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The invention of Zero

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Find Secrets in the Science of Form

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Anxious about Math?

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Type 1 through 7 civilizations

Type 1 through 7 Civilizations

Photo by Pawel Nolbert on Unsplash

In 1964 a Soviet astronomer by the name of Nikolai Kardashev introduced a hypothetical scale that can be used to measure the potential of a civilization based on the amount of energy it can produce. There have been some adjustments to the kardeshev scale over the years, and now it shows the amount of energy required for the types of civilizations and what they are capable of.

The mathematics shows that there should be thousands of types 1, 2, and 3 civilizations, but we just don’t see any. This could be because the transition from type 0 to type 1 is so dangerous. To realize how dangerous it can be, I need to explain what type 0 and type 1 civilizations are.

Type 0 civilization is any civilization that is not capable of harnessing all the energy from its home planet. We are about a .7 because we do collect some energy from the sun, water, and air, but that is not the main source of energy. We choose energy that isn’t renewable and it will one day run out.

Type 1 civilization can gather all the energy that reaches the home planet in the form of solar but it can also obtain the energy its home planet gives off, like thermal, wind, hydro, etc. Physicist Michio Kaku thinks a planetary civilization should be able to control such things as earthquakes, the weather, volcanoes, and would be building ocean cities. If that’s the case, we are not quite there yet. Kaku thinks it’ll take another 100–200 or so years for us to get to Type 1 status. Carl Sagan thought we are currently at about 0.7 on the way to type 1. Type 1 civilization has peace throughout the entire planet, and they also have a universal language.

The reason why where we are at is so dangerous is that we have some pretty powerful weapons such as nuclear bombs, but we do not have the universal peace a type 1 civilization would have. This could be the possible answer for why we don’t see any type 1, 2, or 3 civilizations and an answer for the Fermi paradox. We have the power to commit planetary suicide, but we do not have the universal peace to make sure we don’t do that.

What happens when a type 1 civilization turns into a type 2 civilization? We are likely to leave Earth, looking to draw energy from other planets. If we can become an interplanetary civilization that can make use of the total energy potential of a star, we’d become a type 2 civilization. One possibility to collect the energy from our star is to create a Dyson sphere. A Dyson sphere is a megastructure that would be capable of surrounding the sun and would transfer the energy to a type 2 civilization. Although such a structure like this is a completely unfeasible thing to do, no known material would be able to withstand the sun’s gravity because it would simply get ripped apart and sucked into the sun. However, there are other options, and the one I think is the best is having satellites that acted like solar panels that would orbit the sun transferring its energy for civilization. This would not impact the amount of energy they would be able to collect because you could just make enough of these satellites to pretty much cover the sun. This can be used to spot a type 2 or 3 civilization from great distances. If scientists are looking at the sun and the sun is dulled in any way, this is completely unnatural and it would strongly suggest the presence of alien civilization. Scientists estimate it would take humanity from this point 1000–2000 years to reach type 2 civilization.

Type 3 civilization is capable of harnessing all, or almost all the energy from its galaxy. They would travel using some sort of propulsion technology we do not know yet, being able to travel the galaxy in a couple of hours or days. They would be so far from humanity that we might not even recognize them by that point, becoming some kind of post-biological cybernetic beings. We are talking about a world capable of building robots that would then build a Dyson sphere, or something similar like that to collect to energy from its galaxy. Scientists guess that it could take 100,000 years before we hit this point, but that is a rather optimistic guess and it would probably be closer to a million years before we hit this point.

There is a type of 4,5,6 and 7 civilization. This was not originally on the kardeshev scale as he said that there is nothing after colonizing your entire Galaxy. Type 4 civilization would be able to gather all the energy from the universe and be able to alter it in any way they see fit. Type 5 civilization could do the same but to the multiverse assuming that there is a multiverse. Type 6 civilization is god-level, they can control time and space, and type 7 is so advanced we can’t even imagine it yet.

This may seem a little science fiction, and it is, but scientists and humanity just needed a way to see what is possible for humanity to do and see our progress right now compared to the kardeshev scale.

Type 1 through 7 civilizations was originally published in ILLUMINATION on Medium, where people are continuing the conversation by highlighting and responding to this story.

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Mental Math: A New Divisibility Rule for Three-Digit Numbers (and more!)

Photo by Mike Szczepanski on Unsplash

DISCLAIMER: I am not aware of this proof being published by anyone else.

What is fascinating about mathematics is how a simple rule can open the door to a plethora of others. I find great joy in playing with numbers on my calculator to try to uncover yet another secret. Sometimes, my little conjectures (statements based on a pattern and not solid proof) are ripped apart by the most obvious counterexamples. Other times, I feel so shocked that the pattern I noticed works for more than three numbers (yes, my standards are quite high) that I know for fact there must be something wrong, which there inadvertently is.

Then, once in a blue moon, I find something that withstands test after test. Tentatively, I work out a proof. Let me just say that working out a proof for a conjecture, no matter how silly (as this one is), is perhaps my greatest source of joy in math.

We’ve all learned the divisibility rule of three at school: if the sum of the digits in a number is divisible by three, then so is that number. But what if there is another rule for three digit numbers? I love patterns, so I worked with three-digit numbers whose digits are related in some sort of way.

So, I worked with three-digit numbers formed by consecutive digits. This means that the three digits in a number come right after another, like 123 (or 321, 213, 132, 231, 312 — the order doesn’t matter so long as the digits are right after another).

Punching numbers into my calculator, I found the following pattern:

Any three digit number formed of consecutive digits is divisible by three.

This was a surprise. Unsure whether it was pure luck, I decided to attempt to write a proof. Unbelievably, it worked. Here it is below:

  1. Assume the three digit number has the digits XYZ, where X, Y, and Z are consecutive.
  2. For the sake of convention, let’s represent X by n.
  3. Since the integers are consecutive, then Y = n + 1 AND Z = n + 2
  4. Notice that it does not matter whether the number is XYZ or YZX: it will not change the value.
  5. Add X, Y, and Z. You will get n + (n+1) + (n+2) = 3n+3
  6. Divide (3n + 3) by 3 and you will get n + 1, without any remainder. Since the sum is divisible by three, then the number is divisible by three. It is also shown that the order of the consecutive integers does not matter.


This proof can be extended to six-digit numbers and nine-digit ones.

What are the uses of this trick? Well, not much, if only to avoid tedious addition. But take a moment and think how many other hidden tricks lie out there, waiting to be discovered.

Perhaps the next time you find yourself bored, you can take out the calculator, punch in some numbers, and find your next best pattern.

Mental Math: A New Divisibility Rule for Three-Digit Numbers (and more!) was originally published in ILLUMINATION on Medium, where people are continuing the conversation by highlighting and responding to this story.

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