Leibniz notation in his own hand. Picture from Stephen Wolfram. |

Peter Fielitz and Guenter Borchardt kindly sent me a review of my draft paper and make excellent contributions (thanks also to Tom Brown for a thorough read and commentary). Among other things, they suggest the more pedagogical notation:

P : I_{D} \rightleftarrows I_{S}

$$

which is very good -- and makes more apparent a connection with chemical reactions. The double arrow notation has a unicode representation (however the subscripts D and S are not commonly available unicode).

*P : I(D) ⇄ I(S)*

The information notation

*I(D)*or $I_{D}$ (for information in process variable*D*) would get a bit more unwieldy were we to use variables like*I(NGDP)*or $I_{NGDP}$. The unicode representation was one reason for using the single arrow notation*P : D → S*

despite the notation being overloaded (category theory, functions, maps, fiber bundles). The other thing I did want to make clear was the relationship between the variables in the case of non-ideal information transfer where

*I(D) ≥ I(S)*. However, that relationship is evident in the*D*preceding the*S*.*P : D ⇄ S*

potentially keeping the single arrow notation for non-ideal information transfer. For example, the price level model is:

*P : NGDP ⇄ M0*

One thing this notation helps avoid is concerns about the direction of information flow (source/destination designation) in the case of information equilibrium. Commenter M previously mentioned the lack of symmetry in the single arrow notation as being unclear.

It also helps avoid the overloading problem of the single arrow notation -- so that all we now have to worry about is the overloaded term "information". I thought this post could serve as a reference on information transfer-/information equilibrium- specific notation as well.

The double arrow notation, reserving the single arrow for non-ideal transfer, sounds good. :)

ReplyDeleteI like the new notation. :)

ReplyDelete