Infinite in All Directions: From Copernicus to Clockwork, the Role of Math in Completeness

Infinite in All Directions is The Wire‘s science newsletter. Click here to subscribe and receive a digest of the most interesting science news and analysis from around the web every Monday, 10 am.

Credit: Unsplash/pixabay

Credit: Unsplash/pixabay

From light to darkness

Everyone (reading IiAD) knows about blackholes and how they’re formed – but it seems there’s a different name for a blackhole that’s formed by the infinite compaction of radiation as opposed to matter. Specifically, when matter is compressed into a small volume with density approaching infinity, it forms a blackhole; when radiation is focused into a small volume with energy-density approaching infinity, it forms a kugelblitz. The name is German for ‘ball lightning’, although a kugelblitz shouldn’t be confused with the weather phenomenon known as ball lightning. So in an amateurish-philosophical sense, we can use lots of light to create the paragon of darkness. (And I mean tremendously-stupendously lots, of the order of the output of the Sun over many millennia.)

But yeah – once the blackhole/kugelblitz forms, the properties of the resulting thing are expected to be indistinguishable.


Fearing the night

Let’s be honest. How does it feel when you read something on the web that’s widely shared, featured on 3QD/Boing Boing/Slashdot/wherever-else, but you realise it’s something you wrote about in your tiny blog many years ago and it was read by like four people? Sucks, right? I feel that too, from time to time. But in this case, I have to recognise that this post I’m going to discuss – titled The Coming Amnesia in that subtly ominous way – is actually better elucidated than my own, titled A Universe Out of Sight in the same way, even if the correlation index between them is like 0.8.

Geoff Manaugh and I have both written about how, at some distance point in space and time in the universe, the expansion of the universe will steal away all starlight from us. To Manaugh’s credit, his piece is devoid of equations or scary-looking plots but is brimming with references to ideas in the literatures. In my defence, I have always believed that mathematical literacy is not just important but also necessary as a form of communication in some contexts. You may not be able to read a graph with symbols all over it but if I teach you how to do it and you get the hang of it – nothing like it.

Anyway, some important differences between my and Manaugh’s treatments: in my piece I seemed to have given more credence to the historical record and presumed that scientists of the future will still have ways through which they will be able to determine that the skies of the past were filled with many more stars. Manaugh on the other hand has premised his ‘amnesia’ on a more poetic reading of what’s to come: not such much a forgetting as much as a forgettability, that the imagination of future-thinkers will be crucially lacking in the wonders of the night sky – and perhaps even think about the empyrean as a desolate place to stay safe from, not expand into.

I still prefer my piece to Manaugh’s as far as I’m concerned – but I’m not surprised many more like Manaugh’s better.

Doesn’t make matters suck less, of course.


The Wire Science

The Wire‘s science section is getting its own Facebook and Twitter profiles soon – particularly since we’ve observed that its readership on the site has been comparable to that of the external affairs section (averaged over the last six months). I won’t lie, I was a bit surprised myself. Anyway, it’s good news, and we’re now going to try harder to enlarge our science-reading audience. You’re a part of this so if there’s a feature or something you’d like, please let me know.

And also consider making a donation.


The complexities of colonisation

You’ve heard of the business-development idea called ‘0 to 1’? Its title stands for the phase in which a business idea is born, comes into existence and validates itself, a phase that billionaire entrepreneur Peter Thiel thinks is the most important for a startup because it signifies the act of bringing something new into this world rather than repeating something old. Because once you’ve moved away from 0 towards 1 (FZTO), getting to a 100 will still be easier. And this is where the first metaphor ends and the second begins: that of emergence. Scientists don’t know how intelligence emerges within a complex system largely because the system is built on many simple subsystems. That is, scientists bring together lots of tiny components whose functioning they understand perfectly – but put those components together and suddenly you have something that’s making its own decisions. Somewhere on the way, the synecdoche breaks.

I’m using this portmanteau of metaphors to talk about humans colonising space. On Earth, humans went FZTO over thousands of years – but it wasn’t until recently that they gave a name to what they were doing in this time: terraforming. They were literally paving the way for the Anthropocene epoch. Today, scientists known what we did in the last few thousand years (to some extent) and are more keenly aware of what it takes to set up self-sustaining human colonies in various environments. Fortunately for them – for us – we’ve evolved to live in these environments. What would it be like to colonise other planets?

Other planets have environments that we can’t live in, period. They also have environmental conditions that we’re not fully aware of, whose evolution still presents many unknowns to us. To go FZTO in these conditions will likely present us with the greatest engineering challenges in history – greater than making deserts and oceans liveable for humans, which we haven’t been able to do. That’s not all. Colonising other very-hostile environments comes not only with problems that will force us to advance in leaps to surmount them but also near-certainly confront us with unknown unknowns. And being aware of the consequences of failure makes us less able to tolerate, or survive, unknown unknowns; psychology can’t be ignored. So, like with the mysterious ontology of AI in machines, we may know how to begin colonising a planet – but it’s impossible for us to know how it will shape out over, say, a thousand years in advance. We don’t know what problems will emerge.

As it happens, I was prompted to write all this because of this article on Tor, about the possibility of humans colonising the Solar System. I agree with one of the first comments, that it lacks in imagination. But more importantly, the author’s example of Titan being a better candidate for hosting human colonies than Mars struck me. As I’ve written before, Titan is one of my favourite moons, but just because it has liquid methane on its surface and an atmospheric pressure comparable to Earth’s doesn’t make it easier to colonise than Mars. Mars presents humankind with fewer issues that will have to be solved concurrently than does Titan, and that immediately makes a moon-colony much more costly, likely prohibitively so.

+ H/T Srividya Tadepalli


Garbage graphic

By this point it should’ve become apparent to most people who engage with infographics on a semi-regular basis that there are some rules about what they should or shouldn’t look like, and that your canvas isn’t actually infinite in terms of what you can create that will a) look good and b) make sense – simultaneously. But just when you think everyone’s going to create sane visualisations of data, there comes along one absolute disaster of an infographic to remind you that there’s still a way to go. And when that someone is a media channel the size of News18, the issue at hand actually transforms from being a molehill to a mountain.

Because it’s News18, it’s no longer just about following good practices when making an infographic but also about moving the hundreds of thousands of people who will have seen the infographic (@CNNnews18 has 3.4 million followers) away from the idea that News18’s effort produced something legitimate. Here it is:


Fonts and colours, not bad, but that’s it. Here’s what’s wrong:

  1. The contours of the chicken-leg and the leaf appear to have dictated the positioning of numbers and lines in the graphic, whereas it should’ve been the other way around
  2. The same length represented by 25% for Rajasthan also signifies 31% and 33% for Haryana and Punjab, respectively – which prevents you from thinking that distances within the plot are a reliable measure of anything
  3. The states (in the graphic) from Bihar to Telangana all have less than 10% on the vegetarian side – but the amount of leafy area would suggest these values are actually much higher
  4. If anything, West Bengal and Telangana are the worst offenders: the breadth of leaf they have for their measly 1% is longer than that of Rajasthan’s 25% meat
  5. The numbers say that only four of 21 states have more vegetarians than non-vegetarians – but at a glance you’d think that fraction was closer to 13 of 21
  6. What’s the composite shape of a tilted parallelogram? The graphic would’ve been far more effective in the shape of a regular rectangle lying on its side

In fact, across the board (of mistakes), it seems the designer may have forgotten or ignored just one guiding principle: that infographics should give a clear and accurate impression of the truth as represented by the numbers as quickly as possible. This often requires the designer to ensure that the axes are clearly visible, representations of values through parameters like distance, area, volume, etc. are consistent and predictable throughout the graphic, the representation of relative values is proportionate, colours and/or stylisations don’t mislead the reader, etc.

These are also the reasons why the ‘3D’ pie-chart offered by MS Powerpoint hasn’t found wider use. It offers nothing at all in addition to the normal ‘flat’ pie-chart but actually make things worse by distorting how the values are displayed. Similarly, you take one look at this chicken-leaf graphic and you take away… nothing. You need to look at it again, closer each time, toss the numbers around to see if they make sense, etc. It really just looks like bait with which to trawl Twitter for a flamewar around the Indian government’s recent attitude towards the consumption of meat, especially beef. Seriously: a plain-Jane chart could’ve done this with Raman Singh having said on Saturday that he’ll hang those kill cows in his state, Chhattisgarh.

Also: “So what if it’s a little off the mark to get some attention? It’s done its job, right?” → if this is your question, then the answer is that if you don’t force designers – especially those working with journalists – to follow best practices when making an infographic, you’ll be setting a lower bar that will soon pull a volte face and assault you with all kinds of visualisations conceived to hide what the numbers are really saying and instead play up ‘almost-right’ propaganda. Yes, infographics can quickly and effectively misguide, especially when you don’t have much time to spend scrutinising it. Isn’t that why infographics were invented in the first place: to let you take one look at a visual composition of numerically reasoned information and get a good idea of what’s going on? This is exactly why there’s a lot of damage done when you’re messing with infographics.



Math in lower dimensions

By the way, the Rencontres de Moriond just winded up and if you’re interested in the latest in particle physics and theoretical gravity, I highly recommend checking out the conference slides. I was able to make two articles of three or four presentations – and I’d like to highlight the more recent one of the pair. It was about clockwork theory, and it recalls – or posits or whatever – a notion whose explanatory power I’m only just beginning to appreciate. The notion is called mathematics. I remember how, until class X, all the mathematics we were ever taught at school was closely tied to the real world. In class XI, we were introduced to imaginary numbers – easier to wrap your head around once you know what completeness means. But in class XII, vector algebra came along and I had no idea what was happening.

Three years later, I first heard about neutrino oscillations and it blew my mind. It’s a very physical phenomenon in particle physics that is understood best in terms of its underlying mathematics, not in terms of what can actually be observed happening. It’s a counter-intuitive idea of the world. This ‘first shock’ of non-classicism (I did study basic quantum physics in my first year of engineering but tbh I don’t remember the classes being very memorable) still hasn’t worn off and every shock of its kind since has been yet another first. And like neutrino oscillations, you have clockwork theory – which does away with the naturalness problem concerning the Higgs boson’s mass through a mathematical sleight of hand. It stops us from questioning information that casts doubt on our knowledge by giving us a different way to organise that knowledge. Awesome.

The problem: The Higgs boson is much lighter compared to what physicists think should be its mass given our universe’s size. How much lighter? Given its current mass (~126 GeV), the universe should be about half a foot wide. Clockwork theory makes this a non-problem by giving us a way to understand how the Higgs boson’s mass is in fact quite large but isn’t experienced in the four dimensions we, the observers of the boson, manifest in. So, how does one provide a mathematical recourse to reality? This where it’s easier for me to make my point about the need for mathematical literacy. I’m not asking anyone to try to make sense of how branches of geometry and calculus help us understand higher dimensions. I’m only asking that you try to make sense of how mathematics exists as a bridge between the experienceable and the never-experienceable – a role that is neither complex nor, as we have it, unprecedented.

In the 16th century, Nicolaus Copernicus heralded the so-called ‘Copernican Revolution’ when we publicised his idea of the heliocentric model of the heavens. It conflicted with the then-prevalent Ptolemaic geocentric model. The interesting thing was that Copernicus used the same schema of planetary motions that Ptolemy had used about six centuries earlier; his disagreement with it arose on the basis of how Ptolemy had chosen to explain the motions of Mars, Jupiter and Saturn in the night sky. Copernicus was able to show using his system of reasoning that the paths of all the then-known planets could be explained if Earth itself moved in a larger circle – around a point in space coinciding with the position of the Sun. So of Ptolemy’s failure, the science philosopher-historian Paul Feyerabend writes in his Against Method (1975; p. 141):

Aristotle had already criticised an earlier (Pythagorean) version of it: mathematical harmonies, which are abstractions, reflect truth only if they agree with well-confirmed physical principles. This is a reasonable request; it was used in our own century to reject Schrödinger’s interpretation of wave mechanics. It is reasonable especially for those thinkers who regard mathematics as an auxiliary science that may describe but cannot constitute physical processes.

I daresay higher-dimension mathematics can seem like magic in the lower ones.


Other bits of interestingness

Recommended: The Wire‘s Anoo Bhuyan interviewed the former secretary of the Ministry of AYUSH (he retired on April 1).

Also, an interesting line from a longer blog post on something else:

The quirky thing about science: sociologically, success and failure look pretty similar [from the POV of a scientist, at least in this case]. Either way, it’s time to find a new project.


  • One study – but two press releases reaching different conclusions
  • A new, more effective TB vaccine for India is set to begin clinical trials in June
  • Jeffrey Beall self-published a book on art forgeries on Amazon (hehe)
  • How Madhava calculated pi three centuries before Leibniz did (I asked a math teacher, he said Madhava’s series converges very slowly)
  • “How to hunt for a blackhole with a telescope the size of Earth” – about the EHT
  • Why don’t stromatolites form in Earth’s oceans today as frequently as they did in the past? (What a first-line!)
  • About 11 billion years before 2014, a mysterious X-ray flare erupted in a dwarf galaxy in the constellation Fornax

If you enjoyed the newsletter, please share it with a friend. They can look at previous issues here and subscribe here.

  • Rohini

    NIce! I thought the Madhava article about pi was fabulous, though very short. There are a number of videos on the internet which explores this – and also about the Indian invention of zero as a decimal place holder.
    Its indeed sad that we learn next to nothing about this in our conventional school education.