Are You Calling My Fox Terrier Stupid?

In what he later said turned out to be one of his most popular essays, The Case of the Creeping Fox Terrier Clone in his book Bully for Brontosaurus, the late Stephen Jay Gould explained how the size of the earliest known member of the horse family, hyracotherium (or eohippus to non-pedants), was invariably compared to that of a fox terrier. Gould referred to these sometimes unwittingly plagiarised fox terrier comparisons as clones, although certain other popular science writers would no doubt have referred to the spreading of a successful meme.

Even though the discovery of Flores Man was announced less than a month ago, our diminutive cousin has already acquired a meme of his own: his brain, we are told, was the size of a grapefruit. Some of the more technical articles about the discovery thoughtfully go on to explain that this means Flores Man's brain had a volume of around 380cm³. The comparison to a citrus fruit is sometimes followed by expressions of general incredulity that a human with only a grapefruit for a brain would have been clever enough to make the tools associated with the Flores skeletons—or even to get to Flores in the first place, come to think of it.

But the grapefruit comparison begs an obvious question: clearly, it would be unfair to make direct comparisons between the sizes of our own brains and those of Flores Man—if for no other reason than we are a different, albeit closely related species—but exactly how large would we expect the brain of a one-metre-tall person to be? Or, to look at it another way, if Flores Man was our height, what size would his (or, more accurately, her) brain be?

In scaling things up, it is not uncommon to overlook the fact that there is more than one dimension involved. If you double the (one-dimensional) diameter of a sphere, the sphere's two-dimensional surface area increases by a factor of four (2 x 2), and its three-dimensional volume increases by a factor of eight (2 x 2 x 2).

So, if we were to scale up Flores Man's height by a factor of x, we would expect to see the volume of his brain (and every other organ of his body) increase by a factor of x³.

The following table shows the results of such calculations for various inflated sizes of Flores Man. It's a silly calculation, but somebody had to do it.

Height (m) Brain volume (cm³)
1.00 380
1.05 440
1.10 506
1.15 578
1.20 657
1.25 742
1.30 835
1.35 935
1.40 1043
1.45 1158
1.50 1283
1.55 1415
1.60 1556
1.65 1707
1.70 1867
1.75 2037
1.80 2216
1.85 2406

The above calculations indicate that a 1.55m (5'5") tall Flores Man would have a perfectly respectable (by modern human standards) 1415cm³ brain. (The volume quoted for a modern human brain is typically around 1400cm³—although typical modern human heights are very difficult to define).

Obviously, we can take these sorts of calculations too far—as, indeed, I already have—but they do at least acknowledge an important question: don't we place far too much emphasis on brain size when talking about intelligence? Or, to borrow a phrase more often used in comparisons of other aspects of human anatomy, does size matter?

Clearly, we are far more intelligent than any other living species that we know about. It would also seem reasonable to assume that we are more intelligent than earlier hominids. But Flores Man and some other members of our genus were, for some time at least, our contemporaries, and they shared a close common ancestor with us. So what gives us the right to expect them to be a bunch of grapefruit heads? Surely sheer brain size is far too crude an indication of intelligence (whatever that vague word means).

Yes, I realise I am setting up a straw man here: nobody believes that brain size is the be all and end all of intelligence. But, that being the case, why the great surprise when someone with a brain the size of a grapefruit turns out to have been rather clever? Surely, if anything, it is the complexity of the brain's structure—and the brain's structure itself—that is most likely to have some effect on its owner's intelligence; not simply its bulk. But structure and complexity are a lot harder to gauge from a few ancient bones.

There is a long history of scientists' measuring the size of brains in the assumption that there was a correlation between brain size and intelligence. There probably is some sort of correlation. But there are plenty of other factors that must surely influence intelligence. Did these scientists, I wonder, place such emphasis on brain size simply because brain size was something they thought they could actually measure?

Great Dane & Chihuahua

Canine Einstein and doggy dunce?

It might seem quite reasonable, within our own species, to assume the bigger the brain, the greater the intelligence, but forget about Homo sapiens for a moment and think about our best friend, Canis familiaris: does it make any sense at all to claim that Old English Sheep Dogs are cleverer than German Shepherds? Are you seriously trying to tell me that your St Bernard is smarter than my mum's Cocker Spaniel? Are you calling my hyracotherium-sized fox terrier stupid?

Or, to put it (slightly) more poetically:

If intelligence depended on the size of their brains,
The cleverest dogs would be the Great Danes;
The mutt most lacking in mental power
Would be that minuscule dimwit: the Chihuahua.

Postscript (27-Dec-04):

I said I had already taken my theoretical calculations too far, but it would appear they could do with a little tweaking:

Since writing the above piece, I came across a discussion about the relative brain sizes of different species in Richard Dawkins's new book, The Ancestor's Tale.

Apparently, in the real world (as opposed to the naively theoretical world of my calculations), if you measure the relative brain volumes of different species, they do not increase in direct proportion to the species' overall body volumes, but in proportion to the species' body volumes raised to the power of ¾. Nobody is quite sure why this is, but it is thought to be a trade-off between conflicting needs to scale up certain aspects of the organ in proportion to volume and to scale up other aspects in proportion to area. This ¾-power relationship is empirical, but it seems to hold pretty true for a large number of organs and species. It therefore has a name: Kleiber's Law.

The table below shows the re-calculated expected brain sizes for various inflated sizes of Flores Man, taking into account Kleiber's Law. I would say it still supports my original argument (well I would say that, wouldn't I?): if Flores Man were to be scaled up to have a brain of similar size to a modern human's (around 1400cm&sup3), (s)he would be around 1.80m (5'10") tall—a fairly unremarkable height for a modern human.

Height (m) Brain volume (cm³)
1.00 380
1.05 424
1.10 471
1.15 520
1.20 573
1.25 628
1.30 686
1.35 747
1.40 810
1.45 877
1.50 946
1.55 1019
1.60 1094
1.65 1173
1.70 1254
1.75 1339
1.80 1426
1.85 1517

Post-postscript:

See also:

This article was published on 13th November, 2004.
A postscript was added on 27th December, 2004.
The format of the article was changed (and a few minor amendments were made to the words) on 16th July, 2012, to accommodate a change in format due to migration to WordPress.

3 thoughts on “Are You Calling My Fox Terrier Stupid?

  1. Mona Albano

    One little quibble, since you were discussing language (memes and all): to beg the question is a rhetorical device meaning to assume your conclusion. I think that you wanted "raises the question."

    Reply
  2. Richard Carter, FCD

    Mona, it's come to a sad thing if a website dedicated to Charles Darwin can't acknowledge that languages evolve.

    Your interpretation of the phrase "to beg the question" is undoubtedly the original one, but mine has out-competed it memetically and is now the more common by far. To quote the Concise Oxford Dictionary (Tenth Edition), which I accept as ultimate authority in such matters:

    "beg the question: 1. (of a fact or action) invite a question or point that has not been dealt with. 2. assume the truth of an argument or proposition to be proved , without arguing it."

    The Concise Oxford always puts the most common current usage first in its definitions.

    (I take it that preposition at the end of definition 1 has set your teeth on edge!)

    Reply
  3. Elmer Clyde Hollifield

    brain size is unimportant...humming birds with brains smaller than a pea migrate from canada to mexico each year and find their way back to my house.   i dare any large brained human to do the same......clyde, on the appalachian reservation

    Reply

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