The Speculist: Exponential Life


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Exponential Life

In his speech at the World Transhumanist conference, Ray Kurzweil claimed that life expectancy is currently increasing by 3 months per year. If that rate of improvement stayed constant, my two-year-old son would have a life expectancy nine years longer than my current expectancy when he reaches my current age of 38.

That sort of linear improvement does not upset the status quo. Career and retirement plans would gradually change to accommodate slightly longer lives, but not much else would change.

Fortunately Kurzweil doesn't expect us to stay at the current rate of improvement. He believes that in 15 years life expectancy will increase more than one year for each year that passes. For every year that passes the average person would get at least another year added to their life expectancy. That would be an indefinite lifespan very soon - by the year 2022. That would change everything.

If we placed our progress on a life expectancy calendar – presently we're at March 31... three months into the life expectancy year. December 31 represents the threshold of indefinite lifespans. If Kurzweil's right, how many days improvement in life expectancy will we see added each year until 2022?

365 days – 91 days = 274 days.

274 days / 15 years = approximately 18.25 days/year

But that's linear. When it comes to technological advancement, Kurzweil never thinks linear.

If Kurzweil's forecast is right (that we get 3 months of life expectancy improvement per year now and that we will pass 1 year of life expectancy improvement per year in 15 years), AND if life expectancy improvement is subject to the same doubling trend that we've seen with computers, what would this look like?

life expectancy improvement.JPG

Obviously, this was a job for a spreadsheet. Columns A and B represent the years in Kurzweil's forecast. Column C shows a simple annual doubling trend. Notice that column C is totaled at the bottom. I generated D in reverse order. Starting at the bottom, I calculated 2022's doubling as a portion of the sum of all progress made since 2007. Working backward I did the same with 2021 on up.

The closer I got to the current year, the smaller the percentage. Excel had to resort to scientific notation for 2009, 2008, and 2007.

At the bottom of column E, I placed the number 274 – the number of days improvement in life expectancy per year needed to achieve an indefinite lifespan. Again, working backwards in column F, I showed the number of days improvement we could expect to see each year if Kurzweil is right (and if this improvement were subject to doubling). Column G is where we fall on the life expectancy calendar.

Notice how this could sneak up on us. Imagine some critic writing an article in 2013 about how we're 6 years into Kurzweil's forecast timeframe and we've seen no real progress, "Obviously good ol' Ray is just a lovable crank."

By 2018 the critic might admit that there has been modest improvement, but indefinite lifespans are perhaps a century away, not four years, "Kurzweil's optimism obviously got the best of him with that prediction he made back in 2007."

The progress of the last four years is so explosive that it might take the critic several years after 2022 to admit that we achieved indefinite life spans in 2022.


I wonder how this chart correlates to the increases in life expectancy we've seen in the past century?

That is an great question, but a tough one to answer.

It's pretty easy to find out what life expectancies were in certain years, but how fast life expectancy was being improved - well, we'd have to make judgement calls on that based on subsequent life expectancy numbers.

That's the next post I guess.


According to this graph, life expectancy in the United States has improved about 9 years over the last 57 years.

That's 3285 days increase in average life expectancy over the last 20,805 days. At that rate we're adding a day to life expectancy every 6.33 days. That's about 58 days improvement per year.

This puts our current level of improvement in life expectancy just shy of 2 months per year, not three.

This rate of progress has held fairly constant since 1950 - which is what you'd expect from the early stages of an exponential trend. Of course a critic might argue that it's also what you'd expect from a linear trend. We'll see.

As for the difference between the two months per year improvement v. Kurzweil's three, I wouldn't be surprised to learn that these official life expectancy numbers are overly conservative.

Sorry Stephen, no math cookie for you. "Early stages of an exponential trend" are still exponential. If the rate of progress has been fairly constant, that is entirely counter to Kurzweil's (completely ridiculous) hypothesis.


Sorry D., I almost choked on my math cookie.


The reason an exponential trend initially looks linear in the real world is because the doubling of a very small number yields... another very small number.

.000000002 * 2 = .000000004

That sort of doubling just doesn't get our attention.

It's quite possible that the rate of life expectancy improvement has been doubling since the 50s (and before) but we're only now beginning to take notice.

Life expectancy is a pretty bad measure of how long I will live.

Think of it this way: old people dieing today are influencing the numbers. But their life experience is not the accumulated benefit of today's technology, leading to their death.

They lived most of their lives in a far worse environment. Imagine something as simple as common knowledge about nutrition today -- or about avoiding smoking -- or about getting regular exercise.

I strongly suspect that if a person were to live a lifetime in a snapshot of technology, their age upon death would be far higher than that date's life expectancy.

Now incorporate progress - even linear. I'm planning on beating life expectancy by decades even if there is no singularity.

Stephen, if that were true, then the raw data would clearly show an exponential trend. There is no "early stage" to an exponential trend. At every point t in time, the value of an exponential function f is some X% more than value at time t - 1. In fact, if you take the derivative of this function f, the rate at which the value is increasing is also exponential--meaning that the rate at any point in time is Y% more than the rate at the previous point in time.

You will have to produce this data to support your claim, and have a very strong suspicion it will _not_ show an exponential increase, even for extremely small values of X.

Yet even if it does, it is likely that X is so small that it will _not_ produce enough progress to meet Kurzweil's magic 15 year threshold.

No, in this case (as opposed to the very clear and continuing exponential trend of Moore's law), there doesn't seem to be a shred of evidence to support this contention. It would take a radical and very non-smooth uptick in medicine. I find this highly dubious.

A better analogy for what is about to happen would be the ‘popcorn’ model. Instead of trying to calculate the take-off curve, think of it as kernels of popcorn, where you put the popcorn in the microwave for 5 minutes. Nothing happens for 4 minutes and 40 seconds but at 5 minutes all the kernels pop and you have a bowl of popcorn.


Neither the linear nor the exponential rate of increase is all that accurate; decade-over-decade changes in life expectancy in the US (from 1900 to the present) have
ranged from a loss of 0.3 months per year to a gain of almost 6 months per year.

We could be much closer -- or much farther -- from living practically forever than any set of projections suggests.

I hope we can make it happen, but I'm not going to place any wagers on when.


I'm not making a claim. I asked a question with two "ifs" in it:

"If Kurzweil's forecast is right (that we get 3 months of life expectancy improvement per year now and that we will pass 1 year of life expectancy improvement per year in 15 years), AND if life expectancy improvement is subject to the same doubling trend that we've seen with computers, what would this look like?"

Sounds like you disagree with both "ifs." That's fine. I happen to think differently, but that's okay too.

Clearly something happened in the 20th century (I'm thinking soap and antibiotics were the two most impactful).

Human life expectancy was close late 20's to late 30's for many centuries. Then it more than doubled in the 20th century.

Statistics are not able to expose the underlying causes of the trends. One reason why the trend will likely go ballistic is the explosion in very powerful improvement in neonatal and pediatric care - IE it's mostly first world countries. Further, starvation was normal in 1800...however, by the 1820's starvation itself was dying in first world countries due to Nicholas Apperts epoch making invention of food preservation in bottles (later in cans). This led DIRECTLY to the vast increases in global population by increasing longevity, reducing pathology, inproving the species health overall, and of signal importance, resulting in the exponential increase of computation - collaborative human brains as massively parallel computer...leading to the received wisdom that most of the scientists that have ever existed are still ALIVE today.

So, as various interventions have solved the early probs of early and middle age (yeah I know there's still plenty to do)...the natural effect that we are seeing is more and more research being devoted to the "longevity tail" - ie realizing that aging is indeed a disease and funding the repair, reveral of same. As the money appears, and scientists age, they get wiser and more motivated to themselves survive - and as the field gets more mainstream, the attention/money will become exponential. There are only two outcomes given the current fiscal situation in first world countries - go bankrupt, attack aging directly and scale back social security programs or make euthenasia de rigour.

The first driver that leads to the reversal of aging was the printing press, the main driver was food preservation, refrigeration in transport and home was the third step...augmented computation w/silicon and binary (the fastest growing language in human history bar none) is the final step. Now we're on a roll with aging...the question really comes down to - will you roll with it or will it roll over you :-)

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