibility to get a new outlook for understanding an aspect of exchange as a movement. The problem of transitivity arises because an observer who can describe individual exchanges only as specific parts of the whole exchange tries to describe a general rule. If we take it as a measurement problem, we can positively use the problem of transitivity and construct an internal measurement model in which exchange has the duality, operator and operand. We construct an internal measurement model of exchange as an interaction between cone-relation and equivalent-relation. Then we get patterns named 'particle' that can be interpreted as a rule that can be regarded adaptable for the whole process of exchange, and the particle also has the duality of stability and instability.

Original languageEnglish
Pages (from-to)299-318
Number of pages20
JournalApplied Mathematics and Computation
Issue number2-3
Publication statusPublished - 2002 Mar 10
Externally publishedYes


  • Barter exchange
  • Corn-relation
  • Dynamically changing structure
  • Equivalent-relation
  • Measurement-oriented physics
  • Monetary exchange
  • The form of value

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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