How to Mathematically Predict Potential YouTube Views

Recently, I was looking at my YouTube analytics and I noticed a pattern in my statistics. I figured that I can accurately predict potential views in the future by finding a function that closely correlates to my statistics.

1. I suggest that you go to your analytics and look at your accumulative views (as shown in the videos). Grab a pen and some paper and write down the values. Your x values will be the number of days, and your y values will be the number of views you have acquired on that day. Copy down these values onto the paper.

2. Grab your graphing calculator. I'm using a TI-83 Plus. Press STAT. Press Edit... Plug in your x values in the L1 table, and plug views in the L2 table.

3. To make sure your data shows up on your calculator, press "y=" and make sure that Plot1 is highlighted. To high Plot1, hover the cursor above Plot1 and press enter. Then press GRAPH and dots should appear. You may need to adjust your window.

4. Now to find an appropriate function for your data, press STAT. Move over to CALC. Now there should be a list of functions--quadratic, exponential, sinusoidal, etc.--and choose one that would most likely fit with your data points. If you don't know how these functions look like, then you might have to go through each one and see what function works. Once you found a function press the function. I used ExpReg for my data. Press enter again, and it should give you values for that specific funtion.

5. Now take that data and plug it into the "y=". Press GRAPH. The graph should correlate closely to your data.

6. To look at your projections, press 2nd and GRAPH. An x and y graph should appear. Now you can look at all your projections in the future. The units are in days. For my channel, the function predicts that in 30 days I should have close to 7,000 views!

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Although these stats look promising, it DOES NOT guarantee that you will obtain the predicted views. However, if you continue what you have been doing on YouTube, it is more likely that these predictions can become true. THESE ARE NOT CERTAIN PREDICTIONS!!!

The Mysterious Matter: Dark Matter

According to the renowned astrophysicist, Neil deGrasse Tyson, there appears to be an unknown substance in the universe that affects gravity--dark matter. Tyson claims that physicists have known about the mysterious matter since the 1930s, and they cannot decipher what this thing is. The word itself--dark matter--can be a misnomer because the thing might not even be matter. Tyson says that it should be named "Fred or some other word that has no meaning" (I paraphrase loosely and I'm sorry if your name is Fred) because scientists truly do not what that mysterious thing that alters gravity is. 

I don't know the specific equations that astrophysicists use; however, they do calculations--probably calculating galaxies and planets' movements in space--and they need an added substance to correctly map the universe's gravity. 

Clearly, scientists do not know what dark matter is, but that's the beauty of science; scientists can hypothesize what this substance is or where it comes from. The most intriguing theory--I think-- is the one that relates to String Theory. In String Theory, there is a possibility that there is something bigger than the universe which is known as the multiverse. The multiverse is pretty self-explanatory; it's a place where multiple universes exist and possibly collide. Tyson also argues that this is a valid possibility due to human history. In history, humans have made the false assumption that earth is the largest existing body; however, humans have begun realizing that there are other planets that are sporadically placed in the sky. Humans expanded the universe from earth to its counterparts, planets. It doesn't end there; humans discovered they lived in a galaxy--for sure that's the largest thing in universe, right?. Nope. They, then, discovered there are accompanying galaxies which humans now know this is the known universe. Therefore, there is a possibility that the universe is the limited view that humans see and that there is a larger place than the universe--the mulitverse. Now imagine all these multiple universes as individual bubbles. If these bubbles collide, they create an odd shape such as mickey mouse's head. This leads astrophysicists to hypothesize that the universe is colliding with another universe which causes there to be extra gravity. In String Theory, there is a chance that gravity--or gravitons--leaves from one universe and enters the other. This explains the dark matter issue, but that is not the most interesting part of the theory. If this theory is true, that means there exists another universe and makes humans ponder on how big is this place that humans live in. It truly will make any individual feel small--literally. 

Another question can be answered from this theory is "why is the universe accelerating?" According to Tyson, the universe is accelerating due to dark matter (the universe should be slowing down, but I'll talk about that in another blog post). The scary thing is that the neighboring, unknown universe can affect our universe, and we have no control over it.

The problem with this post is that there is no way that I can make you imagine how big our universe is or even how big our solar system is. It's truly unimaginable. My similes or imagery cannot possibly explain the idea of the multiverse's size. I wouldn't even know what I would be saying if I were able to apply a simile to effectively explain the size of this place. So next time when you look up at the moonlit sky, keep in mind you're seeing an infinitesimally small fraction of the universe, and even a smaller fraction of the multiverse--if it exists--however big those things are because I don't know.  

The Batman Symbol is Mathematical

In a previous blog, I wrote about math's beauty by talking about rose curves (here's the blog post: Who Said Math Isn't Beautiful?). In contrast to math's feminine beauty, math has a second face; a face that says, "I'm a hardcore vigilante that stops evil at any costs--glorious explosions, deadly weapons, sophisticated gadgets, devious plans, etc.--because I can." 

A math teacher decided--on his or her free time--to create a piece-wise equation that generates a symbol that is widely known--the famous Batman symbol. The equation (as seen by the very first image of this post) demonstrates the harshest, ugliest, and the most complex equation--that is legitimate--that anyone has ever seen. The equation is truly a beast. The math teacher didn't state anything that said what techniques he or she used to generate the equation. I'm assuming that the teacher used the basic characteristics of conics--parabolas, ellipses, hyperbolas, etc.--and a whole lot of trial and error. You can see the basic functions in the picture: the blue and red show the simple square root equations, y= √(x); the green portions appear to be parabolas, y=x²; the blue also shows simple linear equations, y=x.

Math can do a lot of crazy things, and a lot of equations do pop out wacky solutions. This equation not only creates a curve that displays Batman's symbol, but also demonstrates a real life application. Although this equation is truly ugly, the outcome is truly fabulous. Who knew that the alphabet soup equation can be tasty eye candy? The equation shows that the horrible situation you're in can become a positive. For example, college students may take several years to graduate and work at a dead-end job but by looking at their prospects motivates them to endure the unbearable times to reach their ultimate goal. The math teacher, more than likely, took painstaking, meticulous time to create this equation, but when it was all done the teacher must have been fully satiated. Although times may be rough, just continue walking down the unfortunate lane because soon there will be a highway to paradise. 

Einstein's Thought Experiment

This morning I woke up in my Buggati, and I was wondering what if my car's speedometer reached the speed of light, 3x10^8 m/s. If my Buggati (I don't really have a Buggati) reached that electromagnetic speed, my car would transform from a Buggati to a DeLorean. However Albert Einstein thought up this scenario with trains or rockets before I did with my fictitious Bugatti.

Einstein's thought experiment derived a time-altering equation by using simple mathematics--algebra and the Pythagorean Theorem.

In Special Relativity, the speed of light is an universal constant; however, in General Relativity, a more complicated topic, light can be altered or bent in space time by gravity. The speed of light is a misnomer because there are other things--gamma rays, radio waves, X-Rays, microwaves, and Gravitons (if they exist)--that have the identical speed. Instead of the speed of light it should be appropriately called the electromagnetic speed.

For time travel to be plausible, the speed of light has to remain constant in any reference frame. For example, there is a car that is traveling at 40 m/s and there is a truck traveling behind it at 39 m/s. The truck will perceive--in its reference frame--that the car is traveling at 1 m/s. However, if the car is traveling at the speed of light, 3x10^8 m/s, and the truck is traveling at 2.8x10^8 m/s, the truck will still perceive the car traveling at 3x10^8 m/s instead of 0.2x10^8 m/s. With that being said, the equation that was derived from the video proves that time travel to the future is possible--not to the past. By traveling at the speed of light, time is infinitely slowed down--basically stopping time. To acquire this speed, however, is completely impractical; it will take an enormous amount of energy to accelerate to the speed of light, and humans--more than likely--will not withstand that force (F=ma).

But that's no fun. Let's say that time travel is possible. With time travel comes interesting paradoxes like the Grandfather Paradox...

or Stephen Hawking's experiment.

Although time travel does not appear possible by the last two videos, keep in mind these videos prove that time travel into the past is impossible. So there is still a chance that time travel into the future is possible.

Breaking Mathematics

There are several dimensions in math--the 0th, 1st, 2nd, 3rd, etc. dimensions. The most interesting one is the 0th dimension which is commonly referred to as a single point in space. A point has no dimension which means there is no measure. If you want to find the distance between two points, you will take the final point minus the initial point. For example, let's say that you want to find the distance between 6 and 2. All you have to do is this simple subtraction: 6-2 = 4. Now instead of finding the distance between two points, we want to find the distance of a single point. For example, we want to find the distance between 9 and 9. So all we have to do is 9-9 = 0. This is good that the definition of a point holds up to this example, but how does it hold up to the number line?

Between two points on a number line, there exists another point between the points. And this can go on towards infinity. So by definition there is an infinite amount of points that make up the number line. But we just proved that a point has no measure? So how does adding up infinite amount points make a measure? It's like adding zero an innumerable amount of times and miraculously appears a unit of measure.

The number line has a unique property. There is no way to determine what the next point is. For example, let's take the number four. The next number can be 4.01, but, actually, there is a number before 4.01 and that's 4.001. So in general, after each integer there is a number that has an infinite amount of zeros with the last number being 1 (i.e. 4.000000000...1). Therefore, between two points there is an infinite amount of points between those two points. Removing a single point from the number line will not affect any measure because there is no length removed, and there are an infinite amount of points that can take the missing point's place.

So drawing a point is impossible. By simply a dabbing a paper--ever so slightly--is still an exaggeration of what a point is. Also drawing graphs are impossible because they are composed of points.

This idea is part of number theory, and this topic almost broke math. Mathematicians ignored this idea and proceeded on doing math. This is a problem because all of mathematics is based on numbers and what they truly are. If this problem was not solved, all theorems, equations, and numbers, will be false. This naive notion of simply accepting the fact that numbers are numbers is horrible way to construct math.

Thanks for those who read my blogs. I want to shamelessly plug my YouTube channel that I recently created. It's just like this blog but in a video format. Here's the link: The Integration Youtube Channel. Hope you guys continue liking my blogs! Enjoy exploring math and science!

Dead or Alive?

Quantum physics generates many profound metaphors that relate to the fundamental functions of the universe and our lives. Imagine a cat within a box that cannot escape. The lid of the box is closed, and there is no possible way of determining the cat's condition--dead or alive--without lifting the lid. This forces the observer to assume that the cat is both alive and dead simultaneously. Fortunately, when the box is open, the cat is alive.

This relates to one of the most bizarre experiments that have been done in quantum physics; it's called the double slit experiment. A physicist, Thomas Young, shot a laser through two narrow slits that landed on a wall behind them. Unexpectedly, the laser created vertical streams of light instead of two beams of light.

For this to happen, light has to be a wave; however, when the slits are a bit wider, the laser creates one stream of light as expected which means light is a particle. In the metaphor, the cat is both alive and dead in the box. The same goes for light; light is both a particle and a wave until observed. Bizarre, light seems to have complete control of it's state; it chooses to be a wave at the quantum level, but also it chooses to be a particle on a larger scale. Why does this happen?

This topic relates more than just to physics; it relates to our lives. We dream of the future; we want to alter the future; we want a pleasant future. However we get caught up in this fourth dimensional lifestyle that we forget about the present. You see, life is full of probabilities. This may happen or that may happen--no guarantee. Instead, you should accept what life throws at you because the most unexpected thing may happen, and that curve ball may hit you in the face. Accept life as it is. Assume that every possibility is equivalent to each other. Prepare yourself for the unexpected. Enjoy life not the dream that may happen.

The Universe is Based on Probability

The quantum world is filled with mystery and wonder. This equation, the Heisenberg Uncertainty Principle, shows probably the most intriguing aspect of quantum physics. In colloquial language, the equation states that there is no possible way to accurately measure a particle's position and momentum at the same time. Now for the mathematics, Δx represents the particles position; Δp, the particle's momentum. The fancy-looking h, ħ, is known as plank's constant which is approximately 6.626 x 10^(-34). To pronounce ħ, say "h-bar." This equation is truly non-intuitive because from the human perspective we can accurately measure an object's velocity, momentum, position, acceleration, and can even predict it's future velocity, momentum, position, etc. by using classical mechanics; however, in the quantum world classical physics breaks down and turns into probability.

Now you may be asking, "why is it so hard to measure these quantities? Don't we have advance microscopes to measure these values?" Firstly, to view an individual particle we need to shed light on it, so it becomes visible. Photons, light particles, can cause a disturbance to the particle's position like when a pool player hits a ball; the ball will accelerate to a different location. Shedding light is equivalent to millions of photons hitting the particle we want to observe. This causes a problem when we look through a microscope. Instead let's just use one individual photon instead of millions to view the particle.When the individual photon bumps the particle, the photon acquires a new direction as well as the particle. So when the photon arrives to the microscope at a new angle, it hits the lens causing it to refract even more (refraction is when light bends). Since we perceive the particle from where the photon is coming from, the measurement is completely inaccurate because of the photon's collision and refraction.

This issue forces us to use probability to locate the individual particle.

This is a probability wave. The probability is measured on the y-axis which is labeled p; the x-axis measures the particle's location which is labeled x. The peaks, or crests, show the highest chances of the particle being at that location. While the bottom peaks, or troughs, show the lowest chances of the particle being there. By using the concept of the derivative, these likely and unlikely possibilities are easy to find (we'll talk about derivatives in a future blog).

That leads us to a question, "is our world governed by probability?" Each human is made up of these infinitesimally small particles, and these same particles have the characteristic of probability. It's like seeing a friend sitting next to you in class, but he can also be sitting across the world in China. Since that probability is extremely low in our perspective, it's almost guaranteed that he or she is sitting next to you. However, having a high probability does not eliminate the other chances. So that very small chance of your friend sitting in china is still plausible. Are we misunderstanding particles' actions? Is there something that controls the universe that deceives us, the observers, to conclude that the universe is based on probability? There has to be something we're missing... I'll leave you with one of my favorite quotes from Einstein.

"God doesn't play dice with the universe." - Albert Einstein