When is a vertebra “horizontal”, part 2
August 28, 2018
Thanks to everyone who’s engaged with yesterday’s apparently trivial question: what does it mean for a vertebra to be “horizontal”? I know Matt has plenty of thoughts to share on this, but before he does I want to clear up a couple of things.
This is not about life posture
First, and I really should have led with this: the present question has nothing to do with life posture. For example, Anna Krahl wrote on Twitter:
I personally find it more comprehensible if the measurements relate to something like eg. the body posture. This is due to my momentary biomech./functional work, where bone orientation somet is difficult to define.
I’m sympathetic to that, but we really need to avoid conflating two quite different issues here.

Taylor, Wedel and Naish (2009), Figure 1. Cape hare Lepus capensis RAM R2 in right lateral view, illustrating maximally extended pose and ONP: skull, cervical vertebrae 1-7 and dorsal vertebrae 1-2. Note the very weak dorsal deflection of the base of the neck in ONP, contrasting with the much stronger deflection illustrated in a live rabbit by Vidal et al. (1986: fig. 4). Scalebar 5 cm.
If there’s one thing we’ve learned in the last couple of decades, it’s that life posture for extinct animals is controversial — and that goes double for sauropod necks. Heck, even the neck posture of extant animals is terribly easy to misunderstand. We really can’t go changing what we mean by “horizontal” for a vertebra based on the currently prevalent hypothesis of habitual posture.
Also, note that the neck posture on the left of the image above is close to (but actually less extreme than) the habitual posture of rabbits and hares: and we certainly wouldn’t want to illustrate vertebrae as “horizontal” when they’re oriented directly upwards, or even slightly backwards!
Instead, we need to imagine the animal’s skeleton laid out with the whole vertebral column in a straight line — sort of like Ryder’s 1877 Camarasaurus, but with the tail also elevated to the same straight line.

Ryder’s 1877 reconstruction of Camarasaurus, the first ever made of any sauropod, modified from Osborn & Mook (1921, plate LXXXII).
Of course, life posture is more important, and more interesting, question than that of what constitutes “horizontal” for an individual vertebra — but it’s not the one we’re discussing right now.
In method C, both instances are identically oriented
I’m not sure how obvious this was, but I didn’t state it explicitly. In definition C (“same points at same height in consecutive vertebrae”), I wrote:
We use two identical instances of the vertebrae, articulate them together as well as we can, then so orient them that the two vertebrae are level
What I didn’t say is that the two identical instances of the vertebrae have to be identically oriented. Here’s why this is important. Consider that giraffe C7 that we looked at last time, with its keystoned centrum. if you just “articulate them together as well as we can” without that restriction, you end up with something like this:
Which is clearly no good: there’s no way to orient that such that for any given point on one instance, the corresponding point on the other is level with it. What you need instead is something like this:
In this version, I’ve done the best job I can of articulating the two instances in the same attitude, and arranged them such that they are level with each other — so that the attitude shown here is “horizontal” in sense C.
As it happens, this is also just about horizontal in sense B — the floor of the neural canal is presumably at the same height as the top of the centrum as it meets the neural arch.
But “horizontal” in sense A (posterior articular surface vertical) fails horribly for this vertebra:
To me, this image alone is solid evidence that Method A is just not good enough. Whatever we mean by “horizontal”, it’s not what this image shows.
References
- Osborn, Henry Fairfield, and Charles C. Mook. 1921. Camarasaurus, Amphicoelias and other sauropods of Cope. Memoirs of the American Museum of Natural History, n.s. 3:247-387, and plates LX-LXXXV.
- Taylor, Michael P., Mathew J. Wedel and Darren Naish. 2009. Head and neck posture in sauropod dinosaurs inferred from extant animals. Acta Palaeontologica Polonica 54(2):213-220.
- Vidal, Pierre Paul, Werner Graf and Alain Berthoz. 1986. The orientation of the cervical vertebral column in unrestrained awake animals. Experimental Brain Research 61:549-559.
What does it mean for a vertebra to be “horizontal”?
August 28, 2018
I was lucky enough to have Phil Mannion as one of the peer-reviewers for my recent paper (Taylor 2018) showing that Xenoposeidon is a rebbachisaurid. During that process, we got into a collegial disagreement about one of the autapomorphies that I proposed in the revised diagnosis: “Neural arch slopes anteriorly 30°–35° relative to the vertical”. (This same character was also in the original Xenoposeidon paper (Taylor and Naish 2007), in the slightly more assertive form “neural arch slopes anteriorly 35 degrees relative to the vertical”: the softening to “30°–35°” in the newer paper was one of the outcomes of the peer-review.)
The reason this is interesting is because the slope of the neural arch is measured relative to the vertical, which of course is 90˚ from the horizontal — but Phil’s comments (Mannion 2018) pushed me to ask myself for the first time: what actually is “horizontal”? We all assume we know horizontality when we see it, but what precisely do we mean by it?
Three notions of “horizontal”

The idiosyncratic best-preserved caudal vertebra of the Snowmass Haplocanthosaurus MWC 8028, illustrating three different versions of “horizontal”. A. horizontality defined by vertical orientation of the posterior articular surface. B. horizontality defined by horizontal orientation of the roof of the neural canal (in this case, rotated 24˚ clockwise relative to A). C. horizontality defined by optimal articulation of two instances of the vertebra, oriented such the a line joining the same point of both instances is horizontal (in this case, rotated 17˚ clockwise relative to A). Red lines indicate exact orthogonality according to the specified criteria. Green line indicate similar but diverging orientations: that of the not-quite-vertical anterior articular surface (A) and of the not-quite-horizontal base of the neural canal (B).
There are at least three candidate definitions, which we can see yield noticeably different orientations in the case of the Snowmass Haplocanthosaurus vertebra that Matt’s been playing with so much recently.
Definition A: articular surfaces vertical
In part A, I show maybe the simplest — or, at least, the one that is easiest to establish for most vertebrae. So long as you have a reasonably intact articular surface, just rotate the vertebra until that surface is vertical. If, as is often the case, the surface is not flat but concave or convex, then ensure the top and bottom of the surface are vertically aligned. This has the advantage of being easy to do — it’s what I did with Xenoposeidon — but it conceals complexities. Most obviously, what to do when the anterior and posterior articular surfaces are not parallel, in the 7th cervical vertebra of a giraffe?

Cervical vertebra 7 of Giraffa camelopardalis FMNH 34426, in left lateral view. Note that the centrum is heavily “keystoned” so that the anterior and posterior articular surfaces are 15-20˚ away from being parallel.
Another difficulty with this interpretation of horizontality is that it can make the neural canal jagged. Consider a sequence of vertebrae oriented as in part A, all at the same height: the neural canal would rise upwards along the length of each vertebra, before plunging down again on transitioning from the front of one to the back of the next. This is not something we would expect to see in a living animal: see for example the straight line of the neural canal in our hemisected horse head(*).
Definition B: neural canal horizontal
Which leads us to the second part of the illustration above. This time, the vertebra is oriented so that the roof of the neural canal is horizontal, which gives us a straight neural canal. Nice and simple, except …
Well, how do we define what’s horizontal for the neural canal? As the Haplocanthosaurus vertebra shows nicely, the canal is not always a nice, neat tube. In this vertebra, the floor is nowhere near straight, but dishes down deeply — which is why I used to the roof, rather than the floor of the canal. Rather arbitrary, I admit — especially as it’s often easier to locate the floor of the canal, as the dorsal margin is often confluent with fossae anteriorly, posteriorly or both.
And as we can see, it makes a difference which we choose. The green line in Part B of the illustration above shows the closest thing to “horizontal” as it would be defined by the ventral margin of the neural canal — a straight line ignoring the depression and joining the anteriormost and posteriormost parts of the base of the canal. As you can see, it’s at a significantly different angle from the red line — about 6.5˚ out.
And then you have human vertebrae, where the dorsal margin of the neural canal is so convex in lateral view that you really can’t say where the anteriormost or posteriormost point is.

Left sides of hemisected human thoracic vertebrae, medial view. Note how ill-defined the dorsal margin of the neural canal is.
So can we do better? Can we find a definition of “horizontal” that’s not dependent of over-interpreting a single part of the vertebra?
Definition C: same points at same height in consecutive vertebrae
I’ve come to prefer a definition of horizontal that uses the whole vertebra — partly in the hope that it’s less vulnerable to yielding a distorted result when the vertebra is damaged. With this approach, shown in part C of the illustration above, we use two identical instances of the vertebrae, articulate them together as well as we can, then so orient them that the two vertebrae are level — that a line drawn between any point on one vertebra and its corresponding point on the other is horizontal. We can define that attitude of the vertebra as being horizontal.
Note that, while we use two “copies” of the vertebra in this method, we are nevertheless determining the horizontality of a single vertebra in isolation: we don’t need a sequence of consecutive vertebrae to have been preserved, in fact it doesn’t help if we do have them.
One practical advantage of this definition is that its unambiguous as regards what part of the vertebra is used: all of it; or any point on it, at the measurement stage. By contrast, method A requires us to choose whether to use the anterior or posterior articular surface, and method B requires a choice of the roof or floor of the neural canal.
Discussion
I have three questions, and would welcome any thoughts:
- Which of these definitions do you prefer, and why?
- Can you think of any other definitions that I missed?
- Does anyone know of any previous attempts to formalise this? Is it a solved problem, and Matt and I somehow missed it?
Answers in the comments, please!
References
- Mannion, Philip D. 2018 Peer Review #3 of “Xenoposeidon is the earliest known rebbachisaurid sauropod dinosaur (v0.2)”. PeerJ. https://doi.org/10.7287/peerj.5212v0.2/reviews/3
- Taylor, Michael P. 2018. Xenoposeidon is the earliest known rebbachisaurid sauropod dinosaur. PeerJ 6:e5212. doi: 10.7717/peerj.5212
- Taylor, Michael P., and Darren Naish. 2007. An unusual new neosauropod dinosaur from the Lower Cretaceous Hastings Beds Group of East Sussex, England. Palaeontology 50(6):1547-1564. doi: 10.1111/j.1475-4983.2007.00728.x
(*) Yes, of course we have a hemisected horse head. What do you think we are, savages?
Down in flames
August 25, 2018
I first encountered Larry Niven’s story/essay “Down in Flames” in the collection N-Space in high school. This was after I’d read Ringworld and most of Niven’s Known Space stories, so by the time I got to “Down in Flames” I had the context to get it. (You can read the whole thing for free here.)
Here’s the idea, from near the start:
On January 14, 1968, Norman Spinrad and I were at a party thrown by Tom & Terry Pinckard. We were filling coffee cups when Spinny started this whole thing.
“You ought to drop the known space series,” he said. “You’ll get stale.” (Quotes are not necessarily dead accurate.) I explained that I was writing stories outside the “known space” history, and that I would give up the series as soon as I ran out of things to say within its framework. Which would be soon.
“Then why don’t you write a novel that tears it to shreds? Don’t just abandon known space. Destroy it!”
“But how?” (I never asked why. Norman and I think alike in some ways.)
The rest of the piece is just working out the details.
“Down in Flames” brain-wormed me. Other than Ray Bradbury’s “A Sound of Thunder” I doubt if there is another short story I’ve read as many times. Mike once described the act of building something complex and beautiful and then destroying it as “magnificently profligate”, and that’s the exact quality of “Down in Flames” that appeals to me.
I also think it is a terrific* exercise for everyone who is a scientist, or who aspires to be one.
* In both the modern sense of “wonderful” and the archaic sense of “causing terror”.
Seriously, try it. Grab a piece of paper (or open a new doc, or whatever) and write down the ideas you’ve had that you hold most dear. And then imagine what it would take for all of them to be wrong. (When teams and organizations do this for their own futures, it’s called a pre-mortem, and there’s a whole managerially-oriented literature on it. I’d read “Down in Flames” instead.)

It feels like this! Borrowed from here.
Here are some questions to help you along:
- Which of your chains of reasoning admit more than one end-point? If none of them might lead other places, then either you are the most amazing genius of all time (even Newton and Einstein made mistakes), or you are way behind the cutting edge, and your apparent flawlessness comes from working on things that are already settled.
- If there is a line of evidence that could potentially falsify your pet hypothesis, have you checked it? Have you drawn any attention to it? Or have you gracefully elided it from your discussions in hopes that no-one will notice, at least until after you’re dead?
- If there’s no line of evidence that could falsify your pet hypothesis, are you actually doing science?
- Which of your own hypotheses do you have an emotional investment in?
- Are there findings from a rival research team (real or imagined) that you would not be happy to see published, if they were accurate?
- Which hypotheses do you not agree with, that you would be most dismayed to see proven correct?
[And yes, Karl, I know that according to some pedants hypotheses are never ‘proven’. It’s a theoretical exercise already, so just pretend they can be!]
I’ll close with one of my favorite quotes, originally published in a couple of tweets by Angus Johnson in May of 2017 (also archived here):
If skepticism means anything it means skepticism about the things you WANT to be true. It’s easy to be a skeptic about others’ views. Embracing a set of claims just because it happens to fit your priors doesn’t make you a skeptic. It makes you a rube, a mark, a schnook.
So, don’t be that rube. Burn down your house of ideas – or at least, mentally sift through the rubble and ashes and imagine how it might have burned down. And then be honest about that, minimally with yourself, and ideally with the world.
If you’re a true intellectual badass, blog the results. I will. It’s not fair to give you all homework – painful homework – and not take the medicine myself, so I’m going to do a “Down in Flames” on my whole oeuvre in the next a future post. Stay tuned!
Diplodocus goes digital
August 21, 2018
No time for a proper post, so here’s a screenshot from Amira of Diplodocus caudal MWC 8239 (the one you saw being CT scanned last post) about to be digitally hemisected. Trust me, you’ll want to click through for the big version. Many thanks to Thierra Nalley for the Amira help.
Further bulletins as time and opportunity allow.
Robin N. Kok asked an interesting question on Twitter:
For all the free money researchers throw at them, they might as well be shareholders. Maybe someone could model a scenario where all the APC money is spent on RELX shares instead, and see how long it takes until researchers own a majority share or RELX.
Well, Elsevier is part of the RELX group, which has a total market capitalisation of £33.5 billion. We can’t know directly how much of that value is in Elsevier, since it’s not traded independently. But according to page 124 their 2017 annual report (the most recent one available), the “Scientific, Technical and Medical” part of RELX (i.e. Elsevier) is responsible for £2,478M of the total £7,355M revenue (33.7%), and for £913M of the £2,284M profit (40.0%). On the basis that a company’s value is largely its ability to make a profit, let’s use the 40% figure, and estimate that Elsevier is worth £13.4 billion.
(Side-comment: ouch.)
According to the Wellcome Trust’s 2016/17 analysis of its open access spend, the average APC for Elsevier articles was £3,049 (average across pure-OA journals and hybrid articles).
On that basis, it would take 4,395,000 APCs to buy Elsevier. How long would that take to do? To work that out, we first need to know how many APC-funded articles they publish each year.
From page 14 of the same annual report as cited above. Elsevier published “over 430,000 articles” in a year. But most of those will have been in subscription journals. The same page says “Subscription sales generated 72% of revenue, transactional sales 26% and advertising 2%”, so assuming that transactional sales means APCs and that per-article revenue was roughly equal for subscription and open-access articles, that means 26% of their articles — a total of 111,800.
At 111,800 APCs per year, it would take a little over 39 years to accumulate the 4,395,000 APCs we’d need to buy Elsevier outright.
That’s no good — it’s too slow.
What if we also cancelled all our subscriptions, and put those funds towards the buy-out, too? That’s actually a much simpler calculation. Total Elsevier revenue was £2,478M. Discard the 2% that’s due to advertising, and £2428M was from subscriptions and APCs. If we saved that much for just five and a half years, we’d have saved enough to buy the whole company.
That’s a surprisingly short time, isn’t it?
(In practice of course it would be much faster: the share-price would drop precipitously as we cancelled all subscription and stopped paying APCs, instantly cutting revenue to one fiftieth of what it was before. But we’ll ignore that effect for our present purposes.)
Caudal vertebrae of Haplocanthosaurus delfsi
August 12, 2018
Tired of Haplo caudals yet? No? Good – me neither. Not by a long shot.
Above is McIntosh and Williams (1988: fig. 10) showing the rearticulated and partially reconstructed tail of CMNH 10380, the holotype and only known specimen of Haplocanthosaurus delfsi, in right anterolateral oblique view. It’s not an original, I plucked it from a PDF scan of the paper. Probably an original reprint would be a lot more clear. In hopes of seeing more, I cropped out the background and tweaked the contrast:
The first 14 caudals are real, the rest are sculpted replicas. You can tell in the photo because the thickness of the supporting rods drops sharply between caudals 14 and 15. That’s not my original observation, McIntosh and Williams pointed it out.
Conclusion? It looks like a pretty good Haplo tail. The first caudal has big, plate-like caudal ribs, which grade rapidly into the normal laterally-projecting stumps in succeeding vertebrae. Caudal 1 also has a distinctly tall, backwardly-curved neural spine, which grades into shorter, straighter spines very rapidly as well. It’s as if the first caudal is built on a typical diplodocoid plan, but the rest are simple non-neosauropod or basal macronarian caudals and they have to switch over as quickly as possible. Both of those shifts happen in the first few caudals in the other Haplo tails, too, with some minor variation among specimens.
I’m sure I’ll have more to say about this specimen in the future, but I’m attending the Flugsaurier conference in LA this weekend so my head is in the clouds. Hope you’re having half as much fun.
Reference
- McIntosh, J.S., and Williams, M. E. 1988. A new species of sauropod dinosaur, Haplocanthosaurus delfsi sp. nov., form the Upper Jurassic Morrison Fm. of Colorado. Kirtlandia 43:3-26.
The Haplo project enjoys a brief interlude in realspace
August 7, 2018

Preserved bits of the Snowmass Haplocanthosaurus, MWC 8028, with me for scale. Modified from Wedel (2009: fig. 10), but not much – MWC 8028 was about the same size as CM 879.
Let’s say you had a critter with weird neural canals and super-deeply-dished-in centrum-ends, and you wanted to digitally rearticulate the vertebrae and reconstruct the spinal cord and intervertebral cartilages, in a project that would bring together a bunch of arcane stuff that you’d been noodling about for years. Your process might include an imposing number of steps, and help from a LOT of people along the way:
1. Drive to Dinosaur Journey in Fruita, Colorado, to pick up the fossils and bring them back to SoCal. (Thank you Paige Wiren, John Foster, and Rebecca Hunt-Foster for an excuse to come to the Moab area, thank you Brian Engh for the awesome road trip, and thank you Julia McHugh for access to specimens and help packing them up!).
2. Take the fossils to the Hemet Valley Medical Center for CT scanning. (Thank you John Yasmer and team.)
3. Find a colleague who would help you generate 3D models from the CT scans. (Thank you Thierra Nalley.)
4. Talk it over with your university’s 3D vizualization team, who suggest a cunning plan: (Thank you Gary Wisser, Jeff Macalino, and Sunami Chun at WesternU.)
5. They print the best-preserved vertebra at 75% scale. (50% scale resin print shown here.)
6. You and a collaborator physically sculpt in the missing bits with some Super Sculpey. (Thank you Jessie Atterholt for sculpting, and thank you Jeremiah Scott for documenting the process.)
(7.) The 3D-viz team use their fancy optical scanner (basically a photogrammetry machine) to make:
- a second-generation digital model (digital)
- from the sculpted-over 3D print (physical)
- of the first-generation digital model (digital)
- made from the CT scans (digital)
- of the original fossil material (physical).
(8.) With some copying, pasting, and retro-deforming, use that model of the restored vert as a template for restoring the rest of the vertebrae, stretching, mirroring, and otherwise hole-filling as needed. (Prelim 2D hand-drawn version of caudal 1 shown here.)
(9.) Test-articulate the restored vertebrae to see if and how they fit, and revise the models as necessary. (Low-fi speculative 2D version from January shown here.)
(10.) Once the model vertebrae are digitally rearticulated, model the negative spaces between the centra and inside the neural canals to reconstruct the intervertebral cartilages and spinal cord.
(11.) Push the university’s 3D printers to the limit attempting to fabricate an articulated vertebral series complete with cartilages and cord in different colors and possibly different materials, thereby making a third-generation physical object that embodies the original idea you had back in January.
(12.) Report your findings, publish the CT scans and 3D models (original and restored), let the world replicate or repudiate your results. And maaaybe: be mildly astonished if people care about the weird butt of the most-roadkilled specimen of the small obscure sauropod that has somehow become your regular dance partner.
We did number 6 yesterday, so just counting the arbitrarily-numbered steps (and ignoring the fact that 7-12 get progressively more complicated and time-consuming), we’re halfway done. Yay! I’ll keep you posted on how it goes from here.
Here’s caudal 1 in Haplocanthosaurus priscus, CM 879. Hatcher (1903) only illustrated this vert in right lateral view, in a drawing by Sydney Prentice (see this post). I showed the vert in left lateral, right lateral, and dorsal views in my 2009 air sac paper (figs. 7 and 9, here). As far as I know, no-one has ever illustrated this vert in anterior or posterior view before.
That’s a shame, because it’s the only first caudal of Haplocanthosaurus with a combination of good preservation and accessibility. The first caudal of the holotype, CM 572, was pretty wrecked and the drawings of it in Hatcher (1903) are largely reconstructions (this is discussed in McIntosh and Williams 1988). H. delfsi, CMNH 10380, has a nice caudal 1 but it’s stuck way up in the air in the mounted skeleton in Cleveland. The Snowmass Haplo, MWC 8028, includes a probable first caudal but it’s not going to win any beauty contests:

MWC 8028 probable caudal 1 in anterior (left), posterior (middle), and right lateral (right) views. From Foster and Wedel (2014: fig. 5).
Oh, and there’s the Bilbey haplocanthosaur on display at the Utah Field House of Natural History State Park Museum in Vernal. It has a very nice caudal sequence, probably the best for any haplocanthosaur, but (1) the specimen is under study by others so I don’t want to say too much about it, and (2) I couldn’t if I wanted to because the caudals are displayed in such a way that only the centra are easily visible.
I intended to talk a bit about the morphology of the first caudal in CM 879 and the other Haplo specimens, but now I’m out of time, so I’ll have to circle back to that in the future.
References
- Foster, J.R., and Wedel, M.J. 2014. Haplocanthosaurus (Saurischia: Sauropoda) from the lower Morrison Formation (Upper Jurassic) near Snowmass, Colorado. Volumina Jurassica 12(2): 197–210. DOI: 10.5604/17313708 .1130144
- Hatcher, J.B. 1903. Osteology of Haplocanthosaurus with description of a new species, and remarks on the probable habits of the Sauropoda and the age and origin of the Atlantosaurus beds; additional remarks on Diplodocus. Memoirs of the Carnegie Museum 2:1-75.
- McIntosh, J.S., and Williams, M. E. 1988. A new species of sauropod dinosaur, Haplocanthosaurus delfsi sp. nov., form the Upper Jurassic Morrison Fm. of Colorado. Kirtlandia 43:3-26.
- Wedel, M.J. 2009. Evidence for bird-like air sacs in saurischian dinosaurs. Journal of Experimental Zoology 311A:611-628.