Unicorns

Charles Arthur (@charlesarthur), reacting to a question from a ten year old, posted the following tweet:

Rhinos have a single horn. Deer have two horns. Why aren’t there unicorns, ie horses (or deer) with a single horn?

— Charles Arthur (@charlesarthur) December 2, 2015

Which turns out, like many “silly questions” to be a rather profound one … and one which I certainly struggled to answer (if you have any more answers or object to any of my reasoning or claimed facts, please comment below).

The initial pedantic responses to the question from various geeks like me (and indeed – in one case - from me) pointed out that rhinos don’t have true horns (their “horns” comprise matted hairs) and that they do usually have two horns (one behind the other). But neither of these observations (relevant though they are) do anything to diminish the force of Charles’s question.

As Charles responded to one claim that rhinos don’t have horns: “let’s impale you on one and see how that goes”.

Lots of creatures have horns, antlers, tusks, swords etc, which I shall generalize to: Pointy Things Sticking Out Of Their Heads (PTSOOTHs). Swordfish, walruses, elephants, deer, narwhals, rhinoceroses, and many others spring to mind in this context.

Ptsooths may be composed of bone, cartilage, hair, skin, or tooth enamel. Ptsooths start out, in evolutionary terms, as small bumps that confer some tiny advantage, and evolve from there. They may serve (or have served in different phases of evolution) various purposes which include: protection from predation, hunting weapons, digging tools, and sexual signalling devices.

The term “sexual signalling devices” covers a multitude of sins here. Huge antlers may signal “don’t mess with me” to rival males (and may be used to actually fight rival males) and “please mess with me” to females. In this kind of situation, runaway sexual selection often occurs and – as with the peacock’s tail – we can end up with ptsooths that are far too big for the purpose for which they originally evolved and that may actually be an encumbrance for the ptsoothholder – at least in its non-sexual life.

But to get back to the real topic here, all vertebrates have basic bilateral symmetry[1]. The symmetry is not absolute. Most men have unsymmetrical testicles and while we usually have two lungs and two kidneys, humans only have one spleen, one penis/clitoris, and (timelords aside) one heart. Our single heart does not, however, offend the basic symmetry of the body as much as many imagine:

[2]

The spleen does:

[2]

But these are soft tissues. Vertebrate skeletons are far more symmetrical and (save for the backbone itself and a few other bits) contain two of everything. In particular, the skull (or at least areas of the skull from which ptsooths grow or could grow) develops (embryologically speaking) from two symmetrical sets of bones that fuse together.

[3]

You can see the join!

Jaws (mandibles), foreheads (frontal bones), crowns (parietal bones) are all made from two symmetrical halves with a join (suture) down the middle. Even “single” skull bones – like the occipital bone at the back of the skull – are formed (earlier on in embryo development) from two (or four) initial symmetrically arranged sites.

So to really come to the point (pun intended) animals with ptsooths generally have two or four or six – ie even numbers of ptsooths – because they grow ptsooths from bits of bone that come in pairs and not from the joints between them.

So this could be why there are no unicorns …… but (to go back to Charles’s initial question) what about rhinos? (Let’s just consider the long front horn or consider Asian rhinos which do only have one horn it seems[4]).

Well because the rhino “horn” is essentially a modified tuft of hair, it was free to start evolving wherever on the skull it wished to. After all, many of us have tufts of hair between our eyebrows or on our noses (which many of us pluck out in order not to further enhance our rhino resemblances). Both single or double ptsooths could be useful and the rhino went for a tandem (or single) arrangement because it could[5].

It should be noted that both rhinos and deer still have bilateral symmetry – if Damien Hirst sawed either in half down the middle he’d end up with two pieces that were essentially mirror images of each other. (By the way, I wonder what he did with the other half of his shark?)

”But what about narwhals (the ‘unicorns’ of the sea)?” I hear you all cry.

Well this is where it starts to get really interesting! (So I hope you’ve persevered this far.)

The narwhal[6] “horn” is in fact a tooth – a left canine tooth to be precise. It grows very long and in a helical fashion. The socket for the tusk has migrated very close to the line of symmetry of the narwhal and grows straight forward – providing the unicorn-like appearance:

[7]

– but narwhals are actually slightly asymmetrical:

[8]

Very occasionally, narwhals grow two tusks, but they never grow a single right tusk or reverse the handedness of the helical twist of either tusk.

Unicorns also have a twisted horns and it is often claimed that depictions of unicorn horns were based on observations of narwhal horns.

[9]

Unicorns, however, twist both ways:

[10]

There again, so does DNA – in its depictions! In real life, DNA[11] only goes one way – the opposite way to the narwhal horn.

The ancestors of modern deer also had tusks[12]. Later they evolved horns and their tusks withered away as their horns grew. I see no reason – in principle – why deer or antelope (or other ungulates) could not have evolved to grow (say) only their left horns and why that single horn could not (with a slight asymmetrical deformation in skull development) have moved over towards the centre of the head. Such a “unicorn” would not be quite symmetrical but, given that they have helical horns, unicorns aren’t really symmetrical either.

In fact, thinking about it, I don’t really see why – if the horn were composed of two fused halves (like the swordfish “bill”) – we couldn’t have had a “unicorn” with a single symmetrical untwisted horn.

Moreover, if the frontal and parietal bones of the skull withered away and the occipital bone filled in for them (stranger things have happened in skull evolution) why couldn’t a single horn develop from the middle of that bone in roughly the right place for a unicorn style horn? I know not.

In conclusion then, I have no idea why there are no unicorns …… perhaps there are!

Postscript: Since writing the stuff above, Rab Austen (‏@RabAusten) has reminded me that the triceratops also had a (front) horn on the midline of its skull. This was a "real" (bony) horn and would - as Paolo Viscardi (‏@PaoloViscardi who has forgotten more about bones than I shall ever learn about them) kindly confirmed - have been formed from the fusing of two symmetrical elements - like the swordfish bill. I'm not sure whether a horn formed like this could then grow with a helical twist (though as Paolo also points out, stranger things happen at sea) but Rab's insight certainly lends support to the claim that there is no reason - in principle - why a horse-like creature could not have evolved a bony horn in the middle of its forehead.

1. Invertebrates often have bilateral symmetry too. Even starfish - which superficially have radial symmetry - have a complicated and interesting way of forming that involves bilateral symmetry. Other invertebrates - snails and sponges spring to mind - break the "rule" in other ways.
2. http://keckmedicine.adam.com
3. http://http://fineartamerica.com
4. Thank you to Steve Jones (‏@TheEulerID) for this information
5. http://news.bbcimg.co.uk
6. Please note that evolution does not work in the way I talk about it (metaphorically) in this post. Evolution has no plan, intent, or purpose. It's all natural (or sexual) selection acting on random mutations, It is, however, often easier to describe what happens in evolution using teleological language - as long as we don't forget that it's just a metaphor! OK?
7. I'm getting all my information about narwhals from Chris McManus's excellent Right Hand, Left Hand which I urge you all to read.
8. https://cdn-images-1.medium.com
9. http://www.mermaidsrock.net
10. http://http://kristell-ink.com
11. OK I'm talking B-DNA not Z-DNA ... pedant!
12. Deer Antlers: Regeneration, Function and Evolution by By Richard J. Goss esp p72 et seq

Also published at Pulling on the corkscrew of life

Homeopathy: Can we believe what we hear?

The BBC Radio Four Today programme interviewed one Dr Peter Fisher (Clinical Director and Director of Research at the Royal London Hospital for Integrated Medicine and a Fellow of the of the Faculty of Homeopathy) this morning (2015-11-13 beginning at 01:33:39).

When pressed on the scientific evidence for homeopathy (the subject of the interview) Dr Fisher had this to say:

"The most recent analysis of all clinical trials of homeopathy conducted by the Robertson Centre for Biostatistics at the University of Glasgow came to a clearly positive result that was published last December."

I thought I might take a look at this paper, so I tweeted Dr Fisher:

.@PeterAGFisher Please could you provide a link to (or ref for) the (+ve for homeopathy) meta-analysis you mentioned on the wireless?

— Dr Mike Ward (@Schroedinger99) November 13, 2015

Dr Fisher kindly got straight back to me:

@Schroedinger99 @PeterAGFisher Sure will dig out and send later. Peter Fisher

— Dr Peter Fisher (@PeterAGFisher) November 13, 2015

I think if I were going on the wireless to cite a scientific paper I should have grabbed hold of a copy beforehand - just to be on the safe side. But perhaps Dr Fisher has a better memory than me. Let us see.

I am still waiting for Dr Fisher to dig out his copy of the paper and send me a link or a reference so I thought I might try and track it down myself.

First port of call The Robertson Centre for Biostatistics at the University of Glasgow. No publications there at all concerning homeopathy - in 2014. So I checked 2015 and 2013 just to be on the safe side. No joy.

I tried another tack and googled "Robertson Centre for Biostatistics" Homeopathy. This led me to this page of the British Homeopathic Association which cites a "Systematic review and meta-analysis of randomised controlled trials (RCTs) in homeopathy". This page and my google search both pointed to the paper below - all roads lead to Rome it seems.

Randomised placebo-controlled trials of individualised homeopathic treatment: systematic review and meta-analysis Robert T Mathie1*, Suzanne M Lloyd2, Lynn A Legg3, Jürgen Clausen4, Sian Moss5, Jonathan RT Davidson6 and Ian Ford2

* Corresponding author: Robert T Mathie rmathie@britishhomeopathic.org

Author Affiliations

1 British Homeopathic Association, Luton, UK

2 Robertson Centre for Biostatistics, Institute of Health and Wellbeing, University of Glasgow, Glasgow, UK

3 Department of Biomedical Engineering, University of Strathclyde, Glasgow, UK

4 Karl und Veronica Carstens-Stiftung, Essen, Germany

5 Homeopathy Research Institute, London, UK

6 Department of Psychiatry and Behavioral Sciences, Duke University Medical Center, Durham, NC, USA

This paper is dated 2014 December and refers to the Robertson Centre for Biostatistics, University of Glasgow and is a meta-analysis of homeopathy studies. I'm sticking my neck out and assuming this is the paper which Dr Fisher referred to ..... but just to be on the safe side I tried to double-check:

@PeterAGFisher perhaps you are referring to this paper: https://t.co/7C2WGJ8vy6 - that isn't from Robertson Centre, but one of 6 authors is

— Dr Mike Ward (@Schroedinger99) November 13, 2015

So far I have not been vouchsafed a reply. If I do hear from Dr Fisher I shall be more than happy to revisit what I say below - should this prove to be the wrong paper.

Assuming it is the right paper, let us list the claims made for it (each in turn):

1. This paper analyses "all clinical trials of homeopathy".
2. The analysis was "conducted by the Robertson Centre for Biostatistics at the University of Glasgow".
3. This paper "came to a clearly positive result".

Does this paper analyse all clinical trials of homeopathy?

No. It analyses some clinical trials of individualized homeopathy. In other words, it does not analyse clinical trials of the homeopathic remedies that the vast majority of people who avail themselves of this type of product consume. It analyses a small subset of trials which involve homeopathic prescriptions individually specified by dedicated homeopaths. We might note here that it is intrinsically more difficult to conduct large scale blinded randomized trials on groups of patients receiving individualized treatments than it is when all patients are receiving exactly the same treatment - especially when that treatment is in the form of tablets. But let's defer judgement on the trial itself. (please see note [1] below)

Was the analysis conducted by the Robertson Centre for Biostatistics at the University of Glasgow?

No. The paper is not listed by the Robertson Centre for Biostatistics as one of its publications. The paper has six authors, one of whom - Suzanne M Lloyd (a statistician) - works at the Centre. The copyright for the paper is actually held by Robert T Mathie of the British Homeopathic Association. Mathie is also the corresponding author.

Oh well, perhaps Dr Fisher just got his words a bit muddled. I probably would if I had to appear on the wireless first thing in the morning. Let us ask the most important question:

Did the paper come to a clearly positive result?

You be the judge:

Conclusions

• There was a small, statistically significant, treatment effect of individualised homeopathic treatment that was robust to sensitivity analysis based on ‘reliable evidence’.
• Findings are consistent with sub-group data [klaxon alert!] available in a previous ‘global’ systematic review of homeopathy RCTs.
• The overall quality of the evidence was low or unclear, preventing decisive conclusions.[my emphasis]
• New RCT research of high quality on individualised homeopathy is required to enhance the totality of reliable evidence and thus enable clearer interpretation and a more informed scientific debate.

A "clearly positive result"? (Even before we analyse whether the evidence presented really supports even these highly tentative conclusions - something I'd like to do later if I get time.[1]) I think the man on the Clapham omnibus would probably conclude that this question deserves a resounding "no" too.

Over to you Dr Fisher!

PS If you listen to the clip you'll hear Dr Simon Singh (@SLSingh) putting the case for science (on behalf of The Good Thinking Society @GoodThinkingSoc) and I should urge anyone not familiar with the arguments surrounding so called "alternative medicine" to read the excellent "Trick or Treatment?: Alternative Medicine on Trial" by him and Prof Edzard Ernst (@EdzardErnst).

[1] Alan (please see comment below) has drawn my attention to this discussion of the paper cited by Dr Fisher which is well worth a read and saves me having to fillet this particular fish myself. And this discussion is followed up with a more definitive analysis of flaws in the paper by Prof Edzard Ernst here: HOMEOPATHY: proof of concept or proof of misconduct?.

Should we renationalize the railways?

(or The Mighty Diamonds and why this leftie didn’t vote for Corbyn [1])

Since everyone else (well Rod Liddle at least [2]) is using music, drugs, and East Germany to illustrate their views about Corbyn, I thought I’d do the same.

I’m not actually going to answer the question I pose – for reasons that will become clear. I simply wish to use trains as vehicles for subjecting Jeremy Corbyn’s views to a bit of scrutiny – pon the lef-hand side[3].

Scroll back to 1982 and, whether you were passing the Dutchie or (more likely) the Kouchie you would probably have (assuming you considered yourself “pon the leff-hand side”) agreed that privatization of British Rail – which began in that year with the selling off of British Rail’s publicly owned catering and hotel businesses – was a “bad thing”.

Public ownership or “socialism” (at least on some definitions of the term) was, pon the other hand, a “good thing”.

But our notions of “good” and “bad” here are problematic – even before we analyse them in any detail. We are already potentially conflating what is (or is not) morally superior with what is functionally superior (whatever our definitions of “superior” in these contexts). Economists on both the right (see eg Friedrich Hayek) and the left (see eg Karl Marx) are guilty (in very different ways) of the same conflation.

Approaching from the right or the left, I think we have to concede that the system of economic organization which is best at generating the most wealth may or may not be best at generating the most happiness for the most people[4]. Of course left and right wingers will care differently about human wellbeing and wealth, but even left-wingers may have to concede that there may, even in a mythical “perfect world”, be a trade-off between what is fairest and what is best overall – a subject which has been analysed in probably the greatest depth by John Rawls[5].

When we do analyse, in more detail, whether socialism is better or worse than capitalism the issues become even harder to disentangle.

Most distinctions between socialism and capitalism can be placed into one of two categories: the ownership category and the control category.

Under capitalism, the means of production, distribution, and exchange are, as we erstwhile socialists all learned, under private ownership. But were they then, and are they now, and what does this even mean?

Some businesses – like the joinery firm I use - are owned by sole traders – as some were in the German Democratic Republic (GDR) or “East Germany” as it was more often known (a “socialist” economy which I happen to know something about). Some businesses – like the shopping chain John Lewis – are workers’ cooperatives – a form of ownership also found in the GDR. Some – like the Coop shopping chain and your local building society - are consumer cooperatives (owned by their members) – see again the Konsum chain in the GDR. Some – like your local Spar – are cooperatives of private businesses – see farming in the GDR. Many UK businesses (very few today) were, back in 1982, still state owned. British Rail for example. This was the rule rather than the exception in the GDR. At one stage British Petroleum (BP) was a wholly state owned enterprise and later (for a while), even after it had gone “public” (ie private), most of its shares were still owned by the UK government. These days, nearly all larger industries in the UK are privately owned, which is to say that they are owned by their shareholders. But who are the biggest shareholders? In many cases these are pension funds that invest in industry and which are, essentially, owned collectively by everyone who has a private or company pension.

So ownership of the means of production, distribution, and exchange is a rather complicated subject – even though I have hardly scratched the surface.

What about control?

During the War (which resulted in the division of Germany and Europe into “socialist” and “capitalist” halves) both sides planned and controlled almost every aspect of production, distribution, and exchange – even though many industries and businesses continued to be privately owned. Even today in the UK, the High Speed Rail link – if it goes ahead – will be centrally planned and controlled by bureaucrats and elected politicians but executed by private firms.

“Central planning” has a bad name, but clearly has a crucial role to play when it comes to a national rail network (and many other areas). What did for the GDR (and similar economies) was not so much the presence of planning but the absence of market forces. Right-wingers ascribe all sorts of magical powers and foresight to capitalists, but I strongly suspect that the main advantage of capitalism is that it employs market forces to control the economic system in an essentially Darwinian fashion and makes competing firms that make the “wrong” decisions at any time extinct. Those “decisions” might as well be – and probably often are – made entirely randomly[6]. As Marx pointed out, capitalism constantly revolutionizes the means of production. Socialism didn’t and was left behind.

So control is complex too and, to a surprising extent, independent of ownership. You could, in theory at least, have state capitalism[7] or, at the opposite extreme, market socialism.

So what’s the best way to run a railway?

I have no idea; nor, I suspect, has Jeremy Corbyn.

I do, however, suspect that Jeremy Corbyn and I both want the same outcomes: a reliable, thriving, efficient rail network that is responsive to social, commercial, and environmental requirements and which treats its own staff well and pays them good wages. I further suspect that many on the right could not give a shit about most of the items in this list.

It is the outcomes we wish to see (I submit) that really (or really ought to) divide left and right in today’s world rather than how we best achieve those outcomes.

Perhaps renationalization of the railways is the best way to achieve those outcomes. Perhaps it isn’t. But that is an empirical question rather than a moral or philosophical question and even if a nationalized railway were better than a private one, I rather doubt that the same would apply to, say, car manufacture or grocery distribution.

Nothing I say above is particularly novel or insightful but Jeremy Corbyn shows no signs whatsoever of having ever considered the issues I raise or having matured his political outlook at all in the years since 1982.

I do not say all this because I have abandoned my left-wing principles over the years. I want the same things that Jeremy wants and that I always wanted: a fairer and more prosperous world. I still don’t want a world where a few people are allowed to shovel money into their own pockets in return for contributing little or nothing to the general good. What I have abandoned is many of the beliefs I once held about how best to get there.

Sometimes you have to “pass the knowledge from the right-hand side”. [8]

1. I am not a member of the Labour Party but had a vote through my Trades Union.
2. You won't believe this story about my friend, Jeremy Corbyn and the owl The real disgust wasn’t about the pig’s head. It was about the awful band Supertramp
3. Pass the Kouchie
4. A vaguely Millsian statement of moral superiority. Other brands of moral superiority are available.
5. A Theory of Justice
6. A train of thought I explore here.
7. In a true rather than an SWP sense.
8. Pass the Knowledge

Our notions of "race" and Wittgenstein on "family likenesses"

[Our] craving for generality is the resultant of a number of tendencies connected with particular philosophical confusions. There is- [....] The tendency to look for something in common to all entities which we commonly subsume under a general term.-We are inclined to think that there must be something in common to all games, say, and that this common property is the justification for applying the general term "game" to the various games; whereas games form a family the members of which have family likenesses. [....]

Ludwig Wittgenstein, The Blue Book, pp 17, 18.

There's an excellent piece from Dr Adam Rutherford in in today's Observer: "Why racism is not backed by science"

in it Adam writes:

We now know that the way we talk about race has no scientific validity. There is no genetic basis that corresponds with any particular group of people, no essentialist DNA for black people or white people or anyone. This is not a hippy ideal, it’s a fact. There are genetic characteristics that associate with certain populations, but none of these is exclusive, nor correspond uniquely with any one group that might fit a racial epithet.

Claims like this seem surprising and counter-intuitive to a lot of people, but the science tells us unequivocally that they are true.

As far as I am aware, the philosopher Ludwig Wittgenstein never wrote directly about the biology of "race", but he did have a lot to say about our use of language and the kind of thinking that underlies our use of language. As ever, I make no claims to do justice to his legacy here, but one of his themes has always struck me as being particularly relevant to our confused notions of "race".

Wittgenstein argued that particular instances of things to which general terms - such as "game" - apply, do not necessarily possess any one feature in common but form a group in much the same way as members of an extended family do when considered with respect to their physical appearances - a shared chin shape here, a shared idiosyncrasy there.

[So here we're going to be using a biological metaphor to illustrate a sports metaphor in order to illustrate a general point about our use of language concerning an apparently biological phenomenon, but please bear with me :-)]

If Wittgenstein is right, then it might be possible (in principle at least) to quantify the extent to which "family likeness" is shared between different particular cases. If we were to label the various features of particular cases of a general term with letters of the alphabet we might come up with something like the following (this is my example not Ludwig's):

1. ABCKL
2. ABCDF
3. ABCGE
4. ABHDE
5. ABCDE
6. AICDE
7. JBCDE
8. ABMNE
9. AOPDE

These nine entities form a group, from which (given no further information) we should almost certainly exclude an entity such as "VWXYZ", and yet these entities have no one feature in common. Entity number one shares three features with three other entities, two features with four other entities, and one feature with one other entity. Entity number three shares four features with one other entity, three features with six other entities, and two features with one other entity. By counting the number of other entities with whom a feature is shared, and adding these numbers together for each entity it would be possible to calculate a "coefficient of shared features" for each entity. In the example provided, the coefficients would be as follows:

1. 18
2. 23
3. 24
4. 24
5. 29
6. 23
7. 22
8. 19
9. 18

It now becomes clear (as could probably have been guessed by simply looking at the example presented) that entity number five shares its features more widely than any other member of the group. If the entities in question were games, then number five might be cricket (which has most features we normally associate with games) and number one might be frisbee (which has players and equipment, but no formal rules, no competition, and no winning or losing*). Whether playing frisbee should be called a "true" game is the kind of issue over which we could imagine disputes. An activity such as cricket (some other examples would serve equally well) is not only secure from such controversy, it actually belongs to the very heart of the concept of game playing**. In the same way, entity number five enjoys a distinct centrality within the family of entities to which it belongs. (Conveniently, in the above presentation, entity number five is also centrally positioned). It is number five which we should choose if asked to pick one example from the above group to serve as a paradigm.

Analysing general terms in this way sheds light on why we have concepts of "racial groups" and think we can describe paradigm examples of members of those "groups" - a "typical negro", a "typical caucasian", or whatever - even though there are no genes which are unique to people we would tend to classify as "black" or "white" or "asian". Even the outward indicators of race: curly or straight hair, dark or light skin, eyes with or without epicanthic folds etc (let alone the complex genetics that underlie such traits) are spread across many different population groups that are often seen as distinct "races".

Let us give Wittgenstein the final word:

There is a tendency [....] to think that the man who has learnt to understand a general term, say the term "leaf", has thereby come to possess a kind of general picture of a leaf, as opposed to pictures of particular leaves. [....]

Instead of "craving for generality" I could have said "the contemptuous attitude towards the particular case".

* This may have changed of course, but it was true in my day :-)

** Even though I have no idea whatsoever what is going on when I watch a game of cricket.