Showing posts with label maths. Show all posts
Showing posts with label maths. Show all posts

11 January 2013

In the beginning

The universe, Part 3
< How does science work?Series index | From the beginning to atoms >

The beginning of the universe is hidden from us although we know it's about 13.75 billion years old. We can theorise about it using mathematical tools, but we can't see it and we can't measure it. Everything began at that point - space, energy, even time itself.

Maths is an essential tool
We can't see the beginning itself. People sometimes talk about the Big Bang and they imagine a huge explosion crashing out into an empty expanse of endless space.

But that's not right. If you see it in that way you are really not seeing it at all!

Nothing existed before the Big Bang. At least no physical thing that we can see or know inside this universe existed.

There was a singularity, though it's difficult to imagine one of those or what it implies.

  • Time began at the beginning, so before the beginning is meaningless.
  • Space began at the beginning, until then there had been no room in which anything could have existed. There was nowhere to explode into.
  • Energy began then too, beforehand there was no energy.
  • And there was no matter because matter is just condensed energy.
  • Even the laws of physics began at the beginning

Time, space, energy and physics all had their origins at the beginning, and we can't investigate that extraordinary phenomenon - the beginning. We can't see it, we can't visit it, we can't measure it, we can't really imagine it. Not only is it far more extraordinary than we think, it is far more extraordinary than we are able to think.

And perhaps the most amazing thing about the beginning is that eventually we came from it; we are here and are able to think about how extraordinary it all is.

Theoretical problems - It's almost as if the universe doesn't want us to understand its origin. Our best models for the earliest moments of the universe are mathematical. OK, really our only models for this are mathematical.

However there's a serious issue, even with that. If at the beginning the universe was infinitely small then some of the numbers in the models become zero, or they become infinite. Not only does the universe seem to explode, so does the maths.

Maths doesn't always handle zeros and infinities especially well, they can be a problem. It makes mathematical models difficult as we try to apply them closer and closer to the beginning. This is driving some mathematicians and cosmologists to think that there may not be a beginning at all, just a certain minimum size and maximum density before which the universe was larger and, perhaps, time ran the other way. Or something.

Is there room for intelligence? - We can only think about it because we are here. There are no other animals on this planet that even know there was a beginning. We are unique on Earth.

I imagine there must be many other intelligent minds in the universe and it's likely that all of them give some thought to the beginning. Each in their own, unique way no doubt. The fact that there is a beginning is one of the reasons I believe in an even greater intelligence that caused the universe to begin. What is certain is that intelligence is almost inevitable given the properties of the universe, but it couldn't appear until a lot of other things were in place.

But for a moment, let's consider the alternative that the universe has always existed and will always exist with new energy and matter appearing to 'fill the gaps' as it expands. In the 1950s and 60s many cosmologists argued this was the case, it was called the 'Steady State Theory'. But it's since been shown to be incorrect.

But if it was correct I would still feel the need for a first cause, a greater power and intelligence to make it exist. So whether there was a beginning or not, I will still believe in a Creator.

What is the alternative? It's all just causeless?

After the beginning? - But there was a beginning, and we can understand some of the things that happened soon afterwards when the universe, time, space, energy and physics were all very new. And you'll be astounded to learn that we understand some things about it even a tiny fraction of a second after the beginning. A much tinier fraction than you think (unless you're a cosmologist).

It all began roughly 13.75 billion years ago. Our Solar System and this Earth are around 4.5 billion years old or about a third of the age of the universe. The universe was smaller then too.

If you made it this far, congratulations! After this things get easier as the universe grows bigger, older and more familiar. Next time we'll pick up the story at that point where we think we know something, and we'll find out just how awesomely near the beginning that is.


Questions:

  • How comfy are you with the idea of a creative intelligence causing this universe?
  • How comfy are you with the idea of the absence of any such creative intelligence?
  • Does your head hurt yet? Go and get a cup of tea, or coffee, or a glass of wine.

See also:


< How does science work?Series index | From the beginning to atoms >

25 February 2011

ARTS - Musical chess!

I thought this was rather neat. Jonathan W Stokes has been experimenting with ways of turning famous chess games into music. It's amusing to see how he does it and the results provide surprisingly good listening.

'The Immortal Game' part way throughSo how did he do it?

The process he chose is quite straightforward. He noticed that there are eight columns of squares on a chess board and also eight notes in a musical octave.

With some rather clever adjustments and using the values of the chess pieces to determine how long each note should be, he transcribed the chess notation into musical scores and then played them on a piano.

Here's my favourite - 'The Immortal Game' played in June 1851, and this is how it sounds on the piano.

Rather delightful!

The full details and a further two examples of the music are available on Jonathan's blog. And if you enjoyed Chess Music you might also like Jonathan's Fibonacci Music!

28 April 2009

Wolfram Alpha

Wolfram Alpha is about to hit the streets (or at any rate, a computer screen near you). The Wolfram Alpha query screenCreated by Stephen Wolfram and his company, Wolfram Research, it will look superficially like a search engine but is fundamentally different in nature.

Like a search engine it comes with a text entry box where you can type in a query, like a search engine it goes away and thinks and then spits out results on a webpage. But what goes on behind the scenes and the nature of the returned webpage couldn't be more different.


Wolfram Alpha depends on two earlier developments from the same stable. Mathematica is software that enables mathematical manipulations to be entered, processed, and displayed on a computer, while NKS (which stands for 'A New Kind of Science') is an alternative to the normal tools used by scientists to model the way the universe works.

Using both of these innovative tools, Wolfram Alpha takes a free text query, decides what the user wants to know, looks up the relevant information in its enormous collection, processes the information to create an answer to the original query, and builds a webpage on the fly to display the response. The webpage may include text, images, graphs and charts etc. The end result is a tailored report that might have been written by an expert. Indeed, in many ways Wolfram Alpha is an expert!

Steven Wolfram is an extraordinary person. He is, frankly, a genius - one of a handful of truly great minds in our own time. He looks at things in new ways and comes up with fresh insights, testing them, proving them, and then publishing them. Here, in his own words, is how he's spent his life so far.

Major periods in my work have been:

• 1974-1980: particle physics and cosmology

• 1979-1981: developing SMP computer algebra system

• 1981-1986: cellular automata etc.

• 1986-1991: intensive Mathematica development

• 1991-2001: writing the book, 'A New Kind of Science'

(Wolfram Research, Inc. was founded in 1987; Mathematica 1.0 was released June 23, 1988; the company and successive versions of Mathematica continue to be major parts of my life.)


You can see right away that he is not a man in a hurry. He is not afraid to spend five years or more on a single project. Learn more about his background and work from Wikipedia.

Not everyone agrees with Wolfram's work on NKS, a range of reactions are included in the Wikipedia article on the book.

In the end, 'wait and see' may be the best advice for both Wolfram Alpha and NKS. As far as Alpha is concerned, we'll all get a chance to try it and draw our own conclusions when it's released. Hopefully that will be next month (May 2009).

Meanwhile you can watch video of Stephen Wolfram demonstrating the new technology at Harvard on 28th April.

For news about the new tool, take a look at the Wolfram Alpha Blog which will be updated regularly with further announcements and background information.

26 August 2008

How many times?

How many times can you repeatedly fold a sheet of paper in half? It's widely accepted that about six or seven times is the maximum possible, and a quick experiment with a piece of writing paper, a sheet of newspaper, or any normal paper you can find around the home will prove that this is correct. Or will it? What does 'correct' mean? What does 'proof' mean?

A mathematician will tell you that however many times you do the experiment and find you can't fold the paper a seventh time, that is not proof. You cannot prove something to be impossible, only that something is possible. Folding a piece of paper six times and failing to fold it seven proves that six is possible, but not that seven is impossible.

Remarkably, someone has managed to fold a piece of paper twelve times! Was there something special about this piece of paper? Yes and no.

The paper was a long roll of toilet paper. The relevant attribute of this paper was not that it was especially thin (try folding a single sheet of toilet paper yourself) but that it was especially long.

Britney Gallivan, a high-school student from California, was not prepared to take 'no' for an answer. She began by developing some mathematics for paper folding, and this showed her that a piece of paper that is long enough can be folded many more times along its width than a shorter piece. Armed with this knowledge she did the experiment - and managed to fold it twelve times.

There are several lessons to be learned from this.

What seems to be impossible may, in fact, be perfectly possible if we go about it in the right way. Technology has shown this to be true over and over again. Here are a few things that were once thought to be completely impossible - travelling to the moon, ships made of iron, building a flying machine, sailing round the world, the earth moving, continents moving, orbiting a satellite.

Common sense often lets us down. It would be a wonderful thing to learn the value of not making assumptions or jumping to conclusions. But we are designed to assume and conclude, this serves us well most of the time and enables us to deal relatively simply with a very complex world.

Britney Gallivan's paper folding achievements are described online. I encourage everyone to read them, if mathematics is not your forte you can skip that part, but please understand that it was the mathematics that led her to a simple, elegant, but entirely unexpected conclusion. With hindsight it seems obvious, but nobody had thought of it before Britney. Clever young lady!

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