Humanist Discussion Group, Vol. 33, No. 663.
            Department of Digital Humanities, King's College London
                   Hosted by King's Digital Lab
                       www.dhhumanist.org
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    [1]    From: William Pascoe 
           Subject: Re: [Humanist] 33.661: mathematics --> ? (59)

    [2]    From: Willard McCarty 
           Subject: The Software Arts (22)


--[1]------------------------------------------------------------------------
        Date: 2020-03-10 02:22:33+00:00
        From: William Pascoe 
        Subject: Re: [Humanist] 33.661: mathematics --> ?

On the mathematics question, it's worth bearing in mind the importance of the
level we are thinking and working at.

Cooking depends on chemistry but most of us seldom think directly about the
interaction of particles or the synthesis and analysis of various compounds when
cooking, beyond applying something acidic, like lemon or vinegar. Normally we
just think basil will go well with tomato, or that if we roast tomato it will
bring out the umami. At higher levels different properties and functionality,
going by different names, are emergent.

If we are drawing on a tablet, does it matter what the maths is? There will tend
to be some range within which the importance of the underlying calculation is
important - if I'm drawing or sending an email I might not care. If I'm using an
app that takes my input and gives an output I might care to know the algorithm
to be sure of its reliability, but even that, and even the level I work at as a
software developer, is 'high' above the sort of mathematics required at the
foundations of computer science. Having said that, some understanding of how the
basics work can provide useful lessons for working at higher levels - how
information theory works provides very useful analogies for UI and UX design
through a deep understanding of what 'information' is and how we design things
like colour and dynamic elements around people's expectations and surprises
(entropy).

There are physical levels of silicon and transistors, mathematical levels of
Turing machines, discrete math, information theory, which translate also into
logic which are all used to produce algorithms and functions at a higher
(almost) human level of languages, which are then used for things useful and
comprehensible to lay people.

Computer science/engineering depends greatly on mathematics. This mathematics is
always dependent on a physical instantiation such as silicon. Much is made in AI
of the importance and potential limitations of both this physical instantiation
and the mathematics it manifests as discrete and linear by contrast to the
highly parallel processing possible in 'wetware'. Some argue it makes all the
difference, others that it's irrelevant. Some that we can make intelligence with
silicon switches and discrete linear computation but that it will be different.
Hayles argues that physical embodiment radically determines
'self'/'intelligence'/etc and that 'mind' is inseparable from the physical
instantiation that determines it.

There are plenty of interesting paradoxes and contradictions. Reason seems
distinctive to humans, a foundation of our ability to reason, and computers
*seem* like minds in that they perform logical operations [Lovelace's notes],
and these are manifested in silicon - yet 'logic' is an emergent property of
massively parallel neural nets, and many people don't understand it, we are
often not good at it, and it takes a long time to learn well. It's only in
retrospect that it appears that we have been using some sort of rules of logic
to reason and to then try to refine them, and (mistakenly?) think that the
functioning of minds must be built upon them. Logic, conventionally understood,
is not foundational to the operation of brains - whereas computers are founded
on logic, with it 'hardwired' into its physical form.

The main thing I want to get across is that the 'level' or micro/meso/macro
scale is an important factor when considering math in relation to humans,
humanities and DH.

Bill Pascoe



--[2]------------------------------------------------------------------------
        Date: 2020-03-09 09:02:58+00:00
        From: Willard McCarty 
        Subject: The Software Arts

Some here will already know about, perhaps even have read, Warren Sack's
The Software Arts (2019), which makes a very important case for the
fundamental role of the arts, and so of the artful humanities, in
computing. It also bears directly on the question of the relation between 
mathematics -- and what is meant by 'mathematics' -- and computing. His 
reach into the sources is excellent and extensive.

A good introduction is his lecture at Berkeley, for which see

https://www.youtube.com/watch?v=0cbMfZRwu5E

Comments welcome.

Yours,
WM
--
Willard McCarty (www.mccarty.org.uk/),
Professor emeritus, Department of Digital Humanities, King's College
London; Editor, Interdisciplinary Science Reviews
(www.tandfonline.com/loi/yisr20) and Humanist (www.dhhumanist.org)




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