Lessons Of The Elections

Substance isn't everything.

Many fellow Labour supporters have bemoaned that Ed Milliband suffered unfairly from a poor public image. Shouldn't it be about substance, not style ? No, it shouldn't - not exclusively. Style matters. A political leader has to be able to inspire people, to not merely motivate but actually make them enthusiastic about things they may have been opposed to - not just to win votes in the first place, but also to maintain support afterwards. That is simply impossible to do with pure rational argument.

I'm a lefty. In fact, I'd have liked even more left-wing policies than Miliband's. But he never inspired me, or persuaded me that he was competent enough to actually make his ideas work, or overcome resistance to them. And if you can't even do that, then no, you're not a good leader. It's a similar problem to Gordon Brown - a tremendously moral man, highly intelligent but a terrible, dreadful manager. He was chronically unable to work well with other people.

Perhaps in a ideal world, everyone would be persuaded entirely by logical argument. But we aren't Vulcans, and failure to acknowledge that is a catastrophic error. Having good ideas is essential, but that doesn't mean anything in a leadership role if you can't persuade people that they're good ideas.


The voting system isn't broken.

Well, not necessarily. The huge disparity between the number of seats won by the Scottish National party (56 - a gain of 50 !) and UKIP (1 - a loss of 1) despite UKIP actually gaining a much higher share of the vote (12% compared to 5%) reveals a very interesting aspect of the first-past-the-post system. Clearly, it is possible for smaller parties to make major breakthroughs. A party which wins a large percentage of the vote but few actual seats is, I submit, not failing because of the system, but failing to understand how to campaign correctly within the system.

Perhaps other voting systems are better or fairer. But the SNP's sweeping victory disproves any idea that a different system is necessary for the success of smaller parties. And, seriously, we recently had a referendum on a different voting system and we rejected it decisively, a fact conveniently forgotten by UKIP. Anyone seeking to change that is going to have a very difficult uphill struggle.

While substance isn't everything, having a single allegedly charismatic leader is only useful if you have other people to back them up - you can't rely exclusively on them to win votes for the other party members.


The voting system is broken.

Or rather, while the system can be fair if you play it correctly, it's not intrinsically a system of proportional representation. It's broken in the sense that currently there are large differences between the share of the vote and the share of the seats that parties win. Even leaving aside the issue of how you play the system, I don't think this is actually such a bad thing. Allow me to explain why I think that if you want to fix the system, you have to be extremely careful about how you do it.

The first-past-the-post system doesn't prevent hung parliaments, but it does make them rare events. It's pretty good at delivering decisive results in favour of one party. Consequently, that's how our politicians campaign and that's how we vote - with the expectation that the party we select will hold office and enact the policies they've put forward. Usually, one party gets a majority and then tries to implement its pledges. Thus, we the people are (in large part) responsible for both choosing the government and its major policies, if not for deciding any specific details.

Where this all goes horribly wrong is when a hung parliament does occur. In that case the system sucks. We don't even get to choose which government is formed (although last time there was really only one practical possibility, a much more even split is possible), let alone which policies we want enacted (this is much worse because the politicians are campaigning in a system where they don't expect to be in a coalition so they don't tell us how flexible they are on most issues). Essentially this gives an unelected government a free hand to choose whatever policies it wants, making the fact that people voted virtually meaningless. No wonder people don't like coalition governments.

The question then becomes : do we want a (more) proportional system of representation, which inevitably means more coalition governments, or do we prefer to occasionally suffer bouts of madness but most of the time get more decisive governments ? While, as I said, political groups do have to work within the established framework of democracy, we also have to recognize that huge numbers of people voted for parties like UKIP which got barely any representation in Parliament at all.

If we do want more proportional representation / coalitions (and I'm not saying I think we do), it's abundantly clear that our voting system is not fit for purpose. We have no way to tell politicians at the ballot box which alliance we prefer, let alone which policies we're voting for. A system where people have a much more direct say in which policies are enacted, rather than which party is elected, might or might not work (that's another issue) but this is simply impossible in the system we have now.

So, to my mind, if you're campaigning for a more proportional system then you should also be campaigning for a better system to ensure that voters get the government and policies that they actually want. Otherwise, we almost lose the "democracy" from "representative democracy" completely - we the people will have little say in which government is formed or what policies it brings forward. Personally I don't want to vote for people simply so they can negotiate policies on my behalf - I want to have a say in how the country is run. Our current system does that since votes for parties and policies are one and the same. By increasing the number of coalition governments, which must necessarily make compromises in ways the voters can't control, proportional representation (without other reforms to the system) could end up making the system more representative but actually less democratic.

In short, voting reform in order to make a fairer system is more complicated than is usually stated. Right now the system is not so broken that this is necessary. Caution is needed.


The left isn't doomed. 

It was an awful election for Labour, but a majority of just five seats hardly makes the Conservative victory any kind of landslide. Labour have recovered from similar defeats before. Moreover, the real disaster area for Labour was not England but Scotland - where they were replaced with a more left-wing party. The political right are currently in the lead, but only just. Left-wing politics is very much alive and well.

Here's the tricky paradox Labour have to very carefully avoid. Scotland voted against austerity and if Labour are to make a comeback there they're going to have to appeal to that ideology. That's widely seen as very left-wing. But simultaneously Labour failed in England by not being pro-middle class enough. Somehow, they need to be more centrist in England and more left in Scotland - or rather, show that anti-austerity measures aren't just about social justice, but fundamentally good for the middle classes. Or, if they don't want to go down the anti-austerity route, then they've got to fight very much harder to convince the Scots that they will make life better for the ordinary voters.

Labour face a major challenge to regain voters at the next election. But, while the SNP are jubilant at the scale of their victory, it should also sound them a note of caution : fortune's wheel is ever turning. Sometimes defeat can be snatched from the jaws of victory.

My own opinion is that to recover from this, Labour needs to get over their moral disappointment in the man who led them to three successive victories, Tony Blair. No, he was not a moral man, but he was a consummate politician. He knew how to win. Better, in my view, to be (seen as) a centre-left winner than a far-left loser.


TV debates aren't all that important, and the parties aren't all the same.

One thing that struck me about the whole campaign was that both sides were struggling to appear as much like their opponents as possible. If you restricted your attention only to the televised "debates", you'd have seen Cameron promoting the most socialist of his welfare policies and Miliband yapping on about the importance of wealth creation. You could easily be forgiven for thinking that both of the main parties are the same.

But the voters weren't fooled. Listening to the questions posed during the debate, it's clear that people had been paying close attention throughout the government's term of office. Cameron was perceived as threatening welfare, Miliband as threatening jobs. Consequently in the debates they both attempted to appear as centrist as possible. Strangely, that Cameron behaved like a child when he consistently refused to turn up for the debates doesn't seem to have done him the slightest damage.

For the second election running, the debates appear to have changed the fortunes of the minor parties not one jot. Last time, the Liberal Democrats saw a huge surge in popularity after their first debate, which completely and utterly failed to translate into winning any votes - indeed they lost seats. This time Clegg cataclysmically failed to undo the damage done by the tuition fee scandal. The Greens, Plaid Cymru, and UKIP all saw no benefit from the debates whatsoever.

Certainly the debates have their place. But it looks to me like it's parliamentary actions over the course of the term that are the real vote-winners. Appearing to be a centre party on a debate isn't enough - if you want to win that coveted centre ground, you have to actually be central. And not go back on your tuition fee promise, of course.


You can't abandon your principles and get away with it.

Some political commentators have said that whenever a smaller political party goes into coalition with a larger one, the result is that it inevitably gets squashed. In this case, I don't agree. I also think Clegg is an idiot if he really believes that losing almost all Liberal Democrat influence was a price worth paying for their being in government, given the appallingly stupid manner in which they shot themselves in the kneecaps. They could still have done pretty much everything they did without committing political suicide.

The Liberal policy of reducing or scrapping tuition fees wasn't just a policy, it was a core principle of the party. It was the reason most people voted for them. The referendum on the alternative vote was important too, but not to anywhere near the extent of tuition fees. Clegg might have been able to get away with not holding the promised referendum if he'd been suitably contrite. Given the choice between an AV referendum (or indeed almost any of the other Liberal policies) and lowering tuition fees, there was really only one option and he took the wrong one.

I liked the Liberals, and I'm disappointed they lost as many seats as they did. But they deserved it. Lowering tuition fees for students may not be the most seriously important moral issue, but going back on that promise was as if Labour decided to privatise the NHS. Politics sometimes necessitates U-turns, especially on flavour-of-the-month policies, but there are limits.

What really was surprising to me was that Clegg stayed as long as he did. I still like Liberal policies, but with Clegg at the helm I simply didn't believe that they meant anything. That total loss of trust made all of their other policies worthless. It was patently obvious to everyone that after that disaster, absolutely no-one else believed Clegg either. If they'd replaced him very soon afterwards, it's possible the blame could have been (correctly) shifted onto him and him alone. As it is, the entire party suffered. Only time will tell if people will believe what the next leader says, or if the damage is more than skin deep.

The Light Of Other Suns

... because outreach articles should have the most pretentious titles possible, obviously...

There is a justifiably famous video comparing the sizes of various objects in the Universe, most notably, stars. If you haven't seen it, I suggest you do so right now. Go ahead. I'll wait.

And that's all well and good, but... just how big are those stars, in real terms ? What would our Solar System look like if we swapped our Sun for Rigel or UY Scuti ?

Long-term readers will remember that I already did this for VY Canis Majoris, then reckoned to be the largest known star.

Since then it's been trumped by the mighty UY Scuti. With this post, I want to do something a little bit different and not just re-render the system with a different star - another wall of fire that's a bit larger than the last one isn't all that interesting. Here I'm going for variety, and animation, because animation is way cooler.

This post is in two parts. First, I'm going to skip ahead to the results because that's what most people are most interested in. The second part looks at how we know these results and some of the pitfalls to be wary of - the short version is that this is only an approximation, but it should be a reasonable one.


1) Lookit all the pretty pictures !

Without further ado, here's the video.

Ah, but maybe you prefer still images ? That's OK, I understand. Here's the first sequence in still form - with extra information added, as a bonus. You lucky people, those chumps who only watched the video don't know what they're missing. We'll get back to the accuracy of this later. Temperatures are in Kelvin; it's easy to convert if you want to. First, the stars smaller than the orbit of Mars (with Jupiter's orbit just visible at the outer edge) :

Note that the parameters don't scale in a nice linear way. A star that's twice the diameter is not necessarily eight times as massive, which is what you'd expect if density remained constant. There are all sorts of reasons for this, not least of which is that the stars themselves are variable, sometimes swelling massively in size and throwing off huge amounts of mass.

Anyway, now we need to zoom out to see the real giants. To properly compare the others, let's start with the Pistol star again.

In the video I show it ending with Voyager 1, which is very much further away again than Pluto (currently 130 AU from the Sun, or 130 times the distance between the Earth and the Sun). If you're wondering, that's only about 0.05% of the distance to the nearest star. So at the speed the camera is moving in the video it would take about 15 hours to reach it.

The advantage of stills is that I can also show you all the views at once. Here's the every star, every planet shot.

Last time, with VY Canis Majoris, people asked about the temperatures of each planet. If that's your thing, have a play with this online calculator. The bottom line is that if you replaced our Sun with a star much smaller or larger than it, we would die. A more interesting exercise for the reader is to calculate the size of the habitable zone for each star.

That about wraps it up for the visuals. If you're really interested in the accuracy, keep reading. If not, here's a short version of some things to bear in mind :

• Large stars have very low densities, so they won't really have a nice well-defined surface.
• Measurement errors in the numbers can be considerable, sometimes as much as a factor of a few. Certainly we know that some stars are very much larger than the Sun, but don't go thinking that VY Canis Majoris is exactly 1420 times larger.
• Stars themselves vary over time ! Most stars go through several distinct phases during their lifetimes, but even within these different stages their size can vary dramatically.
• I only tried to render the size of the stars accurately in the video/image. Everything else - colours, brightnesses, appearance of the planets - is approximate. These aspects are technically much more difficult to depict accurately than size, and that wasn't the goal of the project.
• Orbits of the planets are approximated as circles, which is certainly good enough here. To see more accurate depictions, have a look at this.
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Finally, this set of imagery is only an attempt to compare different stars, not examine how they change over time. Stellar evolution is another topic entirely. Stars are born, expand, explode or collapse... some of them a bright, some dim, some will live for trillions of years while a few will last less than a million. But that's for another post, sometime. Maybe.


2) How do we know what the stars look like ?

One thing I was particularly keen to stress in my original VY Canis Majoris post was that giant stars do not have a well-defined surface. The density is something like a thousand times less than ordinary air (whereas the average density of our Sun is about the same as honey), the gravity in its outer regions less than that of Earth, and the temperature about 3,000 K. Such stars have been described as a "hot vacuum". The extremely low density, high temperature and low gravity mean that they cannot possibly have anything resembling a surface like our own Sun does.

Mmm, that's a seriously hot vacuum alright.

Unfortunately, animating the Solar System with various different stars necessitates a bit of a drop in image quality. Rendering a diffuse object is computationally expensive - about 30 minutes for a single image of VY Canis Majoris. Which means that if I want to animate it, I have to show a surface, because that's much easier to render*. But how does one even define a surface for such a monster, and how is it measured ?

* Unless I want to wait for at least 7 weeks with my computer running at full pelt 24/7. Which I don't.

Well, firstly, it should already be obvious that since stars don't even have a precise surface, depicting one is going to be subject to errors. Lots and lots of errors. This is only ever going to be approximate. The main take-home message - that stars come in very different sizes - is, however, absolutely correct.

You might think that a useful working definition of the star's radius is the point at which it becomes opaque - trouble is, defining "opaque" is tricky. For mathematical reasons, this is usually taken to be the point at which less than 36% of the light passes through unhindered. Exactly how this transmittance varies with radius is complicated and I've no intention of examining this in any detail. This simple definition will have to do.

Anyway, we've got a definition of our "surface", so how do we go about measuring it ? Carefully, that's how. Stars are absolutely tiny compared to the distances between them. Shrink our Sun to the size of an aspirin and Alpha Centauri would be around 300 km away. Even so, it is possible to directly measure the size of a few nearby stars.

Another, cleverer approach is to watch how a star dims when it passes behind the Moon, or how the brightness changes when two stars move past one another in our line of sight. Not easy, but possible.

But the easiest method is to measure the brightness of the star and use a simple relation between brightness per unit area and temperature (which we get from colour) to get the total area and thus convert it into a diameter. Now, this certainly isn't as good as a direct measurement. But deciding what physics to use is like choosing a car : most people would choose the insanely expensive high-performance option if they could, even if they don't actually need it.

Which is fine, I guess, if you're a professional car reviewer or a racing driver or Batman, or something. But if you just need to go to the shops once a week, simpler, cheaper options are available.

The Fiat Panda is no better or worse at getting to the shops and back than a Bugatti Veyron. Similarly, the Stefan-Boltzman law, combined with distance and brightness measurements, allows us to find a good approximation for the stellar diameter. It might not do the job as well as a direct measurement, but it will do. It won't be orders of magnitude wrong, unless we've screwed up the observations somehow. None of our estimates of size will be perfect*, but they will be good enough.

*Another, larger source of error is that some stars vary in size by huge amounts. Betelgeuse, for example, varies in size by as much as a factor of two.

So, we've got our working definition of size and some decent approximations of diameter. OK, we had to compromise on the whole "surface" thing, but now we should try and get the colours and brightnesses as realistic as possible, right ?

Wrong. Sticking with the car analogy, too much realism is like custom-modding a Veyron : very ill-advised. Specifically, it's like adding an extra wheel, filling its tyres with explosives and trying to strap a Shetland pony to the roof - it will make things worse, not better. The result has to be something people are going to want to look at, otherwise everything else is a waste of time.

OK, it's a cow, not a pony. Close enough.

For example, brightness. I've read many sci-fi novels in which the intrepid/hapless explorers find themselves near a red giant star and can see through its outer layers. Perhaps the authors base this on the very low density of giant stars and/or their varying opacity. What they're forgetting is the gargantuan energy output of such beasts. A star which is ten times the mass of the Sun might have a diameter a thousand times that of the Sun but an energy output one hundred thousand times greater*. Which means that the energy output per square metre will be only one-tenth that of the Sun.

* In a few cases, millions. Stars are complicated things.

I say "only" in the sense of "not drastically lower". One-tenth of very very bright is still very very bright. So no, you're not going to be able to see other stars through a red giant. Staring directly at such a star - if you should ever find yourself exploring a distant star system - is a stupid as staring directly at the sun. You is gonna go blind.

Does an object really have colour if it's so bright that you can't look at it... wait, is this some sort of zen ? Can we solve this through meditation and contemplation of the oneness of all things ?

Answer : no.

Anyway, as I said, knowing a star's temperature, it's possible to calculate its "true" colour, or vice-versa. But this is nearly useless since whatever we're supposed to be using to view this blindingly-powerful star will need some kind of filter, which will also change the perceived colour. And then there are temperature variations which will cause strong deviations from the average, which makes calculating the predicted colour very much harder. Never mind that stars don't -  in practise - follow the predicted temperature-colour correlation all that well, or that technically it is not at all straightforward to convert a star's brightness into a format the 3D modelling software can understand, or that getting a camera setting where both planetary and stellar surface features are visible* is not at all simple.

* CGI buffs will notice that I put a little backlighting on the planets, which is not realistic in space. However I wanted the audience to be able to see clear differences in the planets and not just slightly different silhouettes, and this seemed like a good approach.

Basically, there are two solutions : 1) Spend weeks, if not months or years, doing a proper analysis of stellar atmospheres; 2) Make it up.

I went for option 2. It's enough to know that cooler stars look red and hotter stars look blue. Even the most expert viewers will have a tough time saying whether each star has the correct colour, because of the arbitrary, unknown filter choice of the visualisation. So there's really just no point at all in option 1, or even calculating the average colours in a simple way based on temperature. What I've gone for, then, is something which depicts the size of the stars as accurately as is possible, but rendered in such a way as to look engaging for the viewer.

Finally, obtaining the figures. This was done by searching a variety of sources, usually starting with Wikipedia. Estimates in some cases (especially for luminosities and masses) varied considerably for each star, so for these I chose the most common value. Where available figures were limited, I opted for reputable astronomy sites (especially Universe Today and Bad Astronomy) over Wiki every time.

Ask An Astronomer Anything At All About Astronomy (IV)

Five short questions this week as I've been concentrating on an animation which should be done very shortly.

Although I'll continue answering questions wherever I find them, there probably won't be any further updates to the Q&A page for a few weeks. Next week I'm holiday. The week after the week after that I'm on holiday again, which is nice. But in the gap there will be an extra-special Q&A replacement ! On May 22nd, by the kind invitation of Ciro Villa, I shall be appearing as a guest on a Universe Today's Weekly Space Hangout. Join us as I look gormless in front of the camera and babble incoherently about hydrogen !


1) If the expansion of space is speeding up, can it eventually exceed the speed of light ?
Sort of yes, if you like, only not really.

2) In relation to earthquakes, can the Earth's axis change over time ?
God, I hope not.

3) Do astronauts on the ISS age differently to people on the ground ?
A leeetle bit, yes.

4) If the Universe is infinite, does that mean impossible things are happening somewhere ?
It isn't and they're not.

5) Can we calculate gravity on other planets ?
Yes.

I also slightly updated the question, Is the Universe infinite ?

Ask An Astronomer Anything At All About Astronomy (III)

Five questions added to my Q&A page this week, bringing the total to a nice round 50.


1) What happens to galaxies after their central black holes evaporate ?
Nothing, because all their stars will be dead and black holes just aren't that big anyway.

2) If space and time are expanding, how can we estimate the age of the Universe ?
Carefully.

3) How do we know the distances to the stars ?
By drawing big triangles IIIIIINNNNN SPPPPAAAAAACE !

4) Will our Solar System suffer from a space tidal wave ?
Nope.

5) What's the difference between gravitational waves and tidal forces ?
Waves move. Tidal forces are lazier.

The Most Astounding Fact

Neil de Grasse Tyson describes the most astounding fact as being that the elements in your body were created in the white heat of long-dead giant stars.

Though why he feels the need to talk like William Shatner

I have no idea.

It's a pretty neat thing, no doubt about it. But before you get all misty-eyed or swoon from sheer misplaced romanticism, it's worth stating this in another way.

Yeah I've used this before, but whatcha gonna do ?

Even so, it's a great quotable fact. What could I possibly offer to trump this ? Simple.

The sky is dark at night.

If astronomy is the oldest profession (hint : it isn't), then this is surely the oldest observation. It's also, perhaps, one of the most profound. Its consequences are - quite literally - infinitely more significant than knowing where our atoms come from.

Olber's Paradox is breathtakingly simple. If the Universe is infinite in size, eternal, and full of stars, then every line of sight should end with a star. The night sky would be as bright as the surface of the Sun.

From wikipedia.

It would be quite wrong of me to omit this astonishingly good video by MinutePhysics which explains (almost) all the relevant issues in less than 4 minutes. The only downside is that it is, perhaps, a bit of a blitzkrieg of information on some pretty complicated issues.

Let's take a more sedate look at possible solutions to the paradox.


1) The stars are very far away. Duuuh !

This does seem like a good solution at first, because obviously the further away a star is, the dimmer it appears. Right ? Wrong. Well, sort-of wrong. It's true we receive less of the star's energy output, because obviously most of its light never reaches us but just carries on out into the void, so it appears dimmer. That's just simple geometry.

A planet near a star receives a greater fraction of the star's energy than one further away. The energy from the star is spread out over larger areas at larger distances.

But there's another quantity which is more relevant here : surface brightness, or the brightness per unit area. That, it turns out, does not vary with distance at all.

Imagine that you have two large, equally powerful floodlights. One is 10m away and the other is 1000m away. Obviously, the 10m floodlight will be painful to stare at while the the 1000m floodlight won't cause you any problems. But suppose that you hide behind a wooden fence in which there is a very small hole - small enough that you can only see a small part of even the distant floodlight through it. If you look at both lights through the hole, you won't be able to tell which is which. Bizarre, but true*.

* A simplified truth, actually. I'll get back to that later.

Or, to put it another way, the stars we see only appear dim because they also look small. If you made them so large that they would appear as large as the Sun does, they'd also appear as bright as the Sun.

So unfortunately we can't use sheer distance to resolve Olber's Paradox. Booo.


2) There's something in the way.

The Universe is full of gas and dust, and those aren't bright at visible wavelengths. The problem is that given enough time, all of this gas and dust should heat up and become just as hot as the surface of a star. At which point they will also look as bright as the surface of a star. I say "a star" rather than "the Sun" because of course not all stars have the same brightness - but they all, to our eyes, have a high surface brightness. Anyway the same thing applies to dim stars as it does to dust - they'll get heated up by the infinite number of other bright stars.

Dark clouds like this one obscure stars in our Universe, but this doesn't work if the Universe is infinite and eternal. Everything should have reached the same temperature.

One might wonder about black holes, which do not let light escape. If there was a black hole along every line of sight, would it not prevent us from seeing all of the starlight ? Well, perhaps. But this is going to mean having all the black holes set up just right so as to prevent us from seeing stars beyond a certain distance. And the mass infalling into the holes is going to have to be absolutely perfectly balanced to counter their shrinking due to Hawking radiation - otherwise they'll either grow to infinite size and consume everything, or vanish. Which is preposterous given how varied the Universe is on small scales.


3) We're looking at the wrong wavelength.

I myself have made great efforts to point out that the dark night sky we see...

... is only because visible light is not the whole story. If we could see hydrogen gas, it'd look a whole lot different.

But this is missing the point. Although there's a lot of hydrogen gas in the way, it doesn't obscure our view of the stars, so we should see with our eyes a bright sky.

A much more sophisticated argument is that maybe light changes wavelength over great distances, eventually becoming something we can't see. This "tired light" is a discredited alternative idea to explain why distant galaxies look redder. Conventional contemporary astronomy says this is because the Universe is expanding; tired light has it that light loses energy as it travels. Just where that energy is supposed to go I'm not sure.

People sometimes try to use the Cosmic Microwave Background to explain the parodox. The CMB is microwave radiation in the... cosmos... and it's in the background... well we'll get back to that. The point is that this radiation occurs across the whole sky and it's not coming from gas in our own galaxy. When analysed in detail however, whatever it is it simply cannot be from redshifted stars. So that doesn't help us explain the paradox after all.

You can actually see part of the CMB yourself if you don't tune in your TV correctly -  a few percent of the static comes from this. At least it did back in the era of analogue telly. Not sure about this new digital era.

4) Stars don't last forever.

True. We see them exploding all the time. But we also know that new stars are born as well. So if the Universe is infinite, that should still mean that there are an infinite number of stars along every line of sight.

The Crab Nebula, formed by a supernova explosion that was actually observed and recorded in 1054 A.D.

5) Stars don't go on forever.

In one sense this is true : our Galaxy has an edge. But of course, beyond that there are more galaxies, full of stars. So far, there's no evidence that there's any sort of "edge" to galaxies. And if there were, everything should have collapsed into a big ugly heap - the Universe would have a centre which everything would slowly fall towards.

Welsh cosmology is the best cosmology.

Besides, infinite space which just has a few galaxies in it is no way of resolving the paradox - it's simply a way of saying that the assumption of infinite stars is wrong.


6) The Universe is a fractal.

Oooh, this one's interesting ! Remarkably, it turns out that it is possible to have an infinite number of stars in an infinite Universe but not have every line of sight end on a star. One really obvious way to do this would be to have all the stars in a really long line. Infinite stars but lots and lots of dark sky !

Worst. Universe. Ever.

Which is of course very silly because that's just not what we see. Or maybe it is. Maybe all the galaxies we see are part of an infinitely long cylinder...naah. That's just stupid*. For one thing the cylinder would collapse radially down to a line, for another, you'd only have dark sky in certain directions. But more complicated fractals can also allow for dark sky in a more interesting pattern.

* Sometimes, just sometimes, this is a legitimate argument.

Man I hate fractals. They make my head hurt.

This is Fournier's fractal, proposed in 1907 as one possible resolution to the paradox. Clearly it allows large parts of the sky to be dark. It can also be rendered in 3D :

You may wonder if that means that along some lines of sight there'd still be infinite stars and so infinite energy. Tricky. The idea here is that the energy density decreases as you go to larger and larger scales, so the total energy when you sum over infinity is still finite. That's actually a perfectly sensible everyday bit of mathematics for describing continuous functions, but doesn't work for discrete objects like stars. If you have a finite amount of energy, you must have a finite number of stars. Which means there's an edge to the stars, and we get back to the collapsing-heap problem again.

In any case, that's definitely not what the Universe looks like. But the concept is there. I was hoping to be able to find out more about fractals that actually do resemble the Universe, but while there's a great deal of alternative (mostly outright bonkers) ideas about the Universe being a fractal on the internet, I couldn't find a single one addressing this point. Well, I did come across one article modelling a fractal distribution of stars (not the large-scale galaxy filaments), but annoyingly I can't find it again. If anyone can provide simple instructions, I'd love to visualise this - though it's not obvious to me if such a structure is even possible (i.e. stable).

Another problem I suspect with the fractal idea is : why would the Universe remain a fractal ? Galaxies move around quite a lot. Occasionally, stars get ripped out of galaxies. Over infinite time, the nice fractal structure is going to get destroyed, and those blank areas will be filled in.

The Universe is a dynamic place. It's tough to see how galaxy motions are compatible with a fractal structure - what stops distant galaxies from moving into the regions we see as dark ?

Finally, observations have demonstrated that the Universe just isn't a fractal, so this can't be the solution either.


7) The Universe isn't infinite.

We've sort of already covered this one with the idea that there aren't infinite stars. But having a finite number of stars in an infinite void of empty space is philosophically unsatisfying, as well as just plain not working. So, maybe the Universe has always existed but has a limited volume ? The nice thing about this is that space wouldn't need to have any kind of edge - curved space would allow you to travel in any direction and eventually get back to where you started.

Specially modified version of the Virgo Cluster.

The problem is that this doesn't avoid the everything-collapsing-to-big-ugly-heap problem. Einstein's equations show that a static Universe is unstable unless you very carefully tweak things - it's not a natural solution at all.

Now, if you'll remember the very first point, I mentioned that saying surface brightness doesn't vary with distance is a simplified truth. It works in a static Universe. It's not true in an expanding Universe - if space is expanding, surface brightness should vary in a very particular way which we can actually test, and from the results it really does seem that the Universe is expanding (there are also other reasons to believe that redshift indicates expansion and not some other effect like tired light; the cosmic microwave background is also very well explained by this).

There's also a slightly simpler argument to believe that the Universe is expanding. As I mentioned, distant galaxies look redder and this is thought to be because space is expanding, giving them the appearance of moving away from us. Of course, it could instead simply mean that every galaxy is terrified of ours and is trying like hell to get as far away from us as possible.

Worst. South Park. Ever.
This is why I'm not a cartoonist.

That only works if you think our Galaxy is somehow an incredibly special place, which most of us don't. There are good reasons for this - the Universe looks pretty similar in every direction, so it would be extremely surprising if the speed measurements didn't match this. So instead we postulate that it if we were in any other galaxy, we would still see all the other galaxies rushing away, which avoids the weirdness of us having a special position. Remarkably, this seems to work. It really is the case that the Universe is expanding. Even more amazingly, it may even be possible - one day - to measure this expansion directly in real time : to watch a galaxy's velocity change over time as the Universe expands.

And of course, if the Universe is expanding but also finite, then it cannot also be eternal.


8) Energy and mass conservation is for hippy losers ! 

It's true that the collapse-to-a-heap problem of a finite Universe or finite number of stars can be solved, if you provide some force to keep the galaxies moving outward (or to keep the Universe expanding). The trouble is that you could solve pretty much anything by allowing energy to be created - it would be basically saying "because magic". You'd have to have some incredibly good reason why this only happens to keep the Universe balanced, otherwise you may as well throw the laws of thermodynamics out of the window, shout "ALACKAZAM !" and watch them plummet to a firey doom.

All that said, however, the accelerating expansion of the Universe can be explained without violating the conservation of energy. So maybe something similar could stop the Universe collapsing and keep it nicely balanced - if things were set up perfectly. There would be literally zero margin for error, since over infinite time a non-static Universe would either expand to infinity (in which case we wouldn't see any other stars at all) or collapse to a point (in which case we wouldn't see anything at all).

Worse, a Universe in a truly steady state - with star birth and death precisely balanced so the Universe always appears much as it does now - requires violation of conservation of energy.


9) The Universe isn't eternal.

First, let's recap.

• The paradox can't be resolved by the sheer distances to the stars because brightness doesn't work like that.
• There can't be a barrier blocking our view because it would heat up to the same temperature as the stars.
• The sky is bright everywhere at other wavelengths, but the details show that this cannot possibly be due to starlight.
• The finite lifetime of stars doesn't work because stars are also born.
• If the stars only span a finite part of an infinite Universe, they would have all collapsed.
• A fractal Universe might not remain a fractal, and observations show that the Universe isn't a fractal.
• A finite Universe doesn't work because the evidence that the Universe is expanding is very strong, and therefore the Universe cannot also be eternal.

The only thing left is to question the premise of the paradox itself. Maybe the Universe just isn't infinite and eternal after all.

You could, I suppose, argue that maybe the Universe is infinite and eternal but simply doesn't always look the way it does now. After all, we know galaxies looked different in the past to how they do today - not to mention that quasars are only found in the distant (early) Universe - so clearly things have changed :

The "spiderweb" galaxy seen by Hubble, about 10 billion light years away - a chaotic series of galaxy mergers.

The Andromeda galaxy M31, just two million light years away - a stable, rotating disc.

A totally steady state is out. But maybe there's a quasi-steady state of multiple Big Bangs - as the Universe expands and all the stars disperse and die, new material is suddenly created. Well, maybe. The question to ask is whether you prefer the Universe to be infinite and eternal or finite and mortal.

A mortal Universe (finite in time) solves Olber's Paradox at a stroke - or rather, it's more like cutting the Gordian Knot since it effectively declares the paradox invalid. If there hasn't been infinite time, and the Universe has been changing, there's no reason to expect a bright night sky. There was once a time when there weren't any stars, and since then stars have formed so far away that there hasn't been time for their light to reach us yet.

Strictly speaking, a mortal universe doesn't preclude it from being infinite in space. Personally I'd rather it was finite in space as well. I see infinities as problems to be avoided, not solutions to be invoked. They're a useful mathematical trick - but they also let you get away with murder. In an infinite Universe, you can explain any anomaly as being a statistical fluke, no matter how unlikely something is, it will happen somewhere. Which means there's no way of knowing if your observations are telling you something about the underlying physics at work, or if you're just in a really weird part of the Universe. And, of course, this.


Conclusion

Olber's Paradox implicitly assumes that an infinite eternal Universe is preferable. Why, I'm not sure. I suppose it might be nice to think that the Universe will go on and on forever, but personally I prefer the exact opposite. As for whether a Universe that once didn't exist will eventually cease to exist, I've no idea.

Interestingly, those people who are still convinced the Universe must be eternal (google "steady state" and "fractal cosmology") tend to do so because they see Big Bang cosmology as too religious. Seriously. Even the great Fred Hoyle (and he was great, no matter how wrong he was), one of the original proponents of Steady State theory, thought that the idea of a creation was irrational. There are many others on the internet stating things more directly : that the Big Bang is pseudoscientific idea that justifies Christianity.

I wonder what six-day Creationists have to say about that.

Of course, this is not a sensible reason to reject the theory. Things do get created and destroyed all the time, albeit from things which already exist. Most scientists accept the idea of creation from absolute nothingness without believing in a deity as the cause of it. And while religious texts are indeed full of gibberish, the idea that things got created is no more nonsensical than the idea that humans exist - which religious texts also state, but no-one is trying to debunk that.

Debunking the Big Bang because you think it's too religious is a "nuke the whales" policy - it might be fun (those cetacean jerks would do the same to us if they could), but it isn't sensible.

You nuke those whales, Fred. You nuke 'em good.

But whether you believe the Universe is eternal or mortal, finite or infinite (and I'm glad there are people still examining all the options, even if I do think most of them are loony), consider this. The lifetime of stars, the expansion of space, fractal geometry, the very nature of reality itself - all of these are important in understanding why the sky is dark at night. And that's why for me, it's tough to think of a more astounding fact.