That Are Difficult
Throughout history, there have been people who have tried to explain the complexity of the universe, and even something as basic as our everyday reality. While these theories may provide some answers to the mysteries of life, they can also be confusing and boggle the mind. These are 10 of those theories, which are incredibly hard to understand.
10. The Black Swan Theory
Developed by Nassim Nicholas Taleb, a professor of finance, the Black Swan Theory isn’t as hard to grasp as it is to realize its implications. According to the theory, a black swan is an event that is supposedly impossible to predict, but has massive ramifications and then is rationalized with hindsight afterward.
A major black swan event was the 9/11 attacks. If it had been foreseeable that terrorists would force their way into the cockpits of passenger planes, take them over with box cutters, and then crash the planes into American landmarks, then more precautions probably would have been taken to ensure that none of those steps could have happened.
Then after the attacks, experts and pundits weighed in and tried to use hindsight to explain why the attacks happened. Eventually, it seems as if 9/11 was inevitable because poor airline security allowed it to happen. In response to these rationalizations, airline security increased to ensure it never happens again.
Here’s the problem with that type of logic and rationalization: the next major, world-changing terrorist attack won’t be people flying planes into buildings, because we have safeguarded ourselves against that and it won’t be as shocking. It will be some other black swan event that very few people will see coming.
Another example of a black swan event for many people was the election of Donald Trump. Most people did not predict him to be the Republican nominee, let alone win the Presidency. The polls didn’t indicate that he was anywhere near the lead, and even his own party was distancing themselves from him. However, when Trump did win the election, many of the big news organizations and the Democrats attempted to use hindsight to rationalize how he won.
Essentially, the Black Swan Theory is about being aware of what you are not aware of. No problem, right? Nassim’s advice is just to always assume a catastrophe could happen at any time.
9. The Potato Paradox
Let’s say you have 100 pounds of potatoes. These are special potatoes that are 99 percent water weight. Now, you decide to leave the potatoes out to dry, because they taste better when they are 98 percent water. When you go to get your potatoes, how much do they weigh? Logically, one would think that it would weigh a shade lower than 99 pounds, because 1 percent of water weight would be 1.0101 pounds.
Well, the answer is actually 50 pounds. That’s right, by just losing 1 percent of water weight, the potatoes would weight half as much.
It comes down to ratios. When the potatoes are 99 percent water, that means that there is 1 percent solid mass. That makes the ratio of liquid to solids 99:1. However, when it dehydrates, it changes the ratio of water to solids from 98 percent water and 2 percent solids, which is a ratio of 98:2, or 49:1. That means the weight dropped in half to 50 pounds.
In case you don’t believe us, this is the equation:
(99%)(100) – (98%)(100 – x) = x
(0.99)(100) – (0.98)(100 – x) = x
99 – (98 – 0.98x) = x
99 – 98 + 0.98x = x
1 + 0.98x = x
1 + 0.98x – 0.98x = x – 0.98x
1 = 0.02x
1 / 0.02 = 0.02x / 0.02
50 = x
100 – x = 100 – 50 = 50
8. Simulacra and Simulations
Jean Baudrillard was a French philosopher, and one of his most famous treatise is “Simulacra and Simulations,” which was published in 1981. The very confusing theory essentially contends that our reality is fake, and we are so far removed from real life that everything is hyperreal. Baudrillard Even goes as far as to suggest that our life is just a simulation and we aren’t even aware of it.
To illustrate his point, Baudrillard uses a very short story by Jorge Luis Borges called “On Exactitude in Science.” In the story (that is only a paragraph long), there is a kingdom, where they have made a detailed map of the kingdom that is a scale of 1:1. The map is then spread out over top of the kingdom, and after a while people think the map is really the kingdom. He says that our reality is pretty much just a man-made map that is covering real life.
According to Baudrillard, we got to this artificial reality in four steps. On the websiteCritical Theory, they use a pumpkin to show how the steps work, so we’re going to keep with that theme.
- It is the reflection of a basic reality: This is an imitation that is as close as possible to resembling real life. It’s a picture of a pumpkin with no special lighting or filters, just a plain old picture of a pumpkin.
- It masks and perverts a basic reality: The picture has been altered to make the pumpkin look better. Lights are added and it has a nice filter, but it’s still a picture of pumpkin.
- It masks the absence of a basic reality: A picture of a pumpkin pie made from canned pumpkin sitting beside a fresh pumpkin. This gives the impression that the pie is made from fresh pumpkins, even though it’s canned.
- It bears no relation to any reality whatever: it is its own pure simulacrum. This would be a picture of pumpkins with a pumpkin spice latte, which contains absolutely no pumpkin at all. The pumpkin taste is made from spices like nutmeg and cinnamon.
What Baudrillard proposes is that modern reality has as much realness as a pumpkin spice latte has real pumpkin. Our reality, which is constructed by the media and the government, is as real and as authentic as Walt Disney World or professional wrestling.
7. The Dichotomy Paradox
Zeno of Elea was a Greek Philosopher who lived from 490 to 430 B.C. He is mostly known for his riddles and paradoxes, and one of the most famous of them is the Dichotomy Paradox, which means “The Paradox of Cutting in Two.”
In the paradox, Zeno is studying and decides to take a break. For his break, he wants to walk to a nearby orchard. To get to the orchard, he has to walk halfway there, and this takes a finite amount of time. The second half of his journey can also be split into two, and it takes a finite amount of time to walk that distance. Then, the third quarter of the journey can also be split into two.
This is where the paradox arises because distance can infinitely be divided by two, and that would mean that Zeno would never reach the orchard. Because, according to Zeno, if you were to add up all the finite time over an infinite distance, you would get an infinite amount of time and distance, which means that motion doesn’t really exist.
At this point, you may be thinking that Zeno is clearly an idiot (or really,really high) because if you walk from one spot to another, you get there. Nevertheless, the paradox wasn’t solved until over 2,000 years later by mathematician Georg Cantor. He proved that it’s possible to add up an infinite amount of finite numbers.
6. Vasiliev Equations
Unless you’re mathematically gifted and/or highly educated in math, physics is one of the most difficult topics to understand. And one of the most complicated theories in physics, which even physicists have a hard time understanding, is the concept of Vasiliev Equations, which was developed by Mikhail Vasiliev and Efin Fradkin of the Lebedev Institute in Moscow in the late 1980s. If their theory is correct, then it could explain where space and time come from.
George Musser, an editor at Scientific America, decided to take a crack at explaining the theory that many physicists don’t understand. He said that the theory is based on the spin of particles. Basically, all particles of the same type have the same amount of spin. For example, a photon has a rotation of spin-1, which means that it needs to rotate 360 degrees to look the same again. If the particle has a spin-2, like a gravitation, then it would need to rotate 180 degrees. There is also spin-1/2, which means it would need to rotate 720 degrees to look the same. The lowest it can go is spin-0, which is the Higgs field, and it looks the same no matter how it’s rotated.
How high the spin could go is where Vasiliev Equations comes in. They contend that there is an infinite number of spins; however, physicists thought that particles with infinite spin was impossible. For one thing, it appeared to go against the leading fully unified theory of nature, which is string theory. In string theory, if there were an infinite number of spins, then the Laws of Nature would seize up.
However, physicists have recently learned that in curved spacetime, infinite spin rates could be possible. If our universe exists in curved spacetime, then Vasiliev’s Theory would support an important aspect of string theory called the holographic principle; meaning that Vasiliev’s Theory can be reconciled with string theory. But again, that is only if we live in curved spacetime.
5. Maxwell’s Equations
James Clerk Maxwell was only 34-years-old when he published one of the most important papers in physical science, “A dynamical theory of the electromagnetic field.” When it was released in 1865, physicists couldn’t understand the math, and mathematicians couldn’t understand the physical aspects of it. Because it was so hard to understand, it was essentially ignored for two decades.
One person it did inspire was Albert Einstein, who used it as a starting point for his Special Theory of Relativity. In fact, Maxwell was formulating ideas that eventually could have led him to what Einstein discovered, but Maxwell died at the age of 48 in 1879. Einstein wouldn’t make the discovery until 1905.
We won’t go into a lot of detail surrounding the equations, but there are four, which are pictured above. They essentially explain the world of electromagnetics. The four equations describe how electric charges and currents create electric and magnetic fields. It also explains how an electric field can generate a magnetic field, and vice versa.
However, that is just the very basic explanation of what Maxwell’s equations are about. Beyond that, it is too hard to explain and many electrical engineers and physicists don’t fully grasp it. So, yeah, shockingly… neither do we.
4. Gödel’s Incompleteness Theorem
Kurt Gödel was born in Germany, and later immigrated to the United States. He is considered one of the most important mathematicians of the 20th century and he’s also thought to be the greatest logician since Aristotle, who died 2,200 years prior to Gödel being born.
Gödel has a few theories that are hard to wrap your head around, but his most famous and important work, which is incredibly hard to understand, is his Incompleteness Theorem. According to Encyclopedia Britannica, the theorem states:
…that within any axiomatic mathematical system there are propositions that cannot be proved or disproved on the basis of the axioms within that system; thus, such a system cannot be simultaneously complete and consistent.
Did you follow all of that, or did your nose start to bleed while thinking about it, too?
In order to understand the theory a little bit better, it’s best to go back and explain what the mathematical world was like before Gödel published his theory in 1931. Before Gödel, mathematicians thought that all math theories could be solved with proofs that showed them to be correct or incorrect. An example used by the website Number Sleuth is Goldbach’s Conjecture, which is that all even numbers starting with two can be expressed by two prime numbers. For example, 2+2=4, 11+13=24, and 601+797 = 1,398, and so on. Before Gödel, people thought that this could be proved to be correct or incorrect.
What the Incompleteness Theorem did was show that something like Goldbach’s Conjecture is actually impossible to prove, because there is an infinite amount of numbers and if just one even number couldn’t be expressed as two prime numbers, then it would be incorrect. So that means Goldbach’s Conjecture is either true, but isn’t provable, or it is false and the falsehood cannot be proved.
Essentially, what the Incompleteness Theorem proved is that there was a difference between mathematical truth and mathematical proof. Mathematical proof of Goldbach’s Conjecture is that all even numbers up to 4 × 1018 can be expressed by a prime number. However, the mathematical truth of Goldbach’s Conjecture will never be proved to be correct or incorrect. Of course, this doesn’t only apply to Goldbach’s Conjecture, but to all theories in math.
3. The Theory of General Relativity
One of the most famous theories of all time is also one of the hardest to understand: Albert Einstein’s Theory of General Relativity.
Before we get to General Relativity, there are two things we should go over. The first is that in 1905, Einstein published the Special Theory of Relativity, which basically said that time and space are linked. In fact, they are the same thing – something called spacetime. You’ve probably heard Doc Brown talk about that. So since they are the same thing, that means space can’t be warped without warping time, and vice versa. However, the theory had limitations. Notably, it only dealt with constant speeds and it failed to explain acceleration, and acceleration is something that everything in the universe does.
Secondly, before General Relativity, thanks to Newton, the belief was that objects fell to earth because of gravitational pull. However, objects in the universe don’t move because they are pulled; instead they are moved when they are pushed. Think of a rocket – it goes into space because booster engines push it into space. So the idea that gravity pulled instead of pushed was unusual in the world of physics.
This is where the Theory of General Relativity comes in. What Einstein showed is that when mass comes into contact with spacetime, it can warp spacetime. This warping is actually what is causing gravity; space is pushing us down on Earth. This happens because mass will always follow the simplest path in spacetime, but if spacetime is curved, mass will follow that curve toward the object with the most mass. This also means that the further you are away from the Earth’s surface, the slower time goes because time is less warped.
The Theory of General Relativity was a paradigm shift for many people in the world of physics and set the foundation for a branch of physics that is still being used today. However, it is not only the leading theory in physics, it is at odds with the other top theory, which is…
2. Quantum Mechanics
Famed mathematician Richard Feynman once said that “if you think you understand quantum mechanics, you don’t understand quantum mechanics.” So this one is going to be fun!
Quantum mechanics (QM) is the attempt to explain subatomic particles at the nanoscopic level. The mechanics of subatomic particles are different than the mechanics of larger objects. For example, the same rules of size and speed don’t apply. Also, with larger objects, they exist at a specific time and in a specific space. For instance, you exist at this moment wherever you are reading this sentence, whereas the objects in quantum mechanics exist in a haze of probability.
According to Live Science, there are three revolutionary principles of quantum mechanics. The first is quantized properties. According to classical mechanics, properties like position, speed, and color should exist on a smooth, continuous spectrum. However, scientists learned that some properties can sometimes only occur in specific, set amounts. It’s similar to a dial that clicks from number to number. This “clicking” of the dial is what scientists called quantized. Secondly, light, once only thought to be waves, can actually act as both a wave and a particle simultaneously. The third principle is that matter can also act like a wave, but is usually a particle.
Currently, QM is being used to study string theory and loop quantum gravity. Researchers are hoping that QM will be the key to unlocking many of the mysteries in the universe.
1. We Live on the Event Horizon of a Four Dimensional Black Hole
The Big Bang Theory itself isn’t exactly that hard to understand, because the name is pretty self-explanatory. Essentially, everything in the universe exploded from singularity, which was a tiny speck of infinite density. While the Big Bang Theory does explain a lot about the birth of the universe, there are several problems with the theory. For example, it doesn’t explain what caused the Big Bang in the first place.
Since the Big Bang was proposed in 1927, researchers have been trying to figure out a model that would account for these problems. One of the most mind bending theories comes from the Perimeter Institute for Theoretic Physics in Waterloo, Ontario. Their theory is that our universe may be a three-dimensional “wrapping” around a four-dimensional black hole’s event horizon.
Totally makes sense, right? Perhaps we should back up a minute.
According to the Big Bang Theory, our universe exploded out of singularity. Well, singularity is also found at the center of black holes and in our three-dimensional universe, black holes have a two-dimensional event horizon. However, if a black hole had four dimensions, something humans can’t conceptualize but is theoretically possible, then the event horizon would be three dimensional.
Their theory is that our universe exists on the event horizon in a giant, four-dimensional black hole and our Big Bang was actually a three-dimensional “mirage” of a collapsing star in a universe that is profoundly different than our own. After the collapse, our universe expanded and essentially wrapped around the event horizon.
If their theory is correct, and so far math has yet to disprove it, it could also mean that every time a black hole is born in our universe, then it could spawn another two-dimensional universe.