Exponential Growth

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Exponential Growth

Post  Shelby on Thu Aug 20, 2009 6:46 am

My latest writing:


Somethings I wrote in 2008:

dash wrote:..In light of Taleb's crusade against the bell curve, I am particularly leary of the original theorist's introduction of the bell curve in his arguments. Meaning right now I buy into Taleb's criticisms of the bell curve, so I am especially suspect of anything that refers to bell curve distributions as a part of the fundamental argument...

I did not argue that Entropy requires the specific exponentiation of the Bell Curve (Gaussian distribution), but rather that the distributions of populations must have an exponentiation > 2 ^ Y. Power series are thus acceptable.

Long-tail distributions ("black swans" for Taleb) are not distributions of information, but rather noise, because the mutual information of time duration was not considered. In other words, the sampling error was too great due to the short time scale. It is like saying I didn't have to piss for each second of the last 100 seconds, therefore I will never have to piss. But if sample over a few days, we will realize my pissing has a distributions with exponentiation > 2 ^ Y. Btw, I had a long, unfruitable debate with some researchers at NIST working on anti-spam, wherein I made the assertion that Nyquist also applies to the period, not only to the frequency. In order words, we must sample at the longest period in order to capture the signal without aliasing.



[It quantifies the information contained in a message, usually in bits or bits/symbol. It is the minimum message length necessary to communicate information]

There is something very profound you must understand here.

Imagine you have a dice with a perfectly uniform density, thus the probability of landing on any of the 6 sides is equal. Thus the entropy = -SUM( 1/6 x log2( 1/6 ) ) = -6 x 1/6 x -2.58 = 2.58. So it takes 2.58 bits (on/off switches) to represent 6 possible states (number from 0 to 5).

Now imagine a rigged dice, where all the weight was shifted to two sides sand rest of it was hollow, such that the probability of landing on the other 4 sides is 0 (never happens). Thus the entropy = -SUM( 1/2 x log2( 1/2 ) ) = -2 x 1/2 x -1 = 1. So it takes 1 bits (1 on/off switch) to represent 2 possible states (number from 0 to 1).

So it is not the quantity of data or mass (e.g. the 6 sides of dice) that is relevant, but the mutual probabilities of the data occuring (do all 6 sides occur with same probability). If something is so redundant that is always occurs or does not occur, then it adds no useful information.

Again we will go back to my very first retort of dash's concept that MI can be controlled and save the world. The problem is entropy. In order to gain entropy (information), then dash must allow each of his new bots be an independent decision maker. If he tries to control the types of decisions they are allowed to make, then he is decreasing the information (entropy) and forming redundancy.

See the problem is that dash can at best just recreate life and accelerate the reproduction timeline. But he also has to accelerate the learning process. And to do that, he must mix the matter and get out the way. Once he tries to manage the decisions being made by zillions of new bots, then he will have slowed them down to his single mind.

I will be elaborating soon on this math of population growth...it is very profound and explains why the Bible said "go forth and multiply". As it turns out, each new person added to the free market, increases the information content of the world EXPONENTIALLY. But the key point is, that each new person must be free. Controlled bots are not free.

I will be coming back eventually to post more focused on the way that increases in free populations interact with entropy. As a start, remember that N decision makers have an uncertainty based on the number of permutations of interactions they can do. Let us say it is N! (or perhaps it is 2 ^ N ^ 2, or 3 ^ N ^ 2, or 2 ^ N ^ N ^ N but it doesn't matter for sake of my point here). So if we add 1 new decision maker, then the number of permutations increases by:

(N + 1) x N! - N! = N! x N

Since we showed above that entropy is the number of bits need to represent the number of equally likely states, then assuming all interactions among N decisions makers are equally probable (i.e. "100% freedom"), then adding 1 decision maker has increased our number of states by N! x N. Thus the exponential rate of growth of the number of states is greater than 2 ^ Y, thus the number of bits needed is growing exponentially for each new decision maker added.

But the world is not 100% free. We live within constraints, which made some interactions more probable than others, so the information content (entropy) of the existing world is not increasing exponentially for each new person added, but rather the potential energy of (potential contained within) the 100% free market is increasing exponentially. You see the size of the human population is causing the big showdown with the moneylenders. The size of the free market is what is driving all this. It would be much easier for them to control 2 people. Increasing population leads to more freedom, not the other way around.

Understand that increasing entropy (information content) is creating a higher level of disorder. One might get confused, because higher entropy has higher "UNavailability to do useful work". But remember that the world is not free, and thus it is the opposing force of this exponentially growing free market, that can do so much work in the form of the the unfree world doing the work as it disintegrates back to 100% freedom. The unfree world is straining to grow exponentially (probably already stalled, declining, or at best growing much slower than the) juxtaposed against the exponentially growing free market.

dash's goal of increasing the number of decision makers exponentially is noble. He wants to accelerate the exponential growth of the free market. He cleverly understands that the constraints to population growth are just unfreedoms (amount of energy, science, etc). However, I caution dash to know the math, in that unless his decision makers are 100% freedom to learn and make decisions that he is not monitoring, then the permutations of interactions in the population are not growing. He will have achieved nothing, and it would be an extremely wasteful use of energy (meaning the mass of the world will become more redundant and unfree, i.e. concentrated...not free decision makers).

Since mid-80s, I have shared dash's theory that if we can model the
(chemical, mathematical, statistical, topological) learning process of the
brain at the fundamental level, then we could potentially recreate a human
brain. I spent most of my time in college (only showing up to most
classes to take the exams, doing chapters in all niters showing up to
exams sleepless) in my garage or library, educating myself about diverse
applicable topics, e.g. Nyquist limit, filtering theory, wavelets, fourier
transforms, Shannon entropy, simulated annealing, genetic algoritms, etc,
and I bought my first Atari ST computer with the goal of creating a robot
(it had the most processing power per $ at the time). That become the
computer I used to develop WordUp, one of the world's first fully
functional WYSIWYG word processors (predated Microsoft Word going
WYSIWYG), which gained something like 30% worldwide marketshare back in
lates 80s.

dash, I am not arguing against the technological advancements (agreed they
may happen within our lifetimes or sooner).

Let's make sure we understand how economics applies. That is key area
where we are failing to communicate (failing to really hear each other).
>From filtering theory, communication requires us to tune to the same band
frequency (i.e. for us to resonate), else we are just both hearing noise.

Let's make sure we understand how economics applies (to radical,
revolutionary technological change).

The key point of Biblical Capitalism (and scientific economics) is that
the competitive natural selection favors maximum exponential growth (&
decay...exponential S curves).

Properly understanding the prior sentence, could in theory change ignorant
losers into knowledgeable billionaires. Exponential growth applies to
everything in the universe-- even explains the failure of usury & debt
(more on that below). The proper understanding of exponential growth, and
more specifically the competitive natural selection process of the
immutable natural laws, is crucial for understanding how progress proceeds
in our universe. Nevermind the precise correlation to the Bible if you
want, because we can study exponential growth scientifically.

In nature, we need some capital to do anything. Capital is time, effort,
knowledge, resources, etc.. For example, the crucial years (time) from
teenger to early adult (mid-20s for human), are mission critical capital
for a female animal, as her exponential growth options will be altered by
her childbearing years.

This capital is invested (input) in some activity, and the output is the
growth. Thus, efficiency (output as percentage of input) determines the
rate of growth. This is why bearing children is apparently the most
exponential thing most females can do, because if she has more than 2
productive children, mathematical geometric growth results. Men of course
can theoretically achieve even higher geometric growth, because they can
bear children from numerous women simultaneously, but the problem is can
men maximize the feed, care, emotional sanity, social harmony, and
production of such widespread offspring.

So the return (efficiency) on capital invested, determines the growth
rate, and thus determines which activities will dominate.

A human brain (and body) is a machine that attempts to maximize it's
return on capital. The limiting factor appears to be the rate at which
the human can reproduce and learn. So I think the real question dash is
asking is, "can we make machines which reproduce and learn faster than

Why is it that humans have not evolved to be born with a preset
intelligient brain (like an exact copy of their parents)?

As I explained very early in this thread, nature is higly randomized
(always changing, improving, advancing) and thus humans need to be able to
adapt at a rapid rate. This is why each human has evolved to re-learn his
environment. This process of re-learning, which is conceptually analgous
to random genetic pairing in offspring, is how nature experiments so that
the most efficient growth dominates. This is how nature anneals towards
optimization of progress.

I am theoretically confident that the brain could have evolved to learn
faster (chemical processes in neuron cell growth could have accelerated),
but it did not fit the maximal exponential growth in human environment.
Thus I am confident that is may be possible to design a machine that can
learn faster, adapt to it's environment faster, but let's remember that
communication (learning) requires resonance between the learning and what
is being learned from. So if something learns very fast, it does not
capture the same environmental frequencies (experience) as something which
learns more slowly.

Once nature unleashes a new paradigm (e.g. dinasours, or faster learning),
then that paradigm competes to maximize it's exponential growth. We
really can not predict the outcome of fast, self-learning machines. They
would grow as fast as they can, doing anything they can to maximize their
growth. The economics could be quite different than the human growth
economics. But the key point to realize, is their growth will not be
entirely in resonance with (not entirely synergistic, economically
speaking) with humans.

So my point from the very beginning is there is tension between whether
humans maintain control over the new faster learning machines, or whether
the machines learn to maximize their growth and break free from the human

If humans maintain control, then the machines will be subject to the way
humans compete for maximal exponential growth (humans compete for limited
human capital to maximize their exponential growth...mostly the limit of
time until death). NZ Andy and I provided numerous examples of how humans
will pollute the idealized exponential growth of the robots. Remember
dash that your point was the machines should serve the human economics,
not vice versa.

Rather I am theoretically confident that the machines could learn fast
enough to break free of humans, but this would introduce new constraints.
The machines themselves would have some limit to their rate of learning
(e.g. the speed of their simulated neuron growth), and thus the machine
time & resource (capital) economics would be different from human time
(capital), but not infinite. I can not predict the type of world they
would produce, it would probably be composed of faster boom & bust cycles.

Why do we have boom & bust cycles in economics? Answer: friction. (2nd Law of Thermodynamics)

All exponential growth proceeds until the friction becomes greater than
the rate of growth, then the we get exponential decay. Friction is not
just mechanical, but for example even complexity of large populations is a
form of friction.

The usury is form of friction that is opposite of exponential growth.
Humans borrow to get maximize exponential growth in short-term, but this
steals (via inflation) from those who have saved & invested. Thus rapid
exponential growth via borrowing, discourages savings & investment
(everyone must compete to avoid inflation). We need up with a short-term
boost in consumption and production, that eventually peaks and decays.
The reason is it not sustainable is because long-term work (capital) has
been stolen from. This form of exponential growth drives humans towards
wasteful, duplicitous activities, at the expense of longer-term needs.
The fastest growing activities become prioritized, and the slower growing
longer-term activity frequencies are temporarily ignored. For example,
humans may ignore investment in mining for decades, focusing on consuming
cars, homes, consumer goods.

It is possible to create increasing order (decreasing entropy) in isolated systems, by decreasing order in the external system/environment. This is a form of energy exchange. However, such isolated systems are under constant attack by the external environment, which wants to always trend towards decreasing order (increasing entropy), per the natural law above.

Therefor, as isolated systems of increasing order become larger or more ordered, there is increasing risk/probability of decaying back into the decreasing order of the external system. Statistical thermodynamics (entropy) states clearly that the more order, then the higher probability that the order becomes unsustainable.

This is why things in nature must continual to grow, and grow as fast as possible (exponentially!), because life (order) is always fleeting probability. This is why all things in nature follow a S curve of exponential growth, then decay. Because the universe is trending towards disorder always.

Now we can tie this science back into the Bible. All ordered things (wealth, production, etc) that we can do in this world are fleeting. The real nirvana is one of no order, no wants for anything ordered. This is why I theorized that God, and the universe is disorder.


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Resonance is the maximization of mutual information (mutual entropy)

Post  Shelby on Thu Aug 20, 2009 7:13 am

I wrote the following in 2006:


We know that resonance lowers the impedance, or thus maximizes the signal throughput. The above link mathematically relates this effect to mutual information entropy.

Now we come "full circle" back to my first statement of this theory on the forum:


Resonance is a key (pathway) to alternate dimensions (realities).

Energy is organization of matter/reality (entropy).

The difference between between entropies (organizations) is potential energy. The resonance (pathway) between realities is kinetic energy. Resonance is the reciprocal of impedance.

Thus a crystal which would resonate between our dimension and some other dimension (e.g. quantum effects), might yield infinite kinetic energy.

Nuclear energy creates resonance pathway, by a chain reaction of quantum effect (breaking atomic bonds) which lowers the impedance (pathway resistance) for heat (atomic entropy) to kinetically enter our super-atomic dimension.

I think gravity and everything can be explained as resonance. I was visualizing this as infinitely varying sized particles of ether, starting about 1990s. I wrote some on it, but I don't know where I stored it. Might be lost.

EDIT: Did Tesla discover that the speed through the ether varied as a function of the wavelength itself?


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Statisticians believe in the infinity fairytale

Post  Shelby on Fri Aug 21, 2009 3:32 am

The myopia about "Black Swan" events, starts with the most fundamental theorem of measuring:



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Political Economics 101

Post  Shelby on Wed Sep 09, 2009 6:46 pm

Read these about Political Economics 101 (note I have commented on both pages):


Eric Raymond is a famous programmer and writer about technical economics, you can Wikipedia him.


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Conflating Problems

Post  Guest on Wed Sep 30, 2009 11:36 pm

Hi Shelby,

The article linked below illustrates that our past exponential growth IS ALREADY hitting natural limits. I guess it's axiomatic that "sooner or later" sooner becomes now.

From the article:
"Here is an inconvenient truth about renewable energy: It can sometimes demand a huge amount of water. Many of the proposed solutions to the nation’s energy problems, from certain types of solar farms to biofuel refineries to cleaner coal plants, could consume billions of gallons of water every year."

“When push comes to shove, water could become the real throttle on renewable energy,” said Michael E. Webber, an assistant professor at the University of Texas in Austin who studies the relationship between energy and water.


I realise that the mathematics clearly shows the inevitability of hitting the exponential growth "wall" but I find that for me the math doesn't flesh out the reality of how collapse might pan out region to region. This also touches on the issue of how we evaluate strategies to protect ourselves as best we can eg. owning shares in the best gold mine in the world is of little value if there is no water to process the ore.

In order to get a sense of practical impacts of the mathematics I recommend reading Jared Diamond's excellent book "Collapse - How Societies Choose To Fail Or Survive". In the book he identifies and discusses 12 major trends/problems that individually could severely limit the potential for humans to thrive on this planet.

The list includes all the usual suspects such as loss of soil fertility, deforestation, depletion of fisheries etc. Whether one agrees with the science supporting any one individual threat, such as fossil fuel's role in climate change vs sunspot activity, I don't think you could dismiss the majority of the threats he describes.

In showing how these problems interact and conflate he develops one of the central themes of the book ie. if we don't address ALL of these problems we risk collapse.

What are the odds, given recent history and present policy, that we will collectively accomplish this feat? This question then leads me to another question: If not, can we fashion an effective response on an individual and/or local level? FWIW my reading and research suggests that PMs are part of the solution in most scenarios of how this plays out, if only to preserve an objective value over a long period of time.


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re: Confluence of Problems

Post  Shelby on Thu Oct 01, 2009 5:02 pm

angophera wrote:...What are the odds, given recent history and present policy, that we will collectively accomplish this feat? This question then leads me to another question: If not, can we fashion an effective response on an individual and/or local level? FWIW my reading and research suggests that PMs are part of the solution in most scenarios of how this plays out, if only to preserve an objective value over a long period of time.

By spending a week studying the power consumption versus performance tradeoffs for personal computer designs and components for an ideal internet cafe platform, I was able to choose a design that should use 1/2 or less power (which is extra important for tropical country as affects airconditioning needed and especially in developing countries where the electricity cost can be 20% of gross income). I gained performance per dollar also! Usually performance and efficiency are positively correlated. Even in our overall electrical system (generation and grid), moving to nuclear will increase both efficiency, EROEI, and thus decrease cost. Nuclear and hydro-power are the only viable energy sources to displace carbon fuels. Even at $1 capital per installed Watt, solar and wind power are not competitive, except in very remote and low scale applications that the grid can not reach efficiently.

There is plenty enough water, the problem is how we access, use, and dispose (pollute) it. Cheaper electrical energy will help solve this.

However, society tends to move exponential past the useful life of a given energy paradigm, and thus the transistion to the new paradigm usually involves exponential decay of the old without sufficient mass of the new to prevent chaos. These times of chaos are actually remarkable opportunities where vast quantities of wealth are transferred. As I have delved back into computer and software business, I see so many opportunities. I was myopic for the past years focusing only on investing in gold and stocks.

Gold will be important because you can physically carry it with you during that chaos; however, it can not help you take advantage of all the huge paradigm shift business and R&D opportunities right now. And remember that vast majority of people do not have any gold or silver of significance (i.e. if they have 1 - 10oz of silverware or jewelry, silver to $100 doesn't really help sustain a western family). Thus gold and silver hoarders are going to get "their arms burned up to their elbows" (a quote from a former official in Fed or US Treasury, I forget whom exactly). Remember the story of the talents in the Bible. The one who buried his talents was reprimanded by God. I think God allows us to keep enough of our net worth in Gold and Silver to sustain us personally should the chaos goes bezerk. However, putting more than say $50 - $100K (at $1000 gold) in precious metals is going to just make you a target for an angry mob and fascist govt, should that chaos goes bezerk. If you are buying more than that, I hope you are buying in grains (shot) or small coins, so you can basically give it away to society when the time comes. In that case, you would be sort of building a Noah's Ark, in that when the crisis comes you will offer to fund any one who has a business idea. The problem is society scale, you might just have to give it all away. If you expect to just cherry pick and lowball, thus spending your hoard slowly, society will just take it from you. In other words, God gives us talents only when we make them productive.

It is much safer to find paradigm shifting businesses to invest and work in, which will thrive no matter what chaos comes our way. Doing that might just prevent that chaos from going bezerk.

In short, be prudent but don't go overboard. The opportunity cost of the cost basis versus the ROI of expanding your business might be the best determinant (i.e. buying gold means you are not working hard enough to find better ROI investments). Remain productive in real world, don't drift into some gold bug addiction (I had it, so I know what it is). You will know you are addicted when you care what the gold price is. When you are not addicted is when you buy periodically (cost average) and you careless what the price is, because you are buying for security not for appreciation. Read below for more on why we shouldn't buy precious metals for appreciation, only for security...

Right now we have the western largess is deflating:


The developing world is trying to develop fast enough to offset. Are you going to be part of that and help it happen so the world can avoid chaos, or are you going to hunker down and try to make sure your arms get burned up to your elbows by the angry and impoverished masses??

To be or not to be. That is the question.


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