This is a follow-up post to “Greedy reductionism – know any zealots who need a wake-up call?” concerning the whole being greater than the sum of its parts. I received an email from Neil further supporting Tim’s POV, so I thought it would only be fair to post the details…
From: Neil P
Sent: Friday, 30 March 2007 4:03 PM
To: Cassandra Brisbane
Subject: Thought I’d just take umbrage with….I noticed you had your own blog so I took a look.
Tim and I had an interesting discussion about the saying “The whole is greater than the sum of its parts” over email. I originally said that I didn’t agree with the saying, that it wasn’t really feasible and was just bad maths. After thinking about it a while, I came up with this:
As a systems engineer, I can categorically (and beyond shadow of a doubt) state that the “whole is greater than the sum of it’s parts”. I use this quote (from Aristotle) to demonstrate this point in the systems engineering presentations I give.
Case in point. A car. A car is a complex system that relies on the integration of many components to realise its greater function. The engine, on its own, has no real purpose, i.e. without the surrounding infrastructure it has no real use. Similarly the gearbox, the chassis, the doors etc. Even down to the nuts and bolts that bolt it all together. Meaningless as an individual commodity, meaningful in the wider context.
All systems are the same and they do not have to be thought of in terms of cars, planes, trains. The legal system, for example, is the collection of disconnected meaningless things that take on meaning when assembled as a whole.
So in summary:
Don’t argue with Aristotle!
From: Cassandra Brisbane
Sent: Friday, 30 March 2007 4:11 PM
To: Neil
Subject: RE: Thought I’d just take umbrage with….I was just thinking… mathematically speaking, it doesn’t really work. 2+2 will never = 5. As each number has a specific value, the whole will always equal exactly the sum of its parts.
From: Neil
Sent: Friday, 30 March 2007 4:30 PM
To: Cassandra Brisbane
Subject: RE: Thought I’d just take umbrage with….Disagree:
1) 2 apples plus 2 apples is 4 apples. 4 apples constitute the same thing and don’t combine to make anything greater. When you add 1 egg, 1 quantity of flour and 1 quantity of pastry, you may have eight or nine physical items. As individual components, they exist in their own space with a limited meaning. Combined, the systemic meaning changes.
So mathematics does not come into it. It is the intangible nature of the interconnectivity/interrelationship between the components that serve to add the systemic meaning. While I can connect things together and express them mathematically, I can only ever express them as a complex function. Modelling does exactly this. All a model is, is a mathematical representation of a system. I have created mathematical models to show, for a given input, what the given output would be for a system. The systems I reduced to mathematical functions were relatively simple but the mathematics gets tricky. Did you know that 99% of integrals cannot be solved?
So mathematics cannot account for the intangible nature that is associated with the interconnection of independent components. It’s like the soul – tangibly, it weighs 13grams. We can reduce it to meaning. But most academics would agree that the soul itself cannot be expressed as a whole by the assignment of a man-made constant to it. It has an intangible quality that cannot be quantified in itself. Systems are the same.
So, i’ve given the whole thing pretty good coverage, and haven’t censored anything that would make me look uninformed. Because, y’all already knew that, right?
Anyway, I had a look at the usage stats for my blog, and at some of the search string referrers. I don’t know how “superted glasses” brings them to my site. In most cases (as with most searches that lead to blog posts) I don’t think that they found what they were looking for.
It’s totally the weekend right now! I’m totally going to go do some laundry and stuff!