[Humanist] 31.216 on mathematics

Humanist Discussion Group willard.mccarty at mccarty.org.uk
Sat Jul 29 07:56:07 CEST 2017


                 Humanist Discussion Group, Vol. 31, No. 216.
            Department of Digital Humanities, King's College London
                       www.digitalhumanities.org/humanist
                Submit to: humanist at lists.digitalhumanities.org

  [1]   From:    Øyvind_Eide <lister at oeide.no>                            (31)
        Subject: Re:  31.212 mathematical knowledge in the humanities?
                psychology of modelling?

  [2]   From:    "William L. Benzon" <bbenzon at mindspring.com>              (34)
        Subject: On the nature of mathematics


--[1]------------------------------------------------------------------------
        Date: Fri, 28 Jul 2017 08:31:21 +0200
        From: Øyvind_Eide <lister at oeide.no>
        Subject: Re:  31.212 mathematical knowledge in the humanities? psychology of	modelling?
        In-Reply-To: <20170728052905.F1E841ABF at digitalhumanities.org>


> 28. jul. 2017 kl. 07.29 skrev Humanist Discussion Group <willard.mccarty at mccarty.org.uk>:
> 
> […]
> --[2]------------------------------------------------------------------------
>        Date: Thu, 27 Jul 2017 10:49:38 -0500
>        From: Paul Fishwick <metaphorz at gmail.com>
>        Subject: 31.126 unrecognised
> 
> 
> Dear Willard
> 
> To what extent is the digital humanities a creative investigation on how mathematics can
> be included in the humanities? Moretti’s book takes this issue and puts it on the front cover:
> Graphs, Maps, and Trees: Abstract Models for Literary History. Moretti is essentially
> creating an interpretation of the humanities which is guided partially by inclusion of
> mathematical thought. The tools employed by digital humanists can be viewed as applied
> mathematics underneath the layers of software and user interfaces. To see this, we need to
> move beyond the “tool fallacy” (that digital humanities is only about enhancing the
> humanities through digital tools). Behind the tool, we find mathematics and it seeps out.
> Jumping to your last paragraph, I completely agree - there is far too little acknowledgment
> of a true interaction. For example, consider Moretti’s thesis. Maybe we can embark on
> a new education on abstract mathematical structures (e.g., trees) within the humanities?
> The humanities becomes a natural gateway for such exposition. Isn’t that what is really
> going on in the digital humanities, and not just a tool fetish.

Dear Paul,

I think this is a fair point, and I would love to hear from digital humanists who know the situation in Russia better, as (if I got it correctly) mathematics is stronger also in the humanities, and also, the modelling tradition (at least in history) seems to be influenced by that.

Also that the experimental aspects of modelling plays an important role, which leads to complex relationships between models, or between  versions of the same model. You can create a 3D model without ever seeing one line expressed in mathematical language — still, one can argue that the real model is the mathematical expression and the visual model on your screen is a visualisation of it. I have come to see that as a false assumption. The model IS the 3D object in the computer: the visual 3D model is what is created and manipulated in the modelling practice. Mathematics is important, but the relationship is more complex than one being “real” and the other one being just a visual expression of the “real” one. 

The humanities experienced a grand loss when natural philosophy left to become natural sciences. Many a humanities researcher, a philosopher, in the seventeenth century was no stranger to practical experiments and material research tasks — physical model building, practical experiments, etc. 

It is true that many parts of the humanities have had practice elements all the time up until now, for instance, connected to material culture: archaeology, art history, palaeography, epigraphy, etc. etc. But the dominance and the normal practice, so to speak, has been elsewhere. I hope digital humanities is in the process of bringing the practical, experimental, physically playful elements back to the humanities — or rather, to strengthen the practical that was always there, but weak. Even if the experiments and play now to a large extent happens within virtual systems in computers and we also have to find out more about the relationship between the materiality of computational models and the materiality of physical models. 

All the best,

Øyvind 


--[2]------------------------------------------------------------------------
        Date: Sat, 29 Jul 2017 00:00:59 -0400
        From: "William L. Benzon" <bbenzon at mindspring.com>
        Subject: On the nature of mathematics
        In-Reply-To: <20170728052905.F1E841ABF at digitalhumanities.org>


Here’s an interesting interview with mathematician Steven Strogatz on the nature of mathematics. Such as:

> Rigor is only half of what we do in math. Rigor is the over-
> emphasized part of math at the expense of creativity and ingenuity
> and intuition. You know, you might say intuition is the almost the
> opposite of rigor.
> 
> And yet without intuition there is no way of even starting the proof.
> I mean, of course, without rigor, we don't have a proof. So I need
> both. And all mathematicians I think would agree that our subject
> combines creative thinking with critical thinking. There's too much
> talk about critical thinking, or even the way that this subject is
> named here at Cornell. It's considered part of the mathematical and
> quantitative reasoning requirement, the MQR requirement, as if
> reasoning is the only game in town. And it's not the only game in
> town.
> 
> There's creativity that doesn't involve reasoning that involves
> hunches, and emotional feelings, or even body feelings. Like wouldn't
> it be nice if-- you know, there's a kinesthetic aspect to
> mathematical creativity. So, in fact, to exploit that, I have the
> students do some exercises that are literally exercises, that are
> standing up and moving, dancing, striking poses. We did that in the
> recent classes to explore symmetry.
> 
> 
> https://bhi61nm2cr3mkdgk1dtaov18-wpengine.netdna-ssl.com/wp-content/uploads/2017/03/Steve-Strogatz-interview-excerpts-for-website.pdf

Bill Benzon
bbenzon at mindspring.com

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