Showing posts with label initial conditions. Show all posts
Showing posts with label initial conditions. Show all posts

Monday, 30 July 2018

The Anthropic Principle: Was the Universe Made for Us?

Diagram on the dimensionality of spacetime, by Max Tegmark
Posted by Keith Tidman
‘It is clear that the Earth does not move, and that it does not lie elsewhere than at the center [of the universe]’ 
— Aristotle (4th century BCE)

Almost two millennia after Aristotle, in the 16th century, Nicolas Copernicus dared to differ from the revered ‘father of Western philosophy’. Copernicus rattled the world by arguing that the Earth is not at the center of the universe — in a move that to many at the time seemed to knock humankind off its pedestal, and reduce it from exceptionalism to mediocrity. The so-called ‘Copernican principle’ survived, of course, along with the profound disturbance it had evoked for the theologically minded.

Five centuries later, in the early 1970s, an American astrophysicist called Brandon Carter came up with a different model — the ‘anthropic principle’ — that has kept philosophers and scientists debating its significance cosmologically and metaphysically. With some irony, Carter proposed the principle at a symposium to mark Copernicus’s 500th birthday. The anthropic principle points to what has been referred to as the ‘fine-tuning’ of the universe: a list of cosmological qualities (physical constants) whose extraordinarily precise values were essential to making intelligent life possible.

Yet, as Thomas Nagel, the contemporary American philosopher, suggested, even the physical constants known to be required for our universe and an intelligent carbon-based life form need to be properly understood, especially in context of the larger-scaled universe:
‘One doesn’t show that something doesn’t require explanation by pointing out that it is a condition of one’s existence.’
The anthropic principle — its adherence to simplicity, consistency, and elegance notwithstanding — did not of course place Earth back at the center of the universe. As Carter put it, ‘Although our situation is not necessarily central, it is inevitably privileged’. To widen the preceding idea, let’s pose two questions: Did the anthropic principle reestablish humankind’s special place? Was the universe made for us?

First, some definitions. There are several variants of the anthropic principle, as well as differences among definitions, with Carter originally proposing two: the ‘weak anthropic principle’ and the ‘strong anthropic principle’. Of the weak anthropic principle, Carter says:
‘… our location in the universe [he was referring to the age of the universe at which humankind entered the world stage, as well as to location within space] is necessarily privileged to the extent of being compatible with our existence as observers.’
Of the strong anthropic principle, he explained,
‘The universe (and hence the fundamental parameters on which it depends) must be such as to admit the creation of observers within it at some stage’.
Although Carter is credited with coining the term ‘anthropic principle’, others had turned to the subject earlier than him. One in particular among them was the 19th-century German philosopher Arthur Schopenhauer, who presented a model of the world intriguingly similar to the weak anthropic principle. He argued that the world’s existence depended on numerous variables, like temperature and atmosphere, remaining within a very narrow range — presaging Carter’s fuller explanation. Here’s a snapshot of Schopenhauer’s thinking on the matter:
‘If any one of the actually appearing perturbations of [the planets’ course], instead of being gradually balanced by others, continued to increase, the world would soon reach its end’.
That said, some philosophers and scientists have criticized the weak variant as a logical tautology; however, that has not stopped others from discounting the criticism and favoring the weak variant. At the same time, the strong variant is considered problematic in its own way, as it’s difficult to substantiate this variant either philosophically or scientifically. It may be neither provable nor disprovable. However, at their core, both variants (weak and strong) say that our universe is wired to permit an intelligent observer — whether carbon-based or of a different substrate — to appear.

So, what kinds of physical constants — also referred to as ‘cosmic coincidences’ or ‘initial conditions’ — does the anthropic principle point to as ‘fine-tuned’ for a universe like ours, and an intelligent species like ours, to exist? There are many; however, let’s first take just one, to demonstrate significance. If the force of gravitation were slightly weaker, then following the Big Bang matter would have been distributed too fast for galaxies to form. If gravitation were slightly stronger — with the universe expanding even one millionth slower — then the universe would have expanded to its maximum and collapsed in a big crunch before intelligent life would have entered the scene.

Other examples of constants balanced on a razor’s edge have applied to the universe as a whole, to our galaxy, to our solar system, and to our planet. Examples of fine-tuning include the amount of dark matter and dark energy (minimally understood at this time) relative to all the observable lumpy things like galaxies; the ratio of matter and antimatter; mass density and space-energy density; speed of light; galaxy size and shape; our distance from the Milky Way’s center; the sun’s mass and metal content; atmospheric transparency . . . and so forth. These are measured, not just modeled, phenomena.

The theoretical physicist Freeman Dyson poignantly pondered these and the many other ‘coincidences’ and ‘initial conditions’, hinting at an omnipresent cosmic consciousness:
‘As we look out into the universe and identify the many accidents of physics and astronomy that have worked together to our benefit, it is almost as if the universe must in some sense have known we were coming.’
Perhaps as interestingly, humankind is indeed embedded in the universe, able to contemplate itself as an intelligent species; reveal the features and evolution of the universe in which humankind resides as an observer; and ponder our species’ place and purpose in the universe, including our alternative futures.

The metaphysical implications of the anthropic principle are many. One points to agency and design by a supreme being. Some philosophers, like St. Thomas Aquinas (13th century) and later William Paley (18th century), have argued this case. However, some critics of this explanation have called it a ‘God of the gaps’ fallacy — pointing out what’s not yet explained and filling the holes in our knowledge with a supernatural being.

Alternatively, there is the hypothetical multiverse model. Here, there are a multitude of universes each assumed to have its own unique initial conditions and physical laws. And even though not all universes within this model may be amenable to the evolution of advanced intelligent life, it’s assumed that a universe like ours had to be included among the infinite number. Which at least begins to speak to the German philosopher Martin Heidegger's question, ‘Why are there beings at all, instead of nothing?’

Monday, 11 September 2017

Chaos Theory: And Why It Matters

Posted by Keith Tidman

Computer-generated image demonstrating that the behaviour of dynamical systems is highly sensitive to initial conditions

Future events in a complex, dynamical, nonlinear system are determined by their initial conditions. In such cases, the dependence of events on initial conditions is highly sensitive. That exquisite sensitivity is capable of resulting in dramatically large differences in future outcomes and behaviours, depending on the actual initial conditions and their trajectory over time — how follow-on events nonlinearly cascade and unpredictably branch out along potentially myriad paths. The idea is at the heart of so-called ‘Chaos Theory’.

The effect may show up in a wide range of disciplines, including the natural, environmental, social, medical, and computer sciences (including artificial intelligence), mathematics and modeling, engineering — and philosophy — among others. The implication of sensitivity to initial conditions is that eventual, longer-term outcomes or events are largely unpredictable; however, that is not to say they are random — there’s an important difference. Chaos is not randomness; nor is it disorder*. There is no contradiction or inconsistency between chaos and determinism. Rather, there remains a cause-and-effect — that is, deterministic — relationship between those initial conditions and later events, even after the widening passage of time during which large nonlinear instabilities and disturbances expand exponentially. Effect becomes cause, cause becomes effect, which becomes cause . . . ad infinitum. As Chrysippus, a third-century BC Stoic philosopher, presciently remarked:
‘Everything that happens is followed by something else which depends on it by causal necessity. Likewise, everything that happens is preceded by something with which it is causally connected’.
Accordingly, the dynamical, nonlinear system’s future behaviour is completely determined by its initial conditions, even though the paths of the relationship — which quickly get massively complex via factors such as divergence, repetition, and feedback — may not be traceable. A corollary is that not just the future is unpredictable, but the past — history — also defies complete understanding and reconstruction, given the mind-boggling branching of events occurring over decades, centuries, and millennia. Our lives routinely demonstrate these principles: the long-term effects of initial conditions on complex, dynamical social, economic, ecologic, and pedagogic systems, to cite just a few examples, are likewise subject to chaos and unpredictability.

Chaos theory thus describes the behaviour of systems that are impossible to predict or control. These processes and phenomena have been described by the unique qualities of fractal patterns like the one above — graphically demonstrated, for example, by nerve pathways, sea shells, ferns, crystals, trees, stalagmites, rivers, snow flakes, canyons, lightning, peacocks, clouds, shorelines, and myriad other natural things. Fractal patterns, through their branching and recursive shape (repeated over and over), offer us a graphical, geometric image of chaos. They capture the infinite complexity of not just nature but of complex, nonlinear systems in general — including manmade ones, such as expanding cities and traffic patterns. Even tiny errors in measuring the state of a complex system get mega-amplified, making prediction unreliable, even impossible, in the longer term. In the words of the 20th-century physicist Richard Feynman:
‘Trying to understand the way nature works involves . . . beautiful tightropes of logic on which one has to walk in order not to make a mistake in predicting what will happen’.
The exquisite sensitivity to initial conditions is metaphorically described as the ‘butterfly effect’. The term was made famous by the mathematician and meteorologist Edward Lorenz in a 1972 paper in which he questioned whether the flapping of a butterfly’s wings in Brazil — an ostensibly miniscule change in initial conditions in space-time — might trigger a tornado in Texas — a massive consequential result stemming from the complexly intervening (unpredictable) sequence of events. As Aristotle foreshadowed, ‘The least initial deviation . . . is multiplied later a thousandfold’.

Lorenz’s work that accidentally led to this understanding and demonstration of chaos theory dated back to the preceding decade. In 1961 (in an era of limited computer power) he was performing a study of weather prediction, employing a computer model for his simulations. In wanting to run his simulation again, he rounded the variables from six to three digits, assuming that such an ever-so-tiny change couldn’t matter to the results — a commonsense expectation at the time. However, to the astonishment of Lorenz, the computer model resulted in weather predictions that radically differed from the first run — all the more so the longer the model ran using the slightly truncated initial conditions. This serendipitous event, though initially garnering little attention among Lorenz's academic peers, eventually ended up setting the stage for chaos theory.

Lorenz’s contributions came to qualify the classical laws of Nature represented by Isaac Newton, whose Mathematical Principles of Natural Philosophy three hundred-plus years earlier famously laid out a well-ordered, mechanical system — epically reducing the universe to ‘clockwork’ precision and predictability. It provided us, and still does, with a sufficiently workable approximation of the world we live in.

No allowance, in the preceding descriptions, for indeterminacy and unpredictability. That said, an important exception to determinism would require venturing beyond the macroscopic systems of the classical world into the microscopic systems of the quantum mechanical world — where indeterminism (probability) prevails. Today, some people construe the classical string of causes and effects and clockwork-like precision as perhaps pointing to an original cause in the form of some ultimate designer of the universe, or more simply a god — predetermining how the universe’s history is to unfold.

It is not the case, as has been thought too ambitiously by some, that all that humankind needs to do is get cleverer at acquiring deeper understanding, and dismiss any notion of limitations, in order to render everything predictable. Conforming to this reasoning, the 18th century Dutch thinker, Baruch Spinoza, asserted,
‘Nothing in Nature is random. . . . A thing appears random only through the incompleteness of our knowledge’.


*Another example of chaos is brain activity, where a thought and the originating firing of neurons — among the staggering ninety billion neurons, one hundred trillion synapses, and unimaginable alternative pathways — results in the unpredictable, near-infinite sequence of electromechanical transmissions. Such exquisite goings-on may well have implications for consciousness and free will. Since consciousness is the root of self-identity — our own identity, and that of others — it matters that consciousness is simultaneously the product of, and subject to, the nonlinear complexity and unpredictability associated with chaos. The connections are embedded in realism. The saving grace is that cause-and-effect and determinism are, however, still in play in all possible permutations of how individual consciousness and the universe subtly connect.