It’s all Mathematics — What are We Talking About Here?
The Cambrian Room with so much potential, it blew up
I hardly know a thing about you.
If I were to meet you the first time, chances are you will tell me the one name you tell every person you meet for the first time. A name is just a name. I still don’t know you.
If I spend every weekday with you at work, then I get to know some aspects of you. Say, you like having coffee in the morning. Or suits are your thing. Maybe you like having your desk organized.
Now, I cannot compare to your lifelong friend who has known you since you were a child. They have seen you through your relationships, breakups and even attended your wedding.
I have known you for a very short time. So I only know your name. Your workplace buddies know your work schedule and perks. Your lifelong friend knows you don’t like it when somebody calls you past 10 at night.
The point?
In short timeframes, there is little to know. In long timeframes, there is a lot to know.
In the short time I knew you, I got to experience a sample of you briefly. In the long time your childhood friend has known you, they have known you in various scenarios. They have seen sides and thus samples of you for the longest time. Probably longer than your spouse.
With a small sample, there is little to know. With a large sample, there is some level of certainty.
This is the law of large numbers and its inverse, the law of small numbers.
With these examples, you have an idea of what these laws imply. Small samples, high uncertainty. Large samples, more certainty.
As far as small samples go, the smallest sample is one. Less than one and we have no sample. By this standard, the single sample holds the greatest uncertainty.
Now, hold this thought. Don’t forget it.
We’ll use it to formulate our conclusion.
Here’s a thought experiment.
Imagine a room full of blobs of various sizes, shapes, and forms.
This room is always increasing in size. If you walked into the room today and get in tomorrow, you’d notice the ceiling got a little higher.
These blobs have the ability to merge. Yesterday, there might have been a hundred thousand blobs. Today, they are fifty thousand, because some of them merged.
If you were to take the volume of each of the blobs and get the average on day one, you would have a good estimate of the size of just about any blob. The large sample allows you to make this prediction.
However, when you walk in the following day, you find the blobs have merged some more. The estimate you could make on day one is off because the sample size is smaller. You would have to make more computations to improve your confidence in your estimate.
Because you are smart, you manage to do it.
The following day, the sample has reduced even further. Every day, this is the trend.
The only thing you can make out of this is the smaller the samples get, the less you get to know about the blobs. You cannot even know how many blobs formed today’s blob or how many blobs will be present tomorrow.
With a reduction in sample size, you get a lot of uncertainty. Uncertainty speaks of diversity.
Since every day there are more mergers, the diversity potential continues to increase. If one time you find the number has nose-dived precipitously from say 20,000 blobs to 800, the diversity potential should have shot up by several magnitudes.
The diversity potential has exploded.
When we factor in the ability of the room to expand, the actual extent of the explosion becomes bigger. The diversity of the blobs relative to the expanding room is bigger than just the diversity of the blobs without bringing the room into this calculation.
Now,
This is all you need to understand the Cambrian explosion as my theory explains it.
As for Darwin, he had a tough problem reconciling his ideas with the diversity evident in nature.
He thought sexual reproduction would meld traits and dilute extreme properties. This was before Mendel’s discovery — the discrete features of (some) genetic traits — which would have dissolved his issue.
It was not the only challenge Darwin had.
I have found another explanation for the emergence of diversity not related to genes. It follows from the two explanations I used in this post. And it borrows the idea from math.
The expanding room is the universe. Our universe is ever-expanding.
The blobs are organisms. Organisms are always creating mergers in a universe intent on expanding itself and its contents, organisms included. Mergers are a practical solution to avoid this type of death.
With mergers happening in an expanding universe, the diversity potential is explosive.
It is explosive enough to create the diverse forms of organisms registered around 540 million years ago. I am yet to encounter this mathematical interpretation of the Cambrian explosion. I have elaborated on parts of it in my book on evolution.
It is important to appreciate the prevailing theories of the Cambrian explosion. Evolution is complex. Complexity is hardly explained by a single answer. I offer one of the answers to the massive event. The other explanations hinge on the rise in levels of oxygen.
Oxygen was toxic to most organisms back then. Few had the ability to convert it into energy. This was a bigger incentive to merge. The organisms became risk-seeking, according to the four-fold pattern of preference developed by Daniel Kahneman and Amos Tversky.
Merging became a viable solution.
This thought experiment does not explain the emergence of diversity in its entirety. There is one other part to it for it to make more sense. But for now, the take-homes are:
1. Mergers increase diversity from a mathematical standpoint.
2. This has the ability to explain the Cambrian explosion (if you merge it with my previous post).
As the universe expands in length, width, and volume, the diversity potential increase in leaps and bounds.
It’s all mathematics
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