Manifesto for transparent mathematical modeling

Manifesto for transparent mathematical modeling

[Vyacheslav Kalmykov]

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Dear colleagues,

I would like to draw the community's attention to the special role of category theory in the applied race for transparency in mathematical models. This race for transparency is particularly fueled by concerns about the reliability and safety of modern artificial intelligence, which is by nature a "black box". Category theory allows us to view complex systems transparently. Morphisms allow the individual behavior of category objects to be taken into account. Functors and natural transformations make it possible to model higher levels of organization of a complex system. A categorical view of multi-level organization has helped us create cellular automata models of ecosystems. We hope that transparent categorical and cellular automata thinking will expand their representation in science and education.

Kalmykov VL, Kalmykov LV. Manifesto for transparent mathematical modeling: from ecology to general science. Academia Biology 2024;2. https://doi.org/10.20935/AcadBiol6166<https://protect-au.mimecast.com/s/LZJFCjZ12Rfq89xphRWAM7?domain=doi.org>

Kind regards,

Vyacheslav Kalmykov


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Re: Manifesto for transparent mathematical modeling

[Morgan Rogers]

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Dear Vyacheslav Kalmykov,

I find your justification for advertising this work on the category theory mailing list very tenuous. In the paper you link, the only mentions of categories are with regard to R. Rosen's work from the 1950s, and you otherwise discuss only cellular automata with no explicit mention of techniques that are explicitly categorical.

I am also critical of the article overall. Putting aside the bulk of the article taken up with discussion of orthogonal applications of cellular automata, whether historical (applied to "ancient board games") or highly speculative (Wolfram's idea that cellular automata may capture a "code of the universe"), the main contribution of the paper seems to be the proposal of modelling biological systems in this way. In the process, you criticize "black box models" in spite of the fact that besides potentially having more parameters, your cellular automaton proposal is still absolutely a black box model, and moreover one with no accompanying empirical evidence of successful prediction.

While I am by no means an expert in mathematical modelling as it pertains to biology, it is clear that many more biological effects are mentioned (Section 2.6) than can be accounted for by the mathematically vague axiomatization of your model (Section 2.7). Moreover, in spite of the statement made in Section 2.5 that "The theory of the subject area serves as a knowledge base for creating a symbolic mathematical model in that subject area," no direct connection between the theoretical biology mentioned and the proposed model is made.

For these reasons, I discourage my peers from engaging with this work.

Best regards,
Morgan Rogers

On 07/02/2024 02:43, Vyacheslav Kalmykov wrote:
Dear colleagues,

I would like to draw the community's attention to the special role of category theory in the applied race for transparency in mathematical models. This race for transparency is particularly fueled by concerns about the reliability and safety of modern artificial intelligence, which is by nature a "black box". Category theory allows us to view complex systems transparently. Morphisms allow the individual behavior of category objects to be taken into account. Functors and natural transformations make it possible to model higher levels of organization of a complex system. A categorical view of multi-level organization has helped us create cellular automata models of ecosystems. We hope that transparent categorical and cellular automata thinking will expand their representation in science and education.

Kalmykov VL, Kalmykov LV. Manifesto for transparent mathematical modeling: from ecology to general science. Academia Biology 2024;2. https://doi.org/10.20935/AcadBiol6166<https://protect-au.mimecast.com/s/cvQDCD1vRkCVq8oNhWUJQa?domain=doi.org>

Kind regards,

Vyacheslav Kalmykov


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