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, www.rhysy.net



Sunday, 11 November 2018

Now Entering A Seminar-Free Zone

It never rains but it pours ? I seem to have a year's worth of talks compressed into a three-week period, which makes my head hurt.

Last time I went briefly gallivanting around the mean streets of Strasbourg. Exactly one week later I had to repeat the seminar in Ondřejov, because the theoretical physics institute have an annual field trip there. Ondřejov is a small village about half an hour's drive outside of Prague and is home to a pizzeria and the bigger half of the Astronomical Institute but nothing much else. This, as you might guess, is due to the same reason astronomers have a backwards way of measuring brightness and a spectral classification scheme that goes OBAFGKMRN : history.

Ondřejov  (last year) in winter is a bleak place.

A hundred years ago, if you were a Czech looking to set up an observatory, Ondřejov looked like a decent spot. Prague was still small and distant enough to limit light pollution, but close enough to have access to the infrastructure of a large city. You didn't need the kind of massive facilities of today to do valuable science, much less have to set up your telescope at the top of a Chilean mountain to minimise atmospheric effects. So if you were a rich Czech noble (who'd made a fortune making optical instruments to measure the alcoholic content of beer) with a penchant for astronomy, it wasn't a bad place at all. And as it happened that's exactly what Jan Frič was, so he built a small observatory there.


This turned out to be an astute move and the institute grew over the years, eventually transitioning from the old mode of gentleman science into administration by the Czech Academy of Sciences. And since the political forces of history are just as inviolable as the laws of physics, in 1967 the observatory gained a 2m telescope - at the time, the 7th largest optical telescope in the world.


A 2m telescope is not terribly impressive by today's standards, but it's not to be sniffed at either. You can still do perfectly good research with such an instrument. Still, nobody in their right mind would put such an expensive piece of kit somewhere that only gets 60 clear nights a clear. Astronomy, let's face it, is generally something you put money in and astronomy comes out, but 60 nights a year means your money isn't going to get you much scientific bang for your Czech buck*. But history has declared that's what we've got, and arguing against history is largely hopeless. Fortunately, the telescope is facing renewed efforts to maximise the possible scientific returns thanks to the still-youthful field of exoplanets.

* The Sloan Digital Sky Survey is one of the most important surveys of modern times, and that only has a 2m telescope as well, but it's in a much better location with more modern equipment.

Anyway, Ondřejov is a nice place and I figured it would be worth repeating the Strasbourg seminar to a brand new audience and get double the use out of the not-inconsiderable preparation time. Adapting it was more work than I thought : it had to be five minutes shorter, but then I realised there would be undergraduates present as well as academics, so I had to make it simpler too. Which meant a lot more of me giving preliminary practise seminars to empty rooms to get the timing right.

Before the afternoon seminars kicked off, we had a tour of the historic part of the observatory - from the director, no less. Which was very nice, especially because a) I'd never been in any of the old buildings before and b) practically nothing is in English. I still don't know what everything is, but mechanical computers and other instruments from a bygone era are always fun to look at. Here's a bunch of pictures with close-ups of the description panels for enthusiasts.


An early Occulus Rift, which wasn't even in colour.

I want one. Dunno what I'd do with it, but who cares ? I'd look cool doing it.



We should revert to this style because it was the best one, dammit.


Again I've got no clue what this is but it looks nice.

This one I do know : it's a Frič polarimeter, used for measuring the alcohol content of beer. The Czechs still express alcohol content as a polarisation rather than a percentage.
Then there was a seminar by someone else, which was very good, and then there was mine, about which I make no claims. It's always fun to get a large audience to wear 3D glasses and the physical data cube is always a hit. Which is good, because seminar preparation is pretty draining for me. Two in a week would have been a healthy limit really.


By this point I was pretty tired, but prepared to sit through another talk or two. I'd aimed mine specifically at people who might not be observational astronomers by training, as had the first guy, but the others... hadn't. First there was one on relativity, which was very clearly targeted at a highly specialised audience. Which to be fair constituted most of the group but I understood practically none of it. It didn't help that the speaker seemed to be monumentally unenthusiastic, a widespread phenomena that I simply don't understand.

Then there was a break, followed by more talks. I don't even remember what the next one was about at all. Then another talk started, something about molecular physics which looked much more interesting but I was already bored half to death. Mercifully I managed to escape with some other people who were being evacuated back to Prague.

On the train, the relativity dude turned out to be a normal person who just seemed completely exhausted. Fair enough. Our other companion, however, was one of those people you meet in science - someone who's clearly a space alien. In this case he mostly sat in brooding silence, but would occasionally and without any provocation or context start blurting out his hobbies for no reason whatsoever. First we got to hear about rollerblading, which you can at least make some pathetic small talk about, "I suppose it's good exercise"; "not much fun in winter"; that kind of abysmally boring "conversation" that does nothing except expend time and further the progress of the Heat Death of the Universe.

His second unprovoked meanderings were about his efforts to write a novel. Something about a physics lecturer who meets a piano teacher who teaches him the true meaning of Christmas, or to see beyond the equations and how to become socially acceptable. Some pointless nonsense like that. I forget exactly, because it was such a "the hell am I listening to ?" moment that my brain was fighting to decide if that was really what he was saying, whether I might be missing something essential, or if it was just too dang tired and would prefer to just shut down down now if that's not too much trouble.


A fair chunk of the weekend was spent preparing the third talk, a much shorter one at the IT4I supercomputing centre in Ostrava. This one had to be prepared largely from scratch, since it was aimed at an almost entirely non-astronomy audience. It consisted largely of infographics from my last science post, which I think was a good idea. This mini-conference was a one-day event aimed at bringing together users of the powerful computing facilities at Ostrava. This mostly seems to be researchers of the very small : quantum physics and genetics, that sort of thing. So keeping things ultra-basic and simplified is the only realistic way to explain what we did with the ~400,000 core hours in 12 minutes or less.

(The other talks were a mixed bag. Some were good, some were awful, one was clearly intended to be 45 minutes long but the session chair said nope. There was a lot of terminology I didn't understand and some I suspect to be typos : antiferromagnetic, radio zebras, health breast phantoms. Regular physics is weird.)

Preparing the presentation didn't take all that much time, and the nice thing about 12 minute talks is they don't take long to practise. But because the conference was one full day, and Ostrava is 3 hours away from Prague by train, we went there the evening beforehand and left the following morning. The hotel was none too glamorous either.


As for the interior, it looked nothing so much like a badly-converted hospital or dormitory.


The shower refused to point anywhere except at the wall and there were too many noisy students outside to keep the windows open. But it was functional, clean, and I survived.

All this tiring travel and repeated presentation preparation came with a perk : a tour of the supercomputing facilities. These are a very far cry from the mechanical museum pieces at Ondřejov with their punch cards : it still ranks respectably high in terms of modern global performance capabilities and is well-maintained and continuously upgraded. The tour (again by the director !) was excellent. We started with a look at the machines from inside a showroom :


It looks very science-fictiony : kept in darkness behind glass, with enough LEDs to cover a street's worth of Christmas trees.


We spent quite a while looking at it like this, with the director turning on spotlights to highlight specific parts of the machines. Eventually he admitted that these are only for show and turned the lights on properly.


The computer produces so much waste heat that they don't need a dedicated heating facility to keep the staff warm : they just use the water-cooling system that stops the processors from melting. When there's downtime - and as far as I can tell the director was being sincere - they genuinely get cold. The last time they tried to use the more usual radiators they ended up with a minor flooding problem.

The computers also consume a crazy amount of power. To prevent damage or data loss by power interruptions, they have two backup diesel generators. But these take about 30 seconds to start. The gap is filled by a 9 tonne flywheel rotating at 2000 rpm, which, if you've ever seen Robot Wars, you'll know is downright terrifying.

We didn't get to see the generators, but we need see the cooling systems. Unlike astronomical facilities, these are a testament to neatness and good order. Think Half Life 2 if everyone was insanely tidy.



The computer itself is behind glass for a very good reason - the air is hypoxic, with an oxygen content of just 15% compared to the normal 21%. This, apparently, is the sweet spot that makes it difficult for fire to spread but is still enough to work normally. At 13%, on the other hand, you'd pass out. It's roughly equivalent to being at the top of a 2,700m mountain : you notice it, but it's not awful.


You can't help but admire the neatness of the whole thing.

And so then we went back to Prague, leaving the hospotel at a bracing 6:30am.


Could I relax ? Nope, because I had more preparations and only two days to do them in : a public talk at our institute's open day and an escape room. The public talk I simply recycled from a previous one because there simply wasn't time to do anything other than minor modifications and figure out what the hell I was supposed to say. Only the title slide contained any text since that would require additional translation, so I had to re-invent the speech based on the images and movies. It seemed to work though, and 3D movies and props almost always help.


The escape room was a completely new idea that a few of us came up with some months back. Since we're probably going to re-use it, I don't think I should give away too much. It's slightly different from the usual escape room concept where you've got an hour or so to figure out how to escape a locked room (typically themed, with various puzzles to undo locks in a particular sequence). We'd tried one where you have to escape a plane, which was quite fun but the puzzles didn't seem to have much relation to aircraft or the story. We wanted to fix that and make it at least related to astronomy (if not genuinely educational, which would be asking a bit much).

What we eventually came up with was a story of a scientist who's made some major breakthrough but been abducted. The players have the role of his students who come to wait in his office. Instruction by telephone from another scientist tell you that someone's just come to his house and are now heading towards the university. Players get 45 minutes to discover his secret research and email the results (an alien signal) to the outside world before the evil corporation come along to suppress it. The puzzles are astronomy based, including the Hertzsprung-Russel diagram, exoplanet radial velocities and cross-matching galaxy catalogues. And there are also simpler puzzles involving astronomy-themed chocolate. Since this was in Czech, my role was limited to making some of the documents the player's need, including a Pioneer-style plaque identifying where the aliens are from.

I decided the aliens should be like the aliens in Commander Keen but happier.
Which was a lot of fun even to test. The puzzles were more difficult than we anticipated (one test group found an important prop but insisted on putting it back where they found it before using it properly...) but eventually, with enough hints, we got it down to being solvable. The fastest group did it in 30 minutes.

And then I went home and collapsed.


(Normal blog services of extended rants will be resumed shortly)

Sunday, 28 October 2018

Strictly Come Strasbourg Science Seminaring

Hey look, a travel post ! Remember those ? I keep forgetting to write them.

3:30 is not a time that should ever occur in the morning, and if it does, it should only happen because of pub-related shenanigans. Unfortunately, if I wanted an expenses-paid trip to Strasbourg to give a seminar (which I did), I'd have to both avoid the pub and haul my sleep-deprived self out of bed at that ungodly hour onto a plane. Worse for me is that as well as being too paranoid to risk getting the 5am metro to catch a 6:30am flight, I'm so paranoid about missing flights that I barely slept at all. Though sunrise from a plane is always nice, even if you're heavily sleep deprived and irrationally scared of missing flights that someone else has paid for.


Toward the end of the second, mercifully uneventful flight, the little jet descended from the rosy dawn into the grey gloom of Strasbourg.


By Welsh standards, this weather - i.e. not raining - is positively delightful. And it got better later on anyway. From the airport so small you could practically spit from one side to the other, it was a simple ten minute train ride to the city centre station. Which is from the inside an interesting mix of classical and modern architecture, though from the outside is a ghastly monstrosity. It looks a bit like what would happen if you took a graffiti artist, a leading bubble wrap manufacturer, shoved them in a room together and gave them too much money.


Since my seminar wasn't until the next day, I decided to walk to my hotel and see a little of the city before doing anything sciencey. Strasbourg is not quite in the same league as Prague, but comparing any city* to Prague is a bit like comparing landscapes to Switzerland : it's just not fair. By more reasonable standards, Strasbourg is a lovely place with many fine buildings, a nice, compact historic city centre, and very easy to navigate.

* Except Cardiff, obviously.





What I also noticed was that the cyclists put those of Prague to shame. Prague cyclists are all damned aggressive bastards who delight in obnoxiously taunting innocent pedestrians. Yes, all of them. Every. Single. One. They'd probably prefer to mangle themselves and their infernal contraptions in your gizzards than move an inch out of their god-given right of way, preferring to suffer an extended hospital visit than grant a pedestrian the merest moment of admission that they might be at a fault. I, for one, don't like them.

Anyway, Strasbourg cyclists are to be commended. They know that cycle lanes can also be used by pedestrians and aren't always clearly marked. They don't give you any grief if you happen to be in their way. They just quietly and calmly flow around you like a shoal of elegant French fish, and if they have to wait, then so be it. They are truly an inspirational example to us all.

I got to my hotel too early to check in, so I went off to the Observatory instead. This is a grand, historic building, a little complex of old telescopes of various sizes, a planetarium, some gardens with a vegetable patch and even beehives. It's like a little country estate nestled inside the city.



Once you go in through the grand entrance, the first thing you see - the very first thing - is this :


Charming. The sort of thing that would probably be blocked by Facebook's filters, I expect. On the other side is an old wooden telescope, but what the statue's for is anyone's guess. Perhaps it's a sculpture of the unusually hunky astronomer who used to use said telescope. Regardless, it's an impressive building.


My invitation came from Frédéric Marin, friend, colleague, and former housemate. Frédéric's expertise is mainly in X-ray polarimetry of active galactic nuclei. In real terms that means looking at the X-ray emission from the searingly hot gas that orbits supermassive black holes, trying to determine the structure of the gas by other means than resolving it directly because that's fiendishly hard. This relies on relativistic, very high energy physics that's quite different to my own field of nice, sedate hydrogen clouds that don't do anything.

Frédéric also works on Space Nazis studying multi-generational spaceships, looking at how a small population could ensure it was genetically healthy over many centuries. He's found that the smallest number that could reliably ensure everyone didn't die out because of Lannisterism / they had eighteen fingers on each hand or seven malformed penises / inbreeding is about a hundred. More on that in a future post, as we're collaborating on a (submitted) paper about the farming requirements of the Space Nazis colonists.

(I'm exaggerating the eugenic overtones of the necessary breeding program. It turns out the situation wouldn't be all that bad : you would need some breeding restrictions, but actually not that limiting compared to the choices people naturally make anyway)

So we caught up on life, the Universe and everything for a while, discussing the bizarre hiring system for permanent academics in France, possible ALMA observations, that sort of thing. Frédéric is a ridiculously competent, hugely energetic and multi-talented guy who, at 32, is even managing the development of his own satellite. I kid thee not, it's absolutely mental. Then the near-total lack of sleep caught up with me and, fearing that I was about the headbutt the desk as I continuously dozed into mild hallucinations, I went back to my hotel for a very rare mid-afternoon nap. After that I spent considerable time wandering around the nicer bits of Strasbourg, and luckily for me the Sun had come out. Not in the sexual sense though, which was good because that would be really weird.





Of course, no visit to Strasbourg would be complete without seeing its world-famous cathedral with its 143m spire. Fortunately I didn't have to turn back because of snow. Unlike some other churches, it's a genuinely impressive, absolutely monumental mass of gothic stonework. Even after living in hundred-spired Prague, it's well worth a look.





Since time was finite, I decided to spurn the interior and went off to see some more of the city. I think that was a wise choice. Strasbourg struck me as an all-round charming little place, appealing both for tourists and residents.





And so the next day I gave my seminar, which went without a hitch. Normally I practise seminars excessively, repeating them to an empty room at least ten times before daring to speak to an audience, especially one of experts (given that seminars are usually at least 45 minutes long, I'm not sure people always appreciate the time commitment they're requesting when they ask me for a presentation). Fortunately this one was different : I recycled most of it from previous, recent talks, and after only three or four iterations I realised I could say this stuff in my sleep, possibly while gagged and drugged. It was, of course, about the usual stuff, mostly dark galaxy candidates and their alternative explanations.

I was a little wary that the audience might be more hostile than usual. Strasbourg may be a small city but its astronomy group has a lot of prestigious names, and features a lot of outside-the-box thinkers researching modified gravity, planes of satellites, that sort of thing. Regular readers know I'm not exactly keen on those. And the Observatory director is none other than Pierre-Alain Duc, who produced one of the most influential models demonstrating that dark galaxy candidates could be tidal debris.

(I'm not going to try and summarise the science this time, you'll have to consult the links. The rest of this post is mainly for enthusiasts.)

But the lions in this particular lions den turned out to be an affable bunch. There were some questions during the presentation and about 15 minutes of discussion afterwards, all perceptive and relevant. Duc couldn't attend but we had a private discussion for about 30 minutes or so later on. And that was useful too.

One point that keeps being raised about these dark clouds is whether their high spectral line widths could be explained by their actually being several different clouds that are all at the same position but at different distances along our line of sight. I'm confident that this can't be the case. First, there are hardly any such clouds known at all, so the chance of coincidental alignments of multiple clouds is negligible. Second, higher spectral resolution observations don't show any evidence of multiple spectral components. Third, having a series of such clouds along the line of sight but still no connections to nearby galaxies would probably make these things harder to explain, not easier.

So I think I managed to convince people that these things are at least interesting. I'm not at all sure what they actually are, and I played that card very strongly. While I still have some reservations, I lean heavily towards accepting the system that Duc modelled probably is a result of tidal encounters, even if that's not the whole story. But all such clouds ? I very much doubt it. The general view seemed to be that the high-resolution VLA data we've obtained ought to be enough to settle the matter. And my goodness, I'd like to reduce that data but it's a matter of finding time/assistance.

Duc raised a couple of points I wasn't previously aware of. One is that other ultra-diffuse galaxy candidates people have claimed to have hydrogen detections have turned out not to be galaxies at all, but more ragged stellar patches for which the traditional parameters are misleading (like using the mean when you should be using the median, only worse). They are, he says, more likely to be tidal dwarfs than giant galaxies. Though I think the ones we've found, which have enormous amounts of hydrogen with nice clear classical double-horn profiles and continuous stellar discs, are probably much more secure. So I'm confident that a possible connection between very faint galaxies (which we know exist) and optically dark, gas-rich galaxies (for which we have only candidates) is still very plausible. That's extra motivation to publish our observations.

His second point concerns Keenan's Ring. He notes that off-centre rings can indeed be produced by galaxy-galaxy collisions, for example the case of NGC 2992 :
From Duc et al. 2000. Hydrogen contours are overlaid in green on an optical image.
He also notes that the velocity difference from Keenan's Ring and M33 is not so great (~200 km/s or thereabouts). These are good points, and I wasn't aware of the the NGC 2992 system. But could Keean's Ring be something similar ?

I'm skeptical. The ring in NGC 2992 is clearly connected to its parent at two points - no such connection is evident for Keenan's Ring. The NGC 2992 ring is found at identical velocities to its parent galaxy, whereas Keenan's Ring is at completely different velocities with no evidence of any overlap. The colliding galaxy in the NGC 2992 system is obvious, and there's a strong stellar disturbance as well - neither of which is evident for Keenan's Ring. Finally, Wright's Cloud is also close to M33, and it would be a heck of a coincidence if this was unrelated to the Ring - and no such analogue is found in the NGC 2992 system. It's certainly intriguing and that's given me some reading to do, but my immediate feeling is that the differences outweigh the similarities. I don't think we're going to make much progress here without really deep data over a much wider area than we currently have.

In the end, I don't think I managed (or even wanted) to convince anyone that I'd made some shattering discovery or that I had stunning evidence for some alternative theory. But I'd set myself the more modest goal of persuading people that these objects are interesting and worth investigating, and in that I hope I was successful.

There, a post that isn't five hundred pages long and contains a bare minimum of ranting. Don't worry, normal services will be resumed as soon as possible.

Tuesday, 4 September 2018

This Equation Shows You Can't Quantify Everything

Yeah, I used a clickbaity headline. So sue me.

Recently I went on an extensive rant about the fundamental assumptions of science. One of them, I said, was that things have to be measurable. And that's basically true, I think... but there are interesting subtleties. You might well be familiar with the weirdness of the quantum realms, as in the double-slit experiment where "particles" can apparently be in two places at once. What you might be less aware of is that much, much larger things can be just as hard to measure. You really don't need carefully controlled laboratory conditions to see how bizarre reality can get.


Measuring some things is hard...

In astronomy, if you're hunting for galaxies in a new data set, you have to try and estimate these things called completeness and reliability. They're quite simple concepts but they have very strict meanings - thankfully, for once, quite intuitive ones. Consider a naturalist trying to identify some meerkats at a great distance :


There are ten animals here - nine meerkats and one mere cat. Now the naturalist could, if he really wanted, shoot all of them dead or gas them or something, and count them at leisure. In that case there would be no uncertainty at all.

Real naturalists obviously aren't like that. They're more likely to try and count them from a safe distance, say using a small hand-held telescope. Our naturalist won't be able to hold it perfectly steady, it might be a bit blurry, and the animals are probably going to move around a bit - maybe it's getting a bit dark too. His observations therefore have limited sensitivity, resolution, and various sorts of errors. There are all kinds of reasons he might miss or misidentify some of the animals. Maybe he's also very stupid, blind drunk, or simultaneously fornicating with a rhinoceros. Tonnes of reasons.

Hey, I'm not judging.
If the naturalist correctly catalogues the nine actual meerkats, then we say his catalogue is 100% complete : he's found all the animals he was interested in. It doesn't matter if he also thinks the mere cat is a meerkat or if he goes completely mental and decides that some rocks and blades of grass are also meerkats, the completeness will still be 100%.

If, on the other hand, the naturalist is more diligent and demanding, but too much of a perfectionist, he might only identify one meerkat and nothing else. In this case his catalogue will be 100% reliable. The fact he's missed eight other meerkats doesn't diminish the reliability at all, it just means the completeness isn't as good as it could be.

Ideally of course you want a catalogue which is both 100% complete (finding all the meerkats) and 100% reliable (only finding real meerkats). Of course in reality things are never this good. This terminology matters quite a lot... consider this shark-finding drone, which claims to have a 92% reliability. See the problem ? Reliability is independent of completeness, so - in principle - it could be missing thousands upon thousands of sharks !

And that would be bad.
Naturalists at least have the option of going out and catching their subjects, if they really want to. Astronomers don't have that luxury, making it crucial to understand the difference between sensitivity, reliability, and completeness. Sensitivity is about whether it's even possible to detect something at all, e.g. do you have enough light and/or a sufficiently powerful telescope to see the meerkats ? Completeness and reliability, on the other hand, are about whether you actually do detect them. You might have good enough vision and sufficient light, but all sorts of other errors can lead to misidentifications.


...but measuring other things is impossible

It's possible to rigorously quantify sensitivity. Let's switch to astronomy so we can have some hard numbers. In that case, we can quantify very precisely the smallest mass of a galaxy we can ever possibly detect. This is our theoretical sensitivity limit. With the data that we have, we'll never be able to detect galaxies less massive than this - not ever*. But does that mean we will absolutely definitely actually detect things above this limit ?

* As long as we don't reprocess the data in some fancy way. There are various methods for doing this, but they all have associated penalties.

Of course not. It's just like the meerkats : just because you can spot something doesn't mean you actually will. Except there's an added complication here that makes things fundamentally different and more philosophically interesting. We can never know for sure how many galaxies our data sets contain. It's as though we looked at the African savannah and decided that while we couldn't see any, we couldn't quite rule out the possible existence of a gigantic, fifty tonne super-meerkat.

Dammit, internet ! That meerkat is clearly much heavier than fifty tonnes ! Idiots...
One way to illustrate this is through low surface brightness galaxies. Here's an image of low sensitivity of a fairly boring looking galaxy :


My word, that's dull. We could quite easily work out, though, how much light we'd need in any single pixel to be able to detect it. This would be our sensitivity limit : there'd be no way to detect something fainter than the faintest thing we could see in one pixel. This lower limit would be nice and solid. The problem is that this doesn't tell us anything much at all about features more massive than this that we could detect but just wouldn't. And in fact, a much more sensitive survey of the same region found this :


This is an astronomical fifty tonne super meerkat, otherwise known as the galaxy Malin 1. "Low surface brightness" just means that it doesn't emit much light per unit area, like spreading butter on toast so thin you can barely taste it in any bite. Malin 1 is massive, but so spread out it's difficult to see. This is why completeness is, strictly speaking, impossible to measure in astronomy catalogues - and you have to be extremely careful when you speak of sensitivity limits. Sensitivity limits are not at all the same as completeness limits.

To be fair, the way you calculate sensitivity does matter : if you account for the surface brightness sensitivity, then Malin 1 was indeed undetectable in the first image. But that still means you can't give a mass completeness; you can't say, "I've definitely detected all the galaxies more massive than such-and-such", because there could always be something really big but very faint hiding in the noise. And worse, the problem remains that you can never guarantee everything detectable will actually be detected. Let me switch to radio astronomy for this.


Let's do some maths (but nothing difficult, I promise)

That's right : maths. Not math. That would be short for mathematic, and that doesn't make any sense at all.

Anyway, in radio astronomy what you often get is not an image (though of course we can get those too) but a spectrum. This plots brightness at different frequencies. Galaxies emit radio waves at different frequencies depending on how fast they're moving towards or away from us. Individual galaxies have stars and gas all moving at slightly different velocities, so each one is typically detected over some small frequency range. They can look like this, for example :


That would be a nice clear detection, very easy to spot. You can see there's quite a lot of random noise - this is due to a whole bunch of different effects and can never be eliminated completely - but the galaxy itself is obvious. A useful way to measure how detectable a galaxy is is through its signal to noise ratio (S/N). An S/N of 1.0 means the galaxy is only as bright as the typical noise values, so it would be impossible to distinguish from the noise and not detectable. That's what gives us our sensitivity limit.
Examples (fake) of a galaxy at lower and lower S/N levels from left to right.

But what about a completeness limit ? That's harder. A S/N of 2 probably wouldn't be detected either, because the noise level does tend to vary a fair bit. Neither would 3, 4, 5 or even higher values... depending on the frequency range the galaxy emits at. If it's very narrow, then we might need really high values - say 10 or 20 - to stand a good chance of detecting it. The reason is that real data sets are often plagued by very narrow spikes in the noise, due to the natural variation in the noise and artificial sources of interference. In contrast, if the range was a bit wider, it might be quite easy to detect at lower S/N levels.

Here's the equation that we need to understand this :


The numerical constants aren't important. What matters is that the S/N level is governed by distance (d), mass (MHI), and velocity (or frequency) width (W). The parameter σrms is a measure of how noisy the data is, and not important for us.

So let's imagine we have a galaxy at a fixed distance and of a fixed mass, but we're magically able to vary its velocity width. Real galaxies do have different widths because their rotation speed varies, so this example is very much applicable to real observations. This little animation shows what happens as we make the width greater and greater while keeping everything else constant :


We start off with a narrow spike, reach a happy middle where the galaxy is unambiguous, and then we get the galaxy appearing as little more than a bump in the noise. And the mass is the same at every stage. So again, we can't guarantee that we'd detect every galaxy of a certain mass, just because of the variation in galaxy properties. Mass completeness is impossible to measure. Literally impossible - it's not a matter of using different ways to examine the data, because if the galaxy is wide enough then it becomes absolutely indistinguishable from the noise. Objective algorithms and subjective visual inspection are equally hapless here.

Ironically then, this simple equation has led us to immeasurable properties. There are even more - quite a lot more, actually - subtleties to this, but the point has been made. While we can measure reliability by redoing the observations, we can't know if our survey has missed something. So we can't know what the full properties of the real galaxy population are really like. How wide a frequency range can they really span ? How massive can they get ? We can never know for sure.

Which brings me back to my original point. We have an equation - an actual honest-to-God equation, not some namby-pamby wishy-washy handwaving philosophy - showing to us that there are things we can't measure. And I, for one, think that's rather neat.


You've killed science. Please don't do that.

Does this mean I was wrong to say science assumes things are measurable ? Not exactly, but it does need to be phrased more... delicately. We assume physical things are measurable, but not necessarily with perfect accuracy. The Uncertainty Principle already famously puts fundamental limits on things on ridonculosly teeny-weeny scales, but here we have an example of uncertainty on a much, MUCH BIGGER scale. And just as quantum effects tend to reduce us to probabilistic estimates rather than forbidding measurements completely, so it is here, to some extent.

We can't measure the true completeness limit. But we can at least compare the completeness of different search techniques to each other. Remember, we can verify reliability, by doing repeat observations to see if what we find is really there. So by combining all our different search techniques and follow-up measurements, we can at least estimate completeness if not measure it directly, and we can certainly get a handle on which methods are better.

The point is that completeness, while scientifically of undeniable importance, isn't a physical thing. Some properties are innate, others are relational. Take sheep. If we have two sheep charging across the fields at each other, they have both innate and relational properties. The mass of each sheep (or number of atoms if you want to avoid complications like the nature of mass*) is innate. The velocity of each sheep relative to each other is relational, by definition. While every property arguably does have relations to every other, they aren't all intrinsically relational. The number of atoms in each sheep might be related to what it was doing earlier (e.g. pooping), but at any given moment it doesn't depend on the properties of anything else at all. The relative speed of the sheep, on the other hand, is intrinsically a relational property. It can never be expressed except with reference to the other sheep.

* Let's leave the nature of number for now, mmmkay ?



Completeness isn't a physical thing. Is it a relational thing ? Arguably, in some sense. Completeness can be measured as a relational property, by comparing different measurements. But true completeness can never be measured. It's neither physical nor relational : it's conceptual. And conceptual properties, despite being very useful scientifically, can have disturbingly un-scientific aspects...

At least we can quantify completeness, even if we can't know the true numerical value (it's a bit like the difference between countable and uncountable infinities). But consider justice, or guilt, or yellow. Can you quantify them ? Can you put a number of how fair an action is ? Guilt's an especially nice one. If someone was discovered to have aided a criminal, the original criminal's guilt clearly isn't diminished, not even as a fraction of the total guilt, because they obviously wouldn't have diminished responsibility because they had assistance. Guilt isn't like mass or energy, which are conserved - you can't even quantify it at all.

In case you thought I'd gone mad by suggesting colour as an immeasurable quality,
 there are no red pixels in this image.
Are conceptual concepts real ? Clearly yes, but they're non-physical. Which means that reality is more than physicality. And if that seems like a very bold statement on such a profound issue, it probably is. I'll make it anyway for the sake of argument.



What exactly does this mean ?

It depends on how far we can extend this. A pet idea of mine is that notions like these imply that dualism - the old idea that the mind and body are distinct - is true at least in a very limited extent. Descartes had his famous mind-body problem (do read that link), where he couldn't work out how a non-physical mind could apparently control a physical body. Leaving aside the nature of mind and thought, the basic problem seems to be whether the non-physical can ever affect the physical. Maybe :
  • The world is entirely physical, with stuff interacting through direct contact though in ways we clearly don't yet fully understand that gives rise to the mere appearance of non-physicality.
  • The world is partially physical and non-physical. Non-physical properties could either interact somehow with physical ones (e.g. E.M. fields, gravity, ideas of justice, etc.), or simply be non-participating, essentially illusory artifacts, like rainbows. 
  • The world is entirely non-physical : a shard of the mind of God or a high-tech simulation. Causality may or may not be real.
Philosophy has the liberty to explore all of these possibilities and more, whereas science is constrained by the evidence of the time. While the two have undeniably grown apart, and sometimes estranged, I think this is one issue on which they remain inseparable.

Everyday intuition would probably suggest to most of us that the middle one is correct : conceptual properties are real, non-physical, but interact with the world. If we see something that goes against our idea of justice, we may take action to correct it. If our galaxy-finding algorithm performs badly, we may improve it. And we obviously can't act without having observed these problems. So these conceptual properties do have influence... ah. Oh dear.

Stop and think about that for a moment.

These are non-physical, immeasurable things, apparently having a profound effect on reality ! Does this mean there are some things we'll never be able to understand rationally, or simulate ? Is idealism correct after all ? Is the boundary between physical, objective reality and subjective thought more blurred than we might like ?

Which is something I've previously attempted to depict artistically using radio data.
Well, some of those questions are hard to answer. But don't panic ! We need not fear that the woo-woo merchants are about to disembowel science with ritual chanting and whatnot. Even if we grant that non-physical things affect the world, they do so very much indirectly. They affect our mental states, which in turn causes us to take direct physical action. They do not cause galaxies to explode or your cactus to sing or anything stupid like that. And your mental actions don't directly cause any crazy things to happen either. Your dream about the giant wombat with the staple gun poses no threat to society or anything else for that matter. It's a bit like the simple "Change" spells of Terry Pratchett's Discworld, i.e. in Wyrd Sisters the young witch Magrat finds her broom has run out of energy mid-flight :
Some kind of Change spell was probably in order. Magrat concentrated.
Well, that seemed to work. 
Nothing in the sight of mortal man had in fact changed. What Magrat had achieved was a mere adjustment of the mental processes, from a bewildered and slightly frightened woman gliding inexorably toward the inhospitable ground to a clearheaded, optimistic and positive thinking woman who had really got it together, was taking full responsibility for her own life and in general knew where she was coming from although, unfortunately, where she was heading had not changed in any way. But she felt a lot better about it. 
So this doesn't appear to be something that can obliterate the scientific method, or even give it a nasty shock. What it does do is say that the scientific method is potentially limited, that there are some things we can't simulate... at least not mathematically. Which is very interesting, but it doesn't suggest that existing simulations or mathematical analyses are wrong.

Let me reinforce that. That some non-physical states exist, in this interpretation, doesn't mean that every conceivable non-physical state is actually possible, much less actually does exist somehow. You're no more compelled to believe in God or ghosts than you are in a Bose-Einstein condensate lurking in your closet or that you'd find a lump of strange matter in your cheese. Just because something can in principle exist in no way means that it's possible that it does exist*, still less that is actually does. Phew, thank goodness for that !

* E.g. in principle the Moon could be made of cheese, in practise this is impossible.


Some people consider even this limited influence of the non-corporeal to be a step too far. They quite rightly point out that it still doesn't solve the problem of how things of such different natures could interact. Most people, I'd say, are quite happy to let this be, accepting that while they can't explain how the physical and non-physical can interact, they quite clearly do, so nah-nah-nah-nah-nah. A more reductionist perspective finds this unsatisfying. They'd probably point out that E.M. fields and the like can be explained by force-carrying particles, so cases of apparent "spooky action at a distance" can be restored to normality.

Of course, there's more to the notion of action at a distance than E.M. fields. There's wave-particle duality, Many Worlds, pilot waves, and all that quantum craziness, not to mention curved spacetime in general relativity. The reductionist view is essentially that either non-physical things just don't exist - they're a sort of illusion but produced entirely by physical things - or that they do exist but have no influence of any kind, not even mentally. Consciousness, for example, is a process that just observes what physical processes get up to, whilst being completely unimportant by itself.

Here philosophy and science collide head-on, and anyone who thinks they definitely know what the answer is ought to be given a very wide berth indeed. Personally, while admitting that not being able to explain how the physical and non-physical can interact is clearly unsatisfactory, it seems to me at least equally unsatisfactory to suggest the non-physical doesn't really exist. I would even say it's contradicted by not just by advanced contemporary science but also simple relational properties. The reductionist perspective offers no real clue as to where the illusion of non-physical stuff actually comes from. And it seems to me that science does seem to allow things of very different natures to interact - e.g. massless photons can excite electrons, neutrinos mostly don't interact but sometimes do, etc. - even if, again, it can't necessarily explain exactly how.


Conclusions

I don't have any, though I do have preferences.

What seems to be reasonably clear is that some things are unmeasurable and unquantifiable. The consequences of that depend very strongly on the true nature of those quantities.

If, as in my preference, they can affect the world, then this means there's a limit to what we can simulate and describe through mathematical analysis. There would be aspects of the world that no amount of improvements to scientific accuracy would ever allow us to measure, because they're fundamentally unmeasurable. This doesn't imply the reality of any kind of Magical Mystical Woo* : the existence of some unmeasurable things doesn't necessitate the existence of all unmeasurable things. It would just mean that we can't know everything scientifically, no matter how carefully we examine the world.

* Someone should really name their child that. And they should grow up to become a teacher, so that all can benefit from the teachings of Magical Mystical Woo.

Obviously this viewpoint is not without its problems. It wouldn't solve how non-physical and physical things can apparently interact. While we don't necessarily observe the non-physical things, we do conceive them and are thus influenced by them.

The difference is interesting and important. For example if I measure completeness of a survey, or better yet something more mathematically complex that requires extended cognition, I have to write down the number before I can observe it. Doesn't matter how I write the number : I could use ink, bits of pasta, or arrange megalithic stones if I wanted. My brain doesn't care what configuration the number is, it's able to discern the number itself from the infinite different ways it could have been presented. So I'm not observing completeness directly : that's a thing which only arises mentally. It still affects me, but it's very different from, say, a ghost, which would have to interact directly with the observable world to be visible.
Imagining and observing a ghost are clearly different things, despite absurd claims to the contrary.
And this idea wouldn't solve what thoughts are either, or what makes some electrochemcial processes give rise to awareness while others, like those in calculators and possibly in plants, apparently do not. But since this viewpoint holds that some things are unknowable anyway, that ought not to be a major issue... science, so far as I'm aware, anyway isn't yet capable to saying how things of such different natures as photons and atoms can interact. It just describes the ways in which they do.

I also favour the view that our awareness allows us control we wouldn't otherwise have. Extended cognition is a great example : here it seems we actually need to be conscious to make calculations, and we can't act on the results until they are consciously observed. Blindsight is interesting, but this seems more like a flawed consciousness than truly lacking one. Anyway, consciousness isn't exactly a binary state : we may be unconscious while dreaming, but it's hardly as if closing our eyes gives us the mental capacity of a rock. We're still thinking, still perceiving our thoughts. It would seem to me a highly contrived scenario if we could do all this unconsciously but somehow, for whatever reason, just didn't. Much more likely we actually do genuinely need awareness for some things.

That's my view then : not everything is measurable, but I discount Mystical Woo; I believe our mental concepts allow us to interact with the world through our own choices. I don't claim to know how it all works. And this view is somewhat dependent on scientific findings, so I'd have to revise it if suitable scientific models came along.

More reductionist approaches aren't uninteresting, however, but I find them unsatisfactory. I rather like the idea of consciousness as a sort of pure observer that isn't able to influence the world, with everything we think we control being a deception. Yet this seems a strange and completely unnecessary process, and doesn't seem to really do away with the unphysical as it might appear to. It doesn't say anything much about how vast, complex, imaginary concepts arise from atoms bashing about. And anyway pure observation is considered by mainstream science to be impossible.

I'm more intrigued by studies on emergence. Rather than doing away with non-physical things completely, relational, non-physical properties can arise only with sufficient complexity, e.g. two atoms can have relative velocities but enough atoms together can have a sense of social justice and a burning desire for pizza. There are even particularly strange notions wherein complexity is required for emergent behaviour but doesn't directly cause it...

In any case, emergent complexity is intriguing. But it doesn't seem to me to be terribly convincing. I don't think it's going to help with understanding non-physical concepts much at all. Not at their root, at any rate.

So I say the common sense view has it right in this case. Imaginary things are imaginary and exist in a different sense than physical things. They can affect things but only mentally, not directly. It's an open question as to whether, as some have suggested, we might need new physics to explain this. And as for free will, that's a topic for another post.