This video caught my attention. Is there a mysterious universal pattern directing city buses, atomic events and even chicken eyes?
First question: is the pattern above and described in the video below just an artifact, a reflection of the method used to plot the data, and not a real “thing” shown by data?
Is it like a math trick where the input doesn’t matter. Example:
- Have a friend pick a number.
- Tell him/her to multiply their number by 2.
- Ask him/her to multiply the new number by 5.
- Have him/her divide their current number by their original number.
- Instruct him/her to subtract 7 from their current number.
- If the prior steps were done correctly, the right answer will always be 3.
Is a universality graph of probabilities just the inevitable result of looking at any numbers in a certain way?
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This universality curve, looked at another way, seems to occur in cases of randomness where rules or limits prevent complete randomness.
There are many examples, rules imposed by the local environment on randomness.
In the above case with bar code lines, a rule may state that in a random group of lines, no two lines can be closer than one line of blank space. It’s still random, but with some order imposed. Come to think of it, that seems to describe our universe quite well.
Many different types of systems from atomic to biological to cosmological have constraints applied to randomness, so the universality graph does not seem surprising and may just be a mathematical way of saying, “here is a system with randomness which has conditions preventing complete randomness.”
Look again at the graph above showing probability of a bus arrival based on the interval for its nearest neighbor. There are at least two rules applied to what would otherwise be a mirror image curve. 1) There is zero probability that a second bus can arrive when the first is still there, because they can’t occupy the same space (without movie magic or a really bad accident.) 2) Most drivers will be on time following the preset schedule promising a bus every X minutes. 3) it is rare but possible for a bus to be very late, 4) there is a maximum time after which no bus will ever come. (E.g. the bus system is retired, the city is destroyed, the person waiting for the bus dies of old age before it arrives.)
Depending on what data points you use, you could imagine this graph would be quite different. For example, where’s the 2nd hump for when the first scheduled bus doesn’t make it at all, but the next scheduled bus picks people up? That’s why I’m questioning this as a real thing.
Am I missing something about this graph’s mystery for showing a pattern of probabilities in complex correlated systems?
Also note, a “universality graph” is not a universal graph, which is something else entirely. A universal or Rado graph is one that contains all other graphs within it. As you might imagine, it is something so complex that you would draw instructions about how to plot it, rather than actually plotting it.
In mathematics, a universal graph is an infinite graph that contains every finite (or at-most-countable) graph as an induced subgraph. A universal graph of this type was first constructed by R. Rado and is now called the Rado graph or random graph.
Graphs and charts are prone to bias, but some love them.
Regarding the universality graphs, can you think of why in certain cases a probability has a predictably steeper slope on one side of a time curve than another?
That may be the real question regarding this strange universal pattern.