About Exponential Growth, The Universe And Everything
A story on humanity, technology and a fascinatingly true possibility
You probably heard about exponential growth.
It seems to start slowly on a quiet afternoon…
but then it suddenly shoots for the Moon! 🚀
Although the Moon sounds fun, in real life exponential growth behaves a little more down to Earth. It mostly takes part in logistic growth curves, or S-curves. S-curves love to behave like exponentials initially, but after a key inflection point, the growth they display saturates, and a peak threshold or upper limit is finally reached.
“Pure” exponential growth curves that reach all the way to infinity, without necessarily a limit or peak, do not exist in nature. Or do they?
Pandemic infections? S-curve.
There are only so many people to infect.
Moore’s Law for microchips? S-curve.
Modern microchip transistors could only get so small and dense to operate without significantly encountering disruptive quantum effects.
Human population on Earth? Guessed it.
Birth rates are on the decline worldwide, and there aren’t enough resources for an unlimited amount of humans on Earth. Even when our species becomes a spacefaring civilization and we venture far to gather more resources, we’re still limited in space on our home planet.
Exponential growth reaches the TOP, S-curves add an S to make them STOP
For “pure” exponential growth to exist in the universe, there needs to be no physical limit to what it portrays. There must exist an infinity.
The limits of the universe
In our possibly simulated, and yet very real universe, we obsess over approximating reality and its limits. There’s a limit to how small stuff can get, a distance of about 1.6*10^-35 meters, “the Planck length”. Smaller lengths simply make no sense to our conventional laws of physics. There’s also a limit to how large things get, a diameter of about 8.8*10^26 meters, or 93 billion light-years, what we like to call, “the universe”. This length is technically only of the “observable universe”, the part of the universe that we can observe, or see. Beyond what we can see? The actual size of the universe? Is the universe infinite? We simply don’t know.
Assuming we live, laugh & love in a non-infinite & limited universe, the thing that could portray a pure exponential growth the closest, would be what behaves exponentially, for the longest. In other words, the thing that pushes the S-curve’s inflection point, to the limit of time. What is it?
What is the answer to that ultimate question? Some would argue 42.
But we’re not talking about that ultimate question, we’re pondering the following:
What can possibly portray exponential growth for the longest, until perhaps, the “end of all time”?
To answer that question, we must find what has limitless potential & grows like an exponential. One could talk on love, another could say taxes. One could say creativity, another could science.
And one could say intelligence 🧠
Is there a limit to intelligence?
You, reading this right now, use intelligence that’s physically programmed in your brain to do so. Remember that old saying? With great brain-power, comes great intelligence-ability. Is there a limit to the size of a brain? Well, the largest brain of any animal species on Earth is of the sperm whale. It is approximately 6 times larger than the average human brain, or about 3 times larger than yours reading this, nerd.
Size doesn’t matter (in this case)
Sperm whales aren’t for a fact more intelligent than humans. What really matters more for intelligence, is the way the different types of neurons in a brain are arranged and connected — “the architecture”, and their communication speed to each other — “the speed of thought”.
The limit to the “speed of thought”
Humans usually think at speeds of around 180 km/h on average, and peak at 400+ km/h based on several compounding factors. These are the speeds which neurons electrochemical signals (action potentials & neurotransmitters) travel and propagate throughout your nervous system, transferring information in the brain, and sending/receiving it to/from the body.
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Don’t get me wrong, 400 km/h sounds highly ridiculous (and dangerous) in a hypercar on a no speed limit road… but the fact is, that that’s ridiculously slow compared to the speed limit of the universe, 299,792.458 km/second, the speed of light. Electrical signals can travel millions of times faster than biochemical signals, those like in our brains. Namely, computers could process information, or think, incomparably faster than humans. One second for a human, could be a million seconds (~11.5 days) for a computer.
Hence, we arrive at the following conclusion:
The fundamental limit of the “speed of thought”, is the fundamental speed limit of the universe, the speed of light
As a side note, imagine yourself able to think a million times faster, to experience almost two weeks, in the matter of one regular second. The differences are vast. “Small” talk with other humans, becomes “wanting to die of absolute boredom from trying to converse with a statue” talk. The professional term for this time dilating situation is called “Statue Talk”. You can easily experience it yourself, just walk to a nearby vase and put on a happy face.
The limit to “the architecture”
Advanced artificial neural networks in deep learning show, that with fitting architectures and large amounts of model parameters (= the sum of the number of neurons & connections in artificial neural network models), computers can display highly intelligent behaviors. Creating advanced & better architectures and increasing the number of parameters, while using correct training methods and more of the right data, could potentially lead to the display of higher levels of artificial intelligence 🤖
The connections in artificial neural networks are essentially like synapses in the brain. The human brain has about 100 billion neurons and 100 trillion synapses. Meaning, your brain has above 100 trillion “parameters”, arranged and programmed in just the right way by a myriad of interesting factors, including genes through evolution, the behaviors of your parents during childhood, the people you surround yourself with, that one time you did that one thing… (…remember?) and even your very own thoughts. Brains have an ability called “neuroplasticity”, enabling them to physically change and adapt, to transform and reorganize their “model parameters” over time. Along with different functions organs, this is essentially… you.
“Mind-bending, no cap” — Albert Einstein
The artificial brain
Could neural networks parameters be better arranged & increased in number indefinitely? Constantly improving the artificial neural network, artificial intelligence, brain, with an increasingly better architecture and a higher amount of parameters, while achieving the highest “speed of thought” in the universe? If information processing is the source of our and any intelligence in the universe, an artificial brain that can process much more information than humans, incomparably faster with a vastly superior architecture, could lead to a higher form of intelligence. One, that could explore the potentially limitless spectrum of intelligence in an incredibly deeper manner than humanity is ever biologically programmed to.
An artificial general intelligence (an AGI),
limited by the limits of the universe itself.
AI doesn’t need to advance to that level to achieve superiority to humans. In many cases, AI already performs tasks with superhuman intelligence. Once AI reaches a general human level intelligence, it could program itself to be increasingly intelligent. In other words, better in making itself better, or more intelligent at increasing its intelligence. Thus, assuring its possibly limitless advancement, with an exponential intelligence growth curve.
And so, to answer our ultimate question:
Could the intelligence advancement of AGI truly portray an exponential growth curve until the “end of all time”?
Perhaps ⏳
One thing is certain. Only time… will tell.
“… if it’s 42, too” — Deep Thought
