Friday, December 28, 2007

And then time slowed to a crawl

Several years ago when I was a svelte bicycle racer, I was almost involved in a big crash. More correctly put, I was in the middle of a big crash and almost went down myself. It was an early season Cat 4/5 race. For those unfamiliar with bicycle racing, category 5 is the entry level for licensed amateur racers, and category 4 is a Cat 5 racer with some experience in pack races. In peloton racing, position is of utmost importance. Moving up in the pack can be difficult. But there are certain parts of the course (oftentimes) where the road widens, or there's an uphill section, or something else where many racers feel they have a shot to "make their move" and gain better position.

This particular day it was an uphill on the course. At the time, I had been doing a lot of hill training so I was one of the racers who saw this as an opportunity to move up. But as we got to the bottom of the hill, all hell broke loose. There was a crash just 2 or 3 riders in front of me. Everything went into slow motion as the sounds of bikes crashing and people yelling filled my ears. I desperately looked for that opening in the melee as I adroitly fingered the brakes and maneuvered the handlebars. After what seemed like forever, I found my path and threaded my way through as bikes continued to smack the pavement all around me.

Once I was clear of the ruckus, time sped back up to normal speed and I had to sprint up the hill (remember, I used to be svelte) to catch back on to the pack. (It is a common tactic in bicycle racing that when you hear a crash behind you, you take advantage of the opportunity to thin out the pack by picking up the pace)

Did time really slow down for me as that crash was happening? Of course it didn't, but I certainly remember it that way. And I don't mean that I can remember the events in slow-motion, I mean that as far as I recall, they actually happened at that speed. It really feels like I experienced them in slo-mo. But did I? And whether I really did or whether it's just a memory trick, is there any way I could know for sure?

The basic principle behind a slow motion camera is pretty simple. Footage is shot at high speed (say 3x or 5x normal speed) then played back at normal speed. For example, if a sports broadcast is usually shown at 30 frames per second (fps), the network could have a camera that shoots at 90 fps and if an exciting turnover happens, they could play back the footage from that camera at the normal 30 fps and everything would appear to be moving 3x slower. (Super slow motion like the famous clip of the bullet piercing the apple are shot with high speed strobe lights since there aren't any shutters that fast and you need very bright light for such short exposures.)

A spots fan watching the broadcast will have seen both the original play in real time and the slow motion replay. That fan will have memory of both events. But suppose that the only memory was the slow motion memory? In other words, let's pretend that the event, as it happened, was recorded at an accelerated frame rate but then recorded into memory at the normal frame rate so that the recall--even a fraction of a second after the event and possibly even the working memory during the event--would be seen only in slow motion. Wouldn't this be indistinguishable from the event actually having been experienced in slow motion?

These are the kinds of questions I've been asking myself for years now. I had figured that the true explanation was along these lines, but that the slow motion camera analogy was flawed because I knew that that's not how memories are stored in the brain. But it was the best analogy I had.

Then last week I saw this article. There researchers put it to the test.

... to determine whether that distortion meant they could actually see more events happening in time -- like a camera in slow motion -- Eagleman and his students developed a special device called the perceptual chronometer that was strapped to the volunteers' wrists. Numbers flickered on the screen of the watch-like unit. The scientists adjusted the speed at which the numbers flickered until it was too fast for the divers to see.

They theorized that if time perception really slowed, the flickering numbers would appear slow enough for the divers to easily read while in free-fall.

They found that while the subjects were able to read numbers presented at normal speeds during the free-fall, they could not read them at faster-than-normal speeds.

"We discovered that people are not like Neo in The Matrix, dodging bullets in slow-mo. The paradox is that it seemed to participants as though their fall took a long time.

So if memories aren't being squeezed in at a higher rate, then where does the slow motion illusion come from?

The answer to the paradox is that time estimation and memory are intertwined: the volunteers merely thought the fall took a longer time in retrospect," he said.

During a frightening event, a brain area called the amygdala becomes more active, laying down a secondary set of memories that go along with those normally taken care of by other parts of the brain.

"In this way, frightening events are associated with richer and denser memories. And the more memory you have of an event, the longer you believe it took," Eagleman explained.

The study allowed them to deduce that a person's perception of time is not a single phenomenon that speeds or slows. "Your brain is not like a video camera," said Eagleman.

------ snip --------

"It can seem as though an event has taken an unusually long time, but it doesn't mean your immediate experience of time actually expands. It simply means that when you look back on it, you believe it to have taken longer," Eagleman said.

So if I'm reading this right, then the brain is in fact storing more information into memory about the event perceived in slow motion than surrounding events, but unlike the slow motion camera which stores extra frames, the extra information is related to your emotional state at the time. But since your brain perceives time passage as a function of quantity of information, the richer memory is perceived to have taken longer. Now that's wild! So your brain's perception of time is influenced by accompanying information in memory much like your brain's perception of distance is influenced by environmental clues. And so your memory of the relative duration of an event can be tricked muck like an optical illusion can trick your brain about relative length. (hint: the distance AB is equal to BC)

The above article also mentioned that the authors of that study had recently published a related study in the online journal PLoS ONE titled The Effect of Predictability on Subjective Duration. Naturally, I had to go read that study. There were more surprises in store.

But what does it mean to say that subjective time expands? We here set out to distinguish two hypotheses. In the first, perception works like a movie camera: when one aspect of the scene slows down, everything is slowed down. Thus, if a police car launching off a ramp were filmed using slow-motion photography, it would not only have a longer duration in the air, but also its sirens would blare in a lower pitch, and its lights would blink at a lower temporal frequency. In this case, duration, sound pitch and visual flicker all change hand-in-hand. The second hypothesis, in contrast, supposes that different temporal judgments are generated by different neural mechanisms–and while they often align, they are not required to. Thus, the police car may be judged to have a longer duration in the air, even while the frequencies of its sounds and flickering lights remain unchanged. In this paper, we distinguish these two hypotheses by testing the specific entailments of duration distortions, and in this way are able to directly address the notion of “time's” subjective expansion.

In the study, the researchers performed what is called the oddball illusion on volunteers. The subjects were shown a series of images which were all the same except for one oddball image which was shown in the middle of the sequence somewhere. The participants all reported that the oddball image was on the screen longer than the other images although they were all up for equal duration. In a follow-up experiment they introduced sounds. The results are fascinating.

Participants showed no difficulty in discriminating the frequency of the beep accompanying the visual oddball from the beep accompanying the standards (Figure 2b, middle bar). We conclude from this result that the oddball illusion is not accompanied by a concurrent distortion of perceived auditory frequency. This indicates that it is not time in general, but only visual durations in particular, that slow during the oddball.

And surely enough, this actually jibes with my recollection of the crash that day of the bike race. Even as everything around me was happening in slow motion, the crashing bikes and panicked yells all happened at normal pitch and time. I never really realized that until just now. Wow!

Monday, December 24, 2007

Fractal fun

My favorite fractal is the Mandelbrot Set.

Another fun fractal that I like is the Julia Set. What I've recently discovered thanks to someone I was talking to (sorry, can't remember his name) is that there is a section of the Mandelbrot zoom that looks eerily similar to the Julia Set. Look at the Comparison below.

Here's a Julia Set that I generated using GIMP2.

And here's a Mandelbrot zoom generated (by the above mentioned anonymous person) using Fractal eXtreme. (Much nicer quality than my GIMP rendering)

Pretty neat! No?

If you look closely, you'll see that they are different. If you can't see it, look at the center. Here's the Wikipedia explanation.

At first sight, these islands seem to consist of infinitely many parts like Cantor sets, as is actually the case for the corresponding Julia set Jc. Here they are connected by tiny structures so that the whole represents a simply connected set. These tiny structures meet each other at a satellite in the center that is too small to be recognized at this magnification. The value of c for the corresponding Jc is not that of the image center but, relative to the main body of the Mandelbrot set, has the same position as the center of this image relative to the satellite shown in zoom step 7.

While we're on the subject of Mandelbrot vs. Julia, I'll leave you with a Jonathan Coulton fan video of my favorite JoCo song--pay extra special attention to the sound clip at the very end ;-)