S.F. WALKER (Current home page)
Received: 11 December 1980
It is usually claimed that human brains,
and all other brains having two apparently similar halves, have
potential or actual bilateral symmetry More formally, consider a brain with identical halves on either side of the plane X at x = 0 on the left-right axis. In this three-dimensional object points can be identified by the axes z, x, y where z is longitudinal and y vertical.
(1) We begin by assuming that for
every point (z, —x, y) on the left, there exists a
corresponding point (z, +x, y) on the right. This is the
assumption of bilateral or “mirror-plane” symmetry about the
plane X
(2)
(3)
(4)
(5)
(6) In order for P and P’ to be symmetrically connected there must be both a connection PP’ and a connection P’P (see (4) above) and PP’ and P’P cannot follow the same path (see (5) above). Consider the intersections of PP’ and P’P with the plane X. Since the two connections cannot occupy the same point on X, they must occupy different points on X. That is, when x = 0, the y and/or z coordinates of PP’ and P’P must differ. Thus as PP’ approaches X, a point on PP’ must differ from any corresponding point on P’P in its y and/or z coordinate, and therefore at such a point PP’ and P’P do not have mirror-plane symmetry about X (see (1) above).
(7) Both PQ’ and P’Q intersect the plane X, as x changes sign. Since they cannot intersect at the same point (see (5) above) they must intersect X at different points and hence they are bilaterally asymmetrical about X in the same way as commissures.
Countless children must have asked why Alice did not bump
into another little girl when she attempted to climb through
the Looking Glass. Lewis Carroll However, a general rule of asymmetry in vertebrate brains may be applied if asymmetries induced in or by cross- connections are taken into account.
The ubiquity of commissures and
decussations in vertebrate brains is explicable partly in terms
of “crossed lateral control”: sensory information from the left
tends to be projected to the right side of the brain, which in
turn controls the left side of the body, while right-sided
information is dealt with by the left half of the brain
The reason why vertebrate brains should employ the
strategy of crossed-lateral control, requiring the decussation
of both sensory and motor pathways, has always been a
puzzle
It is hard to see how mirror plane asymmetries at the
midline of cross-connections might affect the visible anatomy
of the cerebral hemisphere. However, a significant correlation
has been found
References
1. Dimond, S.,
2. Corballis, M.C., and Beale, I.L.,
3. Galaburda, A.M., LeMay, M., Kemper,
T.L. and Geschwind, N.,
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5. Kappers, C.U.A., Huber, G.L. and
Crosby, B.C.,
6. Weiskrantz, L., in
7. Carroll, L.,
8. Garey, L.J., in
9. Walker, S.F.,
10. Wada, J.A., Clarke, R., and Hamm,
A.,
11. Kemali, M., in
12. Prince, J.H.,
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14. Kerstesz, A., and Geschwind, N.,
15. Sarnat, H.B. and Netsky, M.G.,
16. Kopp, N., Michel, F., Carrier, H.,
Biron, A., and Duvillard, P.,
17. LeMay, M.,
© Elsevier Sequoia S.A., Lausanne. Printed in the
Netherlands.
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