I first state that my domain of interest lies in the understanding of distances in the spatial, geographical domain. This does not involve distances in statistical non-spatial analysis.
Distances in the mathematical sense are characterised by the properties of positivity, separation, symmetry and triangular inequality. In the literature this last property is often wrongly interpreted. I state the hypothesis that the triangular inequality (d(AC)
After six month without answer but with several researchers having expressed interest for discussion around this issue, I come back on the topic.
I have completed this research work on the wrong interpretations of triangle inequality violations and have discussed many consequences of this problem. Basically, what comes out of this discussion is the threefold idea that:
1 distances always possess a character of optimality
2 detours (of path) are contributing to the optimality of distances
3 pauses (in movements) are contributing to the optimality of distances
The result so far of this work has taken the shape of an 'habilitation' thesis attached here. Sorry but it is only available in French. Some articles in English are under preparation.
Thesis Le détour, la pause et l'optimalité, Essai sur la distance e...
I have just submitted two papers for the time being out of three foreseen in English. one for Geographical Analysis expressing the demonstration established in the habilitation thesis. The title is:
"Misunderstanding geographical distances: about three errors of interpretation of violations of the triangle inequality"
and one for the Journal of Transport Geography, focussing on the property of optimality of distances, with the title:
"All geographical distances are optimal"
and the links are given below.
Article All geographical distances are optimal
" All this discussion brings to the idea that distances are optimal in nature, and that in the spatial analysis of transport and mobility, the concept of distance contains an idea of optimality. This idea could link geography and economics through the principle of optimisation in the distribution of activities and the functioning of transport systems "
Interesting work ..... you are probably aware of the fact that the solution to a linear programming "transport problem" links activities with transport systems, and provides a set of prices (dual variables, or shadow prices) that relate to, and are derived from, the transport costs --- those transport costs do not have to obey the triangle inequality.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Quantum Physics
- Quantum Mechanics