I recently finished reading Contact by Carl Sagan. In the book they talk about a pattern in the transcendental number like pi or e, and comment that it is found in base 10 or however many fingers the race has to count with.

When in the end they find a pattern in pi it is in base 11, which I found a strange choice since I can't think of an animal that has an uneven total number of fingers, and I would think that most evolution would result in a somewhat symmetrical design.

Do any animal exist that has an uneven total number of fingers or equal lim, excluding polydactyly and oligodactyly?

  • $\begingroup$ I had a quick look around and I cant see any actual proof that pi has a pattern in base 11 apart from that book ? $\endgroup$
    – exussum
    Jul 19, 2013 at 12:13
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    $\begingroup$ The pattern is a fictional part of the book, but the author based a lot of the information in the book on existing scientific knowledge. There for i found it strange that he chose base 11, and I wanted to know if there where some beings on earth that if they where the dominant spice could have evolved to count on an uneven number of lims, but as Brandon pointed out some count in other ways. $\endgroup$
    – Blem
    Jul 19, 2013 at 17:33
  • $\begingroup$ cf. math.stackexchange.com/questions/460729/… $\endgroup$ Aug 7, 2013 at 1:20

3 Answers 3


Coscinasterias calamaria, the Eleven-Armed Sea Star! (Although I doubt it has much to do with pi)

enter image description here

Image from Wikimedia Commons

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    $\begingroup$ although both C.calamaria and "pi" sound similarly delcious $\endgroup$ Jul 18, 2013 at 14:01
  • $\begingroup$ True, I hadn't thought about the possibility of radial body designs! $\endgroup$
    – user3934
    Jul 18, 2013 at 14:05
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    $\begingroup$ Thanks for the answer, hadn't considered that, now can you teach them to count ;) $\endgroup$
    – Blem
    Jul 18, 2013 at 14:09
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    $\begingroup$ This has 11 votes, so I refuse to add another. sorry. $\endgroup$
    – ghoppe
    Jul 18, 2013 at 16:50
  • $\begingroup$ this is a good answer since bilateral symmetry is what creates even numbers of digits. $\endgroup$
    – shigeta
    Jul 18, 2013 at 17:33

Your conclusion relies on the supposition that all beings must count using their finger tips (or the most paralogous, "finger-like" limb). In fact, even within humans this is not necessarily true: the Yuki native people of California count in base 8 by counting the spaces between their fingers; meanwhile the Oksapmin people of Papua New Guinea count in base 27 (an odd number!) via counting a range of different body parts. One can easily imagine counting in base 20 by counting on fingers and toes. Heck, the Sumerians used base 60. And here's a scheme for counting in base 16 on your fingers.

So, it's entirely plausible to count in base 11, even when assuming morphological symmetry. The beings just need to settle on precisely which 11 parts of their anatomy to count.

As for your actual question, I am unaware of any species with an uneven total number of fingers and I would be surprised if we found one, based on an argument of developmental symmetry and overall (coarse-grained) evolutionarily conserved development plans within major clades of extant animals.

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    $\begingroup$ Really great answer. Thank you for answer what I needed to know and not just what I asked, that is how I personally prefer answer but I see a lot of people who ignore what people need and just answer what they ask for. $\endgroup$
    – Blem
    Jul 18, 2013 at 12:16
  • $\begingroup$ Arguably, the Kobon in PNG have a base 11 (body parts on one side), although it's not exactly a base, because they then count a midpoint before continuing to the other side of the body; thus, while "little finger"=1, "little finger other side"=23, not 22. (Harrison When Languages Die). $\endgroup$ Jul 18, 2013 at 14:26
  • $\begingroup$ Harrison also mentions other languages with uneven bases: 3 (Bukiyip), 5 (many languages), and 15 (Huli). $\endgroup$ Jul 18, 2013 at 14:57

I just wanted to say that I believe you're seeing it from a quite anthropocentric standpoint. It doesn't make much sense to search for patterns like even or odd numbers of fingers or limbs.

If evolutionary tends to result in bilateral symmetry, there is no reason at all why the symmetry should be inconsistent - like 4 fingers on one hand and 5 on the other.

Consistent bilateral symmetry will always result in even numbers:

  • 4 fingers x2 = 8
  • 7 ribs x2 = 14
  • 5 toes x2 = 10

The Eleven Armed Sea Star in @Oreotrephes' answer isn't much of an exception to the rule of symmetry, it's just radially symmetric.


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