3 ms·

In what sense do they mean "begun", as in, that this is a new concept? Some of their citations go back to the 60's and 70's. Engineers have been using block d

In what sense do they mean "begun", as in, that this is a new concept? Some of their citations go back to the 60's and 70's. Engineers have been using block diagrams for.. how long? Venn diagrams were invented in 1880 according to Wikipedia. It doesn't strike me that the use of visual languages in mathematics is particularly new.

spacejunk 7y ago
I think that they mean in this source this /particular/ way of diagrammatic reasoning, as pioneered by Coecke, who literally wrote the book on it (http://www.cambridge.org/gb/pqp http://www.cambridge.org/gb/pqp), although very similar diagrammatic reasoning has been used for some time in Category Theory through string diagrams (https://en.wikipedia.org/wiki/String_diagram https://en.wikipedia.org/wiki/String_diagram).
- GorgeRonde 7y ago
  I think the approach is different. String diagrams is a small DSL while the above is intended to be more foundational and be used to bootstrap and translate between various specific diagrammatic theories (including String diagrams). > The study of each of these ‘diagrammatic theories’, each modelling a separate part of cognitive, physical, or mathematical reality, are currently separate. Our grand vision is to develop a fully integrated framework, in which all of the above can be comprehended and dealt with together. > More deeply, this approach can also be applied to the study of diagrammatic theories themselves [12, 33]. As such, it is its own ‘metatheory’. One major goal of the project will be to understand to what extent this can serve as a foundation for mathematics itself, as a replacement for set theory. Also, as an ironic side note in relation with the article, some of the diagrammatic theories that have been elaborated by this group include diagrams that contain (and not just represent) matrices. I don't know why I'm commenting in this thread, I don't understand anything in these papers, I just know it describes what I see, i.e. the great universal diagram. Don't you see it ?

spacejunk 7y ago

I think that they mean in this source this /particular/ way of diagrammatic reasoning, as pioneered by Coecke, who literally wrote the book on it (http://www.cambridge.org/gb/pqp http://www.cambridge.org/gb/pqp), although very similar diagrammatic reasoning has been used for some time in Category Theory through string diagrams (https://en.wikipedia.org/wiki/String_diagram https://en.wikipedia.org/wiki/String_diagram).

GorgeRonde 7y ago
I think the approach is different. String diagrams is a small DSL while the above is intended to be more foundational and be used to bootstrap and translate between various specific diagrammatic theories (including String diagrams). > The study of each of these ‘diagrammatic theories’, each modelling a separate part of cognitive, physical, or mathematical reality, are currently separate. Our grand vision is to develop a fully integrated framework, in which all of the above can be comprehended and dealt with together. > More deeply, this approach can also be applied to the study of diagrammatic theories themselves [12, 33]. As such, it is its own ‘metatheory’. One major goal of the project will be to understand to what extent this can serve as a foundation for mathematics itself, as a replacement for set theory. Also, as an ironic side note in relation with the article, some of the diagrammatic theories that have been elaborated by this group include diagrams that contain (and not just represent) matrices. I don't know why I'm commenting in this thread, I don't understand anything in these papers, I just know it describes what I see, i.e. the great universal diagram. Don't you see it ?