Category Archives: Uncategorized

Proof that 2=1… or not

Federico Pistono posted about the Wall Street Journal’s opinion piece on science proving the existence of God… or not, so I am going to post (in similar fashion) 2=1… or not.

Many involved with mathematics have already heard of this fallacious proof, however it is an eloquent one and I wanted to share it:

Objective: To prove that all numbers equal each other, namely, 2=1.


1. Let a and b be equal non-zero numbers.

2. Multiply both sides by a

3. Add a^2-2ab to both sides

4. Factor:

5. Divide both sides by a^2-ab

Ah, brilliant, we have just proved step-by-step that 2 is equal to 1. Using these same steps we can prove that any number is equal to each other, right?

Well, obviously, there is something deeply wrong about this proof. Try to consider what might be wrong for a moment, it is a fun challenge. When you’ve done that, continue reading.


The problem in this fallacious proof lies in step 5. In step 1 we stated that a=b, so dividing by a^2-ab would mean we would be dividing by 0. Strange things happen when you divide by 0, and this result is one of them. Therefore, this proof is invalid and 2 does not equal 1. Mathematics is still fundamentally sound and all can remain at peace.

Review: 2014 Goals

As 2014 comes to an end, so too does the possibility of achieving any last-minute goals this year. I recall creating the goal list last December (2013) and mentally visualizing where I would be in preparation for 2015. I wanted to gather an education plan and transfer to a university (accomplished), become financially stable and work part-time to hasten my studies (accomplished), manifest my website into a personal hub of self-expression and utilize it towards my study goals (accomplished),  and learn as much as possible (accomplished sort of =p). However, I also wanted to take a vacation away from everything as I thought I would need to take some time to ‘relax.’ (failed, I don’t know how to ‘relax’) While I did not take this assumed vacation, the reason may be because I did not need to. I was perfectly content with my work-to-play balance throughout the year.

10863784_796039747099353_8167029573984411958_o I start 2015 off in a new home near my place of work and university. I have falling in love with office supplies and now I am the proud owner of three whiteboards in my room. I am within 30 seconds walking distance to UIC’s Richard Daley Library and Learning Center and have a set work and school schedule for the entire year ahead. 2015 promises to be a year dedicated to education for me with all the stars aligning to focus on my long-term goals. Continue reading Review: 2014 Goals

A Discussion on How to break the Cycle of Hatred

This is such a beautiful discussion. Even if you do not watch Naruto, you should be able to understand this discussion.

Will society ever exist in peace and understanding? Is it possible for humans to understand one another? In my opinion, I think it is. In the future, we will communicate in different ways then we do now. Our current communication is harmful to understanding. In a future world, we would communicate similarly to how scientist and engineers communicate. These people transcend language barriers as it is required for their jobs. There is no room for open interpretation in building a bridge.

What is so compelling about this discussion is the reality that both people (Pein and Naruto) suffered from the same societal problems and decided to respond in similar ways. Both idealistic dreamers wished to change the world for the better and create a better future, but failed to understand one another’s past. Similarly, our society creates instances of this exact phenomena. Through poverty, wars, and other problems we are constantly creating hate and people who seek revenge. If we truly want to reach a level of peace, we first need to understand this and wash away the past. Only once we start to treat each human being (note: expand it to every conscious being) like we treat our ‘family members’ will we start down the road of peace. We need to see each other as brothers, sisters, and loved ones and not as ‘outsiders’ to build past this cycle of hatred.

People often ask me why I trust people as I do, and this is precisely why. The world will never get better without this level of trust, and there is too much to gain from trying it out. Trusting others is a prerequisite to achieving a more civilized society.

Math is Beautiful


Mathematics has always been beautiful to me. It has a certain purity in it when explaining the universe that allows no misunderstandings or objections, only truth. In my studies of mathematical series, I’ve finally came across Euler’s Formula and Euler’s Identity. The results of these concepts are truly profound and ought to be understood by every human being on this planet. For some reason, they are hidden away behind complex mathematics, but the logic behind it is rather simple. I wonder how education would change if concepts like these were presented to younger minds from the get-go. Would more people be interested in mathematics and thus, science? I digress…

Euler’s Formula
Euler’s formula can be derived:
1. Using the Maclaurin Series of cos(x) and sin(x).

cos(x) = 1 - x^2/(2!)+x^4/(4!)-x^6/(6!)+x^8/(8!)-x^10/(10!)...

sin(x) = x - x^3/(3!)+x^5/(5!)-x^7/(7!)+x^9/(9!)-x^11/(11!)...

2. Using the Maclaurin Series of e^x

e^x approx 1 + x^2/(2!)+x^3/(3!)+x^4/(4!)+x^5/(5!)+x^6/(6!)...

3. Using the imaginary unit for Maclaurin Series of e^ix

e^ix approx 1 + (ix)^2/(2!)+(ix)^3/(3!)+(ix)^4/(4!)+(ix)^5/(5!)+(ix)^6/(6!)...

By applying the rules of imaginary unit, i, the Maclaurin Series of e^ix can be rearranged to form…

e^ix approx (1 - x^2/(2!)+x^4/(4!)-x^6/(6!)+x^8/(8!)...) + i(x-x^3/(3!)+x^5/(5!)-x^7/(7!)+x^9/(9!)...)

4. Therefore, e^ix = cos(x)+isin(x)

This has plenty of further uses in math, but taking a ‘poetic’ dive into math, let us plug in x=pi

5. e^ix with x=pi




This is Euler’s Identity.

What is profound about this? Well, you are relating Euler’s number (e), an important mathematical constant in finance (namely compound interest), with pi which relates a circle’s circumference to its diameter, with imaginary unit i, which is commonly used in engineering disciplines to find roots of polynomials. You relate these three unique constants of mathematics with the two most simple numbers of one and zero. You are connecting vast areas of life together in one beautiful and simple mathematic equation.

If this doesn’t make you feel emotional in any way, then I don’t know what will. This tells us that the universe, in some way, is connected.

Three Questions: What do you Propose?

Earlier this week, Peter Joseph and The Zeitgeist Movement published a video providing three essential questions regarding the current system that we live in. Essentially, the group is asking for answers to these seemingly impossible-to-answer questions that strike at the heart of the current market system.

I firmly believe that if you can sit through this video and still feel that the current system must be maintained then you are either delusional or ignorant. Possibly, you have an answer to these questions that differs from the answers obtained? If so, feel free to comment via the YouTube link and let them know your answer to these questions.

Direct link:

Read more for Questions / Answers. Continue reading Three Questions: What do you Propose?

The Burden of Proof Lies with The Meat-Eater


It upsets me when meat-eaters ask me why I am vegan. I often respond by turning the question around and asking…

Why do you eat meat when “we are optimized to eat mostly or exclusively plant foods according to the best evidence?” Humans are biologically herbivores. Source


Why do you eat meat when the average meat-eater is responsible for almost two times as much global warming as the average vegetarian and close to three times that of a vegan? Source
Download the PDF Report: Here

Why do you promote violence on me (and others) through unnecessary pollution, deforestation, greenhouse gases, and resource waste? Source

Continue reading The Burden of Proof Lies with The Meat-Eater

How Capitalism Influences Resentment

From time to time, in debating the factors of capitalism with staunch pro-capitalists, I run into the argument that without capitalism there would be no way to properly value someone’s work compared to another persons effort. Examples of this may be where person A and person B work the same amount of time, but person A produces 10x more than person B. Capitalists may argue that person A’s worth is 10x more than person B’s, and demand rightful recognition or ‘pay’. Another extreme example is when one person works 60 hours a week while another person spends all of his/her time watching TV and drinking beer. They argue that without capitalism there would be no way to properly assign value (or resources) to each circumstance.


This argument is highly disturbing to me as it determines one’s worth based on how fast and efficient you can produce things. In a capitalist system, growth is the only concern and if you can’t keep up you are valued less. This type of attitude inherent within capitalism is damaging to our relations with one another. The growing resentment over someone not doing as much work as you is not something that we want to advocate.

I find it largely unlikely that people would exist to simply watch TV and drink beer and have no further desires in a future society built around community, but even if this were the case, I would have no problem with making sure their basic needs are met in a community (food, water, and shelter).
wellfare bullshit 6

Another topic similar regards the welfare state. Many hard-working people complain about paying for the welfare checks of “lazy” people. They blame the poor work ethic and lazy efforts of those without a job while praising how hard they work. In this scenario, they don’t understand how detrimental the current system is on society. Capitalism has created this mess and it will continue to get worse. Before taking a stab at others, remind yourself that it could be you next year on the welfare line when a robot steals your job. Robots don’t care how hard you work, they can work harder. Instead of belittling others, stand in solidarity with your brothers and sisters for an injury to one, is an injury to all. Without this type of attitude, we can’t hope to rise above the vast problems that face humanity.

Pro-capitalists assume the invisible hand of the free market does the job of rewarding those who work hard, however this couldn’t be further from the truth.


Instead of degrading others for doing less than you, or being less talented than you, you should feel fortunate for your abilities to be able to accomplish as much as you do. That’s it. It stops there. Don’t force anything on others, and don’t expect such a high productivity level out of everyone. People have different skills and develop at different rates. We also presently live in a society that ultimately suppresses these things. In a future, community based society, desires and talents will likely flourish. In the meantime, don’t make the mistake of degrading human life because others may not be as disciplined as you are or may not wish to produce as fast as you can. Everyone deserves the right to food, shelter, and water, and we have the ability to make this a reality today.

Welcome to the Mars Project. We have Evolved.

Check out this three-part video series that debunks the idea of claiming human nature  as a reason to eat animals. The typical appeal to human nature fallacy is often used as an excuse animal eaters use to morally justify their choices. The fact is, we have evolved beyond the primitive stage of hunter-gatherer mentality and require a more sustainable and moral approach.

 Part 1 – Introduction

Part 2

Part 3

The Mysteries of Benford’s Law

Benford’s Law, in the most elementary form of understanding, states that the number “1” transpires as the leading digit 30% of the time compared to higher digits such as 9 which occurs 5% of the time. This occurs for all kinds of data sets ranging from electricity bills, street addresses, stock prices, to even physical and mathematical constants. Yes, that’s right, the physical and mathematical constants of the universe follow this mysterious law.












This graph showcases the percentage to be expected based on the results of Benford’s Law. The number 1 representing 30% frequency rate as the leading digit to the number 9 representing a mere 4.6%. Even more strange, the percentage decrease in order from 1 to 9.


The law has been used in court cases to detect fraud based on the ‘plausible’ assumption that people who make up numbers evenly distribute them. It has been used to detect election/voting frauds, fraudulent macroeconomic data, and even scientific fraud.

Continue reading The Mysteries of Benford’s Law

A Science of Morality and Society

Matt Berkowitz “A Science of Morality and Society”

The moment you grant that the worst possible misery for everyone is the worst case scenario we could imagine, and that morality has to do with well-being, you have to admit there are better and worse ways to proceed with respect to morality — which is of course contingent on the laws of nature and the scientific method to uncover.

I. Morals must relate to the well-being of conscious creatures.

II. The worst possible misery for everyone is the worst case scenario we could imagine.

There are better and worse ways to proceed with respect to morality.