I'm reading Ray Kurzweil's book, The Singularity Is Near, and finding it somewhat persuasive. However every once in a while something just looks wrong, and that upsets the persuasivity.

In Chapter 1, he shows various “significant” events in history, like the invention of writing, the development of fire, the Cambrian explosion, etc. He uses the timing of these events to show that change is accelerating:


Image courtesy of Wikipedia.

The thing that occurred to me when looking at the choice of events is that it's a natural tendency to view the world logarithmically. For example, if you ask most Americans about places in the world, they will be able to name the places very close to where they live, the towns nearby, the state, the large cities in the USA, a few very large cities around the world, a few large or important countries around the world, and then places like “Africa” and “Asia”. If you plot the places on a logarithmic chart, you'll get something close to a straight line. If people name astronomical objects, it will be the ones close to us (like planets), the Sun, some nearby stars, and maybe some galaxies. But it won't be some planet in some other galaxy. If people name biological variants, it'll first be the ones close to us (various races of humans), then types of mammals and maybe reptiles, then “fish”, then “bacteria”. It won't start with various species of bacteria or fish. This is because things that are physically or conceptually farther away are resolved in the brain at a lower “resolution”. The closer something is to you, the finer granularity you use to distinguish it from other things.

The same is true for time. For example, Kurzweil's choice of events includes the Cambrian explosion at a very coarse granularity. It doesn't include development of limbs, eyes, skeletal system, muscles, or other events that would've been considered significant if the list was developed back then. Those changes are all grouped together. Similarly, if the list had been developed around the time multicellular life developed, it would have included significant achievements like the development of cell walls, a nucleus, ribosomes, etc.

Things that are farther away are resolved in the brain at a lower “resolution”. The brain's use of variable resolution means that changes from the past are grouped together into larger units, and that makes it look like change was occurring more slowly in the past. I do believe that change is accelerating, but it's not accelerating as quickly as Kurzweil believes.

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11 comments:

John wrote at Sunday, September 25, 2005 at 4:13:00 PM PDT

I was thinking exactly the same thing, Amit. If you ask someone what happened 500 million years ago, maybe they'll say "Mollusks developed eyes". If you ask them what happened yesterday, "Google announced free wifi!"

I think Kurzweil is selecting his data points to fit his theory.

Brandon wrote at Sunday, October 2, 2005 at 11:33:00 PM PDT

I actually saw Kurzweil's talk (where he used this slide), and I was pretty dubious about it too. Kurzweil's answer to this kind of objection is that if you consider multiple different sources' opinion of 'significant', they all list events in near these time periods.

I don't buy that either (largely for the reasons you give), but here's a better graph to consider:

What does a graph of all processing power on the planet look like, over time? What about a graph of total storage? An interesting take on these graphs would be to consider total processing power including that inherent in all the cells on the earth, vs. processing power of just humans, and the same for storage.

I would be willing to bet that both of these graphs are increasing exponentially, and that's what Kurzweil should be pointing to as evidence of radical change. If the computational power available to all humans is set outpace that of the biosphere (or even just the human brain) at some point in the future, that represents some sort of turning point, though I'm not sure want.

Interestingly, there's a study that estimates how much data we produced in 2002, as a species:

http://www.sims.berkeley.edu/research/projects/how-much-info-2003/execsum.htm#summary

Answer: 5 exabytes.

chaitanya wrote at Monday, October 3, 2005 at 8:11:00 PM PDT

Hi, first time here. Was looking around to see what people had to say about the book
I have no problem with his central belief, around which he constructs his life, that at some point there is bound to be explosive growth. It is kind of obvious that science tends to develop with a kind of positive feedback: progress helps progress happen faster. Nor is his idea of the exponential knee fully wrong. It is scale free, but the reference frame Kurzweil refers to here is the AI frame, and the knee is really a perceptual threshold that can still be mathematized. if there were a Ray Kurzweil cave-painting eons ago, he would still have something remarkable to exult about, like fire I guess .The greater question is how individual technologies would develop and morph and here is where he really fails to impress. I wonder if his team of researchers have modeled the present based on the reams of past data and accurately predicted podcasting or blogging.

C wrote at Wednesday, December 7, 2005 at 8:42:00 AM PST

Amit-

This is really more of a question than a comment.

You say you do agree that the pace of change is accelerating, just not as fast as Kurzweil believes. How fast do you think the pace of change is accelerating?

Or, to put it differently, how many key events do you think are missing from the chart? If n is the nth event going back in time on the chart, is the number of missing events between the nth and (n+1)st event linear in n? quadratic? exponential?

Note that I am not referring to your stated examples, such as the development of a skeletal system. I think in fairness, one has to presume that if you thought of it, other experts concerned with thinking of such things would have thought of it too and decided that the event did not meet the criterion to be included. That is, this chart was not analogously about asking average Americans about places in the world...it would be more analogous to asking geography experts about places in the world. (In Kurzweil's example, he refers to 15 different groups of experts, so john's comment about Kurzweil selecting his data points to fit his theory is not compelling.)

So I think what you have to be suggesting is that because of human ignorance, numerous major events are missing from the chart...events that nobody knows about, and furthermore, the number of such events grows with the n defined above. How plausible is it that so many significant events could be so hidden from human research? Is it more speculative to think that so many such events went unnoticed than to think that the list is pretty close and that there aren't really that many missing events?

-a friend of a friend

Amit wrote at Wednesday, December 7, 2005 at 9:06:00 AM PST

Pick a chart point in the past. Let's say the orangutan. What would you list if the orangutan was the endpoint? You'd pick a lot more things that were pivotal in the evolution of the orangutan. Mammals, primates, ability to navigate trees, ability to eat fruit, ability to use simple tools, etc. So the "canonical milestones" would bunch up closer right before "first orangutan", and it would look like exponential growth that was just about to explode right after the first orangutan.

Yes, I think things are accelerating, but I have no good way of knowing how quickly, because I think the choice of milestones is going to be biased towards things closer to us. Notice that "differentiation of human DNA types" is there but "differentiation of orangutan DNA types" is not. And why "modern" physics? The physics of 2000 years ago was "modern" then.

There are many early significant milestones that I'd consider more important than some of the later ones that are missing. For example, the development of the skeletal system is, in my opinion, far more significant than democracy or the number zero. So are sexual reproduction, the development of our body shape (five fingers, four limbs, two eyes, etc.), a digestive system that allows creatures to feed off of other creatures, the development of plants, and the first creatures that could move on their own (as opposed to being carried by ocean currents). And I only listed milestones between the "first multicellular life" milestone and the "Cambrian explosion".

I'm not suggesting that because of human ignorance, there are major events that no one knows about, although I'm sure there are. I'm saying those things somehow seem less significant because they're far away, and they get grouped together in the brain as a single milestone.

C wrote at Saturday, December 10, 2005 at 11:42:00 AM PST

OK.

I think that your view could still be compatible with Kurzweil's conclusion.

The 15 committees that made their own "milestone" chart had some criteria for what constitutes a milestone. What you are implying is that they did not apply their criteria consistently and left off events that met their criteria, or that their criteria is inherently biased toward the recent past.

If you define some criteria that would capture the events that you feel are missing, such as the development of a skeletal system, and that does not have a bias for recent history, then made your own milestone chart, would it show exponential acceleration? (Perhaps you think that the bias is impossible to avoid...but I have a comment on that at the end...)

The exercise you ask to be done to any particular point in the chart has to be done at the same time to all the points to be consistent. And if you get locally exponential acceleration, that really means that the pace of change is accelerating exponentially. It seems still possible that your missing milestones, when all added in, will still show exponential acceleration, although the time between events will be smaller just because you would get a denser chart.

On the other hand, it doesn't seem that likely that 15 different committees would have carelessly omitted events that met their criteria for milestone inclusion or that they used criteria that is biased to recent history or that the number of such missed events increases dramatically as you go back in time (if the missing event number grows polynomially in that n from the last comment, that still represents awfully fast acceleration).

Another comment I have is that perhaps it is a bit crazy to make a chart of milestones going back to the beginning of time. But if that's the case, one could still make a chart limited to say, the last 2005 years. Kurzweil's main focus is the next 3 or 4 decades (though he does comment on some aspects that come hundreds of years from now). Extrapolating 30 or 40 years out from 2005 years of data doesn't seem unreasonable. Perhaps doing this would be somewhat less controversial and I think his argument mostly relies on observations of progress that happened in the last century (such as Moore's "law", the increasing spatial and temporal resolution of brain scans, and the time it takes to sequence DNA).

- C

Andi Silver wrote at Saturday, December 24, 2005 at 1:34:00 PM PST

The points on this graph are necessarily arbitrary and no matter how exhaustive there will always be a huge number of points unnamed and unknown. Likewise quantifying these points in terms of data storage or accelleration must be always involve much educated guesswork.

If it is indeed a logarithmic curve then this will not become apparent to an observer until there are enough obvious points beyond the "knee" of the curve. Even when that point is reached for some there will be others left unconvinced.

I'm satisfied that it certainly *could* be a logarithmic curve. I believe that if it is indeed there will be people swearing that it is not far beyond the point where it is obvious to most...

I'd like to revisit this in a year or five or ten.

Amit wrote at Thursday, December 14, 2006 at 6:04:00 PM PST

Theodore Modis has a much better explanation of why there's no "knee" of the exponential curve.

Anonymous wrote at Saturday, February 6, 2010 at 2:00:00 AM PST

The link for Modis's explanation why there's no knee can now be found here http://www.growth-dynamics.com/articles/Kurzweil.htm

Anonymous wrote at Saturday, February 6, 2010 at 2:01:00 AM PST

The link for Modis's explanation why there is no "knee" can now be found here:
http://www.growth-dynamics.com/articles/Kurzweil.htm

chaitanya wrote at Wednesday, November 3, 2010 at 10:50:00 PM PDT

Hi, first time here. Was looking around to see what people had to say about the book
I have no problem with his central belief, around which he constructs his life, that at some point there is bound to be explosive growth. It is kind of obvious that science tends to develop with a kind of positive feedback: progress helps progress happen faster. Nor is his idea of the exponential knee fully wrong. It is scale free, but the reference frame Kurzweil refers to here is the AI frame, and the knee is really a perceptual threshold that can still be mathematized. if there were a Ray Kurzweil cave-painting eons ago, he would still have something remarkable to exult about, like fire I guess .The greater question is how individual technologies would develop and morph and here is where he really fails to impress. I wonder if his team of researchers have modeled the present based on the reams of past data and accurately predicted podcasting or blogging.