Category Archives: Science

Some Things I Would Have Done Differently in My Pursuit of a Degree in Physics

In pursuing a physics degree, I have stumbled into many problems a long the way. Here are some of them and what I wish I did differently.

1. Start Young

Chances are, if you are reading this, you are not young. This will ultimately end up being a moot point for most of you. However, I am constantly contemplating where I would be if I had started studying physics (really, science in general) at an earlier age.

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Educational Videos (Cauchy-Schwartz Inequality, Binomial Theorem, Hermitian Matrices)

I feel that there is not a large enough presence of proof-based mathematics on YouTube. I would like to try to change that.

Here are a couple new ones I made (Hermitian and Unitary matrix video [not proof based], and Cauchy-Schwartz Inequality) and my most beloved video (Binomial Theorem Proof).

Cauchy-Schwartz Inequality Proof using Inner Product and Complex Analysis

Continue reading Educational Videos (Cauchy-Schwartz Inequality, Binomial Theorem, Hermitian Matrices)

Elementary Proofs in Geometry, a Math Writing Assignment

I am taking a math writing course and our first assignment was to create an essay from lecture notes. This is what I came up with.

Also, a nice read on writing mathematics is found at this pdf:


Elementary Proofs in Geometry Using Features of Pi

Pi is an extraordinarily beautiful number in mathematics. One of pi’s most amusing features is that the measurement of a straight angle is pi radians. Similarly, the sum of the interior angles of a triangle is also equal to pi radians. We seek to prove these facts and use them to determine if parallel lines can ever meet.

First, we will prove that all vertical angles are congruent. After proving this theorem, we will show that parallel lines never meet. To prove this theorem, we will give a definition of what it means for two lines to be parallel and then use the theorem that the sum of the interior angles of a triangle is equal to a straight angle to prove it.

Theorem 1: Vertical angles are congruent.

To prove that vertical angles are congruent we will utilize two axioms.

Continue reading Elementary Proofs in Geometry, a Math Writing Assignment

Just Say No to Solar FREAKIN’ Roadways

solarroadwaysIt is likely that you have already seen the brilliantly marketed Solar FREAKIN’ Roadways video that has helped raise over $2,200,000 for the project.

In the past month, my environmental class linked to this video and I’ve had multiple friends link to this video. In every case, the received response has been overwhelmingly positive.

However, we should be weary of letting the brilliant marketing sway our otherwise logical opinions. Taking a step back, is it really a logical idea? If you initially thought solar roadways were a good idea and perhaps you were even willing to support the campaign financially, consider the actual logic and science behind the project and decide whether the flashy marketing campaign blurred your vision.

Youtube user Thunderf00t, explains the problems with solar roadways in great detail. Some of these issues should have been obvious to the laymen, however, the well-marketed piece has continued to raise money for the project. The creators of this project are clearly intelligent people, but with obvious obstacles like the ones presented in this video, it begs the question of whether they actually believe what they are doing or if they are simply using the lie to deceive the people.

Here are some of my notes/highlights from this video for reference:

1) The main attribute that roads must absolutely have and cannot compromise is that they must durably provide traction for ALL vehicles in ALL environments. Due to this necessity,  roads often need to be repaired. Cheap road repair is still extremely expensive, but replacing roads with high-tech glass bricks would require an unthinkable amount of money. The campaign claims that traction properties are ok, however there has been very limited testing on this property and I can imagine the difficulties that natural erosion and time would take on the high-tech glass. Glass is a relatively soft material, will it truly be reliable with years of usage in a range of environments?

2) Hexagonal tiles are a bad idea. Water will go through the cracks and natural erosional processes exist over time. Having hexagonal tiles will increase these negative properties and will thus need even more (costly) road repairs.

3) Environmentally conscious? Asphalt is one of the most recycled materials on the planet. Once again, the cost of recycling plants needed for this expensive high-tech glass would be astronomical.

4) COST. The solar roadways campaign has set up a part of their website to respond to the (seemingly) wide range of criticism it has received. In it, they state:

But right now, not even we have that information, so if you read an article where a journalist claims to have any data on costs, you can be assured that they have not done their homework and are quoting another unreliable source or they are making up numbers.

They offer no reasonable explanation to the criticisms other than “it has not been worked out yet.” This screams of a desperate dodge to the answer. What predictions on cost have been made? It would take nearly 20 trillion USD to acquire JUST the glass (this does not include any of the high-tech equipment or other materials). This is over 5x the U.S. federal budget in 2013.

5) Typical solar energy problems still exist. Solar power is only generated when there is sunlight. With the (insane) costs of the project, we will still only be generating energy when there is sunlight. It seems vastly inefficient to create roads built with solar panels in areas of low sun.

Power transportation is another glaring issue. The cost of infrastructure to transport the power would need to be taking in account. A power transportation system would have to be built along every road. The amount of material this would take would be ridiculous (metal, resources).

Burying power transmission lines cost about 10x more than hanging them above ground (which costs over $1 million/mile). Another outrageous claim made by the initial marketing video. If this power cannot be transported reasonably, then why generate it in the first place?

Another statement: Will road engineers now need to become electricians?

6) Lighting up roads to create signals and other designs is inefficent. Putting lights in all the roads would be a waste of energy and another insane cost. It is simply inefficient and completely not required for safe and happy roadways. Seeing these LEDs under bright sunlight would be a struggle.

What will be the visibility of these lights? Who cares if we can change the patterns of the roads? Exactly how many roads need to change design on any sort of regular basis?

Another statement: In many of the artistic pictures for solar roadways, the roadways are presented with a dark-green color, however, solar panels are black.

7) The claim that the panels will heat up to eliminate snow is absolutely outrageous. In the northern winters during blizzards when there is extremely little snow, they will use the energy to melt the snow. It requires a very large amount of energy to turn snow into water. This is completely unfathomable to consider. Once again, this process is not needed compared to how we run things today.

8) Will a solar power covered in dirt/oil actually generate enough energy? Roads are extremely dirty and when these panels are covered with dirt, it will generate little energy compared to maximum output.

9) There exists an abundance of better ways to invest in renewable resources and tackle the future energy problems. To consider all the money and resources necessary for this project and utilizing them towards efficient projects would be the best route of action.

To sum up some of the thoughts:

1) The cost is ridiculously high. No, not just high, it is unthinkable.
2) There exists a ton of mechanical problems with the entire project.
3) There are better projects and ideas that will be much more efficient than solar freakin’ roadways.

Essentially, some dude and his wife raised over $2 million using Powerpoint to shovel bunk science to a large amount of people.



Paul Erdös, The Man Who Loves Numbers


I have recently learned about the life of Paul Erdös.

Paul Erdös was a highly eccentric mathematician whose existence could be defined by the pursuit of math.

Here are some excerpts from a review of the book: The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth :

Click here for full article.

“Erdös first did mathematics at the age of three, but for the last twenty-five years of his life, since the death of his mother, he put in nineteen-hour days, keeping himself fortified with 10 to 20 milligrams of Benzedrine or Ritalin, strong espresso, and caffeine tablets. “A mathematician,” Erdös was fond of saying, “is a machine for turning coffee into theorems.” When friends urged him to slow down, he always had the same response: “There’ll be plenty of time to rest in the grave.”

“To communicate with Erdös you had to learn his language. “When we met,” said Martin Gardner, the mathematical essayist, “his first question was `When did you arrive?’ I looked at my watch, but Graham whispered to me that it was Erdös’s way of asking, `When were you born?'” Erdös often asked the same question another way: “When did the misfortune of birth overtake you?” His language had a special vocabulary–not just “the SF” and “epsilon” but also “bosses” (women), “slaves” (men), “captured” (married), “liberated” (divorced), “recaptured” (remarried), “noise” (music), “poison” (alcohol), “preaching” (giving a mathematics lecture), “Sam” (the United States), and “Joe” (the Soviet Union). When he said someone had “died,” Erdös meant that the person had stopped doing mathematics. When he said someone had “left,” the person had died.”


Some YouTube videos that catch a glimpse of the man’s eccentricity:
Note: SF or “Supreme Fascist” refers to “God” or “the higher power”.

Paul Erdös is introducing himself:

Paul Erdös – SF means Supreme Facist

Paul Erdös – The Purpose of Life

Of Rational Communication

rationaldiscussionHaving essentially grown up through the internet, I’ve taking part in all sorts of discussions. Serious discussions and not so serious discussions… all through various means of communication. When I analyze social change and how to best obtain results, the topic of communication remains forefront. How do we communicate most effectively? Do I get my point across properly? It has become clear to me that with the infinite pile of garbage information that exists, communicating in an effective way is of utmost importance towards creating a better future. However, we live in a society that has evolved from dead, inefficient language systems that perpetuate throughout our communication.

I want to be clear. What matters is the full idea and reasoning behind the idea being communicated in an effective and efficient way. This does not imply that both parties uphold perfect grammar or spelling, however, key words must be well-defined and accepted upon in the discussion. It is important to understand that everyone you communicate with has a different background then you. Words, key definitions, slang, and memes that may mean something to you, may mean nothing to them.

“Very few people can communicate with one another.  The only language that’s not subject to interpretation is mathematics, chemistry, basic science, engineering principles, and applied agriculture.  But other than that, many systems today are subject to interpretation.” ~ Jacque Fresco, TVP teamspeak seminar, January 15 2012

As Jacques Fresco states, the best language to communicate with is the language of science as it is well-defined.

With that being said, the ambition of this infographic is to create an atmosphere of rational communication between two opposing viewpoints where an honest, evidence-based decision can be made on the topic of choice. Only when we can communicate properly and be willing to alter our viewpoints, can we make the change that will create a more evolved civilization.

Continue reading Of Rational Communication

Weather is NOT climate and the U.S. is NOT the World.


Welcome to the anthropocene age. The period of geological time signaling impact of collective human activity on biological, physical, and chemical processes. The term ‘anthropocene’ was first used by Paul Crutzen who shared a nobel prize for his work done on chemical mechanisms that affect the ozone layer. Even the most naïve individual would agree that humans have evolved to impact our environment in many ways. While climate change deniers often claim that climate change is ‘just a theory,’ they immediately showcase their lack of scientific understanding. A theory is a hypothesis that has passed numerous tests. This is not a conspiracy, science is not based around opinions and feelings, unlike religion. With this being said, there is two common maxim’s about global warming that need to be analyzed:

  1. Weather is not climate.
  2. The United States is not the world

Climate change deniers love talking about how cold it was in their part of the world during a cold front, but fail to take into account the maxim that weather is not climate. Climate is long-term averages which can fluctuate warming or cooling in the short-term but is ultimately defined by long-term consistencies. For instance, the weather could be experiencing a record-breaking cold front, however, this has little to do with the actual climate of Earth in the long-term. Climate is dependent on the trends and averages, not on the weather you experienced today on your way to work.

Ever since we were able to consider the deeper philosophical questions on life, we had illusions that the universe revolved around us. This train of thought is relevant when deniers speak of weather in their environment as if their weather represented the entirety of Earth. One example of this is how people mockingly react to an extreme negative variation in temperature in their part of the world, claiming, “Where’s my Global Warming?” Ultimately, the Earth is composed of a much larger area then just what goes on in one region and unfortunately, the global temperature is rising.


It is rather naïve to speak of such small regions of the Earth and minuscule measures of time with such confidence regarding a complex issue such as global warming. Atmospheric temperatures may be rising less dramatically, but it is important to take consideration for all heat content on the planet. This chart showcases the large total heat content changes occurring in the various depths of the oceans.
To further understand anthropogenic climate change it is greatly important to understand the aforementioned statements. It is incredibly ignorant to deny human involvement in climate change because your backyard is freezing cold today.

Meet the Dropleton

Science continues to evolve as yet another state of matter has been discovered. On February 26, 2014 the creation of dropletons was announced. Original Source

science-environment-dropleton-it-exists-solids-acts-liquidDropletons apparently behave like a mixture of solid and liquid particles and exist for only 25 picoseconds. Dropletons are as wide as 200 nanometers, about the size of the smallest bacteria, and can be seen with a conventional microscope. Dropletons join plasma and supercritical fluids as newer states of matter that have been discovered. For an extensive list of exotic states of matter check here.