Ask An Astronomer Anything At All About Astronomy (XLII)

Eclipse preparations are in full swing, which is why this post is completely and utterly out of the regular schedule.

1) Could the asteroid belt be the remains of an old planet ?
No.

2) Could ancient massive stars be the progenitors of supermassive black holes ?
Yes.

3) Nuclear bombs used as propulsion ? Are you serious ?
Of course I'm not. I'm not a bloody rocket scientist.

4) Surely we could make the asteroid planet thing work with a bit of imagination ?
Err, yeah, but it would still be the wrong answer.

5) How can tidal locking depend on the brightness of a star ?
Magic pixies.

Let Plato Entertain You (II)

A little while back I wrote up some lessons from reading the first third or so of Plato. Having now completed the entire 1800 page tome, it's time to report on the next bit. In a future third post I'll look at the Republic and Laws, Plato's attempts to design an ideal society. The other works in the final third, quite honestly, aren't really worth bothering with - they're rather long-winded works of theological cosmology and for the most part they're just boring. Republic and Laws, as we shall see, are both an intriguing mixture of wisdom and madness.

It's unfortunate that the Republic is such a popular work. I first read it many years ago as a stand-alone work, but reading it in context is quite a different experience. This post is (partially) an attempt to explain why, without the need for the reader to read the entire thing themselves... though it would be better if you did. If Plato's ideal societies are deeply flawed, then I still contend that the first thousand pages of Plato's works are a monumental achievement. A brief Google search reveals that modern philosophers agree with only about 5% of his work today, but honestly, anyone who thinks that's either meaningful or important wouldn't understand philosophy if it successfully argued that them into a state of continuously questioning their own assumptions.

Here, then, in no particular order, are what I found most interesting in the first, best section of Plato.


Tautological Analysis

This is my term for a common tactic of the Socratic dialogues (I mentioned it last time but it deserves a fuller treatment). The most common manifestation is that Plato's Socrates will ask someone to define a term - justice, courage, virtue, that sort of thing - and they will respond by giving an example-:

SOCRATES : He's asking you not what a fine thing is, but what is the fine.
HIPPIAS : My friend, I understand. I will indeed tell him what the fine is, and never will I be refuted. Listen, Socrates, to tell the truth, a fine girl is a fine thing.
SOCRATES: That’s fine, Hippias; by Dog you have a glorious answer. 

Socrates is of course being very sarcastic in his response, something which happens a lot. He wants to know what fineness itself is, not an example of things which are fine. A fine girl is indeed a fine thing, but she's not fineness itself. Not even if she's Sarah Michelle Gellar.

But nearly. Maybe Scarlet Johannson... ?

That's a facetious example, and there's often a large element of sarcasm and mockery in Plato. Other works are deadly serious, and highlight how deep our assumptions can run. Is justice a good thing ? What about freedom and democracy ? Often they're thoughtlessly chanted as being the defining, crowning achievements about modern civilisation... but they are not goodness itself. Which forces the question as to what the nature of their goodness is, in what circumstances it applies and if there are any situations in which they're actually bad things. But that's for next time.

Plato is famous for this theory of forms : that there are perfect "forms" of ideals like justice, goodness, mercy, beauty and so on, in which individual things can partake. So Mrs Gellar isn't the Platonic form of beauty*, she just shares some aspect of the beautiful. The law courts aren't the ideal of justice, they just have something in common with it.

* With wonderful irony, Plato does go on about the importance of physical beauty quite a lot, while cheerfully acknowledging that Socrates, his hero, was considered to be extremely ugly.

Platonic forms can't exist in the real world. They are, I think, a useful linguistic theory and a way of understanding thought processes, but I wouldn't get caught up in more theological approaches where they actually exist in some higher plane or whatnot. Even though Plato himself tended towards a strongly mystical view of cosmology, which I reject, the theory of forms is extremely useful. Are good things always beneficial ? Must that benefit be immediate or should you integrate over some time ? What if it benefits one person but harms many ? Is pain always bad or is it just unpleasant ? Are bad things always unpleasant ? They can seem like simple, silly questions, but as Plato examines, they are revealed to be anything but. Plato hints at utilitarianism, at one stage (in Protagoras) even praising the importance of mathematics in order to behave ethically :

How else does pleasure outweigh pain, except in relative excess or deficiency ? Isn’t it a matter (to use other terms) of larger and smaller, more or fewer, greater or lesser degree-? And if you weigh pleasant things against painful, and the painful is exceeded by the pleasant — whether the near by the remote or the remote by the near — you have to perform that action in which the pleasant prevails; on the other hand, if the pleasant is exceeded by the painful, you have to refrain from doing that. Since it has turned out that our salvation in life depends on the right choice of pleasures and pains, be they more or fewer, greater or lesser, farther or nearer, doesn’t our salvation seem, first of all, to be measurement, which is the study of relative excess and deficiency and equality ?

How much Plato really believed this is unclear. He often does advocate maximising goodness, especially for the whole population rather than the individual, but he rarely dwells on the prospect of being able to quantify moral actions. And in other dialogues, he's very much against the idea that "goodness" and "pleasure" are the same thing. If you're the sort of person who thinks that terminology problems are straightforward, a few dozen pages of Plato will soon cure you of that.

What I like about this approach is that at his best - which is very frequent - Plato offers a tremendous, somewhat perverse, clarity of thought. Having knowledge means that you know things, right ? And there's no way you can know things you don't know ? OK, then... what does it mean to know things ? Clarity of thought does not mean clarity of conclusions, but this approach of questioning the very basic assumptions forces acknowledgement of one's own ignorance. Which is no bad thing at all.


Conclusions are for losers

Many of Plato's works have no firm conclusion - or they do, but other works reach the exact opposite conclusion. This more than anything else should be borne in mind while reading anything of Plato : for every dialogue, there is an equal and opposite dialogue. In Phaedrus, he goes on for many, many ironic pages that one shouldn't put too much trust in the written word :

And now, since you are the father of writing, your affection for it has made you describe its effects as the opposite of what they really are. In fact, it will introduce forgetfulness into the soul of those who learn it: they will not practice using their memory because they will put their trust in writing, which is external and depends on signs that belong to others, instead of trying to remember from the inside, completely on their own. You have not discovered a potion for remembering, but for reminding; you provide your students with the appearance of wisdom, not with its reality. Your invention will enable them to hear many things without being properly taught, and they will imagine that they have come to know much while for the most part they will know nothing. And they will be difficult to get along with, since they will merely appear to be wise instead of really being so.

Or in other words... Don't. Take. Plato. Literally.

In one of his letters - the editor's notes say we're not sure if any of these are genuine, so bear that in mind - he elaborates further :

On this account no sensible man will venture to express his deepest thoughts in words, especially in a form which is unchangeable, as is true of written outlines... Only when all of these things — names, definitions, and visual and other perceptions — have been rubbed against one another and tested, pupil and teacher asking and answering questions in good will and without envy — only then, when reason and knowledge are at the very extremity of human effort, can they illuminate the nature of any object.

Ironically for a man who wrote so much down, he seems quite sincere when he says that you can't learn everything from books. Yet this is absolutely consistent with his other works, which often reach no conclusion or contradict one another. There are no absolute conclusions beyond all reproach, revision is always possible - and usually stated so : "here is what anyone who disagrees with us will have to show in order to refute our conclusion". Take no text as an authority, question everything. Only through repeated questioning and discussion with others is there any hope of glimpsing "the" truth, if there even is such a thing. It's a echo of one of the most powerful sections of the Apology :

On the other hand, if I say that it is the greatest good for a man to discuss virtue every day and those other things about which you hear me conversing and testing myself and others, for the unexamined life is not worth living, you will believe me even less. What I say is true, gentlemen, but it is not easy to convince you.

Without bearing this in mind, large parts of Plato can seem monstrous. Indeed, even remembering this some sections seem today to be irredeemable, as we shall see.

Plato's world view was undoubtedly complex, both morally, theologically, and rationally. At times it seems like he thought everything was relative, at other times he's a staunch material rationalist (almost an atheist), at others devout (though never the equivalent of a Creationist - he certainly didn't believe that a big beardy Zeus hurled thunderbolts from atop Mount Olympus). Despite his relativist leanings he still seemed to be searching for an objective ethical theory, even if such a theory couldn't be absolute. His theory of forms had led him to the idea that he could never express his deepest thoughts correctly because language is fundamentally limited and flawed : a name is not the same as the thing itself. So as for what he really meant, we'll simply never know.


Rhetoric is the same as pastry baking

He literally says this. Or more accurately, and with that characteristic ironic streak, he says that oratory is the same as pastry baking. So written text can't convey literal truth, and the spoken word is as useful as a pastry. What's a philosopher to do ? Well in Gorgias, with typical wit and verve he goes off on one about pastry baking :

SOCRATES : Ask me now what craft I think pastry baking is.
POLUS : All right, I will. What craft is pastry baking?
SOCRATES : It isn’t one at all, Polus. Now say, “What is it then?"
POLUS : All right.
SOCRATES : It’s a knack. Say, “A knack for what?"
POLUS : All right.
SOCRATES : For producing gratification and pleasure, Polus.
POLUS : So oratory is the same thing as pastry baking ?
SOCRATES : Oh no, not at all, although it is a part of the same practice... I call it flattery, basically.

In fact in context "oratory" really means "rhetoric" - the art of persuasion, though specifically in this case by using appeals to emotion through the spoken word. "Pastry baking" means flattery, in the sense that sweet pastries may taste nice, but they aren't good for you. You might enjoy them for a while, but you can't live off them forever. The art of persuasion is important, but it must be accompanied by a search for the truth. Those who seek to persuade without an understanding of the truth - who just want whatever whimsical fancy comes to mind without caring if it's good for them in the long term - will soon come to ruin. In essence, ignoring the truth and caring only for your base desires is a terribly bad idea.

A more modern way to phrase it is the question, "Do you want to be right or do you want to win ?". For Plato - as it should be for anyone - the only sensible answer is both.

Obvious ? Not really - at least not to politicians of the time, and certainly not to politicians of today. Politics seems utterly consumed with one side being right and the other wrong, and barely pays any attention to the objective evidence at all. The other side must be attacked, whether that's because they're argument is flawed or because their character makes them untrustworthy... whatever. It's not about discovering the best course of action, just about winning. No wonder the world is in such a mess.

One might perhaps conclude that therefore "post truth" and "fake news" are nothing new. And they're not. It doesn't mean that they're excusable, however, or that the current state of affairs isn't worse than it was in the relatively recent past.


Crime never pays

The importance of respecting objective truth ties in with another crucial idea of Plato's : that it's better to suffer an injustice than commit one. I don't mean that it's morally superior - everyone would agree to that trivially - but that it is literally better in every material and spiritual sense to suffer an injustice than inflict one on other people. In Gorgias, Socrates argues that even suffering the physical punishments the law demands (so long as they are truly just) after conviction of a crime is a benefit to be enjoyed by the criminal. The problem is, of course, that for this to work the criminal must understand the punishment. If he does not, then he won't gain anything.

Yes, my good man, I take it that these people have managed to accomplish pretty much the same thing as a person who has contracted very serious illnesses, but, by avoiding treatment manages to avoid paying what’s due to the doctors for his bodily faults, fearing, as would a child, cauterization or surgery because they’re painful... For on the basis of what we’re now agreed on, it looks as though those who avoid paying what is due also do the same sort of thing, Polus. They focus on its painfulness, but are blind to its benefit and are ignorant of how much more miserable it is to live with an unhealthy soul than with an unhealthy body, a soul that’s rotten with injustice and impiety.

Gorgias is a particularly brilliant and lively work. While Socrates often acknowledges that most people disagree with him, what he doesn't seem to appreciate is how many tyrants brought to justice also disagree with him. He argues very convincingly that pleasure is not the same as moral good (of course), but he seems hell-bent that no-one would willingly choose to commit an injustice. And perhaps they don't; perhaps they are truly ignorant of what they're doing, but this is never really convincingly explained. There are just too many examples (then and now) of people who do seem to know that what they're doing is wrong*. But in Plato's view this sort of thing is an abnormality, a sickness of the soul for which there is only one cure :

* His argument would be strengthened considerably if he focused more on the aspect of ignorance required to commit an injustice, the everyday lesser injustices rather than the extreme evils of tyrants and despots, and the extent to which injustice results in the physical, material suffering of the wrongdoer (rather than the corruption of their soul).

For a corrupt person it’s better not to be alive, for he necessarily lives badly.

He means that literally, both for the corrupt person and those around him. Sometimes this takes the remarkably crude theological perspective that evil-doers will be punished in the afterlife. Occasionally it almost takes the from of the "everything happens for a reason" crap that's popular on dumb internet memes. Socrates himself says in the Apology :

I assure you that if I am what I claim to be, and you put me to death, you will harm yourselves more than me. Neither Meletus nor Anytus can do me any harm at all; they would not have the power, because I do not believe that the law of God permits a better man to be harmed by a worse. No doubt my accuser might put me to death or have me banished or deprived of civic rights, but even if he thinks — as he probably does, and others too, I dare say — that these are great calamities, I do not think so. I believe that it is far worse to do what he is doing now, trying to put an innocent man to death.

Socrates had it that if he himself was innocent, then death could not be a disaster. But not just from the religious perspective of being rewarded in the afterlife : Socrates considered the other option, that death is an annihilation :

Death is one of two things. Either it is annihilation, and the dead have no consciousness of anything, or, as we are told, it is really a change — a migration of the soul from this place to another. Now if there is no consciousness but only a dreamless sleep, death must be a marvellous gain. I suppose that if anyone were told to pick out the night on which he slept so soundly as not even to dream, and then to compare it with all the other nights and days of his life, and then were told to say, after due consideration, how many better and happier days and nights than this he had spent in the course of his life — well, I think that the Great King himself, to say nothing of any private person, would find these days and nights easy to count in comparison with the rest.

For Socrates and Plato alike, there is no prospect of an unhappy death for a good man - without any need for the crude notion of being compensated in heaven. Yet Plato (arguably) disagreed that lesser men cannot harm their betters. In a moving passage in Gorgias, Plato has Socrates recount how other great Athenian statesmen had been put to death and so could not have been the skilled leaders and teachers of men that they claimed to be. The reader then realises that Socrates too claimed to be improving those around him yet he suffered the same fate. Plato then has him say, in apparent contradiction to his own words in the--Apology :

If I do come into court involved in one of those perils which you mention, the man who brings me in will be a wicked man — for no good man would bring in a man who is not a wrongdoer — and it wouldn’t be at all strange if I were to be put to death... I’ll be judged the way a doctor would be judged by a jury of children if a pastry chef were to bring accusations against him.

Or is this a contradiction ? Not necessarily, if you accept that "death" and "harm" are not the same thing. Still, it's hardly the "everything happens for a reason" or "there's a Big Plan" rubbish that fills stupid internet memes. It's simply that the accuser would be evil and would accomplish his goal, whereas the noble philosopher is not able to persuade people that he acts in their best interests. Socrates will die, even though he doesn't particularly want to. So a good man can be harmed by a worse... it was hardly the most just outcome possible. On the other hand, Socrates seems to have genuinely believed that by his death the city would be harmed even more than he would. There wasn't any kind of plan or reason at work, but there was an underlying justice. Killing Socrates stopped his advice, which he thought a far worse thing done to his accusers that his own misfortune by merely being executed. If nothing else, it was a remarkable theory to actually put into practise.

Education, Education, Education

Whenever he addresses the topic directly, Plato arrives at different conclusions as to whether virtue can be taught - that is, whether education can improve people. It can make them more knowledgeable of course, but can it make them wiser ? Or does wisdom - knowing how to use that knowledge to achieve the greatest good - come from nature rather than nurture ? Plato never really had an answer.

... at least, he didn't during his direct examinations. Yet the constant implication of his whole corpus is that it can be taught, that by reading and studying his works the reader might become wiser. "A life without self-examination is not worth living" were perhaps truly the words of Socrates himself, but Plato's relentless questioning, considering different perspectives (including ones he clearly disagreed with), his different and contradictory conclusions, his understanding of the importance of rhetoric... these are all hardly the actions of a man who thinks that education doesn't matter. If self-examination is so critical to life, then it follows that everyone should do it.

Many of his dialogues feel like genuine accounts of real exchanges. Even if they weren't, the protagonists often behave so much like real people, it's clear they must have been inspired by actual discussions even if they're not verbatim reproductions. Protagonists get angry and upset, they threaten to leave or even violence. And sometimes - just sometimes - they change their minds. People can be persuaded by the appropriate arguments. Which I think makes the conclusion inescapable : education matters. It can make people better. Though it's worth mentioning that often the participants feel trapped by the logic of an argument but not really persuaded by it.

Quotes (very lightly edited) are from Euthydemus and Gorgias.

An alternative interpretation is possible. In Meno, Plato describes the possibility that learning is actually recollection. The knowledge already exists inside us - or at least the tools to understand it do - so discussion and examination are methods to find out who's best at what, rather than improving people. This would fit with his statements in other dialogues that we should act according to our natures. Education would then still be extremely important, but for the purpose of discovery rather than change. It would be a sort of hunt to find the best young people, and then lock them away to prevent their corruption... though it wouldn't fit with his repeated statements that justice is necessary as a sort of teaching tool in itself, that mends the corruption of the soul.

Perhaps the most direct clues to Plato's beliefs come from his statements about ignorance, a topic about which he had much (probably worth its own post eventually) to say - nearly all of it well worth scrutiny. Ignorance, for Plato, is a vice that actually makes people worse. Knowledge and wisdom are virtues, but they must be properly taught. Upstart youngsters who learn the methods of debate before they're ready like to employ them as a game :

And isn’t it one lasting precaution not to let them taste arguments while they’re young? I don’t suppose that it has escaped your notice that, when young people get their first taste of arguments, they misuse it by treating it as a kind of game of contradiction. They imitate those who’ve refuted them by refuting others themselves, and, like puppies, they enjoy dragging and tearing those around them with their arguments. Then, when they’ve refuted many and been refuted by them in turn, they forcefully and quickly fall into disbelieving what they believed before. And, as a result, they themselves and the whole of philosophy are discredited in the eyes of others. But an older person won’t want to take part in such madness. He’ll imitate someone who is willing to engage in discussion in order to look for the truth, rather than someone who plays at contradiction for sport.

Teaching methods are deemed to be supremely important in his world-building exercises, but in the present context, strictly speaking, he doesn't commit to saying that virtue can be taught. But he's tremendously keen to encourage the practise of philosophy, and thus far there's no hint that any particular group of people would be better at it than any others. In fact there's very little hint of any kind of class system in Plato at all, certainly nothing anyone is born in to. Excessive wealth (which of course would be for the upper echelons of society) is seen far more as a dangerous vice than something to aspire to. Instead of the boring question, "will earning more money make me happier ?", Plato focused on the much more interesting, "can I make myself a better person through learning-?"

Further evidence can possibly be found in Hippias, but we must be careful. Hippias is a an arrogant sophist who boasts of his own money-making skills as evidence for his cleverness. It's with withering irony that Socrates tells him, "The mark of being wise, I see, is when someone makes the most money."*. Yet he also declares that "early craftsmen are worthless compared to modern ones", and, for example, "Daedalus also, according to the sculptors, would be laughable if he turned up now doing things like the ones that made him famous". It's much harder to tell if he was being ironic here. Elsewhere he has nothing but praise for the ancient poets, but sculptors and craftsmen haven't had much of a look in.

* This is coming from someone who shouts loudly and often about wealth not being goodness and poverty not being a mark of stupidity; irony is the only sensible interpretation here.

Well I wouldn't call it a masterpiece anyway.

The argument I find most convincing is one in Protagoras, using a method of Plato's I described last time : consider the opposite case. Specifically, Protagoras argues that OK, perhaps the son of a great flute-player won't necessarily become a great flute player himself even though he has such a wonderful teacher as his father... but he'll become a damn sight better than if he had no teacher at all. Protagoras argues that it's the same with virtue. Education is necessary for people to reach their innate limits, even if it's not necessarily so powerful as to be able to alter those innate limits. You still need education for people to reach their full potential. If you don't teach people how to behave, then left to their own devices they become - in gloriously politically incorrect terms - "savages such as the playwright Pherecrates brought on stage at last year’s Lenaean festival".

A closely related, reoccurring theme is that morality is objective. It's not necessarily absolute by any means : the moral status of any action can depend on context. But if you have the full facts of a situation, you can always assess what's right and wrong. In the Symposium, Plato has Pausanias say :

The reason for this applies in the same way to every type of action : considered in itself, no action is either good or bad, honourable or shameful. Now, in itself none of these is better than any other: how it comes out depends entirely on how it is performed If it is done honourably and properly, it turns out to be honourable; if it is done improperly, it is disgraceful.

You have to be taught how to do things correctly otherwise you'll end up as one of Pherecrates' "savages". But who is to teach you ?


Expert knowledge matters

This is an almost ubiquitous theme in Plato. Virtually every dialogue seems to contain at least one reference to shipbuilders, flute players, carpenters and the like. You don't hire a bricklayer to prescribe medicine. You don't get a philosopher to conduct a choir. You don't hire a shipbuilder to write rhetorical speeches. Unless they're about ships, presumably.

One would think that this would be obvious, but it wasn't at the time and to vast numbers of morons on the internet, it still isn't today. Plato went to extraordinary lengths to refute the then-popular notion of Protagoras that, "man is the measure of all things" : that opinions are the only thing that exist and are true for the individual. This is taken to comical extremes in Euthydemus, in which a couple of sophists declare that everyone knows everything about everything :

But perhaps, Euthydemus, said Ctesippus, you are not uniting flax with flax, as the proverb has it. Because you are making an alarming statement if you say your father is the father of all.
But he is, he replied.
Just of men, said Ctesippus, or of horses and all the other animals ?
All of them, he said.
And is your mother their mother ?
Yes, she is.
And is your mother the mother of sea urchins ?
Yes, and so is yours, he said.
So you are the brother of gudgeons and puppies and piglets.
Yes, and so are you, he said.
And your father turns out to be a boar and a dog.
And so does yours, he said.

Dammit, philosophy !

There's a much more serious discussion in Theaeteus, but even here Plato cannot resist a snarky quip or two. The discussion revolves around whether knowledge is the same as perception and if opinion is the only form of knowledge. Socrates refutes this :

I was astonished that he did not state at the beginning of the Truth that ‘Pig is the measure of all things’ or ‘Baboon’ or some yet more out-of-the-way creature with the power of perception. That would have made a most imposing and disdainful opening. It would have made it clear to us at once that, while we were standing astounded at his wisdom as though he were a god, he was in reality no better authority than a tadpole —let alone any other man.

Here he's taken the idea of expert knowledge and perverted it. If all creatures are the judges of what's true, then human intelligence is equal to that of a god or a baboon. Yet how can Socrates be a better judge of his own health than a doctor ? Plato has Protogoras get very grumpy :

You keep talking about pigs and baboons; you show the mentality of a pig yourself, in the way you deal with my writings, and you persuade your audience to follow your example. That is not the way to behave... I certainly do not deny the existence of both wisdom and wise men: far from it... Now what we have to do is not to make one of these two [men] wiser than the other — that is not even a possibility — nor is it our business to make accusations, calling the sick man ignorant for judging as he does, and the healthy man wise, because he judges differently. What we have to do is to make a change from the one to the other, because the other state is better. 

Protagoras denies the existence of objective truth, but not that some things are better than other things. Therefore some men are better judges than other men, and gods are better judges than baboons (fortunately the ancient Greeks didn't have any monkey gods...), though how one determines who's better without an absolute, objective standard for comparison isn't clear. Plato plays both views off against the other with equal credibility, never trying to make one seem more ridiculous than the other. For a man who vehemently insisted not to take him literally, it's hard not to take him sincerely.

Yet ultimately, reading between the lines, one gets the impression that Plato hated the idea of knowledge as opinion (and especially that false judgement is impossible), but he respected it. There are strong hints in these oft-repeated comparisons to shipbuilders and musicians that he made the now-standard scientific assumption that the external world is real, objective, and measurable (although he toys with the idea that dreams represent another reality in Theaeteus, elsewhere it's pretty clear he thinks they're mere illusions). He holds that you can judge the skill of a shipwright by the quality of the ships that they built - you can judge them on their reputation or examine their ships for yourself. If there is a single key to science, it's this evidenced-based, provisional, objective judgement.

... except, perhaps, where it comes to justice. In Protagoras :

And so it is, Socrates, that when the Athenians (and others as well) are debating architectural excellence, or the virtue proper to any other professional speciality, they think that only a few individuals have the right to advise them, and they do not accept advice from anyone outside these select few. But when the debate involves political excellence, which must proceed entirely from justice and temperance, they accept advice from anyone, and with good reason, for they think that this particular virtue, political or civic virtue, is shared by all.

This is one of those dialogues in which Plato attempts to directly tackle whether virtue can be taught. But whether knowledge in general can be taught (even, as we've seen, critical thinking skills), whether you can objectively examine the world and test it, doesn't seem to be open to much doubt (Theaeteus aside). In Alcibiades, Socrates discusses with the Athenian general what it is he wants to talk about in the Assembly (here edited to remove Alcibiades one-word affirmative answers) :

Then what will they be discussing ? I presume it won’t be building, because a builder would give better advice on these matters than you. Nor will they be discussing divination, will they ? Because then a diviner would be better at giving advice than you, regardless of whether he’s tall or short, or handsome or ugly, or even noble or common. And when the Athenians are discussing measures for public health, it will make no difference to them if their counsellor is rich or poor, but they will make sure that their adviser is a doctor.  I suppose that’s because advice on any subject is the business not of those who are rich but of those who know it.

In general, Plato doesn't seem to have had much truck with the idea that reality is a simulation or the imaginings of a god. Like the idea that the Earth goes around the Sun, this is widely taken for granted these days - but it's very, very hard to prove it from first principles (as we discover at length in Theaeteus and hilariously in Euthydemus), and that's something well worth remembering. You may fairly assume that it's true, but that's not at all the same as proof.

As for the popular idea that Plato claimed to know nothing, this is pure frickin' nonsense. Even in the Apology, when Socrates passionately defends his right to ignorance, he doesn't claim that wisdom is knowing you know nothing. That's only a relative state : it's knowing you know nothing when you actually do know nothing and everyone else thinks they know things but actually know nothing. If they know nothing and know they know nothing but you know something, then you're wiser.

In other words, Socrates only claimed to be the wisest man in Athens because he knew he knew nothing, whereas everyone else professed to know many, many which things they didn't. He never denies that they do actually know some things, especially the craftsmen, it was just offset because of their massive professed knowledge of all other areas which they didn't actually have. The wisest person of all would of course be someone who really did know everything and the best actions to take in all circumstances. In Statesman, Plato advocates for benevolent dictators :

... the truest criterion of correct government of a city [is] the one according to which the wise and good man will govern the interests of the ruled. Just as a steersman, always watching out for what is to the benefit of the ship and the sailors, preserves his fellow sailors not by putting things down in writing but offering his expertise as law, so too in this same manner a constitution would be correct, would it not, if it issued from those who are able to rule in this way, offering the strength of their expertise as more powerful than the laws.

The only way in which ignorance is a virtue in Plato's discussions is when you're aware of it and try to change it, and try to get others to acknowledge their own ignorance when they claim false, damaging knowledge.

I know that's skipping ahead of my stated limit of the first thousand pages, but it sums up the situation very well.

What's frustrating is that we never hear Plato's voice directly, except possibly in his letters although we don't know for certain that they're genuine. So, just like a play, we get to examine all the issues, but not what Plato himself really thinks or prefers, except by looking for trends and persistent themes (of course, he did warn us not to take him literally !). Although it's clear that he didn't claim to know everything, it therefore remains frustratingly ambiguous as to what he did claim to know. What effects had the all-important examination of the self had on him personally ? To what extent should his world-building exercises be seen as hypothetical explorations and to what extent did he think they should be applied practically ? More on that next time.

It's also worth mentioning that the heroic Socrates of the Apology - the one who died not for knowledge but for ignorance and the right to question - re-emerges on many occasions throughout Plato's corpus. He is the principle protagonist in most dialogues, and usually gets the upper hand with all the cleverest arguments. But we also get an altogether more human view of Socrates in the other dialogues. He's sarcastic, mocking, doubtful, unsure of himself (often floored by an opponent's argument and has to sit out the discussion for a while) and sometimes even extremely petty - on one occasion even threatening to walk out if his opponents won't argue on his terms. He achieves moments of greatness, and you could even call him a truly great man, but he's not a saint and his conclusions certainly aren't held as dogma. Dogma, if anything, is anathema to everything the examinations stand for.


Freedom of speech

This one is only discussed directly on occasion. Most notably, a throwaway line in Gorgias :

You’d certainly be in a terrible way, my good friend, if upon coming to Athens, where there’s more freedom of speech than anywhere else in Greece, you alone should miss out on it here. But look at it the other way. If you spoke at length and were unwilling to answer what you’re asked, wouldn’t I be in a terrible way if I’m not to have the freedom to stop listening to you and leave ?

This is the heart of the problem of so many issues surrounding free speech then and now : freedom from versus freedom to, the right to offend versus the right to be offended, freedom of actions versus freedom of consequences. If you force people to listen to things they don't like, you've take a freedom from them. But if people are allowed to speak, what's the point if no-one's listening ? What kind of freedom do they have if, say, they can be fired from their job for saying things people don't like ?

More famously, the Apology is a powerful rallying cry for the virtues of free speech and the dangers of oppression by the state :

If you put me to death, you will not easily find anyone to take my place. It is literally true, even if it sounds rather comical, that God has specially appointed me to this city, as though it were a large thoroughbred horse which because of its great size is inclined to be lazy and needs the stimulation of some stinging fly. It seems to me that God has attached me to this city to perform the office of such a fly, and all day long I never cease to settle here, there, and everywhere, rousing, persuading, reproving every one of you. You will not easily find another like me, gentlemen, and if you take my advice you will spare my life. I suspect, however, that before long you will awake from your drowsing, and in your annoyance you will take Anytus' advice and finish me off with a single slap, and then you will go on sleeping till the end of your days, unless God in his care for you sends someone to take my place.

I tell you, my executioners, that as soon as I am dead, vengeance shall fall upon you with a punishment far more painful than your killing of me. You have brought about my death in the belief that through it you will be delivered from submitting your conduct to criticism, but I say that the result will be just the opposite. You will have more critics, whom up till now I have restrained without your knowing it, and being younger they will be harsher to you and will cause you more annoyance. If you expect to stop denunciation of your wrong way of life by putting people to death, there is something amiss with your reasoning. This way of escape is neither possible nor creditable. The best and easiest way is not to stop the mouths of others, but to make yourselves as good men as you can.

Throughout the other dialogues, Plato considers all manner of crazy ideas. Despite one of the charges against Socrates being impiety, at times he even flirts quite brazenly with atheism. He surely cannot have been unaware of the importance of free speech, how critical it must be to tell people things they don't want to hear without fear of reprisal by the state - otherwise how can people learn and grow ? It ties in closely with his often highly ambiguous conclusions and contradictory statements : being able to explore different ideas, even offensive ones you don't actually believe, is paramount.

Much more on that next time.


Summary

This is an impossibly crude summary of a thousand pages of beautiful dialogue, but there are some reasonably clear overall points :

• Rigour is important. Plato analyses any statement by reducing it down to its most basic components, often to the level where it seems tautologous. He also blends theory (by trying to rigorously define what words mean) with observations (by employing supporting analogies). He never quite gets to the notion that if there's a clear conflict between observation and theory then observation must win (the modern scientific view), but he comes very close.
• Conclusions are provisional. His dialogues sometimes contradict one another (quite starkly) and often fail to reach any definitive conclusion at all. Even those that do usually contain statements about what would be necessary for anyone to refute them. The search for the truth is usually more important than the truth itself. Revising a conclusion is light of new evidence or theory is essential.
• Ignorance isn't bliss. While we can't know everything about the world around us with 100% certainty, we can know some things. Just because some complicated notions (like the concept of virtue or knowledge) are difficult doesn't mean that everything is. You can learn how to build or ship or play the flute and objectively test your abilities. Knowing your own ignorance is important (the Delphic inscription, "know thyself" features several times), but it's even more important to actually try and bloody learn something.

There are other themes which re-occur in the dialogues which are less important in general but are important for anyone to bear in mind if they specifically want to read the Republic or Laws. For example, Plato takes the great poets as authorities on various matters, virtually never contradicting them on anything. He's frequently unsure as to the existence of the gods, veering wildly between a devoted believer and quasi-atheism (even though he never questions the existence of the soul, he does question if it's immortal). Moderation too is a very common theme, often held to be an essential part of virtue ("Nothing in excess", says the Delphic oracle*), as is the notion that things should be done in a certain correct way by experts. Expertise is a common theme; only slightly less common is the idea of elite experts : "in every pursuit most of the practitioners are paltry and of no account whereas the serious men are few and beyond price", he says in one of the more serious moments in Euthydemus. Homophillia runs rampant, to the extent of almost completely ignoring what certain people would deem to be "normal" heterosexuality today.

* But also nothing too little, tying in nicely with the ideas of wisdom being knowledge of how much is appropriate.

The surface level topics of the dialogues vary. They cover rhetoric, theory of knowledge, how to judge expertise, wisdom, the nature of happiness, morality... that sort of thing. Plato's famous forms are woven throughout many different dialogues rather than being given their own explicit section. Don't make the mistake I made of trying to choose a particular topic, because they're all (with the possible exception of Parmenides, which is an exceptionally tough piece about the nature of one) very broad-ranging. In fact, they're like nachos. The surface level topics exist only as a substrate by which to deliver the cheesy goodness of their nutritious subtext - the constant running theme being, "what's the best way to live ?". The answer being, "by eating lots of nachos", obviously.

However, in recent years a rival theory has emerged stating that the best way to live is by teaching your cat to drink wine. I'm not entirely digressing here. Dozens of pages of the text are (I swear !) about the best way to organise a drinking party.

Plato has this other frustrating habit which has a perverse appeal : he'll explain an idea with beautiful rhetoric (often the most commonly-held position on a topic) and them demolish it seconds later with a series of ugly facts or counter-arguments (for particularly extreme examples see Phaedrus and Symposium, both partially about the different kinds of love and both with some of Plato's most eloquent dialogue). This is not a scientific method, of course, but it strongly supports Plato's sincerity to find the truth. While Plato does value both physical and rhetorical beauty, it's abundantly clear that they're much lesser concerns. As Socrates mockingly says of himself in Hippias :

He’s like that, Hippias, not refined. He’s garbage, he cares about nothing but the truth.

Of course, being biased myself, I've picked out the things that I find most interesting and tend to agree with most strongly. Still, I find it hard to imagine that the three main points would be disputed by more serious scholars.

There's one final point that must be made, however, because I think I may have given a rather rose-tinted view of Plato thus far. Some of Plato's throwaway lines are profound, but others are downright mad. For instance, while in Statesman he finds that the best form of government would be a single ruler who was a paragon of wisdom, the next best thing would be a state in which the penalty for disobeying any law is death. He says, as we've seen, that the corrupt deserve death with virtually no analysis of this. There are many hints that he believes that morality is so objective that it should be forced on people against their will. And, as discussed previously, he clearly believes that people are not equal - not merely in flute-playing abilities, but overall some people are better than other people.

Most damming of all is what he does not say, which is anything at all about whether slavery is moral. For other men, imprisoned as they are in the thoughts of their own times, we might perhaps forgive that lapse. But for a man who foresaw the transporter problem through sheer reasoning, who repeatedly stated over and over again that it's a person's actions and abilities that matter, not his wealth or social status, who dedicated himself to the pursuit of virtue... well, for such a man I don't think we can allow the same leeway. Which doesn't negate anything that he did say, but it cautions us to do the very thing Plato advises : continue the process of examination, both of his conclusions and our own.

This Isn't The Law You're Looking For

I have a mental guideline for judging both the accuracy of press releases and scientific claims alike :

The value of a press release and the probability that the reported discovery is correct is anti-correlated with the grandiosity of the claims.

If a press release makes astonishing claims, then the chances are that it's a mistranslation from the original research article. Sadly, scientists tend to be such poor communicators that it's hard to judge if that was the case or not from the press release alone - you have to go back to the source. But the validity of the claim itself doesn't need this, whether it's in the press release or the original paper. You don't need to go back to the source to work out if, "SCIENTISTS SAY BABIES ARE SOLE CAUSE OF HEROIN ADDICTION" is bunk, and you don't need that much prior knowledge to know that, "Our research decisively rules out the existence of gravity" is also bunk.

So when scientists claim in both press releases and the original paper a discovery that's "tantamount to a new natural law", it's pretty hard to take them seriously. Claiming the discovery of a new natural law is pretty close to top of the Tree of Grandiosity. Claiming that you yourself have discovered this law, without there being any previous discussion about it (let alone a consensus) is in the uppermost branches, almost tantamount (see how insignificant that word becomes ?) to declaring, "I AM THE NEXT EINSTEIN ! COWER, BRIEF MORTALS ! LOOK UPON MY WORKS, YE MIGHTY, AND DESPAIR !".

What's this all about then ? Enter the plucky challenger, the Mass Discrepancy Acceleration Relation. Or not, because if you're looking for a concise explanation of what it's all about then you've come to the wrong place. You big silly.


MDAR : The Prelude

Galaxies, we think, are dominated by their dark matter in terms of mass. This still-mysterious and hidden component generally makes up around 90% of the mass of a galaxy, often a good deal more. Since it's gravity (i.e. mass) which dominates how things orbit within a galaxy, the dark matter should dominate internal motions. There shouldn't be much, or any, correlation between the density of normal matter and its orbital speed.

Of course gravity isn't the sole force at work. Stellar winds and supernovae also play their role, sometimes very dramatically. Occasionally we see how huge collective winds from young star clusters (which, like all young offender institutions, contain the most violent and literally explosive youngsters) drive enormous outflows of material deep into extragalactic space. Galaxies are so cool that even their vomit is beautiful.

The galaxy M82 as seen with Hubble. The two red plumes are hot, ionised hydrogen. It's thought that there's an intense starburst region near its centre, where young stars produce enormous winds and explosions that drives material outwards. 

Such winds are often produced near the centres of galaxies, where the star formation can be particularly vigorous. But there are other ways to produce a so-called "Active Galactic Nucleus". Indeed these days the term AGN is almost synonymous with another spectacular phenomenon : a supermassive black hole.

Hercules A, which features huge jets (see in radio emission in red) thought to be powered by matter orbiting around a black hole.

But such features are by far the exception rather than the rule. Many galaxies have star formation, of course, but at nice sedate levels. It also tends to occur somewhat randomly, so it's rare to see it driving large-scale outflows. The exact details of how and where stars form are complicated, to say the least.

So in normal galaxies it's the dark matter which should dominate. And it does, in that the rotation speed seems to require this enormous amount of extra material to prevent galaxies from flying apart. Yet when we look at the rotation speed in more detail, we see something more complicated. We don't usually see nice smooth curves describing how the rotation varies throughout the galaxy - we see little wiggles.

Rotation speed against distance from the centre for a bunch of galaxies, from this paper. The dots are the measurements, the solid lines are model fits. The wiggles are small, and the measurement errors of comparable size (the authors note that the true uncertainty may be about twice as large as these "formal errors", which in my experience is a good rule of thumb).

The size of the wiggles appears to be correlated with the mass of gas and stars, as though the stars and gas were influencing the dark matter. Which they shouldn't be able to do, since there's so much more dark matter than normal matter. It's not quite like throwing the proverbial peanut at the proverbial rhinoceros - a bag of sugar would be a better analogy.

It probably wouldn't be a good idea, but it's safe to say that the 1 kg bag of sugar wouldn't be able to move two tonnes of rhino except by annoying it.

How strange is this ? It's hard to say. It's one of those problems that occasionally flares up from time to time but few people regard as extremely serious - I show an example in point two here. The wiggles are intriguing, but they're not that large. And the authors of the above study note that there may be selection effects at work that mean the correlation isn't real.

But it's still intriguing. There's another, much stronger apparent relation between normal matter and galaxy dynamics (i.e. the dark matter) : the Tully-Fisher relation. This isn't subject to all the small-scale measurement errors or problems of star formation or other processes that might affect internal motions in very localised regions, because it's a relationship between the maximum rotation speed of a galaxy and its total mass.

Just as in the pages of any celebrity gossip magazine, so relationships in astronomy are equally complicated. OMG, is that line width just a proxy for rotation ? I don't think the resolved observations are going to be happy when they find out about that ! And have you seen the stellar mass getting off with the neutral hydrogen ? Things are getting steamy gassy !

What I mean is, originally the relation was found by comparing the rotation speed with the brightness of a bunch of galaxies :

From the discovery paper. It looks more complicated than it is. It's just plotting brightness (on the vertical axis) against rotation speed (on the horizontal axis).

As usual, some words of caution are needed. This quantity "LOG ΔV" means how fast the galaxy appears to be rotating, but direct rotation measurements are hard. That requires painstaking observations of the galaxy's speed at each point within the galaxy. It's much easier to observe the whole galaxy at once, which gives you a "line width". This is equivalent to the maximum difference in speed along the line of sight.

Say the galaxy is rotating at 200 km/s. One half will be coming towards you at 200 km/s and the other away from you at 200 km/s, and your measured "line width" will be 400 km/s. The correction is a bit more complicated than just halving the line width, because the galaxy might not be directly face-on. But this correction is relatively easy. Also, at high widths you can be pretty confident you really are measuring rotation, because unless you've got one of those cases of particularly windy galaxies there's not really much else that could create such a high line width besides rotation.

Things get trickier when you start going to lower line widths. There, rotation might not be nearly so dominant, so your assumption that you're measuring rotation is much more questionable.

Using line width rather than true rotation is done for convenience. Similar, brightness was used because that's what's actually measured rather than stellar mass. Converting brightness into the more physical parameter of stellar mass is possible, but needs some assumptions about how many massive stars there are, how many faint ones, their colours, etc. You can do it, but you need more than just one observation for this - you need to use lots of different wavelengths to properly measure the different stellar populations.

Once you make these corrections, however, something remarkable happens. There seems to be a very tight correlation indeed between the total mass of stars and gas and the rotation speed. And most interestingly of all, galaxies which don't fit the normal brightness-rotation relation do fit the mass-rotation relation !

Left : using the stellar mass (effectively, brightness). Lots of galaxies (highlighted in green) don't fit this otherwise nice relation. Right : using the total mass, combining the mass of stars and gas - now those errant galaxies have been brought back into the fold.

This "baryonic Tully-Fisher relation" (baryonic just being a fancy word for "normal matter" suggests that there really is something funky going on here. No need to worry about the problems of little wiggles - the total mass of normal matter seems to correlate very well indeed with the overall rotation. And it's the total mass that's key - stellar mass by itself doesn't work.

 Later studies found that the scatter in the relation can be reduced quite a bit with more accurate corrections - there might not be any intrinsic scatter at all ! You'd think there'd be some variation, but apparently not.

Let me emphasise this. It turns out this galaxies like this...

... sit on exactly the same relation as galaxies like this :

About a factor of 10 difference in rotation speed, 50 in size and 10,000 in stellar mass... yet they still lie on the same relation. What's particularly weird is that it's quite easy to show that the Tully-Fisher relation should have scatter, but it doesn't. The only way to make this work if there's strange "conspiracy" between the normal matter and the dark matter, which doesn't really make physical sense. What's going on ?


Behold, The Mass Discrepancy Acceleration Relation !

I SAID, BEHOLD !!!

We've so far seen different variations of the same problem : the normal matter seems connected to the dark matter in a weird and unexpected way. We've also seen how the way we examine the problem changes how we think about it. The observational parameters that we have may be convenient, but they aren't the most basic physical properties which are at work here.

The MDAR is an attempt to reduce things down from the measurements we get directly from telescopes to the actual underlying physics : acceleration. Knowing the size, rotation and mass at any point in a galaxy, it's possible to work out how fast it's accelerating, i.e. the force it's experiencing.

"But wait !", I hear you cry. "Surely there's a problem with this ? After all, the mass in a galaxy is rotating in an unexpected way, that's how we know there's dark matter there."
"Indeed," I respond, "but what we can do is compare the expected acceleration (based only on the mass of the normal matter) with the actual acceleration based on its measured speed."
"Gosh !" you reply, "that's jolly clever."

Yes it is. The MDAR cuts through the problems of interpreting the observational parameters by bringing it back down to the physics - and it doesn't need many complicated assumptions to work these out either. The result, as shown in that famous "new law of nature" paper by Stacy McGaugh et al., is very impressive indeed.

On the horizontal axis, the expected acceleration due to the mass of the normal matter ("bar" = baryons = normal matter), On the vertical axis, the actual acceleration from the speed measurements ("obs" = observed). There isn't a nice straight slope : the important thing is that there's a trend at all. Knowing the mass of normal matter, you can predict its true acceleration.

That's just about one of the clearest results ever. At least, there's hardly any scatter and everything follows a nice trend, over a factor of about a thousand in acceleration (if not more).

Let me further emphasise how odd this is. It's a bit like being told a few basic bits of information about a horse - how large it is, how many legs it has, typical horsey sort of things - and then being able to work out exactly how fast it's going... even though no-one told you that the horse is on the back of a truck. It's weird.

To be more accurate, what the MDAR says is that once you know the theoretical acceleration of some matter, based only on the mass of that matter and its distribution, you can accurately predict its true acceleration. The problem is that no-one told you that there's also so much dark matter present that it should be dominating the acceleration, not the matter you can see. So again, it's weird.

But we like weird. Weird is cool.

Still, what does it actually mean ? In fairness, apart from the extremely silly comment about a "new law of nature", I have no complaints about the rest of the paper. I can even understand why one would be tempted to make such a comment as this (later on they call it, "a sort of Kepler's law for rotating galaxies"), but you shouldn't actually do it. The discoverers may of course hold any private opinion of "their" (see later) discovery's importance that they wish, but it's the scientific community that should be the public judge of it - not the original authors. Inevitably, however honourable their intentions, it comes across as arrogance and hubris.

Still, the authors note three possible interpretations of this result :

1) It's just the way galaxies form. That is, it can be explained using entirely conventional physics and standard models of galaxy formation. The authors aren't happy about this because of related, long-standing problems with those models.
2) It indicates that there's something we don't understand about the dark matter. Maybe it really is influenced by or somehow relates to the normal matter in a way other than purely through gravity as in the standard model. That's possible, but it would make the already complex models even more complex.
3) It undermines the dark matter paradigm. A perfectly legitimate interpretation since it seems to suggest a direct connection between the normal matter and the rotation speed, in seemingly direct contrast to the predictions of dark matter. Alternative theories of gravity like MOND might provide the answer. MOND did actually predict this relation decades ago, much to the irritation of dark matter supporters. It even makes intuitive sense in a MOND perspective, since in that scenario there isn't any dark matter - only normal matter causes acceleration.

All of these are valid possibilities. Taking this result in isolation and at face value, the second two are the most natural. But the dark matter paradigm is a formidable edifice indeed, and it's a foolish astronomer who would rush to declare it dead because of any one issue.


Not such a mysterious mystery ?

Actually Stacy McGaugh likes dressing as a monster and scaring off his competitors...

What quickly followed in the wake of McGaugh's publication was a series of papers showing that actually the first possibility - that the standard models could explain everything - worked just fine, thankyouverymuch, we don't believe in MOND in this neighbourhood, we're Baptists....

Not quite. Of course, I'm not suggesting that either dark matter or MOND are any kind of a cult or religion or even ideology, as regular readers will well attest to. But there was certainly more than usual element of humanity creeping in to the normally stoic research papers and analyses. Perhaps it was due to the fact that this was coming from McGaugh, a highly respected researcher who normally manages to straddle the dark matter and MOND camps without winding anyone up the wrong way, using this frankly ridiculous phrase.

The first criticism came not from angry dark matter "believers", as you might suspect, but from a much more unexpected source : Milgrom, the creator of the MOND theory !

If McGaugh used a single poor phrase, Milgrom took it to a whole new level. For example, "It is anything but a newly discovered relation"; " These results, indeed, constitute a triumph for MOND"; "McGaugh et al. have chosen to obfuscate the MOND roots of their analysis"; "No other possible origin for such a function is known"; "There is no other paradigm, certainly not the dark matter paradigm, that dictates this form."; "McGaugh et al. seem to try to justify their suppressing the role of MOND"; "the data itself is not even theirs". It was essentially the arXiv equivalent of an angry blog post. Worse was to follow, but we'll get to that.


He's already got one ! It's very nice !

Let's try to divorce the angry ranting from Milgrom's claims themselves. First the claim that it's not a new discovery, for which Milgrom cites no less than eight papers. Indeed, we've already seen how the rotation curve wiggles and Tully-Fisher relation can be seen as one way to describe this relation. I couldn't access one of the papers, but the others don't plot this precise relation though they do describe something similar... except for one. This paper by Wu & Kroupa from 2015 plots exactly the same relation as in the McGaugh paper. Look, here it is :

Is it fair to claim that this result was well-known though ? Hard to say. Certainly the other forms of this MDAR are well-known, and McGaugh describes them himself in the introduction. But this particular form ? I don't think so. The Wu paper has been cited 20 times (a very good rate - better than any of mine ! - but not astonishing) and McGaugh (until this year) was never on any paper that cited it. Wu notes that a similar study had been done in 2006, but that references a conference proceedings. People often deliberately avoid these as they're seldom up to the same standards of rigour as normal papers, so although it should be cited it's understandable that it was not.

The Wu paper is 17 pages long and quite technical (and doesn't call this relation a new fundamental law of nature !), so you'll have to forgive me for not reading it thoroughly*. As far as I can tell, it only cites that conference proceedings in support of this previous formulation of the MDAR. But it also notes that the standard "mass discrepancy relation" is basically the same thing. That relation definitely is well known, but this particular form of it ? Probably not. Milgrom is correct that McGaugh should have been more explicit about describing the MDAR as a well-known problem, but it seems forgivable that he might not have known that this plot had already been produced. I've met Stacy McGaugh a few times and Pavel Kroupa many, many times, and while I'm not privy to their private communications, I can't say I've ever noticed Pavel being upset that Stacy didn't cite him.

* For all other papers I read them in their entirety, quite carefully, before referencing them. That's why these posts are infrequent.


Been there, done that

What of Milgrom's claim that McGaugh "suppress" the role of MOND in their analysis ? No, sorry - this one is silly. McGaugh says it directly in the paper : "Indeed, our results were anticipated over three decades ago by MOND. Whether this is a situation in which it would be necessary to invent MOND if it did not already exist is worthy of contemplation."

That seems like plenty of endorsement and acknowledgement to me. And since it's a letter, space is at a premium so brevity is crucial. It's folly to ask for anything more in the space available.


A mysterious mystery gets less mysterious

Which brings us to the third, most important claim by Milgrom : that there's no way the dark matter model can account for this result. The first challenge to this came out within weeks of the McGaugh paper. Keller & Wadsley used standard dark matter simulations but with better physics for the normal matter, and they were able to reproduce the MDAR strikingly well.

McGaugh's observational result is on the left, Keller & Wadsely's simulation on the right.

What was the secret to this astonishing success ? Unfortunately, they're not very clear on that one. They state only that it's due to, "simple dissipational collapse of gas", which means that the gas can cool and lose energy, but that's not a tremendously detailed explanation.

More convincingly, they show that this relation would look very different in the early Universe, when star formation was higher and those huge windy outflows were much stronger. In their simulations, this relation evolves over time, starting out quite different (because of the strong stellar winds) but then evolving naturally into the relationship we see today (as the winds die down). So I'm sold on their simulations reproducing the results, but I don't think they give any sort of reason why this relationship exists. Ho hum.

Milgrom flew into an outright rage at this point. The reason appears to be that the original title of the paper contained the phrase, "La Fin Du MOND ?". In fact the paper barely even mentioned MOND at all - it was much more focused on showing that the standard model could produce this MDAR.

But Milgrom's wrath was terrible; his retribution swift. He said that authors "smugly suggested" that the end of MOND was nigh (they didn't, they just asked a question); that they only "claim" to have simulations which show the presented results (this is - ouch - tantamount to calling them liars); that the reasons for the agreement were "trivial" (they weren't and aren't); that they had too few galaxies in their sample and no dwarf galaxies (this was true in the first draft but corrected in later versions); that they made "unwarranted extrapolations, they seem to imply that CDM [the standard model] is consistent with all the observed galaxy properties predicted by MOND" (absolute nonsense, they did nothing of the sort); and made some odd comments about the choice of which parts of the galaxies to sample (which the authors describe well and they seem fine to me). He even made a bizarre comment about the simulations trying to make guesses as to "unknowable events and processes" - which is frankly laughable. All simulations do that; if we knew everything that was happening, we wouldn't need simulations !

Milgrom's only objection of any real substance, so far as I can tell, was that half of the galaxies used in the simulations did not have realistic rotation curves. Yet the other half did. To my mind, they showed convincingly that this result dropped out naturally from their simulations, with absolutely no attempt to force things to work.

At this point one has to wonder, "Milgrom, what are you on about man ? Did Keller deliberately run over your dog ? Did Wadsley break your house and burn your legs down ? 'La Fin Du MOND' might be a bit snarky - condescending even - but come on, it's not that snarky."

Anyway another paper came out a bit later, from another team using a completely different set of simulations, measured in a different way... and what did they find ? Guess what. Pretty much exactly the same as Keller & Wadsley !

Well well well, doesn't this look eerily familiar.

Unfortunately this paper, lead author Aaron Ludlow, didn't really offer much more in the way of what causes this relation either. But they offered some hints. They say that it doesn't really matter what "scaling relations" the galaxies in their simulations obey - that is, how much normal matter they contain at different total masses - they all obey a relationship like the one seen in the graphs. Maybe not the same one though. They're not quite as clear as I would like on this point, but they seem to say that if the galaxies in the simulations obey the scaling relations that normal galaxies do, then they reproduce the observed MDAR. There's nothing profound about it; it just happens naturally.


EDIT : Some considerable time later, another paper came out which does a much better job of explaining why this happens. You can read my detailed summary and find the original paper here. In brief, there are a few things at work. Detectable galaxies can't form in the largest or smallest halos (they either don't accumulate enough gas, or so much gas causes runaway star formation and stops any more gas from getting in), limiting the acceleration baryonic matter ever experiences. And the acceleration withing each galaxy varies in a characteristic way depending on the distribution of dark matter, which in turn controls the distribution of mass. There are some important subtleties explained in the link, but if you want my opinion (and I guess you do because you're still reading) this is a convincing explanation.


Which doesn't mean that it disproves MOND or proves the standard model : it's not even that useful. In fact, as a way to test between them, it appears to be utterly useless. Even without fully understanding its cause.

The next response was published early this year.... unfortunately. Well, unfortunate in the sense that all the players involved decided to put their papers on the pre-print hosting service arXiv before they were accepted for publication. This is an unfortunately common practise, occasionally justified (if you've made a fun discovery and you want to stake your claim to it, or if you need help from the community and don't have many of your own personal contacts) but not usually. The result was that each of the papers went through several iterations all responding, very confusingly, to different iterations of the other papers, which all took different amounts of time to get through the review process. It's all a bit of a mess, really.

Not quite this messy, though.

On this paper the lead author was a certain Federico Lelli, with McGaugh taking a back seat. It has the catchy title, "One Law To Rule Them All", which is at least a little bit humorous, but then they go on to again say that it's tantamount to a natural law. You bunch of bloody muppets. Don't get get how damaging this stupid rhetoric is for science communication ?

Anyway, the "original" McGaugh paper was just a letter, which are short reports on particularly exciting things. The Lelli paper is the more detailed follow-up (and this time it does cite the earlier discoveries of this relation). Much more detailed. Despite this single daft bit of drama, I'm forced to admit that it's a first-rate paper. It's clear, detailed, well-explained and readable. All the figures that you might want are there. Many different interpretations and parameterisations have been explored.

By far the most interesting result was this plot :

It's the same MDAR we've seen umpteen times already, but now with the addition of dwarf spheroidal galaxies. These are galaxies which are dwarfs... and spheroidal. Photogenically they're deafeningly dull.

But they are nevertheless extremely interesting and confusing little buggers. As we saw last time, sometimes the faintest galaxies are interesting precisely because they're so bloody faint. Which in this case is because they're a good test for very low accelerations. Did McGaugh cheat by not including them in the original paper ? No, not at all. The problem is that they're so faint you can only estimate accelerations at the outermost edge. Essentially, the provide only a single data point each, whereas for all the other galaxies it was possible to estimate accelerations in many different places. And one of the really neat things about the MDAR is that it really seems that it's acceleration that matters. The overall properties of each individual galaxy don't seem to be important at all - if the predicted acceleration is the same in two galaxies, then the actual acceleration is the same, no matter the total mass or size of the galaxies.

Except for these pesky dwarf spheroidals, it seems. Since they're so faint, they're hard to measure, so their data isn't as reliable. But when the selection is limited to the sample where Lelli et al. believe the data is of the highest quality, it still seems that they deviate from the relation and have more scatter (right hand panel, above).

If we're feeling very stupid indeed, we might take this relation at face value. We'd conclude, "HAH ! You SUCK McGaugh ! There's no law there at all ! How can acceleration behave differently in different galaxies ? That's feckin' stupid. Jeez, I don't know why I wasted my time on this."

And that definitely would be a very stupid thing to do. Even in the high quality sample, the observational errors are still large. So we just don't know if there's a stronger intrinsic scatter there or not, as yet. But is there a systematic offset, a flattening of the relation at low accelerations that would mean we wouldn't have to change the laws in different galaxies ? Possibly. Lelli & Co. think so, noting that the they can't fit the same equation for the dwarf spheroidals as for the rest. They're also very cautious about the nature of these objects, and it's possible that because they're so faint they might actually be more disturbed than we think they are, in which case we wouldn't expect them to obey a nice relation.

That's one possibility, but it's not the only one. Lelli et al. note that it could be explained in the standard models if there's some sort of threshold for how much dark matter you need to form stars (which is not crazy - dark matter clouds which are too low mass might never accumulate enough gas to form any stars at all). Certainly if this deviation (especially the scatter) is true then it does make it much less likely that this points towards any new physics - it looks much more like the galaxy assembly process might somehow be to blame.

On the other hand, it could point out unexpected physics of the dark matter or even gravity itself. If you change the form of the MDAR just slightly, Lelli says you can get the dwarf spheroidals to agree with the normal galaxies pretty darn well :

What they do in the above plot is very clever. They now combine the expected acceleration due to the normal matter with the expected acceleration due to the host galaxy, for satellite galaxies. For some reason that seems to work. It doesn't get rid of the high scatter, but it does put everything on the same overall relation. That does rather suggest that the original form of the MDAR isn't such a fundamental law after all - it seems that something more funky's going on. The physical motivation of combining these two quantities is, in my view, highly questionable, but we'll get back to that shortly.

The other option suggested of the dwarves not really being stable - well, they're famous for going "swimming with little hairy women", so that's not such a surprise - has recently been examined in another paper by Fattahi et al. (still under review !) :

Observations on the left, simulations on the right. The satellite galaxies in their simulations are being tidally disrupted and deviate from the MDAR, whereas isolated galaxies aren't and don't.

It's fairly okay, I guess, but it's not a fantastic agreement. They show that these gravitational encounters can cause more scatter, but they don't reproduce the size of the scatter very well. Also, Fattahi seem to be unaware that Lelli already plotted this strong scatter, saying that it, "seriously calls into question the idea that MDAR might encode a `natural law'". I agree, it does call it into question, but they don't cite the Lelli paper, which is very strange. On the other hand, one of the few possibilities the Lelli paper doesn't discuss is that these galaxies might indicate that it's not really a law at all. And if you compare the simulations with only the high quality dwarf spheroidal data (scroll up a few figures), you'll see the agreement is very much better.


Summary

So what's going on ? Does this discovery have any hope of being a new natural law, or is it just wild-eyed crazy hype ? Does it provide evidence that our theory of gravity is wrong or not ?

Currently I'd have to say "no". It appears to be useless : it's been reproduced directly in two independent sets of standard model simulations, and occurs without tweaking them to make it work. It's true MOND predicted it well ahead of time*, but dark matter - thus far - appears to be doing an equally capable job of reproducing it. So there's no clear reason to prefer one to the other.

* However, as far as I can tell none of these current papers actually show the specific MOND prediction, nor do they explain whether MOND predicts the flattening seen at the low acceleration end with the dwarf spheroidals.

Lelli raise some objections to the dark matter simulations. Unfortunately, because everyone did this silly thing of posting every version of their paper online before it was accepted, Lelli's objections (like Milgrom's) are no longer accurate. For instance he says that Keller & Wadsley only use giant galaxies; in fact they now use a range of galaxies with the largest being more than 100 times as massive as the smallest. Most of Lelli's objections to Ludlow's work seem to be more nit-picking than anything else - the size of the scatter isn't quite right, the measurement techniques weren't quite right. This doesn't seem critical to Ludlow's conclusion : that some version of the MDAR arises naturally in standard simulations, though the precise relation does depend on the galaxy parameters.

You might think that the galaxy mass range objection also isn't critical. After all, if you go to large enough distances from giant galaxies then you experience very low accelerations, so you don't need to simulate a dwarf galaxy to fill in the faint end of the MDAR (this was also one of Milgrom's objections). Indeed this is true, and exactly what was done in the earlier version of the Keller & Wadsley paper. And you'd surely think that if it's really due to new physics, then acceleration is acceleration wherever you are. It shouldn't matter if you're inside a giant galaxy or a mouse's fart : as long as you only calculate gravity, the results should be the same using the same laws.

PHYSICS !!!!

This is true in the standard model. But it is not true using MOND, which predicts that the behaviour changes depending on the distribution of matter. As Lelli say, in some versions of MOND the acceleration, "could vary from galaxy to galaxy or even within the same galaxy". Although not strictly the same, that's what motivated their choice to include the acceleration from the host galaxy that brings the dwarfs back into agreement with the MDAR. So MOND's prediction of the MDAR is based on a totally, radically different approach to the standard model. That's why it's important to test if dark matter's predictions do still hold true in very low-mass galaxies. Lelli's objection is still valid in that the simulations haven't shown what should happen over the same galaxy property range as is actually observed, though it should be noted that when Kelly & Wadsley took their simulations to less massive galaxies they found exactly the same as for the giants. It feels just a little bit desperate to suggest that a problem might crop up if we just keep doing the same exploration of ever-lower masses.

Personally I don't like the MONDian approach. Classically we're used to physics being the same everywhere in all conditions : sure the final numbers depend on the precise conditions, but the underlying processes never vary. With MOND it's more like (though not quite the same as) the idea of physics changing locally to give different result : gravity works differently depending on the local conditions, albeit in a predictable, ordered way. I find this deeply unsatisfying. Sure, of course the Universe might work like that, but I'd put that one in the "last resort" options box.

Many objections MONDers have to the standard model are now beginning to feel a bit dated. Not so very long ago, dark matter simulations could only use dark matter. But for several years they've been able to employ ever more complex physics of the gas and stars. It's true we don't fully understand many of these processes, and there are many parameters we don't have independent constraints for. But that doesn't invalidate the success of the models, nor does every minor failure point to a fundamental problem. MOND still doesn't have any published simulations using the complex gas physics, and when it does it's going to have just as many difficulties as the standard model.

The Fattahi paper (not yet accepted for publication) claims to have found a "possibly insurmountable" challenge to MOND. The rotational speed of those same faint dwarves appears to be in very stark disagreement with MOND's predictions even if you account for the MONDian weirdness. It's intriguing, but MOND has survived such challenges before... somewhat. I'm not at all convinced that the MOND interpretations of some phenomena are nearly as sensible as devotees seem to think they are.

Whenever I do these posts about whether dark matter is really real, I like to stop and see if anything I've read has caused me to re-evaluate my position. The approach I like to try and numerically quantify which I prefer the most, because that forces room for doubt. Last time I ended up increasing my bias towards dark matter from 75:25 to 80:20 in favour of dark matter versus something else (I reserve about 5% for MOND, so it's really 80:15:5).

This time, nothing has changed. All that analysis has been essentially for nothing, because neither side has any advantage over the other.

Is there at least any scope for future developments ? Well I'd like to see a MOND group actually show their predicted MDAR instead of just claiming that they've got one. Or a dark matter group do simulations of those very faint dwarf galaxies. But these are at the "it might be nice" level. What I suspect will happen is that we'll see a few more papers on this over the next year before everyone becomes horribly disillusioned, gives up and goes home.