Eternal, unchanging, omnipresent? That’s true of maths as well as of God.
Do you need a Universe for maths to exist in? I don’t think so. Do you need a moment for maths to exist in? Er, don’t think so either. Time can flicker away, stop, start, accelerate, slow down, be intermittent, go backwards and maths would continue its brute existence.
All you need for maths to exist is a single idea, ‘logic’. Once you have the idea of logic, all possible maths is both inevitable and necessary. I don’t think, for example, you need beings to think mathematical thoughts, or a Universe to write them down in. Every number, every infinity, every theorem, every possible consequence of every possible set of axioms must eternally exist in its complete perfection quite apart from this universe of time and space.
Nothing exists before Maths, and nothing can exist that is in some sense post-Maths, because Maths is a different order of a thing than Creation or Time. Maths does not create itself, slowly building itself, like Creation might. In its unchanging totality Maths cannot not exist, and it cannot not exist regardless of whether it is being observed, or whether there is or isn’t a universe.
So maths is eternal, unchanging, omnipresent and necessary.
The ontological ‘proof’ of the existence of God is a cousin to this proof in that it also talks about God being necessary. Most days, when I try, I do not understand the Ontological Argument. Occasionally I think I get an understanding glimpse of it, but then the clouds roll over again.
But that fact that I know of something that is infinite, eternal, unchanging, perfect, complete, omnipresent and necessary–Maths–makes me think that ‘proofs’ like the Ontological Argument may (as apparently even Bertrand Russell admitted) ‘have some legs’.
(If you want to wade into the Ontological Argument, try here.)
My blog’s theme, thought of by someone else and expressed better
Above all, trust in the slow work of God.
We are quite naturally impatient in everything
to reach the end without delay.
We should like to skip the intermediate stages.
We are impatient of being on the way to something
unknown, something new.
And yet it is the law of all progress
that it is made by passing through
some stages of instability—
and that it may take a very long time.
And so I think it is with you;
your ideas mature gradually—let them grow,
let them shape themselves, without undue haste.
Don’t try to force them on,
as though you could be today what time
(that is to say, grace and circumstances
acting on your own good will)
will make of you tomorrow.
Only God could say what this new spirit
gradually forming within you will be.
Give Our Lord the benefit of believing
that his hand is leading you,
and accept the anxiety of feeling yourself
in suspense and incomplete.” Pierre Teilhard de Chardin
Some years just stick out in the cultural memory. 1812. 1914. 1945.
How about 2007?
The idea that ‘the future is here, it is just unevenly distributed’? Thomas L Friedman in his book Thank you for being late seems also to suggest that 2007 was the year the future started to get distributed.
This is also so scarily not-that-long-ago, as history goes, that I remember lots of it.
Late 2006: Google bought YouTube
Late 2006: the Internet had more than 1 bn users for the first time
Sept 2006: Facebook, previously just for students, was opened to the world
Jan 9 2007 at the Moscone Centre in San Francisco, Steve Jobs introduced the iPhone to the world: I remember watching the preasentation on my mac.
2007 Twitter spun off from an earlier startup and started to scale globally. I remember joining Twitter shortly afterwards courtesy of the Guardian’s Tech Weekly podcast — and finding nothing going on, came off again.
2007 AT&T found a way to use software to expand its capacity. Its throughput of data increased 100,000% (in Friedman’s words) between Jan 2007 and December 2014
2007 Amazon released the Kindle.
2007: Google launched Android.
Spotify (though Friedman doesn’t mention it here) started in late 2008.
Of course other dates in 2007 may also make a mark on history:
Bulgaria and Romania join the EU, marking (in the light of future events) its maximum extent?
BNP Paribas blocked withdrawals by three hedge funds that were drowning in sub-prime mortgages, triggering the financial crisis.
(And there was a school shooting in the US, only a couple of dozen dead, not news at all.)
Am enjoying Thomas L Friedman’s Thank You for Being Late which, at root, only tells us the boring story that the world is changing fast and how to adapt to it. What makes Friedman’s book interesting is his observation of how fast it is changing, and the thought that many things (laws, culture, life) have not caught up. Being a three-time Pulitzer prize winner, Friedman has some great examples too. Here’s one.
Lawrence (Larry) Summers, was a treasury official in the US. In 1988 — just 30 years ago — he was campaigning for the ill-fated Michael Dukakis and was picked up at the airport in a car with a phone in it. He was so excited that he used it to phone his wife and tell her.
Just nine years later, as deputy health secretary, Summers visited Cote d’Ivoire to open a village health care project that had been funded by American aid money. The village was remote enough for him to do the last part of the journey by canoe. As he was getting into the canoe for journey home, someone handed him a phone saying ‘Washington has a question for you.’ The world had gone from a carphone being an exotic luxury to a phone in every canoe in just nine years.