Fourth dimension (March 2001)
Scientists have known since the time of Galileo Galilei that the giants
of mythology were impossible. Today, they know equally that the monster animals
sometimes depicted in movies cannot exist. consider, for example, monster
movies with giant ants scaled up in a huge size attacking cars and people.
If these larger-than-life ants had the same proportions as their much smaller
counterparts, their legs would break with the first step. To be much larger
than life-size, an ant's exoskeleton would have to be disproportionately
much thicker compared to that of a smaller ant.
In the same way, if humans were scaled up to giant size as they were in
mythology, and as they sometimes still are in movies, their hearts wouldn't
be able to circulate blood properly and they would die of a heart attack.
This scaling is known as the
dimension because it relates mass to the other three dimensions -
width, length and depth - and in the animal realm, the laws of scaling have
been well known for more than a century. Yet only recently have plant biologists
become aware of these laws' importance throughout nature.
Now Karl J. Niklas and co-author Brian J. Enquist have shown, in the online
version of the Proceedings of the National Academy of Sciences (PNAS),
evidence of a fourth spatial dimension in plants, based on mathematical
equations. The paper, ''Invariant scaling relationships for interspecific
plant biomass production rates and body size,'' will be published in a
forthcoming issue of the print version of PNAS. The abstract is located at
and at the time of writing, the text was also available from a link on that
The finding could be important in environmental and ecological policy, as
well as the science of evolutionary biology. In the future, plant scientists
will have the ability to
develop mathematical models to make predictions in such areas as standing
forest biomass and growth. They have shown that plant growth increases at
three-quarters the rate of plant body mass, the same scaling relationship
as for animals. For example, as a redwood tree grows in size over centuries,
its rate of growth gradually slows down according to this very precise
Says Niklas, ''Our data say that growth rates are indifferent to other biological
differences across species. In scaling, a tree is a tree is a tree.''
Note: for general access to the PNAS, refer to
http://www.pnas.org/, or for readers in
Europe, Asia, Australia and South America, use
http://intl.pnas.org/ for faster
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