First off, here is a gif that will show you exactly what the Mandelbrot set is all about, and how stunning it is:

As you can see, the set repeats variations of itself infinitely. This is a very fancy gif. Why stop here? Let’s find out the math behind this incredible discovery.

The Mandelbrot Set

The Mandelbrot set is a very famous assortment of complex numbers named after mathematician Benoit Mandelbrot. Wikipedia’s definition of the Mandelbrot set is: 

“The Mandelbrot set is the set of complex numbers for which the function  F_c (z) = z² does not diverge when iterated from z=0“

When first glancing at this, unless you have a solid background in mathematics, this may seem like a group of letters and numbers glued together at random…

However, there is no need to panic, as we’ll go through each definition thoroughly. By the end of this article, you’ll be able to interpret Wikipedia’s definition effortlessly. 

Complex Numbers

First of all, we must take into consideration a number line: the visual representation of… numbers on a line:

We are representing “natural numbers“. These include positive numbers, negative numbers, decimals, and so on. 

On the line, we can also position things like squared roots, for example, the squared root of 1, which is 1, and so on. 

However, what we cannot position on the line is the squared root of negative numbers. This is because when you square negative numbers, the final result will always be positive. 

For example:

2^2 = 4

-2^2 = 4

This means the squared root of, for example, -1 is unobtainable. However, mathematicians have established that the square root of -1 does exist, and its value is i.

The letter i stands for “imaginary” and its values are not included on the number line. However, if we draw a perpendicular axis things change.

Instead of a number line, we now have a complex number plane, which is the combination of natural and imaginary numbers. Every number on the number plane is technically the combination of a natural and imaginary number.

How do we know what numbers belong to the Mandelbrot set? Let’s figure out what functions are first.

Functions

A function is a relationship between two given numbers. Functions apply a predetermined set of rules to a set of numbers. Let’s take an example:

As you can see, we use x as a placeholder for any number. An input of 2 would result in an output of 4, an input of 4 would result in an output of 16, and so on. 

Verifying if a number belongs to the set

To verify if a number belongs to the Mandelbrot set, we use the function we mentioned at the beginning of the article:

First, we assign z a value of 0 (that’s the rule for the function to correctly work), next, we take any complex number (c), for example, 1, and add it to z. We then take the result and insert it into the function, iterating it. If the function keeps returning non-consistent values, then we know the complex number we picked does not belong to the Mandelbrot value.

However, with certain numbers such as -1 and start iterating them, we will notice a certain pattern repeating itself: the results of the function will always be either 0 or 1. This means -1 is part of the Mandelbrot set

Conclusion

The Mandelbrot set is one of modern mathematic’s greatest discoveries. It is amazing to think about how much it took us to find it.

We had to invent computers, graphical processing software, and so on. This shows just how little we know about our universe, and how much more there is to discover

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Quantum locking, or flux pinning, is the phenomenon where a superconductor is “pinned” in space when placed above a magnet. Flux pinning could be helpful in many operations in space, such as docking and on-orbit assembly, require two or more bodies to be nearby. These tasks require high-level precision, as well as intense control abilities. This is where quantum locking kicks in.

A superconductor flux pinned on top of a magnet

What is Quantum Locking?

As previously mentioned, quantum locking is the process in which a superconductor is placed above a magnet. The superconductor then proceeds to “pin” itself in space. Flux pinning only occurs on type-II superconductors, due to their magnetic penetration abilities. 

How does Quantum Locking work?

Quantum locking describes the interaction between a superconductor and a magnetic field. The magnetic field provokes current vortices in the superconductor which resist the change in magnetic flux, happening on top of the superconductor’s surface. This causes a stiffness effect that influences the motion of the superconductor across the magnetic field’s surface. 

The Applications of Quantum Locking

In the future, we could implement quantum locking in numerous sectors, such as lifts, frictionless joints, and transportation. One example of transportation could be a modified version of the MagLev system, called Maglev Cobra. This system is currently being developed by the Federal University of Rio de Janeiro and aims for a smaller form factor than existing urban rail systems.

Conclusion

Quantum locking has a place in future technologies we should keep investigating. Frictionless transportation and precise aircraft construction are some technological advancements we wouldn’t want to miss out on.

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As fun of an idea it may sound, scientists and researchers are looking into transforming cloning humans into a reality. Let’s dig deeper.

What is Cloning?

Cloning is the process of producing genetically identical individuals of an organism. Mother nature has already figured out a way to do it, with many species of trees and plants. This is done through something called asexual reproduction, where offsprings arise from a single organism. 

A question someone may ask is: “Why don’t all living things just clone themselves, instead of having trouble finding partners? Wouldn’t it be more efficient?” If you think about it, evolution is based on the mixing of two different genetic heritages, where the stronger characteristics survive. Without normal sexual reproduction, there would be no evolution, therefore, no progress.

Why should we clone ourselves?

Leaving aside the comfort aspect, which is not achievable due to ethical problems, clones could be used in long term missions in space, once we will have the capabilities of building powerful and long-lasting spaceships. Other than that, the other possible uses of cloning are full of controversies and ethical issues, so we haven’t come to a conclusion

Uses of cloning

Cloning has excessive usages in various fields, such as medicine, agriculture, biology, etc. 

For instance, cloning could be used to clone endangered species, organ transplants, and possibly, immortality. The question is if you were cloned, would it really be you?

How cloning works

In 1996, cloning was revolutionized, when Ian Wilmut, at the Roslin Institute in Scotland, successfully cloned a sheep, named Dolly. Dolly was, in fact, the first animal to have ever been cloned. 

Wilmut and his colleagues transplanted a nucleus from a mammary gland cell of a Finn Dorsett sheep into the enucleated egg of a Scottish blackface ewe. The nucleus-egg combination was stimulated with electricity to fuse the two and to stimulate cell division. The new cell divided and was placed in the uterus of a blackface ewe to develop. Dolly was born months later.

Dolly was shown to be genetically identical to the Finn Dorsett mammary cells and not to the blackface ewe, which clearly demonstrated that she was a successful clone (it took 276 attempts before the experiment was successful). Dolly has since grown and reproduced, a not-so-typical “and they lived happily ever after” scenario, but still valid.

Conclusion

Cloning will probably help us reach some state of immortality in the future, however, ethically speaking, machines and IA are, in our opinion, a better option.

Sources: wikipedia.com, britannica.com, learn.genetics.utah.ed, digitaltrends.com, science.howstuffworks.com

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 A theory proposed by Enrico Fermi, an Italian-American physicist, suggests the apparent lack of evidence for extraterrestrial civilizations elsewhere in the Milky Way galaxy despite the high probability of these existing is paradoxical.

Basic Hypotheses

These hypotheses demonstrate how weird it is that we haven’t been visited by other life forms yet.

• Multitude of Stars – There are billions of stars in the galaxy that are similar to the Sun and many of these are way older than the sun
• High numbers – Because there are so many, there is a higher chance some of these stars have Earth-like planets
• Wiser Civilizations – Because these planets are much older than Earth, the civilizations may have developed interstellar travel

Based on these logic-based hypotheses, Earth should have already been visited by some form of extraterrestrial civilization by now.

The Kardashev Scale

The Kardashev scale is a method of measuring a civilization’s technological advancement. This is done by categorizing civilizations into 3 categories, based on the amount of energy they are able to use.

• Type I civilization – this type of civilization can use and store all of its planet’s energy. We are not quite there yet, but we are slowly getting closer (we’re roughly at 0.7)
• Type II civilization – this type of civilization would be able to store and use all of their host star’s energy
• Type III civilization – this incredibly advanced civilization would be able to access such power comparable to that of the entire Milky Way galaxy

Although these civilizations’ energy resources sound hard to believe, you must keep in mind they got roughly 3.4 billion years more than what we got. In 3.4 billion years, we might achieve such levels of greatness… If we don’t extinguish ourselves.

The Fermi Paradox

So, if there were Type III civilizations in the universe, or civilization advanced enough to have figured out interstellar travel… Where is everybody?

All we can do for now is suggest a series of possible hypotheses, and explanations, based on the information we have. However, in this article, we are going to explain the main ones, as well as the most interesting ones.

There are no signs of higher civilizations because there are no higher civilizations

Mathematically, this hypothesis makes no sense, as there are supposed to be so many higher civilizations that even if 99.9% of all of these did not come into contact with us, we would still have met the other 0.1% by now. This must have been caused by something else. This something else is known as The Great Filter.

This sets an imaginary filter that causes civilizations to die out whenever they try to acquire a major evolutionary leap. The situations are the following:

• We are rare – we have already passed this great filter and it is, therefore, behind us
• We are unique – we are the first civilization to have ever passed this filter. This would explain the absence of other life forms visiting us
• We are not there yet – the great filter is ahead of us and it’s going to exterminate us

The Type II and Type III civilizations are out there but there are logical reasons why we have not heard from them

• We were not here when they visited – humans have been around for roughly 50,000 years, which is very little, compared to Earth’s total lifespan
• Our galaxy has already been colonized but we are in some rural area of the galaxy – we might be so distant from the galaxy’s urban zone that there is no alien influence here
• Aliens stopped thinking about colonizing and are just enjoying themselves – why bother searching the emptiness of the universe if you are living a utopia? Makes sense
• We might be too primitive to perceive them – our intelligence may be proportional to ants compared to theirs. Even if they tried to communicate we wouldn’t understand
• We are in a simulation  – read more here

Conclusion

This article is very intense, but it gives you an idea of what the Fermi Paradox is, as well as all of its related theories. It gives some simple rational motivations for why we haven’t met aliens yet. 

Sources: www.waitbutwhy.com, islandone.org, wikipedi.com, seti.org

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There are an estimated 100 billion in our galaxy alone; considering the fact that there are about 10 trillion galaxies in the universe, that adds up to a total of 1,000,000,000,000,000,000,000,000 stars. We know they did not just appear out nowhere, so how did they form?

Initial Ingredients

Just like many things in the universe, stars start as really small. In this primordial state, they are just particles floating around in vast clouds of dust and gas. 

These nebulae remain cold for an uncertain amount of time and then stir up. This is due to the disturbance generated from a streaking comet or the shockwave from a distant supernova. These forces move the cloud particles, making them move faster and collide more often. These particles then form groups which then grow more mass, therefore increasing the gravitational pull.

Growth

As the primordial star gains more mass, for about one million years, its center becomes denser and hotter. This group of particles then grows into a small but dense body called a protostar. This keeps on gaining mass, as its gravitational pull increases. 

When the protostar becomes hot enough, it starts an atomic reaction, called nuclear fusion. Its hydrogen atoms start fusing, producing helium as a consequence, as well as an outflow of energy. 

However, to be able to contrast the now increasing inward gravitational pull, the star still needs more outward energy. 

Stabilization

Finally, after millions of years, the star stabilizes. This happens when enough mass collapses into the protostar and bipolar flow occurs. Bipolar flow is when two massive gas jets erupt from the protostar, blasting the remaining gas and dust away from its surface. Once the star stabilizes, it reaches a point where its output exceeds its intake, meaning the outward pressure from the nuclear hydrogen fusion fully overcomes gravity’s inward pull.

Death

The star will stay roughly the same until it will run out of fuel. The lifespan of a star depends on its mass. A sun sized star would take about 10 billion years to die out.

Conclusion

Stars are definitely something particularly astonishing. Their lifespans’ steps look simple, yet they take billions of years to take place. 

Sources: wikipedia.com, www.universetoday.com, science.howstuffworks.com, nasa.com

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Basic Idea

As soon as computer power got strong enough to handle simulations in the 1990s, and technological progress kept getting quicker and quicker, people started wondering if in the future we would’ve been able to simulate our universe. As soon as that hypothesis came into mind, people also started wondering if we were the ones being simulated. When movies like “The Matrix” came out, people became more and more obsessed with this “simulation idea” and what was behind it.

Supporters

Tech Billionaires such as Elon Musk have openly stated their support for this theory and have popularized it. Even world famous Astrophysicist Neil deGrasse Tyson thinks it is very likely that some advanced future civilization developed advanced computer simulations.

Many people in the Silicon Valley have actually become quite obsessed with the simulation hypothesis. Two tech billionaires have gone so far as to secretly engage scientists to work on breaking us out of it. Of course, that may not make a huge ton of sense as breaking us out of it would cause a “termination of the program” which would end up destroying us all. 

Elon Musk actually thinks being in a simulation is something we should hope for. If this were a simulation, we could save ourselves from the end of civilization by creating another indistinguishable from reality simulation.

Our creators

If we actually were in a simulation and we got to know the creators of it, they would surely be some incredibly intelligent beings, possibly not too different from us. If you think about it, mammals have a very similar DNA to our own, however, we are able to understand concepts they will never even get close to understanding. If this were the case for our creators, we would look like dogs compared to them.

Conclusion

We are probably living in a simulation. If in 10 years we were able to upgrade basic calculation devices to computers able to handle AI we think that in 14 or more billion years or more these “creators” were well able to simulate us.

Sources: www.nytimes.com, scientificamerican.com, snopes.com, seeker.com

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