Mathematics and technology

I love mathematics. I love technology. Therefore I agree wholeheartedly with this piece, which explains that there are no technological shortcuts in the learning of mathematics, and many technological hindrances.

Good quote: "earned fluency is the only way to understanding". A calculator can tell you the answer; but plenty of hard work with pencil and paper is the way to understand the answer. Confusing those two concepts is fatal.

On the subject of mathematics, here's a link to an article I wrote a few years ago, "Creation and Mathematics".

Darwinism and Dawkins versus Mathematics

Here is a very interesting job advert. Two professors at St. John's College, University of Oxford, are looking for two assistants to help them do research into the mathematics of population genetics and Darwinism:

http://www.sjc.ox.ac.uk/3498/RA%20in%20Mathematics_FPs.pdf.download

Three things are particularly noticeable in the description of the job:

• The two professors are doing research that they hope will lead to mathematical support of Darwinism - i.e. they are friends of Darwinian theory.
  
• They frankly admit that mathematical geneticists "mainly deny that natural selection leads to optimization of any useful kind", and then go on to explain, equally frankly, that Richard Dawkins' arguments in his seminal work, "The Selfish Gene", are not supported by known mathematics.
  
• The description proceeds to explain that they are looking for mathematics that will provide a basis for many of the concepts that are the Darwinian philosophers' stock-in-trade. Or in other words, stating the implication of that, they admit that as yet, the stock-in-trade conversations of Darwinian philosophers are not grounded in any known mathematical reality.

Note again the first point: these aren't enemies of Darwinism looking to do research to tear it down. They are its friends, looking for the research to establish it, and along the way candidly admitting that the mathematics to do so does not exist and the idea is generally contradicted. And remember, these aren't clowns; these are mathematics professors at the wealthiest college in the UK's top university...

I've just hopped over to RichardDawkins.Net to see if the great non-existent misotheist has republished the job announcement yet. Seems he hasn't got round to it....

What has Christianity got to do with mathematics?

Just added to my website: "What has Christianity got to do with mathematics?". This article aims to give a brief, non-technical answer to the given question.

A Mathematical Universe

My first love in academic study was mathematics. At school I drank it up, and I studied it for my degree at university.

Mathematics, Realism And Theism

Mathematics is also a very interesting field if you have an interest in philosophy and questions about design in nature. Almost all mathematicians are in practice realists - they believe that as they make progress in their field they are involved in discovering and not in inventing. (See here for more on this distinction). That is, they act and research as if there is already a transcendent, pre-existing mathematical universe "out there" that is waiting for us to find and explore it. The opposite of that is behaving as if mathematics is our arbitrary toy, to be played with, deconstructed and rebuilt as we please. Shall we adopt the convention that 2+2 = 5 from now on and see where that takes us?

In my observation most "mathmos" haven't done much by the way of questioning themselves over this realism - they just accept it. If, though, you want to have a coherent and comprehensive view of reality, you have to start looking at this. In my view, the atheist materialists who have tried to explain their view of reality are in an exceptionally weak position when they seek to explain mathematics in non-transcendent terms. Mathematics resists, at multiple levels, any attempt to treat it as an arbitrary invention of the human mind. Almost at every turn it cries out "I was here before you, and I am bigger than you!". Maths is a very theistic subject!

Abstract or Concrete?

What I wanted to talk about here though was down a little bit of a different track. It is about the connection between mathematics and the physical universe that we live in.

Mathematics is, from one angle, an entirely abstract subject. When we do algebra, we are manipulating symbols on paper - but we are really talking about something that exists behind the symbols. Mathematics basically has its seat of existence in the mind, and not on the paper. I can of course always add two apples to two apples and will always get four apples (an inconvenient truth for the atheists who want to argue that mathematical truths are not transcendent!) - but as I do so I'm conscious that there is a notion of "two-ness" or "four-ness" that goes far beyond the tasty bits of fruit and is independent of them. If I add two oranges to two oranges I get four of them as well. The more complicated the mathematics gets, the more obvious this becomes. I can move from the simple adding of objects to a dimension up and do calculus to work out the area under a graph. I can then accelerate to five or six dimensional spaces and work out their corresponding concept of volume. I can work out the properties of completely theoretical objects. you get the idea. Mathematics speaks to us of an ideal reality which depends on the mind.

We've already said more than that, though. Whilst it depends on the mind, mathematics also seems to have an unbreakable link to the physical world. In the most simple example, there's something about those two oranges that has the notion of two-ness. The notion of two-ness is contained, but not exhausted, by them. I can create a two-dimensional shape that is approximately (but never exactly - because we live in a world of discrete atoms and molecules) equal to the one in the equation of the graph I was using. This is all simple enough. What is more breath-taking, though, is to understand that correspondences between abstract mathematics and the physical world have also been discovered in far more complicated cases. In some areas, mathematicians discovered new theorems in highly abstract areas that nobody thought would ever turn out to have a practical application - but in fact they actually perfectly described physical phenomena observed decades later. Do you get that? Away in his dusty study somewhere, the mathematician was working on a problem that was thought to be far too abstract to have any real application. Some time later, a physicist realised that this bit of mathematics was the key to something that he was observing. Quantum physics provides a number of illustrations of this.

Summing Up...

I hope you're still with me! The point here is this:

Observation one: Mathematics has its seat in minds. Observation two: We also now know that mathematics is also embedded at a fundamental and essential in physical reality. Inescapable conclusion: Physical reality is the product of a mind.

As a Christian I believe that all knowledge can only ultimately be rightly understood when we see its integration point in our Maker. Or in other words, unless we begin with God in everything, we'll eventually go wrong somewhere down the line. When I say things like this, a response I often get is "but lots of knowledge is neutral and has no religious implications. Take maths - 2+2 is 4 whether you are a Christian or an atheist!" Above I've explained just one reason why that answer is on a wrong track. The objectivity of mathematics and its fundamental connection to the physical world are two more places where God speaks clearly - and leaves the atheist without excuse. They cannot be accounted for on purely materialist assumptions. Mathematics is universal, transcendent, comes from a mind, and is embedded at the deepest level in the world we live in. Mathematics speaks clearly of the immense and wonderful mind of the one who is.