The Evolution of Mathematics on Planet Earth

tumblr_ncxcqixe9k1qzy92fo1_1280

math-heartMany people couldn’t imagine Math and Biology going out on a date. Flirting with each other from time to time…maybe. But a date? Never! Math is precise, abstract, cool, and distant. Biology is messy, unpredictable, prone to mood swings, and chemically dependent…as it were.

But this may be changing.

“The conversion of biology into a more quantifiable science will continue to the extent that it might even become the main driving force behind innovation and development in mathematics”

Philip Hunter

Let me explain why I think Math and Biology are ultimately compatible, and in fact, part of a Single Reality.

tumblr_my165xRv5f1swaxzgo1_250

I have written a few articles on the subject of math, and raised questions as to the universality, truth-status, and God-givenness of Math. Here is something to consider about Math and Biology:

Math Evolved in the Biosphere

Let’s start with numbers. Imagine a mother crow busily feeding her three chicks. She would become worried if she came back to her nest to suddenly find two chicks instead of three.

House_Crow_feeding_chicks

She would know there something is wrong with this picture…because crows can count (they can subitize small numbers, like about 2 or 3).

How did it come about that some animals, like crows and humans, can count? First of all, in order for intelligent beings to be able to count, they have to live in an environment where countable objects are found, and where counting has some evolutionary benefit. Consider a gaseous planet where fluids intermix and there is no way to detect a “thing” or “event” and to compare that with another “thing” or “event”. In this kind of world, there is nothing to count.

seahorseFor that matter, it is unlikely that an intelligent entity that can count could ever evolve on such a planet in the first place, because structure and differentiation at some physical level are required for living things to bootstrap themselves into existence.

Theories of autopoiesis, negentropy, and the emergence of mind from matter rely on the existence of a prior structure to the universe where it is possible for self-regulation, and self-creation to arise. One might say that the origins of life had a head start long before those first molecules started dancing together and accidentally reproducing. Maybe it wasn’t such an accident after all.

imgres

…which brings me to a core concept: since Earth’s biosphere gave rise to animals that can count, as well as those things that can be counted – at the same time, we must understand ourselves as in and of the biosphere – we and it all evolved together: one did not come before the other.

70212-1024x603Which came first: the chicken or the egg? Neither. They have both been in a continual state of becoming since egg-like things and chicken-like things have existed. And if you go back in time far enough, these things look less and less like chickens and eggs.

We animals have evolved to understand containment, and that is partly because hierarchy evolved within the fabric of physical biology. We know what it means for something to be “inside” or “outside” of something else. We clumpify, categorize, differentiate, compare, and identify. All animals need some degree of this compartmentalization of nature in order to operate within it.

We cannot separate our math from the environment from which it evolved. The very foundations of math evolved within the bodies and minds of animals as a part of evolution. At least this is what several recent scientists and philosophers are suggesting. (Mathematicians are more likely to claim that math is universal, constant, and unchanged by biology.)

OctoMath

In a previous article I consider what kind of math would have emerged if octopuses has evolved to become the complex and dominant species on earth, instead of humans. This is not so hard to imagine, considering how intelligent they are.

Screen Shot 2015-08-10 at 12.19.31 AM

Would an advanced octopus race have stumbled upon complex numbers? Would they have become as obsessed with the Cartesian coordinate system as we are? Since they have no skeletons, would they have formulated a geometry based on angles and lengths? Of course we can’t know, but it is likely that they would have created some math concepts that we may never achieve. And that would be because the long history of math that we have built and that we rely on to create new math has taken our brains and societies too far away from the place where an octopus-like math would naturally arise.

mouroborobius2Now consider aliens from a completely different kind of planet than Earth. What kind of math would originate in that world? Many people would argue that math is math and it doesn’t matter who or what discovers or articulates it. And there may be some truth to this. But we can only hope and imagine that this is the case.

Until we meet aliens from another planet and ask them if they understand and appreciate the fibonacci sequence, I have to assume that their math is different than ours.

What do you think?

(I would have consulted one of my octopus friends on the subject…but I don’t speak their language).

The Future CAN Change the Present (Terrence Deacon’s Incomplete Nature)

DIn his book, Incomplete Nature – How Mind Emerged from Matter, Terrence Deacon tackles some of the deepest and gnarliest philosophical questions about life and mind, and how they emerge from the physical world despite the fact that the laws of physics can only explain lifeless, mechanical processes. Regarding the second law of thermodynamics, which states that everything is in an eternal state of eventual decay, Deacon says this:

220px-TerryDeacon“There is the dead, pointless, uncaring world and its rules, and the living, striving, feeling world and its rules, and the two seem to be working in quite contradictory ways. Because the spontaneous order generation that is so characteristic of life and mind runs counter to this otherwise exceptionless current of nature, it demands that we take seriously the possibility that our usual forms of explanation might be inadequate. When unrealized future possibilities appear to be the organizers of antecedent processes that tend to bring them into existence, it forces us to look more deeply into the ways we conceive of causality and worry that we might be missing something important.”

I am in the process of re-reading the book, which is fat and dense.

b

Deacon makes little attempt to help the reader by phrasing his sentences and paragraphs for easy digestion. Subsections are rare, and I feel like I’m often wading in a vast ocean without a view of an outcropping to pause and catch my breath. I beg for a period, perchance a comma. But despite the relentless texture of the writing, what Deacon has to say is inspiring…almost breathtaking. Actually, the breath-taking happens after I allow Deacon’s ideas to percolate in my mind during a short walk – which I find necessary for getting the depleted oxygen back into my brain.

…which reminds me of a core concept of the book. Billions of years of evolution have gone into the making of this unlikely spacetime dynamical event, which is me: a fully conscious human who happens to be writing words for you to read at some point in the future. The fact that I can choose to go for a walk for mental and physical health, and maintain my equilibrium (on many levels of consciousness, mostly un), is nothing short of a miracle. This is especially true when you consider the general trajectory of atoms in the universe.

31d377bBut in fact it is not a miracle. It can be explained with a systems-attitude overlaid on top of physics that includes emergence. “Emergence” is so wonderfully explained by Daniel Dennett in his descriptions of skyhooks and cranes. Here’s my take on the topic: when a higher level of structure emerges in the world, it reaches down to manipulate the lower levels that brought it into existence – it regulates and modulates those lower levels for its own survival. Then another level of emergence comes into being, and begins to regulate and modulate the previous structures. This upward cascading of order – this ever-complexifying hierarchy of constraints – is particular to life and mind, and it runs counter to the entropy that is the general rule of the universe. This is sometimes referred to as negentropy.

fdd042bb5ac4e50236974f747f0fdb8cI had previously struggled to understand the “incompleteness” aspect of Deacon’s thesis. In the first part of the book, he spends a lot of time re-stating the notion of things that “aren’t there” or that exist “for the sake of something missing”, after only briefly defining this concept up-front. In my first reading I had started out with a limp. Perhaps some training wheels with familiar language would have helped, as these are new and subtle ideas.

This is not unlike a small criticism from Daniel Dennett, in a book review. Overall though, Dennett’s review is very positive. In fact, Dennett says the book has him re-examining his fundamental working assumptions. When something rocks Daniel Dennett’s world, you stop and take notice.

The Future Does Change the Present

illusionLiving things have inner representations of the world they find themselves in – that’s part of the holographic picture of life. For us humans, these representations are not just in our brains; they are infused in our technology – distributed throughout our extended phenotypes. Organisms with minds not only put a lot of effort in trying to predict the future (which is necessary for survival), but they act in accordance to those predictions.

This has the effect of creating alternate futures – of changing the course of events – based on something represented in the mind of the organism – represented but not actually “there” (though it could be there in the future). I believe this is what Deacon means by incompleteness, things that are missing, or, in his own words: “absential features“.

RV-AE885_BRAIN2_DV_20111111015014According to Raymond Tallis in a Wall Street Journal book review, An absential is a phenomenon “whose existence is determined with respect to an . . . absence.” This sounds somewhat opaque but captures something essential to mind. In the push-pull universe of mechanical causation, only that which is present shapes the course of events. In our lives, by contrast, we are always taking account of things that are no longer present or not yet present or that may never come to pass. Thus “absentials” include our beliefs, the norms to which we subscribe and those great silos of possibility such as “tomorrow” and “next year.”

Screen Shot 2015-07-25 at 9.30.00 PMAlan Kay is once said, “The best way to predict the future is to invent it“. This is not just good advice for entrepreneurs; it might also be the motto for all living things. How else can we explain the fact that life on Earth has continued to exist for billions of years, with robust self-similar structures that persist for several millions of years – gradually changing, only to become better at predicting the future.

Why do we not expect every living thing to quickly dissolve into a gas, or at least some entropic state of uselessness? This is what classical physics would predict for such a rare, unlikely, and delicate assemblage of molecules. The answer is that living things have their futures infused into their DNA, their minds, and their societies. We fight the force of entropy, and we succeed.

For the most part.

Physics does not (at least not yet) adequately explain how the future effects the present. For this reason, Deacon is helping to build the foundations for a new kind of physics (or perhaps a new kind of meta-physics), which includes…

you, me, our consciousness, and everything that has meaning.