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> "math-lite" The series is intended for a general audience and starts by laying the groundwork necessary for exposition of this paper: [1]. Article 4 [2] expl

> "math-lite" The series is intended for a general audience and starts by laying the groundwork necessary for exposition of this paper: [1]. Article 4 [2] explains why it is introduced this way. > end up just rehashing standard mathematics in opaque ways It's just an explanation of string diagrams [3][4], pretty transparent and standard. I find it funny that your response to this is so similar to that of the abacists to Fibonacci.[5] [1]. https://arxiv.org/abs/1403.7048 https://arxiv.org/abs/1403.7048 [2]. https://graphicallinearalgebra.net/2015/04/29/dumbing-down-magic-lego-and-the-rules-of-the-game-part-1/ https://graphicallinearalgebra.net/2015/04/29/dumbing-down-m... [3]. https://ncatlab.org/nlab/show/string+diagram https://ncatlab.org/nlab/show/string+diagram [4]. https://en.wikipedia.org/wiki/String_diagram https://en.wikipedia.org/wiki/String_diagram [5]. https://graphicallinearalgebra.net/2015/04/26/adding-part-1-and-mr-fibonacci/ https://graphicallinearalgebra.net/2015/04/26/adding-part-1-...

imvetri 6y ago
Funny thoughts have truth in them. Can you share what truth did you realise ?
spekcular 6y ago
I don't believe the exposition is written well (judged as either an exposition of linear algebra or just the graphical calculus the article develops). But this is perhaps a subjective point, and others here have already commented on this in detail. More importantly, I would like to remark that string diagrams are not standard. The vast majority of mathematicians have never read the definition of a string diagram (or even a monoidal category), precisely because it is not standard and not needed for most (any?) useful mathematical work. They also have obvious disadvantages when compared to the usual notation, as I pointed out earlier. When I read articles by category theory boosters, I get the sense (rightly or wrongly) that they think the world revolves around them and they have stumbled onto some deep and fundamental truths. This is not the case. It's a niche of a niche.
- graphlinalg 6y ago
  It's interesting to suddenly get all these hits.. I haven't touched the blog in a long time. I'm sorry that you didn't find it well-written -- it wasn't written with you in mind. Originally I wanted to write about my research in a way that was understandable to a lay person, but I quickly abandoned that and went for the mythical "second year undergrad" level. You have pretty strong thoughts about what is "useful mathematical work". Are you the high priest and decider of the usefulness of mathematics? To be honest, it almost sounds like some category theorist was super mean to you... One more thing. Arguments like "niche of a niche" are sociological - just because something is niche doesn't mean it's not important (or, god forbid, fun!). Maths is one of the most conservative fields in this sense; what is and is not considered "standard" is extremely political.
  - stablenode 6y ago
    "Are you the high priest and decider of the usefulness of mathematics? To be honest, it almost sounds like some category theorist was super mean to you..." Interesting and totally not ad hominem response... I believe Kevin Buzzard (an actual mathematician) had a few words about this last year: https://youtu.be/Dp-mQ3HxgDE?t=1039 https://youtu.be/Dp-mQ3HxgDE?t=1039
    - feanaro 6y ago
      Given the tone of the poster who this reply was for, it seems entirely warranted.
      - stablenode 6y ago
        feanaro: fine, if you think so. I find it interesting that actual mathematicians working in Category Theory, such as Tom Leinster (who wrote a lovely little introductory text on Category Theory [not covering monads though] and made it freely available on arXiv: https://arxiv.org/abs/1612.09375 https://arxiv.org/abs/1612.09375) are able to engage in polite discussion about the contentious viewpoints on the use of CT without resorting to personal attacks (see 2-3 minutes from his talk from a few years back: https://youtu.be/UoutGluNVlI?t=410 https://youtu.be/UoutGluNVlI?t=410) ... which stands in sharp contrast to some of the evangelists, whose attitude in response to criticism often reeks of arrogance and puts people off taking CT seriously, which I think is a great shame.

imvetri 6y ago

Funny thoughts have truth in them. Can you share what truth did you realise ?

spekcular 6y ago

I don't believe the exposition is written well (judged as either an exposition of linear algebra or just the graphical calculus the article develops). But this is perhaps a subjective point, and others here have already commented on this in detail. More importantly, I would like to remark that string diagrams are not standard. The vast majority of mathematicians have never read the definition of a string diagram (or even a monoidal category), precisely because it is not standard and not needed for most (any?) useful mathematical work. They also have obvious disadvantages when compared to the usual notation, as I pointed out earlier. When I read articles by category theory boosters, I get the sense (rightly or wrongly) that they think the world revolves around them and they have stumbled onto some deep and fundamental truths. This is not the case. It's a niche of a niche.

graphlinalg 6y ago
It's interesting to suddenly get all these hits.. I haven't touched the blog in a long time. I'm sorry that you didn't find it well-written -- it wasn't written with you in mind. Originally I wanted to write about my research in a way that was understandable to a lay person, but I quickly abandoned that and went for the mythical "second year undergrad" level. You have pretty strong thoughts about what is "useful mathematical work". Are you the high priest and decider of the usefulness of mathematics? To be honest, it almost sounds like some category theorist was super mean to you... One more thing. Arguments like "niche of a niche" are sociological - just because something is niche doesn't mean it's not important (or, god forbid, fun!). Maths is one of the most conservative fields in this sense; what is and is not considered "standard" is extremely political.
- stablenode 6y ago
  "Are you the high priest and decider of the usefulness of mathematics? To be honest, it almost sounds like some category theorist was super mean to you..." Interesting and totally not ad hominem response... I believe Kevin Buzzard (an actual mathematician) had a few words about this last year: https://youtu.be/Dp-mQ3HxgDE?t=1039 https://youtu.be/Dp-mQ3HxgDE?t=1039
  - feanaro 6y ago
    Given the tone of the poster who this reply was for, it seems entirely warranted.
    - stablenode 6y ago
      feanaro: fine, if you think so. I find it interesting that actual mathematicians working in Category Theory, such as Tom Leinster (who wrote a lovely little introductory text on Category Theory [not covering monads though] and made it freely available on arXiv: https://arxiv.org/abs/1612.09375 https://arxiv.org/abs/1612.09375) are able to engage in polite discussion about the contentious viewpoints on the use of CT without resorting to personal attacks (see 2-3 minutes from his talk from a few years back: https://youtu.be/UoutGluNVlI?t=410 https://youtu.be/UoutGluNVlI?t=410) ... which stands in sharp contrast to some of the evangelists, whose attitude in response to criticism often reeks of arrogance and puts people off taking CT seriously, which I think is a great shame.