# The Trouble With Exponential Growth, from Jim Sogi

April 23, 2014 |

People generally cannot understand or have difficulty understanding or picturing exponential growth. There is a story about the inventor of chess when the King condescendingly asked him what he wanted for a reward, the inventor replied that he would like the number of grains of rice, which when starting with only one grain, doubled in amount for each square on the chess board. The King laughed and thought he got off so easy. This same inability to picture compounding growth interferes with a long compounding hold of financial assets.
The same lack of ability to see compounding growth applies to study of past growth. People understand linear growth more easily.

## Vince Fulco writes:

The inability to see compounding growth interferes with the study of nearly everything I might add. We tend to think that evolution is responsible for much if not all of the world that we see, a function of random mutations that have a selective advantage. Consider, after all, the universe is about 18 billion years old. In seconds, this is 60 x 60 x 24 x 365.2425 x 18 x 1,000,000,000 = 5.68e17.

"Random mutations with a selective advantage." Yes indeed. A thousand monkeys wailing away on typewriters will eventually happen upon Hamlet.

So let's examine that (it provides an insight into the astounding character of exponential growth James writes about here). Only considering the line "To be or not to be," which comprise 18 characters. We will consider the space a character, and make no distinction between upper case and lower case, require no punctuation, but rather a keyboard for the little apes having only 27 keys. The probability of any one monkey typing only this line is 27 ^ 18 = 5.81e25

To put the relative differences into perspective, if I could take a thousand monkeys, 18 billion years ago, and permit them 5,000 keystrokes per second, we would have about an even money bet that, without regard to case or punctuation they might, with a probability of about .5, come up with something like "to be or not to be" and much less all of Hamlet.

Natural selection, whereas I do not contest its existence, does not explain a whole lot as clearly not enough time has elapsed since the big bang.

I'm wrestling constantly these days with allocation structures based on similar matters, where a copula of discrete outcomes (say, the copula of rolling a pair of dice) posses 21 possible, distinct outcomes such that the branch out across elapsed consecutive trials gets unfathomably large quite rapidly. Even with parallel processing (more monkeys, more typewriters) the problem reduces, but the scale remains too enormous still as a result of astounding nature exponential growth.

## Henry Gifford writes:

The relatively new field of epigenetics has some very interesting answers to the astute observation that random mutation alone would have taken too long.

## Stefan Jovanovich writes:

So, one starts with a "known" fact that is not a fact at all — monkeys sitting at a typewriter writing Hamlet. Then, one proves mathematically that the fact is not probable; and that, in turn, raises a question about the validity of the current best hypothesis for explaining the organic world around us — namely, that through natural competition fortunate mutations win.

It seems to me that we are all saddled with two very stupid terms and our minds wear them like blinders - Marx's word for the results of enterprise ("capitalism") and the Darwin's unfortunate choice of the word "selection" for his title. "Evolution", especially in the eyes of its admirers who try to turn its theory into a fact, somehow takes on the certainty of religious moral authority; it "explains" everything just as Marxism does. No, it doesn't; but Darwin's theory does withstand the Shakespeare test. For one thing, there is no evidence that any monkey of sense would go near a typewriter.

If Marx fudged the data wherever possible to make history say what did not, in fact, happen, Darwin did the very opposite. He thought there could never be enough data to "prove" his hypothesis; but he did take heart that there was, at least not yet, no data that proved it wrong. He does seem to have realized that he had been proven wrong in his choice for the title for his first edition. But he deserves a pass for that.

In choosing On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life, he was not endorsing the Southern way of life or Dickens, Carlisle, Kingsley and Ruskin's defense of Governor Eyre. Hardly. Darwin was one of the very few people who had the courage to speak up, along with Huxley, John Bright, and John Stuart Mill. In using the words "race" and "species" Darwin was using the biologist's definition - could male and females produce offspring. In the rare times when he was asked about human "races" Darwin was genuinely bewildered by the question; there was, in his view, demonstrably only one human species/race.

That leaves the point HG notes. Useful mutations may have had their randomness accelerated.

"Timescales of Genetic and Epigenetic Inheritance":

"According to classical evolutionary theory, phenotypic variation originates from random mutations that are independent of selective pressure. However, recent findings suggest that organisms have evolved mechanisms to influence the timing or genomic location of heritable variability. Hypervariable contingency loci and epigenetic switches increase the variability of specific phenotypes; error-prone DNA replicases produce bursts of variability in times of stress. Interestingly, these mechanisms seem to tune the variability of a given phenotype to match the variability of the acting selective pressure. Although these observations do not undermine Darwin's theory, they suggest that selection and variability are less independent than once thought."

## Jeff Watson writes:

We should revisit the Second Law of Thermodynamics, and how some scientists speculate that it enables the formation of life itself. There is some very good peer reviewed literature regarding the second law and life.

Anyways, there are some very interesting challenges to Stanley Miller's glass jar filled with water, methane, ammonia, and hydrogen.(I believe he got his PhD from the same place as the Chair). In Miller's experiment, he blasted it with an electric arc for a long time, and out of this primordial soup arose half the amino acids required for life.

Fifty years later and biochemists and physicists today are on the verge of creating an artificial organism that meets all the criteria of life.

In evolution it's the survival of the fittest, so how come so many species still exist?

## Gary Rogan writes:

There are multiple niches in the environment, so species specialize.  The famous Darwin finches were shown to adapt their overall size and beak size to different sub-environment both geographically and on the same island.  It's the same reason why Toyota doesn't operate supermarkets or Procter and Gamble doesn't own any airlines.  It's easier with conglomerates: at least they can get specialized departments, but imagine a lion competing with heat-loving microorganisms in under-water vulcanoes.

Now the jumps: just because not all species that died out left any identifiable remains, doesn't mean they didn't exist.  The absence of evidence is not evidence of absence.

## Bruno Ombreux writes:

Why is it hard to believe that matter will organize itself into a more
complex form when a very high temperature source of energy is in the
sky?

Matter will organize itself when it is in an open system subjected to an energy gradient. See Prigogine's principle.

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