At the Eighth International Conference on Complex Systems
in June, an entertaining late-night conversation among participants
centered on whether the principles of complexity science are a human
invention or some basic truth we've simply discovered as we've learned
more about the world.
This echos a debate that's been raging in the field of mathematics for years. In the August 2011 issue of Scientific American,
Mark Livio explores this question, "Is math an invented set of tools,
as Einstein believed? Or does it actually exist in some abstract realm,
with humans merely discovering its truths?" He writes that we accept the
view that mathematics is the language of science and expect that its
grammar explains experimental results and even predicts novel phenomena.
He quotes Albert Einstein who said, "How is it possible that
mathematics, a product of human thought that is independent of
experience, fits so excellently the objects of physical reality?"
Livio describes the way that math captures the natural world as
"uncanny." In the end, he concludes that "mathematics is an intricate
fusion of inventions and discoveries."
can we credit the power of mathematics to capture critical aspects of
the world to help us understand it while appreciating the capacity of
mathematicians to produce new knowledge that helps us create it? It's a wicked question.
In The Daily Galaxy,
Josh Hill raises questions that challenge both sides of the issue. For
those who believe these mathematical truths are purely discoverable,
where, exactly, are you looking? And for those on the other side of the
court, why cannot a mathematician simply announce to the world that he
has invented 2 + 2 to equal 5? "If a mathematical theory goes
undiscovered, does it truly exist? Maybe this will be the next "does a
tree falling in the forest make any sound if no one is there to hear
one of the world's most distinguished mathematicians says, "I like to
think of mathematics as a bit like geology or archeology, where you're
really exploring beautiful things out there in the world, which have
been out there, in fact, for ages and ages and ages, and you're
revealing them for the first time." Nobel laureate Frank Wilczek
believes that "Inventions have to come from somewhere so they could be
inspired by natural phenomena. ... You can invent [all kinds of] axioms,
but most of them won't be interesting. And the ones that are
interesting are discoveries, so even the inventions have some element of
discovery. So as I said, mathematics is more discovered than invented,
and this only makes it more so."
This debate is a great example of what Plexus Advisor, Scott Kelso
calls a "complementary pair." Mathematics - and complexity science -
could be seen as both discovered and invented. Kelso has developed an
empirically-based scientific theory of how the polarized world and the world in between can be reconciled.
and his collaborator, David A. Engstrom, coined the term "squiggle
sense" to describe the sense of the inextricable, complementary dance of
contraries. The notion of the 'dance' goes beyond the familiar notion
of "both/and" inherent in wicked questions to highlight the importance
of the dynamic relationship between the ideas. This fits with Livio's
conclusion about the nature of mathematics, "A pattern emerges: humans
invent mathematical concepts by way of abstracting elements from the
world around them - shapes, lines, sets, groups, and so forth - either
for some specific purpose or simply for fun. They then go on to discover
the connections among those concepts."