To Infinity and beyond

 I’ve had this statement on my mind for what seems an eternity – you know, like when we can't get a song out of our head. And sure it’s a classic Buzz line courtesy of toy story and itself a variation of "Beyond the infinite" as it appears as a title card in Kubrick's 2001: A Space Odyssey. It’s quite possible that Buzz is showing everyone that he can do the impossible and cross any asymptote, something that a curve approaches, as it heads towards infinity.

And, it’s that time of the year when one can get back into the business of writing, doing physics and thinking beyond the curbs and bliss of the daily grind. This means hard thinking; my hobby-horse, the nature of time. That illusion or a trick of mind that presents us with a persuasive, ever meandering, passage of time. Here I’m talking in the tradition of Plato, we find time, mathematics and all else on a higher plane that our mind sees into, by a process not unlike sense perception. And I suppose, the inter-play between time and space, the time-space manifold, Riemannian geometry is/was there for Einstein to see.

One of Gödel’s less well-known papers is a 1949 article called, “A Remark on the Relationship Between Relativity Theory and Idealistic Philosophy.” In this paper, Gödel attempts to show that the passage of time is indeed an illusion. The past, present and future of the universe are just different regions of a single vast space-time. Time is part of space-time, but space-time is a higher reality existing outside of time.

For many, including Gödel, mathematics, even the mathematics of the infinite, was an essentially empirical science. But when we begin to talk about infinite numbers that the trouble really begins. Cantor’s Continuum Problem is undecidable on the basis of our present-day theories of mathematics. For a Platonist like Gödel, this means only that we have not yet “looked” at the continuum in a hard enough way.

Time paradoxon

For the great part of this past summer I’ve been talking and writing about what we have come to understand of time. Not so much about the passage of time, or our perception of time but rather, the more lofty notions, space-time. We know for example time slows at higher speeds of the reference frame relative to another. This (time dilation) is explained in special relativity theory. But what of the psychology of time? We have all, at one time to another; acknowledged how quickly time seems to be breezing by. Time seems to pass by quicker as we grow older. Time flies when we’re having fun, where did this year go, etc.

Time paradoxon is relevant for understanding our perception of time. It seems, according to Bruss and Ruschendorf of Universite Libre de Bruxelles and Universitat at Freiburg that while time periods which are filled with interesting activities pass by quickly, these periods are felt in retrospection as having taken longer than less eventful periods. Hence, in retrospective, the feeling of time duration is in general different from its perception at the time of the very same period. One convincing explanation of this is that human beings remember, first of all, major events of their life. Periods of these major events are memorized in a particular way and leave an accessible track on the human mind. Moreover, the meaning of a major event changes naturally in time. A first event of a certain type has a greater chance to be felt as major than similar events later on in life. Therefore a month in childhood or adolescence is usually felt much longer than a month in adult age. The feeling of time is thinned out in a quite natural way. On the whole the phenomenon seems almost unavoidable. Taking these arguments together gives additional support to the idea that important or new events and their pattern of occurrence in life play a dominant role for the individual perception of time.

Time and time again

For years - any opportunity I have to do any serious thinking typically and inevitably circles around time. What is it, was it always there, how do we perceive it, how is time intertwined by space (space-time) etc. And if we subscribe to Einstein's theory of relativity, there was no such thing as time before the big bang; there was no "before." Time (and space) started at a singularity (with the laws of physics broken down).

And more so, is time a feature of the universe that can be understood independently of a conscious being. That is, can we make sense of time when everything about time is perceived and processed through a lens of brain architecture?

We know for example time is processed across a a highly distributed system involving the cerebral cortex, cerebellum and basal ganglia. One particular component, the suprachiasmatic nucleus, is responsible for the circadian (or daily) rhythm, while other cell clusters appear to be capable of shorter-range (ultradian) timekeeping.

Different types of sensory information (auditory, tactile, visual, etc.) are processed at different speeds by different neural architectures. Our brain, it seems, has learned how to overcome these speed disparities, to create a temporally unified representation of the external world.

In the popular essay "Brain Time", by David Eagleman, he suggests that "if the visual brain wants to get events correct timewise, it may have only one choice: wait for the slowest information to arrive. To accomplish this, it must wait about a tenth of a second.  As long as the signals arrived within this window, viewers' brains would automatically resynchronize the signals". He goes on to say that "This brief waiting period allows the visual system to discount the various delays imposed by the early stages; however, it has the disadvantage of pushing perception into the past. There is a distinct survival advantage to operating as close to the present as possible; an animal does not want to live too far in the past.

Therefore, the tenth-of- a-second window may be the smallest delay that allows higher areas of the brain to account for the delays created in the first stages of the system while still operating near the border of the present. This window of delay means that awareness is postdictive, incorporating data from a window of time after an event and delivering a retrospective interpretation of what happened."

Competing models of time perception

Anyone that knows me will know my fascination with time. Not how we go about measuring time but time it self. Here there are 2 equally important paths of endeavor. One is that of a global scale and involves the very nature of the universe; Space-Time continuum and General Relativity.  The second is equally baffling – how does the brain code time.

There are multiple competing models of time perception with no real consensus. For example we know that the Suprachiasmatic nucleus uses environmental cues, most importantly light, to determine the time of day and year thus coordinating circadian rhythms. This however is more about tracking time and less about perception of time. Also, this may not be the structure that links events to time – i.e. history.

According to a recent MIT study groups of neurons in the primate brain code time with extreme precision. Institute Professor Ann Graybiel says “All you do is time stamp everything, and then recalling events is easy: you go back and look through your time stamps until you see which ones are correlated with the event,"

Neuroscientist Paul King of the Redwood Center for Theoretical Neuroscience at UC Berkeley explains fast time interval estimation (sub-second) to be important for timing complex behavior and playing musical instruments. Slow time interval estimation may be important for planning the day, although daylight and hunger can provide cues. Intervals greater than a day may rely on observing the repetition of day-night cycles and seasonal changes.

The above diagram shows the accuracy of time interval estimation for humans and other animals, along with proposed neural mechanisms for each time scale. Slow time scales (hours) are at the top and fast scales (milliseconds) are at the bottom. It’s a fascinating model.

The conundrum of time

There wouldn’t be too many people who haven’t at one point or another wondered if there was ever a time before time. And it really doesn’t matter if you’re a Christian, of the catholic persuasion, a Zen Buddhist or a non-believer – it’s a conundrum that’s occupied the minds of the greatest philosophers and perplexed scientists as far back as Newton and contemporaries. I know I asked my father when I was about ten years old “Who created God if God created everything…” for I was told at Sunday school God created a mature universe and mature life from nothing in less than 7 days, less than 10,000 years ago.

So was there a time before time? Did time begin for example as a by-product of a very early universe? Of course one can ask, without a prime mover what ever happened before the birth of the universe.

The difficulty is of course because we don’t have the mental architecture to hook our thinking about it. It’s a bit like the edge of the world question. Back in the day when we thought the world was flat, we wondered if the sea poured over the edge. Discovering that the world is a sphere gave us; a model of the world that explained neatly that there is no edge.

One would have to think that with the appropriate mental scaffolding we might be able to answer the question – was there a time before time. The answer may well be in the depth of the Big Bang, General Relativity and Quantum Mechanics. 

General relativity unified time and space giving us a space-time continuum while Quantum Mechanics describes the unbelievably small dense universe. We think that in the first moment of the big bang, all the matter and energy that are in the universe today, existed at a single point, impossibly dense, inconceivably hot, and dark. Space began to expand at a speed faster than the speed of light.

At a trillionth of a trillionth of a trillionth of a ten millionth of a second after the big bang the universe was small enough to be described by both General Relativity and Quantum Mechanics effectively supporting 4 dimensions of space and none of time. So as we backtrack to the earliest of time – there may well have been no time and instead 4 dimensional Space. Substituting time with a direction of space is somewhat similar to the problem of the edge of the world. It is only [later] that we humans begun to realize that time and space are one and the same.