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!

*****PLEASE READ*****

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 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.

Who Said Math Isn't Beautiful?

Who said math couldn't be beautiful? Math comes in various shapes and sizes that are very attractive: triangles, squares, prisms, parabolas, waves, spirals, and even flowers! Actually, mathematicians don't call them flowers; they call them rose curves. Here take a look!

This is a rose curve that follows this equation r = cos(4θ). The reason why the curve appears like this is because of polar coordinates. Polar coordinates spice up the Cartesian plane by replacing rectangular coordinates--x and y--with θ and r. θ is the angle from the positive x-axis to any given point; on the other hand, r is the length measured from the pole (or the origin) to the given point. As you can see functions like these are cyclic which causes the curve to repeat patterns; in this case a rose petal repeats itself as θ increases from 0 to 2π radians (or 0 to 360 degrees). Pretty cool, huh?

For more generalized equations to make rose curves, follow these formulas: r = ksin(nθ) or r = kcos(nθ). The constant, n, determines how many petals the rose curve will have. If n is an odd number, the curve will have n petals. If n is an even number, the curve will have 2n petals. The other constant, k, determines how long the petals will be from the origin. Before drawing rose curves on graphing calculators, be sure that your calculator is in radian mode and using polar coordinates!

Polar coordinates can create more wild shapes, but I'll save those for future blogs.

These curves alter people's perception toward math. People see math as black and white, and they don't see its true color. Hopefully, these petals pretty-up the conventional y = mx+b. Truly, math is full of boring (most may think) equations, but it's these boring equations that make the world beautiful. Just take a second and look around you. You don't just see a computer screen, a desk, a table lamp, you also see math's product. Look outside. Our whole world is governed by mathematics: fractals, bell curves, infinite series, parabolas, inverse square laws, derivatives, integrals, geometry etc. Take the time to look at math, analyze math, and soon you will lift the veil of boredom and find a beautiful figure underneath it. 

Infinite Sums are Weird

What if I told you that 1-1+1-1+1-1+... = 1/2, and I proved it?

So lets take an infinite series, S.

S = 1-1+1-1+1-1+1-1+...

Now lets factor out a negative one from the second term to infinity...

S = 1-(1-1+1-1+1-1+...)

The grouped values are identical to the original series, S. 

S = 1-S

Now with some help from algebra, we can solve for S.

S = 1-S

2S = 1

S = 1/2

Therefore,

1-1+1-1+1-1+... = 1/2

Who knew? Well actually this is categorized as mathematical hocus pocus because this breaks math. In order to use the basic properties of arithmetic (i.e. associative property, commutative property, etc.) the series has to converge. For a series to converge the sum of the infinite series has to add up to a finite number. In this case, we are unsure what the series converges to because it can add up to 0, 1, or 1/2--which is it? If you want to see a visual proof on YouTube check out this video.

Euler, a mathematical gangster, disobeyed the rules of mathematics and found even more surprising values for infinite sums. He concluded that 1+2+3+4+5+... = -1/12. Although this sounds nonsensical, this does apply to quantum physics. Physicists go by the rule that says nothing in the universe has an infinite measure, and these insane values surprisingly appear in their experiments. Although I don't know the details or the direct application to the field, I find it amazing that there is physical proof of nonsense existing. 

Physics generally follows this order: develop an equation and experiment with it (or vice verse). Excitingly, physicists found that math is wrong--in the quantum world--and experiments are correct. Usually, math is correct and the experiments are wrong. This is mind boggling because which one should we believe? 

In our lives, we know what's nonsense and what's correct. However, our field of view is limited from our frame of reference. A human experiences the universe on a human level. If we break out of this perspective and look from a planet's perspective our view changes dramatically. We'll see--as a planet--empty space and feel like we're floating amid nothingness. We'll see our counterparts: stars, asteroids, galaxies, planets, etc. Or instead of a planet's perspective, we look through a quantum perspective. We'll see particles whizzing by, we'll feel the electrical force, and we'll possibly see other dimensions (as theorized from String Theory). What if we take this a step further? What if there is a world smaller than the quantum world or a realm larger than the universe? Is this where all the mathematical hocus pocus is spawned? 

I'm an advocate for being open-minded. I like to accumulate many theories, ideas, and suggestions and determine which is correct and wrong (based on my opinion). This is not only limited to math and science, but also to real life situations. Teachers may provide life lessons in their classrooms and so do parents in their homes. People completely ignore the teacher and follow their parents advice because it's ethically correct--some may think. I believe that one should not completely ignore suggestions due to bias or alleged nonsense; instead one should take in both and generate a more appropriate conclusion. The same goes for math and science. Who knows? Maybe there are parallel universes, time travelers, different dimensions, green aliens, flying pigs, etc.