Wednesday, October 05, 2011

Dark Energy - the basics

The Nobel Prize for Physics was awarded yesterday for the discovery of dark energy in 1998.

What is dark energy? Do we really need to just accept that it's complicated and freaky, unless we're boffins?

I don't think so.

It's an apparently constant 'energy' per unit volume of space, which causes space to expand.

In 1915, Einstein developed a theory of gravity, out of essentially nothing more than the assumption that the laws of physics in free-fall are the same as those without gravity.

One of his very clear conclusions was that dark energy – which he called a "cosmological constant" – could be a physical aspect of gravity. It emerges naturally from following through the logic from that one starting point.

The question of how to follow the logic is the tricky bit... but unless you're masochistic or deeply suspicious or fantastically curious and patient, it's ok to just think of it as something that's been accepted as a logical implication for nearly a century, and go with it.

So it's been there in the standard modern theory of gravity since the very beginning, although there was no evidence that it was anything other than zero until 1998. It's not a new thing - it's just a part of the nature of the force of gravity.

It's the part of gravity that causes space to expand so that very distant things accelerate away from each other.

I think calling it 'energy' and 'dark' makes it sound freaky and mysterious and new and unknown.

What's new is that it's been measured. Nobody expected it not to be zero, but it's not; and now we can't just pretend it's not there any more. And this is what the winners of the Prize – Perlmutter, Riess and Schmidt – with the help of many, many others, have given to the world.

It's not some kind of bolt-on to the laws of physics to explain something nobody understands – not in any way. It's a sophisticated measurement of something surprisingly simple, and what's more it's an interpretation that's been verified by many other independent observations of what's out there.

And yes, lots of research needs to be done to check that it's not this kind of field or that kind of modification or that it's doing this or that crazy thing, which is very important and great fun for the scientific community... but as it stands, there's no evidence for anything beyond good old gravity, doing its good old Einsteinian thing.

And if it turns out that it is as simple as that, then it means the fate of the universe is that clusters of galaxies will separate over time until they're no longer visible to each other.

Within clusters of galaxies, which is where we live, dark energy doesn't really do anything at all. (Apart from handily ensuring that the entire rest of the universe won't come falling in and crush us at some point in the future!)

I (try to) study this stuff, so it's fascinating to me. The details of the logic of the theories can be daunting, but I like to think that the real substance of ideas like this are accessible to anyone. But perhaps this belief just helps me feel less isolated from those not mad enough to dive into it all in detail.

If you kinda knew all that, and have been trying to come to terms with how it all fits together and the various questions and apparent paradoxes it throws up, the excellent Sean Carroll has provided a very clear and detailed FAQ.

Saturday, October 01, 2011

Census of the Dead as the Living Reach 7 Billion

A question for Hallowe'en. For each person alive on Earth, how many ghosts are there? And what are they like?

If you want to skip the numerical details, click on Ghosts.


The Population of the Living

The human population of our planet has increased at a tremendous rate over the past few decades, and is poised to exceed 7 billion.

You may find people are telling you when this milestone be reached, but let's be honest: nobody can truly say they know what year it will happen, never mind what day. We may well already have passed it.

The world population at any time is probably known to an accuracy of little better than ±1%. Wikipedia's page of world population estimates gives a selection of independent estimates of the world population at different years, and the agreement for recent years is around ±0.5%, which means an uncertainty of ±35 million people.

The rate of increase is something like 217,000 people per day, so if we wanted the date when the population of the world exceeds 7 billion, realistically we're looking at an uncertainty of nearly six months either side.

Nevertheless, it's sometime about now, and it's a significant event, so it's good to have a date to focus our attention. The United Nations has chosen 31st October 2011 as the day on which world human population will nominally exceed 7 billion.

There's a lot to be said about the implications and consequences of this vast and still growing number of people. You'll hear plenty about carrying capacity, fertility rates, resource crises and environmental concerns over the coming weeks, along with the inevitable speculation about what drastic measures might be needed to deal with it.

So far as I know, the only large-scale socio-political force that is known to put the brakes on population growth is long-term investment in and commitment to the education and health of women. Which is hardly a drastic measure. Hopefully the news will focus on this, and how we can help; and hopefully at least some journalists will try to recognise other valid perspectives instead of just pressing the easy sensationalist hype button. Let's see.

That aside, what intrigued me today is something altogether different.

(The choice of date by the United Nations may have something to do with it.)

The Population of the Dead

If there are 7 billion people alive on Earth, how many people have ever lived?

This report by the Population Reference Bureau, which is discussed in this article in Scientific American, gives us an answer. (There may well be alternative studies which are more recent, more thorough or more objective in some other way, but I haven't seen them. I'd welcome comments from anyone who can put this in a bigger context.)

Their result is that 106.5 billion people were born between 50,000 BC and mid-2002.

Is this realistic?

The authors don't give an estimate of the degree of uncertainty in their figures, but they have modelled the population based on assumptions that appear to be reasonable.

The most significant assumptions are the very rough values they've chosen to use for birth rates, which are listed in the table on their report. To my eye, they seem to be on the high side, implying very high rates of infant mortality. If anyone has any clear ideas as to how world average annual birth rates per 1,000 of the population would have varied over history and pre-history, I'd be interested to hear them. I could re-run the authors' model with different birth rates if there are good reasons to do so.

Meanwhile, I'm taking the view that their figures are fine, though perhaps veering towards the high end of what's feasible, and presumably with an uncertainty of a few tens of billions.

One thing I will briefly look at – because it's interesting – is the date range of 50,000 BC to mid-2002 used in the report.

1. Adding in the period mid-2002 to 31st October 2011

This is fairly easy to do. The worldwide birth rate over that period has decreased steadily from around 20.8 to around 19.2 per year for every 1,000 of the population, so let's call it 20; the population has risen from 6.22 to 7.0 billion, so let's take an average of 6.6 billion over a period of 9.25 years. This gives a figure of 1.22 billion births, which we should add to the result.

2. Adding in the period before 50,000 BC

If we extend the period back to the origins of Homo sapiens around 250,000 years ago, or of the genus Homo 2.3 million years ago, or to our diversion from chimpanzee cousins around 5 million years ago, even with a tiny population, the total number of births during these enormous timescales would substantial.

The population is thought to have dropped to around 10,000 in 70,000 BC due to extreme climatic changes following a catastrophic volcanic event. Before this period, the number of humans is estimated to have been around 50,000.

Using the authors' suggestion of a birth rate of 80 per year for every 1,000 of the population, the number of births prior to 80,000 BC is in the region of 4 billion births - and deaths - per million years. If we went back five million years, we'd be adding something like 20% to the total. But that's pushing the limits of what we consider to be human further than we might wish: if we went any further than that we'd implicitly be including chimpanzees. It's a matter of taste where we choose to stop, but if we're talking about humans, it definitely won't be further back than that.

To summarise:

107.7 billion people (give or take a few tens of billions) were born between 80,000 BC and 31st October 2011.

Perhaps 20 billion homininans were born in the 5 million years prior to that, of whom around 0.8 billion were Homo sapiens going back to 250,000 BC. If we stretch our human period back to around a million years to start including some close relatives, we bring the total to 111.5 billion.

Of the 111.5 billion who have been born in the last million years, 7 billion are alive, and 104.5 billion are not. Which means...

For every human being alive today, there have been about 15 who have died.


So each of us can be allocated 15 ghosts of humans past. Assuming we are to share them equally, which seems only fair.

Who were they?

Using the table in the report, our ghosts were born as follows:

7.4 of them before 1 AD
3.8 of them between 1 and 1200 AD
1.8 of them between 1200 and 1650
1.0 of them between 1650 and 1850
1.0 of them after 1850

The last figure tells us that, of all people born since 1850, half are alive now. (The total number of births since 1850 comes to 13.92 billion.) Which means each of us can have only one ghost of a person born since 1850.

We each get one ghost of someone born in the period 1650-1850 too.

If we allocate a period to each ghost, the distribution would look something like this:

1 born after 1850
1 born between 1650 and 1850
2 born between 1150 and 1650
3 born between 200 AD and 1150
4 born between 1400 BC and 200 AD
3 born between 7000 BC and 1400 BC
1 born between 1,000,000 BC and 7000 BC

The last guy in the list may or may not have actually been Homo sapiens – it starts to get blurry here. And there may even be another couple of fairly closely-related hominids kicking around from earlier still.

(The splits at 1400 BC and 7000 BC follow from the assumption of steady exponential growth between 8000 BC and 1 AD, which the authors of the report used in their model.)

The other thing we can say, of our 15, is it's likely that:

5 or 6 survived to adulthood
3 or 4 died in childhood after the age of one
and 6 died before reaching the age of one
That's two baby boys and two baby girls from earlier than 200 AD
and one baby boy and one baby girl from after 200 AD.

And those are our ghosts.

As the Northern Hemisphere approaches the dark nights of winter, and the veils between the worlds of the living and the dead are at their thinnest, as our Pagan friends would say, we could take this opportunity to each bear in mind our 15 ghosts.

To consider the lives they had, the world they lived on, the world they've passed down to us, and what we might do now that we're in it. To consider how we might choose to leave our world for those who will later think back to us, wondering what we were doing and thinking as we watched the world pass 7 billion.

I'm not an artist – numbers and abstractions spark my imagination. But it occurred to me that some people might want to sketch their ghosts, in clothes or settings for their period; or else do some unpredictable creative thing to acknowledge them. If you do, send me a link.

And happy Hallowe'en – or however it is that you choose celebrate this time of the year.

Don't have nightmares. They were humans just like us, after all.
Be good to your ghosts and they'll see you right.