“You believe in the God who plays dice, and I in complete law and order in a world which objectively exists, and which I, in a wildly speculative way, am trying to capture. I hope that someone will discover a more realistic way, or rather a more tangible basis than it has been my lot to find. Even the great initial success of the Quantum Theory does not make me believe in the fundamental dice-game, although I am well aware that our younger colleagues interpret this as a consequence of senility. No doubt the day will come when we will see whose instinctive attitude was the correct one.” – Albert Einstein, 1944
I don’t believe in God. Or, more accurately, I’m more likely to believe in Calculus.
I didn’t want to come to this conclusion – that the universe is merely just math and science, and we are all just random, predetermined points playing out an exponential symphony of growing cacophony under the umbrella of “order” – but in spite of rampant optimism, I stand corrected.
I’ll be brief in my findings, and if time permits or the demand for a more elaborate and constructive illumination exists, we’ll come back to this at a later point.
I want you to take a look at the chart above. It is your generic graph illustrating exponential growth. It is the most important piece of imagery you’ll ever see.
Every exponential graph like this contains the following characteristics:
2. An X and Y-axis
3. A curve whose slope consistently increases at an increasing rate
4. An asymptote which the near-vertical part of the curve can never touch.
Let’s discuss each of these parts quickly.
1. Origin – The point from which the curve originates. The meeting of the X and Y-axis. For nearly every system occurring naturally and of human construct, there is always an origin. The invention of currency, the first of the species, the Big Bang, absolute zero. Origins are the point at which something comes from what initially appears to be nothing – but actually more accurately occurs from a confluence of other systems reorganizing and resetting their own disorder. Stay with me here.
2. X and Y-axis – An X-axis is a linear (theoretically, at least) measuring piece (often time, but could potentially be anything) and a Y-axis is a level or quantity of some kind. the X-axis exists independently, Y must always depend to some degree on X.
3. A curve whose slope consistently increases at an increasing rate – Check out the curve. Seems to continue to arch further and further up as you move from left-to-right across the X-axis, correct? That signifies exponential growth. This is an important concept. Perfectly linear growth does not exist. The problem with most humans is we base most assumptions upon perceived linear growth. This is laughable. Population growth, currency devaluation, heat, technological advancement and evolution are just a few of the multitude of examples of non-linear, exponential growth. We’ll illustrate a few of these examples below.
4. An asymptote which the near vertical part of the curve can never touch. – At some point, the graph points up so drastically that it becomes near vertical. The point at which the curve can no longer sustain itself, and it reaches near infinite levels of growth is called an asymptote. For simplicity’s sake, let’s assume it’s the far right vertical line of the chart listed above. That red line will never touch it, for it is the limit of the graph.
Got the math down? Great. Now, for a bit of science.
First, the chemistry. There are two important laws of which to take note here. The Law of Conservation of Matter and the Law of Conservation of Energy. They relate to each other an important way.
The Law of Conservation of Matter states that “During an ordinary chemical change, there is no detectable increase or decrease in the quantity of matter.”
The Law of Conservation of Energy states that “Energy cannot be created or destroyed, but can change its form.”
Subsequently, the total quantity of matter and energy available in the universe is a fixed amount and never any more or less.
This is important to the concept of our graph for the following reasons:
1. Since there is no creation or destruction of mass or energy, no origin point can exist independently of other graphs of other systems.
2. The X and Y axes can run through multiple phases, systems and courses in conjunction with reason #1. (Time on the X-axis is a fantastic example of this. Time doesn’t start and stop when systems start or stop. It’s a metronome. It’s independent of other variables.)
3. An asymptote has the potential to function as the Y-axis for another related system or graph.
And it is point #3 that harkens back to Einstein.
There is one final piece to the puzzle. “What happens at the asymptote?”
Quantum Mechanics is a hard concept around which to wrap one’s mind. A brief, perhaps overly simplistic overview goes something like this:
A particle appearing at any given discrete point in time and place is probabilistic in nature, and is dependent upon a variety of interrelated factors including energy and field strength. Energy exchanges will always be discrete because standing waves only exist at discrete frequencies (a common graspable example given is a guitar fret-board, where you can move your finger around in a given fret and still produce the same note).
To illustrate this more concretely, although humans have evolved over the past few million years and bare little resemblance to the original homo sapiens, we are still considered human. Many different permutations, but still falling in the same general bucket. Now, let’s put this all together.
The above is a water phase diagram. Note that it contains all the characteristics of the graph we’ve discussed earlier.
1. There are three origin points: the intersection of the X and Y-axis (absolute zero), the triple point and the critical point.
2. An X and Y-axis (Temperature and pressure.)
3. Curves that increase at a consistently increasing rate. (Two of them, in fact!)
4. Asymptotes at which the curve can never touch. (No water ever exists solely at the triple point or critical point, for water can never be both solid and liquid, solid and gas or liquid and gas. It is either one or the other. The dotted line illustrates the clear divide between solid and liquid if you’re not convinced by the points.)
It is also important to note that the quantity of water within this graph never changes (as it is neither an X or Y-axis variable), satisfying the Law of Conservation of Matter. Also, the quantity of energy within the entire system never changes … only whether the energy is stored as potential energy, or in use as kinetic energy as temperature and pressure increase. This satisfies the Law of Conservation of Energy. Ok, that’s basic high school chemistry. You didn’t come here for that.
Finally, due to Quantum Mechanics, it’s important to note that water can only be justifiably bucketed into three phases. Solid, Liquid and Gas.
There’s your illustration … here’s your mind-blowing application.
The following graph represents an exponential system:
Yeesh. That doesn’t look very encouraging. It’s world population.
The origin point is the birth of the first human. The X-axis is time. The Y-axis is the amount of people inhabiting the pebble we call Earth. The curve is in red. The asymptote is, well, pretty freaking soon. Due to a finite amount of resources such as food, water, energy and inhabitable land, the collapse of the system nears closer and closer. Don’t panic yet, as there are plenty of other related systems that may kill us off quicker.
Hey everybody! It’s the national debt! It’s also increasing roughly exponentially.
The origin point (not pictured) is the first printed U.S. Dollar. The X-axis is time. The Y-axis is the amount of debt carried by our entire country. The curve is the upper limit of the purple. The asymptote is, well, also pretty freaking soon. Due to the federal reserve banking system (itself a human-constructed innovation allegedly created to curb debt spending and prevent devaluation of a gold-backed dollar, which confoundedly produces money backed only by debt), and an increase in spending that far outweighs the increase in income and credits earned by our government and industry, the collapse of the system nears closer and closer. A collapse of the U.S. currency (97% devaluation since 1913!) could come as the Fed releases more money to cover existing debt … thereby creating more debt.
Now, let’s get really mind-bendingly abstract.
Evolution & Technological Advancement. Astronomer Carl Sagan once offered up a “cosmic calendar” to make it easier for you or I to visualize the events of the history of the universe. Goes a lil’ something like this:
“The year would begin on January 1 with a bang – the Big Bang. Nothing much would then happen in our corner of the universe until about August when the sun would make its appearance. The earth itself wouldn’t show signs of any life until November—when the first multicellular organisms begin wiggling about. Dinosaurs show up around Christmas Eve. At 10:15 AM on December 31, apes would appear; humans would begin walking upright at 9:24 PM; modern civilization would appear at 11:59:20; Rome would fall at 11:59:57; and the Renaissance would occur just one second before midnight.
Rather amazingly, everything else – the printing press, the steam engine, electricity, the computer, the Internet, the human genome project, stem cell research, nanotechnology, etc – would be squeezed into the last second.”
Indeed, he’s not the only person who shares this view.
If you accept the notion of evolution, you will agree that the earliest life appeared on earth approximately 4 billion years ago. Complex cellular organisms showed up 2 billion years ago, and the first multicellular organism about 1 billion years ago. The first reptiles and dinosaurs made their appearance 300 million years ago; the first primates 40 million years ago; homo sapiens appeared 160,000 years ago; Cro-Magnon man 40,000 years ago; and modern civilization as we know it began about 10,000 years ago.
Wow. Sketched out, the shape of that graph would look an awful lot like all the previous charts we’ve shown.
Related to that, there’s the example of the logarithmic timeline. You can view a simple one nearly anywhere, but for ease of use, here’s a link to one presented by Wikipedia. (Yeah, it’s accurate. You’ll see.)
This flips the concept of exponents upside down, because in this case the distance in time increases backwards exponentially (a logarithm) to make the technological advancement seem more linear. If you were to sketch time linearly, the technological advancements would be exponential. Note that a logarithmic scale never actually gets to zero. This is the origin point! Thus, illustrating backwards the theory that an origin point itself lies on an asymptote, perhaps as the limit of another related system! Just as in water phases and quantum mechanics.
Again, with respect to evolution and technology … it would seem as though we’ve neared the asymptotes, and that a collapse of the current status quo is imminent, and other novel exponential systems will rise. But what does it all mean?
Systems, both human-constructed and some naturally-occurring, are nearing their boiling point. The 20th century produced greater war-related destruction than in all the centuries preceding it. Climate change and natural disasters are more devastating than ever. A freshman in college going for an IT degree will see roughly 50% of their knowledge become outdated by their junior year. Our national debt will once again smash a record high. The gap between the rich and poor grows astronomically. There have been more medical advancements within our generation than in all generations preceding it.
With every breath we take, we draw nearer to the potential for a superhuman species, for the collapse of our ability to sustain ourselves, to live to be 200 years old, or to blow our entire planet off it’s axis. And, mathematically and mechanically, there’s nothing we can do to stop it.
“I never think of the future. It comes soon enough.” – Albert Einstein