Dear Francois,
Thank you for your message. I'm happy to oblige. It makes more sense, however, to take things in reverse order.
First, my apologies. Spell checking corrected ‘mereology’ in my last post to ‘metrology’ (science of measurement!).
The post should have said ‘moving between set and *mereological* mapping of concepts.’
The difference is that ‘sets’ comprise collections of distinctly defined objects. Some sets may overlap and an object may be in more than one set. Set theory is relatively straightforward as the relationships between different sets are straightforward. In contrast, ‘mereology’ refers to the way that some things are ‘parts’ of a ‘whole’. This is a complex issue and very different from ‘sets’. For more detail see http://plato.stanford.edu/entries/mereology/
Where mereology (and sets) become interesting is when designs and their behaviours become discussed. This means they become abstractions that are also part and parcel of theories, concepts and layers of higher-order meta-theory representations of behaviours of lower-order theory functions. For example, an iphone enables communication, and results in increased or reduced social capital. This is part of a higher-order understanding of the dynamics by which communication affects social behaviours, or an even higher order theories about the dynamic behaviours and consequences associated with communications between human, animate and inanimate elements. The part/whole issues are complex and subtle - and different from simple set formulations. This extends all the way down to the physical realm of cups, saucers and handles, or iphones, icons and apps.
Getting a handle on mereological/set maths is crucial in many aspects of design. Recently I've been using web scraping software to gather research information for some design research. It demonstrates the difference between part/whole and set relations. For example, in designing a process to collect data about research publications, the title, author and abstract have part/whole relations to each publication, yet the books themselves fall into sets . Get them confused and there is an awful data tangle!
There are many similar examples in, e.g., graphic design, information architecture, design management, and design of socio-technical systems.
P.S. I see you are back safely from Rwanda. Well done.
Best wishes,
Terry
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Dr Terence Love
PhD(UWA), BA(Hons) Engin. PGCEd, FDRS, AMIMechE, MISI
Director,
Love Services Pty Ltd
PO Box 226, Quinns Rocks
Western Australia 6030
Tel: +61 (0)4 3497 5848
Fax:+61 (0)8 9305 7629
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-----Original Message-----
From: [log in to unmask] [mailto:[log in to unmask]] On Behalf Of Francois Nsenga
Sent: Sunday, 27 April 2014 11:18 PM
To: PhD-Design - This list is for discussion of PhD studies and related research in Design
Subject: Maths, the language for everyone, including (fine) artists?
To many among us, the following enumeration of what, to you, seems 'crucial', alas it does mean much until, if you can spare the effort, you provide to laypersons that we are, further explanation on each of these
points:
"Crucial seems to be is mastering abstraction and meta-abstraction along with predicting dynamic behaviours in multi-dimensional spaces, going beyond linear four-dimensional understanding of the world, understanding and using limits and disjoints, moving between discrete and continuous, combinatorics and design theory (different from what is known as design theory in the design industry) , understanding the calculus of change and feedback, and moving between set and metrological mapping of concepts."
Best regards!
Francois
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