Follow the reluctant adventures in the life of a Welsh astrophysicist sent around the world for some reason, wherein I photograph potatoes and destroy galaxies in the name of science. And don't forget about my website,

Thursday, 26 July 2018

I Read Edward Gibbon So You Don't Have To

Literally. There is no point anyone reading this book unless they're an actual historian.

Pretty much any history of Rome will mention, at some point, Gibbon's mighty tome, often in exalted terms as though its sheer magisterialness can be absorbed through osmosis. Well, as y'all know, I prefer to read the source material myself. They usually turn out to be a darn good read and (sometimes) the modern interpretations aren't quite up to scratch.

See, the other thing that pretty much any history of Rome will go on about is how gosh darn amazing Gibbon is. Peerless rhetoric, they said. A masterful command of language and persuasion, they said. "I devoured Gibbon", said Churchill. "An undisputed masterpiece... a work that will only perish with the death of the language itself", it says on the back of my paperback abridged edition. You can see why I was particularly eager to read this one.

Well, I'm here to tell you that they're all wrong. It's a crappy book full of dreary, inscrutably dense and dry prose and whoever did the editing of this particular version ought to be thrown to the lions or given some other suitably Roman punishment.

I suppose competing in the modern incarnation of Gladiators would be appropriate.
This particular version is a hefty 40% or so of the full work; a mere 1,056 pages making it a positively light read compared to Plato's 1,800, my last big read. But Plato was lively, engaging, occasionally funny (and not dry humour either), deeply analytical and a work of genius. Gibbon, on the other hand... well, imagine the most stereotypically boring librarian you can can conjure up and pretend you gave them unlimited funding for twenty years to write an encyclopedia about cabbage production. That's roughly what you get from Edward Gibbon.

Now, I'm not sure how much I should blame Gibbon and how much I should blame the editors of this cut-down version, but I'm pretty confident that both of them are morons so I'll blame 'em both. The editors because their chapter selection sucks, and Gibbon because during his twenty year project he apparently never learned how to explain things clearly, use commas correctly, stay on topic, assess relevancy, or have a single damn analytical thought in his life.

Gibbon's greatest strength is also his greatest weakness. His History is one of pure observation. As a compendium of citations with raw descriptions of what happened, it is indeed peerless and will never be surpassed. The amount of reading and note-taking the poor sap must have had to do in an age before the invention of ctrl+f should give everyone horrifying nightmares. The problem is that that is literally the only good thing about it.

Take his legendary rhetoric. At best, this is vastly over-rated. It's not that he didn't know how to turn a phrase so much as it was that he wouldn't stop doing it. Ever. Who needs clarity when you can have pseeudopoetry ? Except that it's rather worse than that... it's more pseudo-poetric ramblings. The occasional flash of rhetorical brilliance can't compensate for the impenetrable fug of verbal diarrhoea that fills most of the book. The real annoyance is that there's just enough good stuff in there - whole chapters, even - that I can't blame this on the writing style of the age. Some parts of the text are crystal clear, flowing narrative. The rest is what I'm calling Gibbonish... not exactly gibberish, but sort of half-narrative, half general commentary that ends up as the worst of both worlds. So focused is Gibbon, nay obsessed, with constructing rhetoric that it feels almost like deliberate obfuscation. It's not text you read so much as parse. And that quickly becomes mentally exhausting and whatever godforsaken point Gibbon was trying to make is utterly lost.

In particular, while the description of what happened is usually okay, deciphering who did what to who is often a fiendish challenge. For example Gibbon is overly-fond of referring to "that person", rather than saying, "he" or "she" or whatever. It feels lazy and weird, exactly like this cat :

"Yeah, it was that guy. You know, the emperor. The one with the shoes."
And it's much worse if multiple groups are interacting. Trying to understand which group did what is less of a challenging read and more of a decryption exercise from Bletchley Park's glory days. Often I found myself completely befuddled as to who attacked who and frequently baffled as to which side even inflicted an apparently decisive victory, and sometimes if was a victory at all or if everyone just went home for tea instead. Gibbon might very well have penned the least pedagogical history of all time.

Then there's his analysis. Other works I've read - most notably Peter Heather's Fall of the Roman Empire - have been quite insistent that Gibbon largely attributes the causes of the collapse as primarily internal discord and Christianity. But Gibbon actually has very little explicit to say about this, and nothing at all about the deepest underlying causes. As an analyst he is hopeless, as a philosopher he is a non-entity.

And what little Gibbon does have to say just isn't terribly convincing. He paints a reasonable picture of an arrogant Rome in a state of decay following the Antonine Emperors. The problem is that he then seems to describe a reasonable successful recovery during the following century, making that particular little episode not really very important in the grand scheme of things. And a grand narrative is something Gibbon singularly fails to deliver. It's just a case of "this happened, and then this happened, and then this, and then there were some angry barbarians for some reason."

Now I can't avoid mentioning the problems of this cut-down version, just in case I'm doing poor Gibbon a massive disservice. I might be. The way this edition has been abridged is by presenting a selection of chapters in their entirety, with brief notes describing the omitted chapters. These chapter selections are simply awful.

Several included chapters are almost entirely irrelevant, have no meaningful context, and often they don't relate to the Empire at all, much less its downfall. Chapter 21, for example, is exclusively devoted to some stupid old priest who (so far as I could tell) did absolutely nothing and died. Later chapters are about the rise of the Prophet Mohammed and the crusades, which would be pefectly fine in the context of the end of the Byzantine Empire except that's not how they're told. They're just about those particular episodes for their own sake, and I'm pretty sure some chapters don't even mention the Romans at all. And dammit, I don't care about some stupid priest who did absolutely nothing and died, or even the Crusades : I want to hear about the goddamn Romans. You're a moron, Gibbon, and I don't like you.

Gibbon covers the fall of both the Western and Eastern empires. One might imagine that an edited version would focus on either one of these, and that's mostly what's done with this edition, but reeeeally badly. Crucial chapters detailing how barbarian tribes became incorporated into the Western empire are cut, so we go from the empire having some minor difficulties to suddenly OMG there are barbarians everywhere and where the hell did they come from ? 

Admittedlyone does get a nice sense of the empire transmuting into something different in its last couple of decades, dissolving rather than falling... it's clear that by the nominal end the Empire was already quite, quite dead, the deposition of "Emperor" Romulus Augustulus a mere formality. Very good. But how did it come to that ? All those critical decisions in which Rome failed to properly deal with the massing barbarian tribes... those chapters are completely missing. And that sucks. The most important part of the story is gone. Why ? Buggered if I know.

Later on we miss out all the best bits of the Byzantine Empire as well, and that sucks too because it's a damned epic story : the Eastern Empire's spectacular (but tragically brief) recovery after its near-fatal wars against Sassanid Persia has been called one of the greatest military comebacks of all time. But we don't get any of it in this edition, we just skip straight to Mohammed, the Crusades, and the final siege of Constantinople. It's bloody stupid, is what it is.

I somehow doubt that the missing chapters would help that much though. Gibbon is at least half decent at writing narrative, so as far as individual stories go, he's fine as long as he doesn't slip into Gibbonish. Not brilliant, but okay (if you want a modern writer who could kick Gibbon's ass, I recommend the aforementioned Peter Heather, Tom Holland and Roger Crowley; Lars Brownworth tells a really gripping tale but I have my doubts about his accuracy). The chapter on the rise of Islam, for instance, is very long but a thoroughly good read, and Gibbon - never one to be shy of judgement - does at least venture some interesting commentary on the character of Mohammed.

But what about analysis ?

Nope nope nope nope nope. Gibbon doesn't do that; the closest he gets is judging people's personalities. Sorry Gibbon, but there's more to an Empire than the quality of its Emperor. How about some thoughts on what forces were at work to influence the choices of the soldiers when they brought good and bad emperors to power ? Under what conditions were emperors able to control their armies rather than the other way around ? What about the state of the legions and their organisation over time ? The economic forces ? The social changes ? Why did Rome, otherwise masterful at exporting its culture to distant lands and assimilating others into its vast edifice, later do such a crappy job of incorporating barbarian tribes when its Empire was still powerful ? No, no discussion of that. The person who read more of the original source materials than any other also seems to have thought about them the least. Even the final chapter, where Gibbon ventures to describe the conditions that led to Rome's ruin, is disappointingly and almost comically literal. He describes why the city itself fell into ruin, of which the causes are pathetically trivial : buildings fall down, it's a thing that they do.

Thanks, Gibbon. Thanks so much.

Of course you could read between the lines and infer your own hypotheses, which is what later historians have done. But that really is a job for historians, as without a starting point this ain't so easy. Comparisons and analysis of a stated position are relatively easy : if Gibbon were to say "Christians did it", you could point to examples of where his evidence supports the claim and examples where it doesn't. Then you can sum up and decide if this idea makes sense overall. Spotting the possible underlying trends from the raw facts - especially with Gibbon's focus on individual character rather than systemic trends - is much more difficult, and because Gibbon's text is largely drier than the surface of the Moon, I'm not going to try.

Even at a much more trivial level this edition is unnecessarily difficult to read : I'm talking about footnotes. I can understand why these are useful in a historical narrative where you want to state important caveats without interrupting the flow of the story. Fine. But the editing here is pretty horrendous; 95% of the footnotes are bibliographic references but some do contain interesting additions that are worth reading. It would not be a monumental task - seriously, the work of a week or two, and if anyone wants to pay me money then dammit I'll do it myself to prove it - to arrange these to appear at the bottom of the relevant page so that the reader doesn't have to treat the work as a gigantic flip book, leaving the bibliographic references at the back for the historian. Oh, and most of the non-English language footnotes have been translated, but some haven't and no explanation is provided. It's weird and silly and I don't like it.

How to summarise this nine month endeavour of mine ? Well, sorry Gibbon, but I'm rating your life's work 3/10. Low on clarity, long-winded, and while there are indeed flashes of genuine rhetorical brilliance, they're rarer than sightings of Bigfoot being abducted by a flying saucer. Obsessive descriptions of irrelevant minutiae are hardly a substitute for deep analysis, a fact obvious to just about everyone except Gibbon. Go away and read the dictionary instead. You'll learn more and make more friends.

Thursday, 12 July 2018

Ask An Astronomer Anything At All About Astronomy (XLVII)

Catching up on a remaining bunch of questions. As always, click the links for full answers, and if you want even more, have a browse through the enormous Q&A main page. Current grand total : 436 !

1) How hot does a pole get moving at mach 1 through the atmosphere ?
Ah, should I make an innuendo or a casually racist joke, or both ? SO HARD TO CHOOSE !

2) Are eyepieces overrated ?
Yeah they suck.

3) To stop the xenomorph infestation, should we nuke the ISS from the ground or from orbit ?
From the ground, because we don't have any nukes in orbit.

4) Are there really only four planets in the Solar System ?

5) You're lying about the size of Betelgeuse.
No I'm not.

6) What do you think of detecting belts of exoplanetary satellites to find aliens ?

7) Did you predict the battle of Callisto from the Expanse ?
Well I predicted a battle...

8) Could you make a colonial spaceship smaller using frozen genetic material instead of a living crew ?
Yes you could.

9)  Do you have to time everything just right to dock with a rotating space station ?
Yes, but it's not that bad.

10) Is the radial acceleration a good method to choose between the standard model and modified gravity theories ?
No it sucks.

11) What do you think of this paper on missing matter ?
It's OK. 7/10.

12) How much stuff has been found by microlensing ?
Not much.

Monday, 9 July 2018

Ask An Astronomer Anything At All About Astronomy (XLVI)

Yeah, I know, these aren't updated very much. I think I have to change the schedule as weekends are seldom available to update things these days. Still, it's not like there's been an absence of questions ! Here's a round-up of the last few months (I still have more stockpiled, but I reckon twenty is enough to be getting on with). As always, click on the links for the longer, generally less sarcastic answers, and have a browse of the enormous Q&A page. Current total stands at 425 questions !

1) Are you a rah-rah scientist ?

2) Is that my timeline of the Universe Stephen Hawking is using ?
Yes it is !

3) Your Discovery variant of Orion is all wrong.
Blame Kubrick.

4) What's neat about this galaxy without any dark matter ?
It looked like it was really cool... but it wasn't.

5) The galaxy can't have more than one black hole !
Err... yes, it can.

6) Can you make a side-by-side 3D version of this galaxy fly-through ?

7) Is this the Andromeda galaxy ?

8) What do you call it when you reach the point of closest/furthest approach to a black hole ?

9) Is every round object a planet ?

10) Is mainstream science being a douchebag by pretending the Big Bang is real ?
Umm, no.

11) Don't quasars disprove the ages of distant galaxies ?
What ? No.

12) I've disproved the expansion of the Universe !
No, you haven't.

13) Is the Cosmic Microwave Background homogeneous ?
Yes, very.

14) How come distance doesn't matter for surface brightness ?
Geometry works like that.

15) Wait, are your sure distance doesn't affect surface brightness ?
Yes. There are lots of subtleties but they can be accounted for.

16) Could time dilation affect our estimates of star formation rate in distant galaxies ?

17) Isn't space a vacuum, so how come turbulent clouds don't just fly apart ?
It's not a perfect vacuum, just a very good one.

18) What shape are black holes ?
Very, very pointy.

19) Is this asteroid impact video accurate ?
It's not bad.

20) What's the data set shown in this pretty movie ?
Your mum.

Tuesday, 5 June 2018

H One

Richard Feynman was both a great scientist and a wonderful philosopher of science (though he was also, and it's worth bringing this up a lot more often, a dick). The imagination of the artist is of course a very interesting thing indeed, and scientific and artistic creativity aren't always so unlike each other. For actual science, imagination is by necessity tempered by observation. But for data visualisation, sometimes it's better to let imagination off its leash and run wild and free without giving a flying poop about whether it's "useful" or "relevant" or not. I'm a firm believer in the principle of doing things because they are cool. All that spin-off gubbins can come later, or not at all.

Do you think this crocodile cares that data isn't uniformly sampled ?
No, neither do I.

A long time ago in an institute far far away, I made an abstract visualisation about neutral hydrogen data. Five years later, software, hardware, and techniques have improved quite a bit, so I decided it was time for another one. In general I think art should stand up on its own and let the viewer decide how they want to interpret it, but if and when an explanation is required, it'd better be a bit more than, "old clay pipe stuck in festering monkey's uterus" or whatever crap the modern art world is currently plagued with. So if you want, you can view the final video product below and walk away. Or, if you prefer, you can keep scrolling and look at some additional pretty pictures. If you're really enthusiastic, you might even read some of the accompanying text, think about the philosophy behind this, and then watch it again. I'll be asking a lot of questions here and answering hardly any of them. Be warned.

The main purpose of this work was to show how different data visualisation methods let us perceive the same data sets in radically different ways. In principle, scientific conclusions should be limited by the data itself. In practise, the process of interpreting the data is creative and subjective. This can be true even of numerical analysis of very simple data sets - raw numbers, by themselves, tend not to be terribly inspirational, restricting the contextual environment of the data to existing ideas. And more trivially, as we all know, statistical analyses of larger data sets can all too easily lead to conclusions which are objectively constructed but simply wrong. All interpretations are ultimately subjective because interpretation is never done by the data itself, but always by human judgement.

How you perceive the data is therefore freakin' important. It strongly affects which conclusions you can find and even consider, shaping your worldview. Data visualisation has many exploratory and communicative purposes : to help discover what the data set contains, to compare different observations and models, to persuade others of whatever conclusion seems most probable, and, not least, to inspire new ideas. Creativity is a complex process, but it's fair to say that most people are far more inspired by visual imagery than mathematical text : the former is, after all, something we're much more evolved to process, since cave art tends to have more pictures of mammoths and stuff than differential equations.

And we're now in an era where data sets of millions of data points are commonplace. It's true that we're going to have to adapt our analysis methods to deal with the new problems associated with big data, but it doesn't mean we can stop looking at the data : not now, not ever. Rather it means that we have to come up with new visualisation methods, which will affect both our hard scientific conclusions and purely philosophical interpretations.

Here then is my offering to attempt philosophy through art driven by science. I'll briefly describe each sequence of the movie both in terms of the aim of each sequence and the method of its construction. I finally managed to get myself to learn Python for Blender > 2.49 for this (all of which is rendered in Blender, mostly in 2.78), so I've included links to scripts where useful. All of the data sets used here are, as is my speciality, 3D neutral atomic hydrogen data cubes. Again, links to public data sets are provided where available.

As this might interest different audiences, each section has a separate description of how the image was rendered which is written for Blender specialists and can be skipped by everyone else*. The main point is that these data cubes are three-dimensional maps of the hydrogen gas in different parts of the universe. Imagine them as a sort of slightly unconventional atlas. Every page shows a map of the density of gas at exactly the same locations in space, but at very slightly different frequencies. This corresponds to velocity, which, depending on the data set, can tell us how fast the gas is rotating and/or its distance away from us.

* Originally I had this fancy thing of using buttons to hide the text, which worked brilliantly for about twenty minutes and then stopped for no reason whatsoever. So I'm afraid you'll have to skip this the old-fashioned way. "Computers are logical", they said. "They give repeatable, objective results", they said...

Too Much Information

We begin with a Matrix-style shot, panning back from a single number to a whole array of text. This is of course a cliché, but a very useful one. The data that we have to process is, ultimately, just numbers, so in a sense this is the simplest and most natural form of data visualisation. Yet we very rarely use this for large data sets, because, unlike characters in the Matrix, we can't train ourselves to automatically see "blonde, brunette spiral, elliptical galaxy". We are compelled to process the data in different ways in order to make any sense of it.

Note that I said the data we have to process. Whether the data itself is really all numbers or not is another matter entirely. What we're ultimately processing is radio waves or photons (or particles, but let's not even go into how we're fundamentally unsure about the nature of the stuff we're measuring) from the sky, which induce minute electrical currents that experience an enormous amount of complex processing before they're reduced to the final numbers we get to muck around with.

So are numbers, in some sense, a very literal, accurate representation of reality, or are they as flawed as any abstract representation, like language ? Are they continuous or discrete ? One view is that because you can't contain infinity in a finite volume, physical properties - length, height, weight, acceleration, charge, etc. - can't have infinite precision. The problem with this is how you'd ever prove that volume is truly finite, that you can't just keep dividing space up into ever smaller parts. And if reality is continuous, that implies all the problems typically associated with infinities. So you can certainly represent data with numbers, but whether than means the world really is made of numbers or they are merely conceptual mental constructs is far less clear.

How it's made

This shot (the above image is actually from a later sequence) attempts to make sense of the data in a few different ways. First, I used this script to slice the data set into a series of text files. Each one contains a 2D slice of the 3D data, one for each frequency (velocity) channel. I've cheated here - despite appearances only one slice is ever visible, with each frame of the animation increasing the visible channel. The script to create the text grid is available here and the animation script is here. Rendering a true volume of text is just too computationally demanding, so I used two planes, one above and one below the text objects, with a mirror material to create the illusion of extra depth. This uses a very simple render layer setup to hide one of the planes, which you can find an example of here.

The first sequence in the movie uses data of the Triangulum galaxy M33 available here. As the animation proceeds, the height (as well as the value) of the text is adjusted to correspond to its intensity, so you get a hint of a Matrix-style surface effect. I wanted the visuals to be driven as much as possible by the data, but I allowed myself a fair amount of "artificial" window dressing if I wanted to make a particular point. In this case the text has some random value variation to give it a more "Matrixy" appearance, since the numbers in the font I used weren't particularly unusual to look at.

The M33 text only samples a small fraction of the full data set, mainly because my first script was flawed : it links each text object to the scene as it's created. Later I realised it's very much faster to create the object and link them to the scene all at once, which made the image shown above possible. That one uses private data of the Pegasus cluster. Each of the whiteish columnar features is a galaxy. Whereas M33 is nice and close and well resolved by the Arecibo telescope, these guys are much further away. We detect them over many different channels because they're rotating, but they're essentially just blobs in the spatial plots - hence the long, cigar-like features.

Even with the improved script I couldn't render all the data at full resolution - it's just too large to display everything as text. The galaxies, however, are unresolved, so they did require the highest resolution or they wouldn't be shown at all. So I clipped the data : the brighter flux, corresponding to galaxies, is sampled at the maximum resolution possible, whereas the fainter noise is much more restricted. Creating the appearance of the galaxies as textual surfaces (rather than volumes filled with text) was done by restricting the flux shown to a narrow range, so the interiors are avoided. The appearance of the galaxies was animated by this very simple script which just controls their visibility.

The Dark Tower

We next get a transition from representing the data as numbers to a landscape, via a brief transition sequence I'll describe later. A happy rendering accident produced the murky scene that resulted, giving a slow, reluctant change from text to surface. Of course the data here still is numerical, but this has a completely different feel to it. I liked the idea of thinking of these highly abstract slices of data as real places. Of course they are places, but a diffuse, gaseous galaxy is conceptually different from a rocky landscape. And you don't even need the concept of a number to understand a landscape. Do our minds even quantify things at all, or are they making relative comparisons in some other way ?

I played around with this quite a bit. In the video we get this gloomy blue scene, blurring the line between discrete surface and volumetric fog - a running theme of the project. I'm fascinated by how continuous data can emerge from seemingly incompatible discrete points. Eventually we see the data (the same as in the first sequence) rendered in the style of a barren rocky desert, albeit with some reflections to keep it suitably surreal. At the end the sky changes from a clear blue sky to one filled with clouds generated from hydrogen data from our own galaxy : a hydrogen sky illuminating a hydrogen landscape, data of the same type shown with starkly contrasting methods. Altering the colour scheme is also fun.

As Above, So Below

Minas Morgul

Interestingly, despite having looked at this data (as above, of the Triangulum galaxy M33) a lot, I've never noticed the twin peaks here before. So in some cases you really do get new information by changing your visualisation method. Which makes one wonder if and why it's more legitimate to view your data as a landscape, map, or volume. What exactly do we mean when we ask what the data really looks like ? Why do our minds perceive things as colours and not as heightfields, or smells, or boredom, or homoerotic ennui ?

For example, imagine that you had extremely densely-packed nerves in your fingertips. You could in principle receive tactile information as though you were seeing it, though no photons would be involved. Similarly, photons received by your eye could trigger the same sensation as when you touch something, though this wouldn't be accessing the same information as from a direct physical interaction. Or your brain could directly generate maps of emotion rather than brightness and colour. It's hard to imagine finding your way around based on how hilarious/erotic you find your surroundings, but why not ? It would be the same information as you have now, just processed differently. Indeed many animals lack a sense of sight entirely and get by just fine on smell and touch; others, such as sharks, have electrical senses quite beyond our ability to imagine. Does their electrical sense feel similar to touch, or is it as different from touch as touch is to sight ?

Synaesthesia, where one sense triggers another, is sort-of what I'm getting at. Blindsight, where the brain process signals from the eyes only at an unconscious level, is perhaps closer but still an imperfect analogy. My questions are more why we should consider our senses legitimate at all. To what degree are we experiencing the real world ? How does our perception shape our view of it ? Why do we only perceive things in such limited ways ?

All this comes about from spending too long looking at those channel maps. False colour images are one thing; maps of the motion of an object are quite another - and they all give real information. For comparison, here's how I would normally render the above data set :

So which one is real ? A mind-wrenchingly difficult question. None of them show the data as it would appear to our eye, but on what grounds do we grant visual sense a special privilege ? None, really. Maybe one day we'll have the equivalent of a Copernican Principle but for senses, holding information from smell and taste to have the same level of validity as that from photons.

How it's made

Rendering data as a landscape is fairly easy - I just used each channel map to displace a grid mesh vertically. Stupidly not realising that Blender can now easily do this for animated textures, I wrote a couple of Python scripts : one to create the initial mesh which you can find here, and a second to animate the meshes which you can find here. Pointless, but it got me learning to code in modern Blender at long last.

The hydrogen sky data is taken from the Leiden Argentine Bonn survey and is available here. The data files are equirectangular so are easily mapped to a sphere in Blender without even needing UV mapping. To create the colours, I used a classic technique where different channels contribute to the RGB components separately.

I had a happy accident creating the murky appearance. I found that if you enable indirect lighting and ambient occlusion, and completely surround your objects with some closed mesh (which must be traceable so it can cast shadows), you get this wonderfully gloomy appearance. I never bothered to figure out how to change it, but fortunately it looked nice to me anyway.

Infinity Sphere

This works a little better as an animation but the stills are nice enough, I guess. As the hydrogen sky appears to set, we change to the reverse angle - a view from beyond the sky, with the hydrogen data mapped onto a sphere. Now here I'll admit I've used something that looks pretty rather than being driven directly by the data. The sphere is between two reflecting mirror spheres, so you get a series of "infinite" (well, okay, about ten) reflections fading into the finite volume of the sphere. This merges the smooth, solid appearance of the sphere with the diffuse nature of the hydrogen, combined with strange distortions from the spherical reflections and a deliberately ambiguous sense of motion.

It's true that slapping on a pair of shiny spheres might not be necessarily the most informative way of viewing data. But to hell with that ! You're look at a series of literally timeless photons that have, from their perspective, instantaneously travelled fifty thousand light years to be intercepted by a series of reflective metal surfaces in order to cause a small, measurable electrical current and then re-emitted as photons on a computer monitor and finally viewed through twin organic, refracting lenses which transform them back into electrical signals and then... lord knows. What exactly is strange about throwing a couple more reflecting spheres in there, hmm ?

More Than Darkness In The Depths

How it's made

Not much to say about this one - LAB data again, with offsets to generate the RGB channels, and a couple of reflecting spheres, with a similar render layer setup to prevent the outer one from being visible.


Next comes a very different style of sequence. Here the transition from an initially sharp, discrete, digital mesh to continuous volumetric cloud is very explicit, and hopefully very hard to pinpoint. You ought to be able to definitely say that the end points are discrete or fuzzy, but not determine where one begins at the other ends. Towards the end, you might spot hints of a crystalline structure that I'll return to later. I liked this sequence, but I wanted to exaggerate the effect still further.

If there's anyone ought there still suffering the naive impression (as I certainly used to) that once you've got a data set, you pretty quickly understand it, this may hopefully cure them of that.


The Fires of Mordor


The same data set with the same colour scheme, but the final image has the faintest material stripped away, revealing an inner core much cooler in appearance.

How it's made

This sequence relies on the volumetric rendering techniques of FRELLED, which renders volume data a series of transparent planes. With enough planes the appearance of a continuous volume can be faked very convincingly at low computational cost. Modifying this to initially appear solid was done by the simple approach of removing most of the planes, making the visible ones opaque, and using the build modified to show very discrete, square sections of the data that gets gradually filled in. The data set used for his one is from the VLA GPS survey of our own Galaxy.

The only quirk I encountered was towards the end of the sequence, where I wanted the data to fade out. Since this is a realtime render I wanted to animate the clip alpha value, which to my surprise I found was impossible. Also, the tooltip in Blender that tells you how to access this via Python just doesn't work. Eventually some Google searching gave me the correct answer, so here's a script to show how this was done. The sudden drops in intensity are not deliberate but a result of the very low alpha value of each mesh, which means that Blender can't set enough precision on the Clip Alpha value to give a smooth transition. Not what I was aiming for, but I liked it.

Non Spectral Lines

After another Matrix-style shot, we now get something very different. Instead of turning the data into a landscape as in the first sequence, now we see a series of advancing lines, rendered with infinite reflections. This is easier to explain with something we briefly saw in the second sequence where the M33 data gradually turned into a landscape :

Phantom Spectra

Normally with these data cubes we plot spectra. These show how the intensity of a source varies with frequency, which gives us clues to its rotation and total mass. The lines above are different, they are non-spectral lines that show how the intensity varies with position on the sky. Such plots are sometimes made in astronomy, but my point here is again that rendering the same data in a slightly different way produces a conceptually different result. All that's been done is to restrict the data displayed and we get a sort of electrical appearance, very different from the landscape we had before.

You might also have noticed another phase during M33's lines-to-landscape transition sequence :

Spectral Surface

Here we see the same landscape but rendered as a partially transparent surface, with transparency depending on viewing angle. This helps to make the transition from lines to surface as gradual as possible.

How it's made

It was easy to modify the landscape scripts to restrict the meshes to a series of lines, and the creation script can be found here. For the M33 sequence these are trivially animated by just controlling their visibility (via layers rather than display) based on the current frame - a single velocity channel is used, so the height of each line never varies. That script can be found here. For the Pegasus sequence (the one with reflections), the lines are animated both in space and velocity channel. Each line that appears advances through the spatial and velocity pixels of the cube simultaneously, reversing direction whenever it reaches an edge. The animation script to do this is available here. The semi-transparent landscape is made using a very old "X-ray" technique for which you can find an example file here.

Crystalline Hydrogen

Next we return to the crystalline sequence show earlier, but this time attempting to make it explicit in a single frame. I wanted something that appeared diffuse and continuous one one side, but discrete and crystalline on one side - structured and structureless in the same form. This I found could be done by removing certain parts of the data. Again, there's no clear point at which one can say that the object is solid or gaseous. The idea of a crystal of gas is very appealing to me. What two substances could be more different ? Yet here they are, reconciled harmoniously. Or at least as good as I was able. One day it might be fun to improve the crystalline appearance and merge the shadeless material of the volumetrics with something with specular reflections and other crystalline effects.

I'll admit that thoughts about mind-body duality, the apparent contradiction where mental, non-physical concepts somehow control physical ones, was more than a little influential here. Since I've decided I have absolutely no clue how this works (and will greet anyone claiming they've got an easy answer with a shifty-eyed look), I'm not even going to attempt a speculation. What the hell is a thought, anyway ? How can I experience something via electrochemcial reactions whereas a plant or a calculator apparently does not ? Is our conscious perception just an emergent phenomena of a flabbergastingly complex web of reactions or something more mysterious ?

And then I got to thinking about blindsight again, wondering if perhaps we all do this constantly - only being truly aware of our surroundings for brief moments yet still receiving external information unconsciously. Can we truly be called intelligent if all we do is, like a camera hooked up to a monitor or computer screen, process data ? Where does data processing end and true consciousness begin ? Is objective intelligence possible or does it innately require subjectivity and bias ?

Buggered if I know. But I like the idea of a crystalline gas. Maybe the subjective and objective aren't so diametrically opposed as we think. Or then again maybe they are. I dunno. What am I, a magician ?

I also experimented with this display technique using M33, so here's yet another render showing how different the data can appear.

How it's made

The crystalline hydrogen sequence uses Milky Way data from the GALFA-HI survey. This is rendered using FRELLED, but with some modifications. Each image plane is heavily subdivided - not to the extent of having as many vertices as data points, but pretty heavy (there a few million vertices in the scene). The first part of the sequence is easy : all the planes are parented to a empty, which is scaled down heavily in the vertical direction so the stretched data is compressed to the size of the visible area.

Making the data look half-crystalline is more subtle. Each mesh has a randomised build modifier. I wrote a Python script to alter the length of each build, depending non-linearly on the channel number but always keeping the same starting frame and random seed. This gives the appearance of long "crystals". Build modifiers were then applied at a well-chosen frame so that they were no longer animated, and the clip alpha script was used to fade everything out. You can get the build modifier script here - it was quite carefully calibrated to work on this data set, mind you.

Ghosts of Virgo

In the next sequence we return to the idea of data emerging from a surface. Once again the surface represents a particular velocity channel of the data, but this time it's shown as a solid, reflecting pool rather than a wall of Matrix text. Galaxies emerge as partially transparent surfaces, this time showing their true spectral information. As with some of the other sequences, it can take a little while before the eye understands what it's looking at. What's particularly fun about this sequence is that these galaxy surfaces are genuinely useful ways of analysing the data - this is something I'm working on currently.

How it's made

The "surfaces" are actually a series of contour plots, one at each channel of each galaxy, extruded to look like a surface. They've got the X-ray material applied whereas the flux surface is simply purely reflective. This data is from the Virgo cluster and is available here.

Broken Cloud

At the end of the Virgo sequence we again see LAB data fade into the sky. Suddenly we see the view from beyond the spherical sky, but this time rendered as a volumetric cloud. The simple, almost cartoonish sky is replaced with something far more dramatic and weird, yet it's the same data set. There's a mixture of the diffuse and discrete, coupled with strange sort of turbulent motion.

How it's made

This uses a modification of the FRELLED technique I describe here (and formally here), mapping the data to spheres rather than planes. Since the data is from the whole sky, this is better for removing its distortions. The weirdness of the motion arises partly thanks to a strongly varying camera field of view and exploiting Blender's problems of sorting multiple layers of transparency. That is, transparent meshes only display "correctly" (if there even is such a thing) from one direction. With spherical meshes, one can peer through meshes that would otherwise appear dull and boring by using the clip alpha value in combination with simple distance clipping.

Eye of Harmony

We now fly through the LAB data. Everything is once again smooth and continuous with no hint of flaws in the data.

Xeelee Tunnel

We stay with the LAB data for the endgame. Again we see a confusing, now especially asymmetric, view of data that is sometimes discrete and sometimes diffuse, often dark but occasionally flaring into waves of bold, primary colours, before finally fading back into nothing.

Reality Bomb


Shattered Mirror

The Dream Is Collapsing

How it's made

This sequence worked out far better than I dared hope. Blender can't automatically displace spherical textures - they have to be UV mapped for this to work. But all it is is the colourised LAB data displacing a sphere. Originally I just wanted to show the hydrogen as an object, something you could conceivably hold rather than a place you could visit. I found than the interior of the sphere looked so much more interesting than I'd anticipated I abandoned my original idea and went for pure surrealism. This uses a wide angle camera moving on a complex orbit, together with distance clipping and an reflecting icosphere for the background. There are just two meshes in this scene, but it looks like so much more.


Data visualisation is the best thing ever. It just is. But if you think about it for too long, you end up spouting pretentious twaddle about "infinity" and "consciousness". You start muttering dark things about how life is a crystal and all knowledge is subjective. Pretty soon you go Full Philosopher, start asking random people on the street if they've ever wondered how language constructs reality, and eventually do all kinds of weird things a normal person should only do under the influence of psychoactive drugs, like pretending to be a small hummingbird named Hilda. At that point it's probably time to stop and go and plot some dang graphs.

Tuesday, 1 May 2018

The Assumption

Thank you for that helpful contribution, Dr Zoidberg.
Pseudoscience, stupidity and wrong-headedness are some of my favourite topics. Over the years I've looked at the different flavours of wacky beliefs people hold, the way they express them, and the reasons they come to some truly bizarre conclusions. While true idiocy should not be disregarded, by and large even intelligent people can be guilty of wanton stupidity. This obviously includes me, so you have to take everything I say with that in mind.

But there are a couple of Aeon essays going around right now which I think go too far in this regard. Both make the same essential point : that fringe lunatics and the like are basically normal people, but with different - possibly much higher - standards of trust and objectivity than the rest of us. This is a comforting thought, because it means that "we don’t have to attribute a complete disinterest in facts, evidence or reason to explain the post-truth attitude". They've just got the sources wrong, but are fundamentally open to rational argument and persuasion.

The essays are intelligent and persuasive, and the second in particular has many other points I entirely agree with. But this main point has a strong feel of being written by someone who has heard about loonies, but never actually gone and engaged with them. It might well apply to the silent majority of those who merely tacitly endorse fruitcake ideas - I certainly don't dispute there's some merit in it - but I doubt very much it applies to the vocal ringleaders.

So here I want to tackle a couple of important points. First I want to look at the underlying assumptions of science itself - not the messy process of actually doing science, but the most basic, fundamental assumptions of all. Then I'll see if these people are behaving in a way that is fundamentally compatible with scientific practise or if they reject this at a deeper, more fundamental level.

1) What is science made of ?

Another thing that helped prompt this post was a recent conservation with a very good friend of mine who happens to be a staunch atheist. He holds, essentially, that certain beliefs shouldn't be given the benefit of the doubt - that the scientific method must be correct almost by definition. Here I shall show what assumptions this rests on, but, much more fundamentally, why these premises are indeed (and can only ever be) assumptions, and why this is in fact a far more scientific approach in itself - and why it may not even be possible to do science if you don't make these assumptions.

To do this we'll need a basic working definition of science. Of course such a definition could easily take up an enormous amount of discussion by itself, so I'll just propose what I think is a useful, rough and ready description that should convey the essential meaning but might not stand up to rigorous philosophical scrutiny. Proof-reading this post when it was nearly done didn't reveal any obvious flaws, to me at least.

Science, I'd say, is the process of using rational methods to find out whatever is true about the universe. It doesn't necessarily always or entirely use rational methods (you can get lucky and literally dream up the correct answer), and likewise it doesn't always or entirely examine the real universe (you can construct theoretical models based on scientific principles but not expect them to apply to reality). I employ the word "process" in the definition because any process is unavoidably an extended, prolonged affair (not a discrete momentary act) and scientific examination can be incredibly complex. Yet if at some point a technique neither uses rational methods - if you've dreamed up or guessed an answer you still have to test it in a rational way - nor attempts to apply its findings to the real world, it is surely not science.

This definition is very broad, and arguably includes a lot of the so-called "humanities" subjects while excluding mathematics. You could, for instance, do a rational examination of a poem to analyse its sentence structure, or, oh, I don't know, a statistical examination of Plato. But in general I'd say that while there might be a scientific component to these topics, they also have other essential components of their own, such as subjective feelings and intuition. They could be seen as a mirror for science in that respect : they might not necessarily exclusively rely on emotions or internal reality, but they do require them at some point in their own procedures.

It should be apparent that this in no way disparages either science or the humanities, nor insists on firm boundaries between the two. They are both useful and valuable in their own fields, which sometimes overlap. Both can make use of (while being essentially distinct from) the other.

So what assumptions are implicit in this working definition ? Well, given the rather inexact nature of the definitions, the assumptions must be somewhat questionable as well. Still, this doesn't preclude an attempt at finding at least some of the underlying postulates on which the scientific method is founded. In less dedicated posts I've casually stated that science assumes the world is objective, measurable, and real, so let's use those as a starting point. Bear in mind that these assumptions apply only when someone is actually doing science, not necessarily all the time in everything they do. They do not have to be absolutely convinced of their unequivocal truth, they just have to (at the very least) accept and entertain these notions while engaging in scientific examination. That's what an assumption is, after all. I was also strongly reminded of this by this excellent online philosophy course, which really rams home the message that proof, in the strictest sense, is arguably impossible.

i) Objectivity

All forms of science, even those which examine the mind, are based around the notion that there is a world outside our heads. The world is, at least when we examine it, absolute. It does not depend on our own feelings and limited perceptions, except in that our own feelings and perceptions are part of the world. These may serve to limit our understanding, but they do not directly influence things beyond our direct, immediate, physical control. Being angry can cause us to smash things, but anger itself, when stripped of all its secondary effects on the body, causes no change except within our own minds.

Consider the alternative case in which the world was internal and that the only things which genuinely existed were our perceptions, if reality were nothing more than a dream, an illusion, or a simulation. Our thoughts, feelings, and truth would be indistinguishable. We could never know for sure if other people existed or if anything at all was truly independent of us. Reality could keep changing continuously and we'd have no way of knowing if our memories had changed. Two plus two could equal four, or five, or an exploding hippopotamus. There would be no reason whatsoever to presume the world was logical or meaningful.

That's the extreme case. A far more common alternative to the assumption of objectivity is that reality is a sort of objective illusion, which is internally largely and logically self-consistent. This shadow world is very much like our own, but because the physical laws which govern it are somewhat arbitrary and capricious, they can often be suspended. The world is occasionally haunted by ghosts, monsters, gods and demons with supernatural abilities, but most of the time logic prevails.

An even more extreme version has it that no such entities or other spooky phenomena exist and that the world is in fact basically the same as what we see, except that we're just a brain in a vat or a subroutine in a program. This is essentially pointless because there's no real difference between the observed and real worlds in that scenario except in matters of detail - if the observed world is illusory, there's not much reason to assume that brains or subroutines even exist externally, yet that is the usual presumption. But more on that later.

In The Matrix, the real world may be less pleasant than than the simulation but it's fundamentally the same - indeed it's based on a real, documented past. But there's no particular reason this should be the case : if absolutely everything is an illusion, what grounds do you have to suppose that reality operates logically ?
Objectivity itself is comprised, I think, of two other assumptions which do not always require each other. In its usual sense, what we mean by objectivity is that the world is both independent of and external to our thoughts and feelings. These are not quite the same thing. It's possible in principle to make an objective, logical, and even correct assessment of one's own internal feelings, all by oneself, without being influenced by those feelings - strictly speaking objectivity does not require externality, though often this makes things far easier. The externality of the world means that it exists outside our minds. This by itself does not require independence from our minds, since conceptually the world could be external but still directly dependent on our beliefs.

It's important to realise that being objective is not the same as correct. For example, one can construct a weather forecast, or a horoscope, that's entirely objective but completely wrong : neither independence or externality are sufficient for correctness; objective procedure is not at all the same as objectively correct. But a world that is by its very nature not objective cannot be analysed scientifically at all : you can't even have objective procedures, much less correctness, if reality is itself not objective.

So why is the objectivity of the world an assumption ? For the very simple reason that it's impossible to prove it's true. The conceptual possibility of the alternatives is itself sufficient to discredit any notion that the objectivity of the world is provable. If you were being continuously manipulated by Descartes' evil demon, or living in an even more complex and convincing version of the Matrix, you'd have absolutely no way to know about it, let alone demonstrate this to others. Given these two possibilities, that the world is or is not objective, we've no choice but to assume one or the other - there is absolutely nothing compelling us to choose one over the other save our own preferences. But for science, we must assume the former. To do otherwise is to replace objectivity with magic, but to not recognise that an assumption has been made is to fall victim to dogma, absolutism, and preclude the legitimate possibility that the world is fundamentally unscientific. And excluding possibilities without evidence is intrinsically an unscientific procedure, which is why our only hope lies in recognising the assumption that we're making. This doesn't mean we can't fervently believe our assumption is correct, we simply have to acknowledge that it's an unprovable belief.

If the boundary between objective, scientific reality and subjectivity is somewhat blurred by the idea of internally consistent illusions, it is at its fuzziest when dealing with quantum effects. There are, in fact, variants of the subjective nature of reality that are entirely reputable within the scientific mindset. The two most prominent interpretations of the weirdness of quantum reality are the Copenhagen Interpretation and the Many Worlds Interpretation.

The former essentially says that observation determines reality, which, even if not excluding the role of purely mechanistic observations, necessitates a role for conscious observers as well (though this does not forbid conscious observers from themselves being only a peculiar variety of mechanical constructs). The latter interpretation says that there is no unique reality and that all possibilities occur. If conscious beings have any sort of free will, then in this case their choices determine their experienced reality, but no more or less than any other possibilities arising from purely physical mechanisms.

Thus both have a role for minds, albeit rather weakly, and while both are considered extremely controversial (and sometimes deeply unsatisfying), both are also generally accepted as legitimate scientific philosophies. Neither suggest any direct role for emotion, only observation and choice. Most importantly of all, neither say that our subjective, internal reality is what directly shapes the external reality - they are simply weirder and more elaborate pronouncements that our interaction with the external world controls it, though in a very much stronger way than through simple physical control of our bodies. One may argue from other reasons why these ideas are not scientific, but purely from the perspective of objectivity, in my opinion they are sufficient.

ii) Measurability

The external, independent world must also be measurable. The world itself must be fundamentally capable of being measured, if only in principle - practical difficulties do not concern us here. And the observer themselves must be capable, with sufficient effort, to be able to make those measurements accurately. Of course this does not preclude them from making errors, but their own perceptions must be generally reliable enough that they can correct themselves meaningfully. Repeat observations of deterministic phenomena may give rare outlying values because the observer had an angry cat suddenly drop on their head from time to time, but the usual state of affairs is that their measurements are reasonably accurate. Errors can, in principle, be corrected through repeat observations.

Again quantum effects might seem to derail this pleasant idea, and to some extent this is true. The Uncertainty Principle does not forbid us from conducting accurate measurements, but it does limit our precision. In some circumstances, we can only give probabilistic estimates rather than hard values. It doesn't say that we can't measure things at all, only that we can't know their values to arbitrary precision. Which in general is also true of classical physics, since our measuring equipment is inherently limited anyway. That a particle might actually be a probability cloud is, from the perspective of pure measurement, not actually so different from us not being able to measure it with infinite precision and accuracy.

Clearly though, not everything is measurable. We cannot fly into the centre of the Sun or a neutron star and report back, because we'd die - and anything entering a black hole is doomed. However, with the notable and important exception of singularities, all of these are measurable - we assume - in principle. That is, their substances possess definite or at least probabilistic properties. Only singularities seem to defy this basic requirement, where conventional theories lead to infinities that are by definition impossible to measure. Most people believe this points to a flaw and/or incompleteness in the theory rather than reality having some rare exceptions which are inherently unmeasurable.

Simulation of what it would look like inside a black hole. Though the properties of space and time start to become fundamentally different within the event horizon, it's only at the singularity itself where they truly break down.
The role of the observer in this ties back to the idea of objectivity. Although they do have moods, biases, and incorrect ideas (and these internal constructs are themselves not necessarily measurable), this does not influence the external world directly. We cannot know for certain that each and every measurement was made correctly, but we instead have to assume that they were done with reasonable accuracy unless we have good evidence to the contrary. We again can't be sure that an evil demon isn't manipulating reality, or that we aren't living in an illusion with our memories being continuously replaced from moment to moment. We have to assume that this isn't true, that reality isn't so transient and our own skills are not so deeply at fault.

Without this assumption we have absolutely no basis for any of our conclusions at all. An unmeasurable world would have no basis for comparison, no justification for logic, and would be utterly inscrutable to analysis by any kind of rational methods. We have to assume that the world is measurable and our measurements are meaningful, otherwise the scientific analysis is impossible. And again, this is unavoidably an assumption because by definition we have no way to prove that this is really the case.

iii) Reality

Thus far we have a world which is largely external to and independent of our own subjective beliefs, save some small overlap wherein we, as part of that world, are able to influence it. The world is measurable and our own ability to measure it is generally accurate. If we open the box to examine Schrodinger's Cat, we might be influencing the state of the cat or selecting which universe we inhabit (though surely, as someone once quipped, it doesn't take the creation of entire universe to kill one cat), but in both cases we still have an objective and measurable reality - even if our measurements are neither always complete, precise, or accurate. Our perception is limited, but not wholly wrong.

But do we really have to assume that this external world is in some sense real ? Obviously something does exist. In principle we could be living in a fantasy constructed inside the true reality, and if it was as self-consistent as it appears to be, then we could scientifically analyse the nature of that fantasy without being aware that it was not, in that strict sense, real. The assumption that we are in the "true" reality is one of convenience, otherwise our entire analysis is meaningless as it tells us nothing about the truth of the universe - which is the explicit goal of science.

I suppose if you were happy enough to analyse a fantasy, you could get away with rejecting this assumption, but the point is that the fact we are in the "ground state" of reality has to be an assumption. It cannot be proven. This is subtly distinct from the notion that the world we see is objective, since we could in principle inhabit a world which is indeed external to ourselves and independent of our minds but still, in effect, someone else's fantasy. The assumption that our observations are of something real gives our findings an important additional level of meaning, since it follows that we are understanding what's really going on - not just studying the elaborate playpen constructed for us.

That said, it is possible to scientifically analyse a fantasy. Theorists do this with numerical models all the time, yet eventually they expect their results to be compared and contrasted with observations. If those observations are themselves another model, then in what sense have we made a meaningful comparison ? I would say that comparing two models to each other is a qualitatively different activity to comparisons of models with reality - even though the operational procedures might be identical. If you don't know which one is real, it's impossible to say which one is better in absolute terms. You can only make relative comparisons, which are not the same thing at all. So while this might be the least important of the assumptions underlying science, in my view it is still a necessary one.

Combining these three assumptions raises an interesting philosophical question which I shall only mention in passing : where do our imaginary, immeasurable mental constructs - justice, duty, mercy, the tooth fairy, that sort of thing - fit into all these ? They clearly exist in some very broad sense, but obviously not the ordinary physical one. For that matter we could argue that mathematics itself - the foundation of measurement ! - is a mental construct that just happens to apply to the external world. And where does the external world end and the internal world begin ? What, when you really get right down to it, exactly is a thought ? How does an electrical current in the brain become something so much more than that ? I for one have absolutely no effin' clue, so it's way easier to just say, "External world = real; Internal world = something else. Bam. Done, bitches."

All of this analysis suggests at least one additional assumption that I feel fairly confident about.

iv) Logic

This is a running theme in the above discussion but has not been stated directly. If the world is independent of and external to our minds, measurable and real, this still does not preclude it from being fundamentally illogical. It could be a mass of daffodils one minute and full of screaming badgers the next. At any stage it would be measurable, but it would be proceeding in a completely illogical fashion (unless someone can devise a logical theory of spontaneous badger generation, but the deeper point should be clear).

Therefore the assumption that the world proceeds logically, with cause and effect, is distinct from the others. Mathematics, we assume, does apply in the real world given the appropriate numerical parameters and an accompanying account of the physical processes. Our understanding of both maths and physics need not be complete in order for us to assume that the world is indeed governed by them. We need not even fully understand logic itself (certain quantum phenomena and time travel to the past may be regarded as unsolved problems), but a universe that proceeds on capricious, arbitrary whims or without some kind of underlying reason to it cannot possibly be analysed in a scientific way.

Reason, of course, is a loaded term, often conflated with deliberate purpose. Certainly the ancient philosophers (and the religious today) thought that an ordered universe was impossible without a divine will to control it. Modern scientific thinking tends to the opposite view : that a potentially capricious supernatural deity could lead to disorder and chaos, and that to suppose they had some grand scheme in mind is an assumption that science is justifiably unwilling to grant.

No, reason in this context really means something far more basic - the mere notion of causation itself. Nothing happens, we assume, without something to cause it. Hume pointed out that we cannot actually prove causation in the very strictest sense - we only directly observe correlation. This makes our notion of a logical, coherent universe another assumption, though only in the sense that we cannot absolutely prove something totally unpredictable won't happen at any moment. Few people indeed would grant that causation itself is on unstable ground, though in the most rigorous sense it isn't actually proven.

Note that science also, in a strict sense, does not preclude there being an intelligent, careful being directing everything, thus being the root cause of absolutely everything - it neither rejects nor accepts this possibility but simply ignores it as irrelevant. Instead we only assume that cause and effect do actually operate, that one thing can cause another, that nothing happens without some cause - though that can frequently be fantastically difficult to determine.

v) Finite

Thus far I think my series of assumptions are all reasonably safe, and that though some might contest certain aspects of what I've described, few scientists indeed would disagree with the main points. For this final point, I'm likely venturing into far more suspect territory.

We do not know for certain that the Universe is finite in spatial extent. There is however very compelling evidence that is is finite in time and expanding, strongly implying that it is also spatially limited (though not necessarily bounded). If true, the content of the Universe must also be finite, though enormous. In such a case it becomes easy to understand what we mean by a fraction - half of all the stars might be red and half might be blue, the fraction of stars with planets is some number, etc., because the total number of things is fixed.

It's far less obvious if we can assign fractions in the case of an infinite universe - the measure problem. While some infinities are bigger than others, and you can do some mathematical operations on infinities, defining fractions turns out to be especially difficult - perhaps even impossible. Just as with singularities discussed earlier, infinity introduces an unmeasurable aspect to the universe, with all the problems that entails. Recall that singularities are generally supposed to not really be of infinite density as relativity predicts, but indicate instead some flaw in the theory that has yet to be resolved (whilst granting that the theory may be useful and correct in other cases). In the case of an infinite universe, or multiverse of universes, this escape clause is not possible. Thus an infinite universe becomes unscientific because it would be fundamentally unmeasurable.

Worse, its contents would become unmeasurable. A probability value is a type of fraction, and if you can't have fractions, you can't assign probabilities. If you flip an infinite number of coins, an infinite number of them will land heads up, another infinite set will land tails up, another infinite set will land edge on, and yet another infinite set will spontaneously quantum tunnel through the floor... Events that normally happen frequently in the quantum world but that have insanely small probabilities at macroscopic scales would not longer be limited by their fantastic unlikeliness. In some parts of the Universe broken eggs would reform into their original structures, water would freeze at boiling point, and the Loch Ness Monster would eat everybody.

Oh, you could save us from this hellish death of causation easily enough, but the price would be high indeed. We could, by an incredible fluke, just happen to be living in a region in which everything proceeded exactly as though causation meant something when in fact it was all due to random chance. Whilst such a scenario would still concede that the world was objective, it would utterly abandon any notions of measurability, logic, and in a certain plausible sense it would also relinquish the idea that it was real : how can you say which one of an infinite number of absolutely identical objects is the real one ? "Real" and "copy" cease to mean anything at that point. Everything we value most about the scientific endeavour would be gone.

Therefore I say that the Universe should be assumed to be finite. If we don't, we risk making science both pointless and impossible. Once again though, we cannot really prove the Universe isn't infinite in extent (or, strictly speaking, in time), so we must take this as an assumption. It's also important to note that infinities can be merely bothersome in some cases and even useful in others. The problems only occur when infinity is used to abuse probability, such as in the Many Worlds scenario where literally everything only ever happens by chance. Similar abuses are possible in samples which are merely very large, if one resorts to saying that an unlikely event only happens through chance and does not seek an underlying physical explanation. Great care must be taken to distinguish between truly random processes (in which exploiting the effects of chance is legitimate) and physical processes which occur repeatedly (in which case chance plays a role, but physics must also be accounted for).

An infinite, fractal or otherwise repeating universe could perhaps be made logical if the more probabilistic elements of quantum theory could be rendered back to something strictly deterministic. Like a sine wave or the Mandelbrot Set, such a universe need not contain necessarily everything conceivable, or random events happening without cause, but only feature endless variations on a theme. Some events permitted by quantum theory that are currently thought to be fantastically unlikely would have to be made truly impossible for this to happen. The size of the universe at any given moment would have to be finite in order to solve Olber's paradox, and you'd probably need some sort of cyclic process in order to prevent it either expanding or collapsing to oblivion. The problem of unique identity would still remain, and since we don't have a handle on the underlying cause of causation itself, I'm not convinced there really would be a way to prevent ludicrous events happening for no reason. I treat this possibility with the utmost caution.

Can these assumptions be disproven ? 

I've stated elsewhere that scientific theories can disprove their own more superficial own assumptions, such as the existence of dark matter or the age of the Universe - provided of course one remembers that assumptions are being made. What about these much more fundamental ideas ? Recall my attempt at a definition of science : the process of using rational methods to find out whatever is true about the universe. If we make all of the above assumptions, and then conduct our scientific inquiries in accordance with the vast array of other scientific principles and practises we need to carry out an investigation, is it ever possible that we could actually disprove any of them ? Could science actually disprove itself ?

I believe the answer is yes. There is little point in carrying out a scientific inquiry if you limit the conclusions you're allowed, though of course some conclusions are very much harder to reach than others. But we probably could disprove all of the above assumptions, thereby ending the use and value of science. Again, we'd have to remember that these are assumptions in order to be able to question them at all, but, being so fundamental to the scientific process itself, only a fool would demand anything less than the very best evidence possible before they decided that issues so basic ought to be scrutinised to explain their apparently incompatible observations. It would be an act of truly monumental stupidity to declare that because an observation can be explained by abandoning these foundations of science, that they are necessarily flawed - literally anything could be explained in this way. What we absolutely must not do, however, is to declare things to be impossible because our assumptions forbid them. That would be the most unscientific approach of all.

Here are some ways I suggest we might be able to disprove our assumptions, at least in principle.
  1. Objectivity. The independence of the external world could be disproven if someone's thoughts and feelings could be demonstrated to control it without any apparent causal connection. The externality could be disproven if their imaginings and reality could not be distinguished, if their thoughts could become physical constructs at will.
  2. Measurability. Like the single standing stone of Lancre which is so magical no-one is able to count it, measurability could be disproven through the existence of an unmeasurable object. That is, under conditions where measuring devices survive and function correctly, something must be shown to be unmeasurable (giving different results to the same observers using the same methods), be that either probability measurements or more definite numbers.
  3. Reality. If the visible external Universe suddenly stopped existing, or a supernatural phenomena such as a ghost or a demon was well-documented, this would be powerful evidence that what we generally observe is not the deepest level of reality. In the latter case it would have to be shown that the observations really do defy logic. In the former, in which an individual or group awake from a dream, then provided the "real" world was shown to be at least as coherent as this one, then there'd be (at least) no way of knowing which one was real, and good grounds to doubt that either of them were the ground state.
  4. Logic. As above, the existence of phenomena inexplicable by causation would satisfy this one. Most supernatural phenomena would fit this category, though some might be possible to explain rationally.
  5. Finite. This one is much harder. In principle in an infinite universe we could be inhabiting a region where all of the other assumptions permanently appear correct by chance alone. While we can say that observations are consistent with a spatially and temporally finite universe, we strictly speaking can't rule out that either of those might be deceptive. It is even possible that both are infinite, given that the outrageously improbable events allowed by quantum mechanics must occur somewhere in an infinite realm. I think it might be genuinely impossible to really prove that this one either way. The situation would improve considerably if we could somehow presume that the rest of the universe was similar to our own and evolving in a similar, logical and consistent manner. 
I write this very much in a contemporary context. As hinted at, it's unlikely that it's a black and white case of science being valid only if these assumptions are correct, but useless if any of them are not. In the past the logical and rational philosophers accepted mind as intrinsic to the ordering of the cosmos (it would be a step too far to ever call this a scientific assumption, however); if we constructed a virtual reality that was as convincing as this one we'd have to concede that our reality was unlikely to be the true one; if the measure problem could be solved through advancements in mathematics then infinity would no longer pose such a challenge; maybe it would even be possible to devise an alternative to logic itself. It's a fascinating question as to how far the modern scientific approach can be warped before we'd have to say that it was no longer providing the same basic intent or functionality as it does currently. But that is beyond the scope of the current post.

While I was writing this, The Conversation produced a nice little article in like vein which will bring us on to the second topic. This article points out that one flawed argument used by those who deny (some or all) scientific findings exploits the assumptive nature of science : if you don't really know anything without making these assumptions, then your inherent uncertainty, they say makes my position stronger. The error is that questioning these most basic assumptions actually makes any other counter-position possible, which is very different from saying that it makes any one particular counter-position more likely. If you don't know anything, then anything is possible. Why does the Flat Earth get more of a claim to correctness than an invisible jelly monster that's controlling everyone's minds using insane sausages ?

This alludes strongly to the power endowed in science by these assumptions, which I shall return to later, without undermining its even more fundamental basis of philosophy (which, as a quest to discover how we can know anything at all, is granted by its very nature much greater freedom to interrogate the principles of science - it does not have to automatically accept them itself). If, and I stress if, you can shift the arena of debate into the rational or irrational sectors depending on the issue at hand, then all sides are forced to acknowledge the assumptions they're making. This is a powerful asset in any debate. So now we should turn to the second topic, and whether this or other approaches can help those who accept the scientific world view in operating with those who don't.

2) What about the people who challenge these assumptions ?

So we've established a not wholly unreasonable definition of science and a set of assumptions on which it relies. We've shown that these are indeed assumptions, at least given our present understanding. But it's absolutely to vital to remember that within those assumptions, science is fully capable of establishing its conclusions with extreme confidence and even exact proofWithin these assumptions, but only within these assumptions, and accepting that it is neither complete nor perfect, the scientific method is an undeniable work of astonishing achievement.

What, then, of those who reject those conclusions and the arguably related phenomena of people with other (e.g. political) beliefs that make no damn sense ? Are these deep, intelligent thinkers who have thought carefully about the basis of science and then rejected it ? Or are they are just bloody mad ?

Nutters versus the truth

While the first of the Aeon essays is concerned explicitly with pseuodscientific, irrational beliefs, the second is more focused on the political arena and people not hearing opposing viewpoints. Yet both claim that their respective groups of apparent nutcases are actually just people with different standards of truth. They state that these people behave rationally and sensibly, but simply reject certain sources and insist on more rigorous levels of proof than the rest of us. I shall concentrate on the second essay, as it goes into considerably greater depth than the first. I apologise to the author if they were more strictly intending their essay to apply only to the political arena, but I do think that bullshit and post-truthism result from common causes both in politics and pseudoscience.
We don’t have to attribute a complete disinterest in facts, evidence or reason to explain the post-truth attitude. We simply have to attribute to certain communities a vastly divergent set of trusted authorities. Listen to what it actually sounds like when people reject the plain facts – it doesn’t sound like brute irrationality. One side points out a piece of economic data; the other side rejects that data by rejecting its source. They think that newspaper is biased, or the academic elites generating the data are corrupt.
The trouble is that if you actually do go and engage with people, you will find that they generally are being wholly irrational, and all too often it sounds very clearly like brute, outright stupidity. In my experience hardly any of them are really more concerned with being objective than the rest of us. Flat Earthers, in particular, tend to be religiously motivated, and like Creationists, will automatically disregard anything from any source whatsoever that contradicts their existing view. Even their own senses cannot be trusted, because, to be blunt, "God did it". Such a reasoning is by its very nature not objective in the slightest : indeed, it is an explicit denial of objectivism.

Other crackpot viewpoints tend to be of similar ilk, albeit with superficially different motivations : they tend to try to alter the facts to fit their views rather than the other way around - committing that unpardonable sin of thinking that what they already know is a fact, and so anything that contradicts it must be wrong by definition. They cherry pick to an absurd degree, holding whatever supports their view to be unimpeachable but anything else to be obviously wrong, with little consistency as to which source supports or disproves them. But the essay has a strange and unjustified insistence that they behave otherwise :
And, in many ways, echo-chamber members are following reasonable and rational procedures of enquiry. They’re engaging in critical reasoning. They’re questioning, they’re evaluating sources for themselves, they’re assessing different pathways to information. They are critically examining those who claim expertise and trustworthiness, using what they already know about the world. It’s simply that their basis for evaluation – their background beliefs about whom to trust – are radically different. They are not irrational, but systematically misinformed about where to place their trust.
Well, no, not really. They may well have a capacity to process information to form and evaluate conclusions in a logical manner, and I'm sure at least some of them really are, in effect, simply victims of chronic misinformation. But I think it would be a terrible mistake - or at best an oversimplification - to infer that this is what happens in the majority of cases.

Those who aren't interested in challenging their own views are not really being rational at all (or if you prefer, they are not engaging in critical thinking). If you go around only seeking out sources which support your existing view and insist that others must be discredited by definition of their obviously wrong conclusions, without examining the reasoning behind those conclusions, you are hardly being rational. You have already formed a viewpoint and are being an evangelical activist. You are not interested in the truth unless you actively examine contrasting viewpoints and try your best to give them a fair hearing. These people aren't "engaging in critical thinking" in the slightest - there's no real skeptical inquiry going on, they are simply rejecting sources based on their content.

Scientists behaving unscientifically : how to engage a scientist in debate

To be scientific about opposing viewpoints, you have to try and search for your underlying assumptions - ideally the deepest assumptions of all, ones you might not even be consciously aware of - and examine their effect on your conclusions. Scientists hold even empirical measurements as potentially subject to revaluation*, but they don't reject (though they may not immediately entirely trust) them because they don't like them. In contrast, continuously rejecting a conclusion on the basis of what it says without ever examining how it was formed is an entirely different, wholly unscientific approach.

* You might wonder, then, how there can be any facts at all in such a system. At a deep level, we might say that instead of the measurement itself being a fact, it was only a fact that someone claimed to have reported a measurement of a particular value. You can probably see that if we took this too far we would indeed be left with nothing - how do we ever trust anyone's measurements ? This again alludes to measurability as an assumption, and the shallower, more practical consequence is that we simply have to trust that values were reported correctly (see below).

Note the emphasis in that last point. While thus far I've largely been describing ideals, now comes the time when we must temper them with practicality. That is, no-one has unlimited skills, resources, or patience. Someone only need apply the assumptions and goals of science when they are actively seeking to undertake science, not when they're deciding what to eat for dinner. Likewise, if you're arguing with someone on the internet, you have no good reason to feel entitled that they should respond as a paragon of scientific virtue if your argument defies all scientific principles.

Furthermore, scientists do not go around questioning absolutely everything the whole time, because that is unproductive and stupid. It is absolutely integral to the scientific process, though not an innate feature of science itself, that some ideas can be rejected after suitable examination. Without this, progress would be impossible. Had we possession of some perfect artificial intelligence, we might just continuously feed it data and it would continuously re-evaluate all conclusions, but alas we have only our meagre, mortal brains to actually understand what the data means. It's a consequence of the assumption of measurability that we simply have to trust that measurements are generally reported correctly.

Questioning the very basis of science is a fine thing in a philosophy lecture or even in the much lesser medium of a dedicated blog post, but you can't expect everyone to do this either constantly or on demand. Within the scientific world view there are some conclusions which are very much stronger than others, and if you suddenly come unasked out of nowhere and challenge them with little or no evidence, you can't expect a warm and welcoming reception. Scientific conclusions are hard-won, and it is sheer folly to abandon them at the slightest provocation. Furthermore, individual scientists very often do hold those basic assumptions as ideological beliefs, which you can't very well expect them to alter on your say-so, but more on that in a bit.

So what if you do want to go and engage a scientist in an open discussion ? By far and away the best means to challenge them is the conventional arena of scientific debate : the peer-reviewed publication. This sounds pretty extreme, but it's the best method to be be taken seriously. It is, after all, how mainstream conclusions were formed in the first place. In some ways it's an astonishing level of double standards to demand that you can circumvent this as though you had a note from mummy.

But far more common, in my judgement, are people who aren't out to actively discredit science, nor are they genuine pseudoscientists or highly intelligent people who for whatever reason have got some wrong-headed notion stuck in their brains. Most people just aren't that interested. Rather, all they want is a bit of speculation and perhaps some insight into something they've got a passing interest in; they don't have the same level of expert knowledge, but they are at least somewhat curious about other possibilities. They may have a preference for one over the other but not necessarily a dogmatic conviction. Or, as the old saying goes, when all you've got is a hammer, everything looks like a nail. Most people don't need to be hammered, they need to be listened to and engaged using techniques of reasoning. It would be absurd to expect such people to suddenly spend years of their life learning things they have only a passing interest in, and equally preposterous to dismiss them completely - that should be reserved for the most extreme morons who really are rabidly anti-science. Great care must be taken to distinguish between people behaving (temporarily or chronically) anti-scientifically, saying that the principles of science are wrong, and unscientifically, where they say that they are merely inapplicable.

Therefore, if you want to engage in the more common but less rigorous debate with strangers on the internet, the premise and informality of discussion needs to be stated. I discovered this first hand not so long ago, and could have saved a lot of bother if I'd paid more careful attention. The poor bloke was at pains to state that he didn't want me to accept something as true, but just assume it was for the sake of discussion.

Being incredibly dense, I didn't realise this until he basically shouted it at me with a megaphone. Finally the light bulb moment occurred and I realised that I could proceed without professing some belief I didn't hold. I felt both assured that I was not going to be subsequently held hostage to my idle, frivolous speculations in the future, but was only engaging in an enjoyable, rewarding form of play : whilst entertaining the possibility of a different world view, I wasn't being asked to abandon my own. Had this chap proceeded in the more usual way of mouthing off about dogmatic, closed-minded scientists not listening to opposing viewpoints, it would have been just another slanging match; insisting that one already knows the answer will cause scientists, just like everyone else, to become defensive. It also helped that I already thought of the instigator as a basically decent guy who wasn't on an anti-science crusade.

Dealing with different conclusions

Another scientific dispute settled with brutality and shocking violence.
As regards both alternative scientific theories and political viewpoints, it is certainly possible to reach radically different conclusions based on the same data; I don't mean to suggest that anyone deviating from the scientific consensus (or indeed my own strongly left-liberal political leanings) is being a moron. Far from it. For example, of the people who regularly engage on my threads, I think just about every single damn one of them has got at least one opinion on which I think they're being really quite thick. This doesn't mean I don't like them, because, you see, the reverse is also true : I don't think I entirely disagree with any of them. Everyone's got something useful to say about something. And yes, I'm sure quite a few of them think that on a least a few issues I'm behaving moronically - and of course some fraction of this will be correct. You know what ? That's fine. We don't have to "agree to disagree". We can simply disagree, and still be friends. Unless you're a Nazi, that is.

Now this doesn't mean everyone is going to eventually come to the same conclusions or hold no moral convictions or ideals whatsoever; this, as the second Aeon article points out, would be "more than we could reasonably expect of anybody". You can't expect everybody to hold rational views about everything unless you're a total plonker. But, it's good practise to remember that some people disagree because they too are critical, rational thinkers who've taken the time and trouble to examine issues in detail, but that doesn't oblige you to agree with them. All that can be reasonably expected of a genuine truth seeker is that, circumstance and time permitting, they engage in a sincere effort to find the truth and honestly question their existing views.

For example, I've got followers (and in turn follow) people with whom I profoundly disagree regarding, say, Brexit, gun control, abortion, religion, capitalism, gender equality, UFOs, free speech, etc. I don't think most of these people are lesser idiots who are stubbornly refusing to see reason, I just disagree with them. That said, there are some views and combinations of views which are red flags. I'm unlikely to befriend someone who disagrees with me on all of the above issues (there's no point in just constantly having an argument), and there are some views so utterly stupid that I would seriously question the intelligence of anyone holding them, just as I would if someone told me that water isn't wet*. I think it's both reasonable and unavoidable to have some beliefs that just won't budge.

* Let's have no smart-alecy BS about wetness being perception, thankyouverymuch.

Recognising when things are hopeless

All that being true, I find it undeniable that some people are virtually lost causes, unless one is prepared to invest a truly enormous amount of effort into changing their minds. The second Aeon essay makes the important distinction that there are two kinds of limiting thought bubbles that people fall into, though I prefer my own terminology to describe them.

The simplest kind of bubble is one in which opposing viewpoints are not present. This is what I would call an echo chamber-: you're just hearing the same ideas repeated. Other ideas are excluded and never enter your social circle, not necessarily because you're attacking them but because you simply ignore or aren't even aware of them. Even the wisest people of all can only process the information they have access to.

The second kind of bubble is more sinister. Members of this are more like cultists : it's not that they merely disregard or even attack other viewpoints, but they attack other people because they hold opposing views. Those inside this kind of filter bubble are already aware of the opposing arguments but reject them. They do listen, but they take alternative views as evidence of the bias of the other side and do not ever entertain the possibility that they might be correct. In effect they have been inoculated against outside beliefs, allowing them to hear them but never accept them, even provisionally. They have made a far deeper ideological shift - they are so convinced they already know the facts, that anything challenging those facts is wrong by definition. The essay goes on to describe how it is possible, but exceptionally difficult, to reason with such people.

Do scientists sometimes fall into in such bubbles ? Inevitably yes, including the second. Even within science there are different modes of thinking at work. The best kind, in my view, is of a philosophical nature - a position for once which is neither at the extremes nor in the middle of the spectrum. These scientists sometimes stop to consider their underlying assumptions, the nature of the reality in which they operate, and entertain opposing viewpoints from time to time for the sake of curiosity. The curious, philosophical scientist is never stuck for very long with a dogmatic conviction, though they may weight some possibilities more strongly than others, and few if any are always questioning everything - that really would lead to being so open-minded your brains fall out. It's just that they are able and willing to do so from time to time.

The more sinister kind of thought is scientism. These kinds of scientists can be extremely intelligent and skilled at processing data to form a conclusion. They may even be genuinely curious in certain matters. But they are rarely of a philosophical inclination; they do not stop to consider their underlying assumptions or even admit they are making assumptions at all - their conviction of the five assumptions discussed earlier is so strong that they think of them as factual, and therefore anything going against them is wrong by definition.

There is a middle ground, of course. Such people accept the basic assumption of science as assumptions, but are disinterested in ever examining them. They say that propositions which violate these assumptions are inherently unscientific, and therefore it's beyond the remit of science to study them. They stop short of actually attacking unscientific ideas and world views because that holds no appeal to them either. This perspective is closest to the scientific approach itself, but arguably not as beneficial as the more philosophically-minded scientist.

Discussion serves multiple purposes

While in any debate it's very bad form to attack your opponent rather than their argument, it's nonetheless important to establish the nature of the person you're interacting with and the intention driving the discussion on all sides*, including your own. The latter isn't always obvious. For instance, for as long as I can remember I've been asking my mum questions and sometimes I don't agree with her answers. Her invariable, legitimate response has always been : "well why did you ask me then ?". After several decades, a lot of higher education and philosophical ponderings, I think I may finally have an answer.

* While it's worthwhile to be aware of the different ideals of how to respond to something you disagree with, this won't help if you don't also understand who you're dealing with. The idea that "small minds discuss people" is nonsense. Don't let the need to avoid insulting the other side prohibit you from trying to understand them.

In this context there are three sorts of discussion. One of these is education : the person asking a question wants an answer and expects the other person has it. They accept that they themselves don't already know the answer and want to learn what it is, requiring an external source to provide it or instruct them how they might find out. People often tend to assume that's why people ask questions in the first place, but this isn't always so - hence my mum's mild indignation. If the question isn't asked, or the debate is not entered, in a spirit of true and free inquiry, then it's not acceptable to give any-old answer. It's only in the mode where one side presumes the other has a greater knowledge and understanding that they surrender their own right to examine the response.

The second sort of discussion is where someone already believes they have the answer or at least a part of it. They might be asking further questions to evaluate their own (self) knowledge against other people, seeking to establish if their (own) views are consistent. They may also be unconsciously aware that they already hold a position on something, but they are not actually cognisant of what it is. This discussion is one of self-discovery, to raise their deeper view to a more conscious level. It might also be that the person already has all the necessary mental equipment and inner beliefs in place to form a position, but they are lacking some knowledge to fully formulate it, and they want another person's more developed opinion to help them construct their own. The point is that people can be participating in this kind of investigation without even being aware of it - and often the unfortunate matriarch will be equally clueless as to what's going on. It's certainly not the default assumption usually adopted during a discussion. While I was deep in my readings of Plato, I tried on a few occasions to actually participate in discussions like this. But, not being quite able to articulate what I was doing, I stupidly forgot to attempt to, making the conversations helpful but with more ruffled feathers than I intended.

(Of course there's another more trivial interpretation of why people ask questions and reject answers : they may not know the right answer, but they know enough to determine which one is wrong. If I ask why the sky is blue, and you say it's because it's full of smurfs, then I'm justified in rejecting your explanation even though I myself might not know the actual reason. I'd obviously overestimated your intellectual prowess.)

So long as one is aware of the purpose, the first two sorts of discussion can be highly productive. However the third sort, which is very common, is much less useful : activism. The first two types occur between the sorts of people who are, at least at an unconscious and basic level, willing to change their minds. The latter happens when someone has already made up their mind and wants to promote their own viewpoint, with no expectation that someone will seek or be able to persuade them in the process. They are explicitly saying, "here's what I think and why you should agree with me, I don't need to think about it myself any more"*. This mode of thinking is not wholly awful, but it is very difficult to change someone's opinion on that particular matter.

* Nothing is more irritating than clickbaity internet articles that do this. There's a world of difference between saying, "here are the facts and some interpretations, draw your own conclusions", "here's what I think about this", and, explicitly, "here's why you should think the same as me". Persuasion is respectable goal, but such an obvious declaration smacks of propaganda and devaluing disagreement. Strong convictions are best expressed implicitly, unless you at least make an effort to be tactful towards your opponents.

Activists are tough. Yet, if you are convinced that their viewpoint is wrong and needs to be dismantled, you could begin by undermining the factual foundations of their conclusions. Starting by attacking their ideology is rarely a good idea - this is usually a core part of a person's identity, and their very physiology is telling them not to believe you. Paradoxically, while people don't like explicitly being told what to think, they can be tremendously vulnerable to manipulation. A summary of some techniques can be found here. In brief : tackle the "facts" they think are true which have lead them to their own conclusions and beliefs, and let them come to their own conclusions independently (or at least think they have). If at all possible, don't leave a gap - argue for uncertainty, but present possible alternatives without enforcing them. Try and understand their deeper beliefs before attempting to change their more superficial conclusions. You may not have to shift their more valued ideology at all, if you can demonstrate that an alternative conclusion is compatible with it. Examples can be found here.

All this shows why discussions about post-truth and bullshit are so important. If people don't even care about the facts, then arguing with them rationally is useless. Most probably, some do and some don't. It's not that those who don't can't be reasoned with, it's just that you need to use more emotive techniques for them - otherwise they will view you as a cold, unfeeling monster. Conversely, appealing only to emotion to those who are more concerned about facts will be equally unsuccessful - they'll think of you as a wishy-washy ignorant woo-woo merchant. Pick your battles carefully, and seek to engender a sense of goodwill. As the second Aeon article rightly states :
We don’t simply trust people as educated experts in a field – we rely on their goodwill. And this is why trust, rather than mere reliability, is the key concept. Reliability can be domain-specific. The fact, for example, that somebody is a reliable mechanic sheds no light on whether or not their political or economic beliefs are worth anything. But goodwill is a general feature of a person’s character. If I demonstrate goodwill in action, then you have some reason to think that I also have goodwill in matters of thought and knowledge. So if one can demonstrate goodwill to an echo-chambered member, then perhaps one can start to pierce that echo chamber.
This also hints at why the method in The Conversation will only be of limited help : only a small subset of the Flat Earth ilk will be vulnerable to realising that abandoning the scientific method leads to abandoning all scientific knowledge. That small group will be those who have fallen victim to chronic misinformation, and/or have simply not realised the magnitude of the broad implications of their specific claim. These kinds of people have indeed not much abandoned the tenets of science : they only inhabit echo chambers, not cult-like exclusion bubbles.

In contrast the majority of pseudocscience acolytes unfortunately have begun to reject logic and rationality, but not entirely. Most, perhaps, are not wholly irrational, so in that sense the Aeon essays have a point; they selectively cling to logic even while denying its broader findings. If you tell them that the Flat Earth requires entertaining a host of other (scientifically) ludicrous other ideas, they'll only respond with mountains of "evidence" as to why their particular theory is correct and all the other are bollocks (trust me, I've spend far too much time around such people), not so much accepting or discarding scientific methodology as wantonly abusing it. Pseudoscientific findings are engendered by psuedological methods : rational here, irrational there, without consistency. This is what makes it so frustrating to come to grips with - believers clearly are inherently capable of behaving reasonably, it's just that on some issues they absolutely refuse to. They are highly reluctant to concede that their views necessitate that the world is not the objective, logical place they would (often) genuinely prefer it to be, because they don't really understand what we mean by objective or logical - they're rarely capable of grasping the basic assumptions of science.

The most extreme variety of all are actually sometimes more intelligent : they recognise that they're being irrational and that proposal doesn't fit in the remit of science. These people rarely try and persuade scientists, dedicated to rationality, that they should be irrational instead - because they know the response will be a straightforward, "no". It is perhaps inherently flawed to suppose that you can reason rationally with people conscious that they have rejected rationality, and vice-versa, so neither side is even capable of interacting much with the other. In my experience such people range from the utterly bizarre, who have rejected logic for reasons not even they understand, to deep, ferociously intelligent philosophers. For all that the world makes little sense and has seemingly little coherency without a scientific approach, and that self-consistent theories are only possible within the assumptions of science, the Universe is under no obligation to behave as we would demand of it.

3) Summary and Conclusions

It's all tremendously confusing. But there are quite a few take-home points from all this. First, let's sum up the nature of science and its assumptions :
  • The scientific approach and world view rests on key assumptions that the world is objective, measurable, real, logical, and finite. All of these (and perhaps others) are inherently unprovable - if any of them were not true, it would be extremely hard and likely impossible to guarantee that the world behaves in accordance with modern scientific notions. Ultimately, they really are, and can only ever be, assumptions. There is no question of "admitting" they're assumptions, because they simply are so.
  • Within those assumptions, science is a truly formidable edifice. That is not to say it is even remotely completely or perfectly accurate - its very nature demands flexibility. Yet it is capable of remarkable levels of confidence : if it can rarely give a complete or unequivocal answer, still it can give an answer which is sufficient for the basis of actions.
  • Science is capable of disproving itself, at least in principle. It absolutely does not follow that any viewpoint requiring scientific assumptions be suspended automatically disproves science, just that that viewpoint is fundamentally unscientific.
  • While science might never be able to deem that its key assumptions are really true, there are ways in which all of these assumptions can be tested. However this is dependent on the system itself, not the people participating in it. Dogmatic thinking can ensnare anyone, scientists and non-scientists alike, if they confound their unprovable assumptions with facts. 
And then we should break this up for readability, and move on to what we've learned about people both doing science and disagreeing with it. Those conscious of the scientific method and philosophy behind it will be aware (at some level) of the assumptions they're making and tend to admit them; crackpots seldom do. If you can manage to get people to admit what assumptions they're making, and thus shift the debate to the arena of rationality or irrationality as appropriate, you've gone a long way to getting them to start thinking. Which is, and I can't stress this enough, absolutely no guarantee they'll be any good at it. Anyway :
  • Scientists are people too. You cannot expect them to be wholly rational about absolutely everything, nor infinitely patient or available on demand. While some are abject ideologues, convinced that rationality is magically a fact by definition, others are very much normal people just getting on with their job, neither crusading for rationality nor attacking dissenters, ignoring rather than examining or championing the underlying basis of the process. Others, perhaps the majority to different degrees, are philosophical and curious, but even these are not performing seals obligated to abandon cherished assumptions through pure whimsy, any more than an artist should be expected to work "for exposure".
  • Debating scientific issues with doubters ideally requires an understanding of oneself, the other side, and the purpose of the debate itself. Some people are just misinformed about methods and facts, victims of echo chambers. Others are in a more cult-like state of indoctrination : the aggressive activist style of thinking makes them resistant to counter-arguments and even bolstered by them
  • Even the most rational of people do not necessarily agree on everything and may hold strong opposing convictions on certain topics. Someone who is in "activist mode" will be very hard to persuade and the method used highly dependent on the individual. Scientific conclusions cannot be fought with irrational, emotional arguments, and irrational, emotional arguments cannot be countered with cold logic. 
  • ... but if you do have to argue with an activist, don't try and go straight for the ideological jugular. If possible, instead try and undermine the factual or emotional basis of specific conclusions little by little. Argue for uncertainty but present alternatives, preferably ones compatible with existing ideologies. Demonstrate goodwill, don't criticise someone's intellect (even, or especially, if they don't have much of one) or tell them what particular fallacy or bullshit tactic they're using, and remember that changing their superficial conclusions may be much easier than altering their deep-rooted ideological beliefs. Hold your own convictions, don't tell them what to think, and try and lead them to form a new conclusion by themselves. Get them to entertain hypotheticals.
  • If you yourself venture into activist mode at times, never sink into this permanently. Always allow yourself a space in which to coolly and soberly reflect on yourself away from the judgements of others, entertaining alternatives if, for nothing else, than for the sake of fun. Feel free to fail. Improvement is only possible through change.

One of the main criticisms levied against the fundamental assumptions of science is that this seems to undermine the scientific world view. In my opinion, it does the exact opposite. It neither weakens nor cheapens the scientific achievement, but instead strengthens it immeasurably : the fact that its assumptions are disprovable is a tremendous power scarcely found in any other cosmogony; the admission that they are unprovable is a testament to its genuine commitment to truth and a powerful shield against dogmatic thinking. It opens new possibilities without abandoning the old, enforcing the strength of its conclusions without necessarily labelling dissent as heretical. And within those assumptions, it restores science to something like, though very much messier than, our schoolbook picture of a process of testing, falsification and proof. Absolute right and wrong becoming comfortingly achievable again, albeit rare, whilst not denying shades of grey nor, paradoxically, insisting on unquestionable doctrine. It really is the best of both worlds.

There is little sense in battling those who truly deny science by using scientific methods, any more than one would expect scientists to be coerced by irrational drivel; rather, they should be persuaded that its benefits do not exclude the virtues of more intangible perspectives. Argue factual and rational disputes primarily using scientific methods, and emphasise the emotional and moral aspects for debates which are driven by those quandaries. Allow the humanitarian and scientific viewpoints, which are not mutually exclusive nor incompatible, to flourish in their respective arenas, and instead of the forlorn hope of winning an impossible battle when ideological clashes do occur, seek instead compatibility and deny the conflict. The extremists, and the extremely stupid, are virtually beyond salvation, but the clash of the reasonably capable and ideologically less motivated (a conflict weaker in dispute but more numerically significant), might just be largely averted.

Finally, this acknowledgement of these assumptions - leaps of faith for some, entertaining notions for others - offers the prospect of a world which is richer, more wonderful, and more terrifying than found in any dreary textbook, religious text or cultist lunacy. It is partly through this admission that the scientific process ceases to become another means of control, yet another belief system using knowledge and belief to oppress rather than enrich, and transcends to a philosophical, genuinely curious search for the truth. That is the power of questioning the most basic assumptions of all, opening possibilities beyond intellect or fanaticism. No other human endeavour is so liberating, so unifying, as this unlimited, astonishing exploration of the reality of ourselves.