Scientific American - February 2019

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about the lab-sized one. Worse still, even
if you determine whether the lab-sized
sample is gapped or gapless, this could
change just by adding a single extra atom.
It’s important to emphasize that no
materials anyone has encountered in real-
ity display this perverse behavior. But we
can look for simpler systems that exhibit
similar physics, and we have made some
progress on doing so in a follow-up paper.
Durham’s scenario is somewhat similar
to what we describe: In principle, given in-
finite time, the speed of light is no obstacle.
A time limit would be qualitatively similar
to imposing a finite size limit, equal to time
multiplied by the speed of light.

DOWN UNDER DEVELOPMENT
In “Body Balance” [Advances], Maya Mill-
er reports that developmental biologist
Alberto Roselló-Díez and his colleagues
found that when they suppressed growth
of a limb in a mouse fetus, the surround-
ing cells communicated with the placenta,
which slowed down the growth of the oth-
er three limbs to keep them symmetrical.
This mechanism for maintaining sym-
metry in development would, however, work
only with placental mammals. How would
marsupials manage this coordination?
DAVID WEINTRAUB Edison, N.J.

ROSELLÓ-DÍEZ REPLIES: It is worth not-
ing that even though they lack a true pla-
centa, marsupials do form a yolk-sac-de-
rived placentalike structure. And where as
the most obvious mechanism we found in-
volves the placenta, this does not mean it is
the only one. It is possible that other organs
with a key role in body growth, such as the
liver, also participate in the systemic re-
sponse triggered by a local injury. They
could do so either in parallel to the placen-
ta or at subsequent (postnatal) stages once
the placenta is no longer present.

ERRATUM
“The Unsolvable Problem,” by Toby  S. Cu-
bitt, David Pérez-García and Michael Wolf,
should have worded a mathematical state-
ment about deriving the number 1 from
any whole number in this way: “If you
take any whole number and divide it by 2
if it’s even or multiply it by 3 and add 1 if
it’s odd, and then repeat the process, you
always eventually reach the number  1.”

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