The Daily Stumble #2: Mint Graffiti

Today’s 5th stumble is Mint Graffiti from the site MintLife.

This page many humorous examples drawings on dollar bills. The best one is Bender’s applause sign above, seen briefly above, and shown more clearly here:

But a close second is:

This was just hilarious. It isn’t the first time I’ve stumbled upon so-called “mint graffiti.” In fact, there are many pages of people doing creative things with money, drawing silly stuff or even folding bills origami-style into bizarre shapes.

The previous Daily Stumble was “Slow Time.”

People Who Agree With You for the Wrong Reasons

Yes, I’m attempting to write a post that talks about both politics AND religion. Yep, the two most heated things that always lead to flame wars on the Internet. In one post.

The Two Types of Disagreeing

We’ve all had those moments we just flat-out disagreed with everything someone said. No matter how many facts we throw at them, they never seemed to listen. And they probably thought the same about us. The argument turned into full-blown war, and we were ready to start throwing punches at each other.

But we’ve also had those debates where we disagreed with them, not in a hostile way at all, but in a calm, mature, intellectual manner. We realized some of the things we said were wrong, and so did they. And while we still had our differences in the end, we felt more connected and felt that we had uncovered some truth out of it. This is the good type of disagreement.

The Two Types of Agreeing

There’s the intellectual style of agreement as well, the good kind. You try to teach your kid about gravity, but she is skeptical, so you encourage her to try to throw a ball so high that it won’t return, to disprove gravity. She quickly learns that no matter how hard she throws it, it will always fall back down. Finally, she ends up agreeing with you, having learned a valuable lesson out of it.

Then there’s the wrong kind of agreement. The kind when once she becomes skeptical of gravity, you only assert that it’s true and don’t give any reason or evidence for it, and you say “Believe it, or else.” Of course, this example is pretty silly because no one needs to threaten someone else to get them to believe in gravity—there is overwhelming evidence for it everywhere on Earth. I’m really setting this up for matters which have no evidence or are misunderstood.

Agreeing Due to Party Alignment, Not Due to Facts

I’m going to go with politics first, and then religion. I consider myself to be a moderate liberal, but I usually don’t care about politics that much. However, sometimes when people talk about politics in stupid ways or completely misunderstand their political party, I do care. I don’t want them making misguided decisions in the ballot.

It’s common for liberals to criticize conservatives for outrageous claims, but many of these liberals don’t understand that they themselves also make outrageous claims. They say how bad conservatives are, but then when someone asks them what has Obama done in the last 4 years, they are silent. Not that Obama hasn’t done anything—he’s done quite a bit. But some of these liberals are just clueless about their own party and seem to vote Democrat just because their friends do or because they think Obama is charismatic.

These people annoy me greatly. They might agree with me, but for all the wrong reasons. For instance, I know people who like to make fun of Rush Limbaugh, despite never having read anything he wrote and never listening to anything he said, and rely instead only on what other people said of him. If you disagree with Rush Limbaugh because you disagree with his views, that’s fine. I respectfully disagree with much of what he says. But if you disagree with him just because it’s cool to disagree with him, then that is pathetic.

It seems that respect is all but forgotten in this era. I can disagree with someone but still understand what they are saying, and admit that some parts of what they say are correct. But respect doesn’t seem to be mainstream anymore. Case in point, in Obama’s 2008 election victory speech, he began in a noble manner by making a respectful statement about McCain’s campaign. But what did the crowd do? It booed him very audibly. And in McCain’s defeat speech, when he congratulated Obama, he got loudly booed by his crowd as well.

What has politics become, a spectator sport where you boo the other team, or boo anyone who says shows respect to the other team? If anything, Obama and McCain’s respect for each other in that moment of the election gives me some hope for the American political system. However, the behavior of the crowd does not.

Agreeing Due to Authority, Not Due to Evidence

Now for religion. I am an atheist. I don’t believe in god for the same reason I don’t believe in Santa or an Invisible Pink Unicorn or the Flying Spaghetti Monster or an invisible fire-breathing dragon. Simply, I believe it is childish and immature to believe in something that has zero evidence, just because other people believe in it.

That said, I am not claiming that Christianity is inherently bad. Despite its numerous provocations, injustices, and wars, I do not know where the world would be right now had Christianity not existed. Without its teaching of generosity and kindness to primitive cultures (and then enslaving them), civilization may not be as advanced as it is. However, given that we have already reached an early Space Age, where technology and the search for knowledge can unite us in place of the mass belief of ancient myths, I question whether Christianity will be of use for much longer.

So if you tell me, “I am a Christian because the moral system is wonderful,” then that is great. But if you say, “I am a Christian because there is evidence that God exists,” then I will facepalm, because that is like saying, “I believe in the Invisible Pink Unicorn because there is evidence that the Invisible Pink Unicorn exists.”

On the other side, people who believe in atheism might agree for the wrong reasons, though not usually, as they tend to be more open-minded. Saying “I am an atheist because there is no evidence of God” is perfectly fine, but saying “I am an atheist because Christianity is evil” is not a valid reason. However, I don’t know of anyone who actually believes that, so as far as I know, there are no atheist “extremists” like there are religious extremists.

So as far as this section goes, I cannot really talk about the atheist side as there are no examples of belief for the wrong reasons that I know of. Instead, I can try to empathize with the religious side and think about what they would consider to be belief in god for the wrong reasons.

The first one is probably believing in God for fear of ending up in Hell or some other divine punishment. That would be a terrible reason to believe in something, simply out of fear of threat for not believing in it. This is one reason I have a problem with Pascal’s wager (the other being that it can just be applied to other religions, forcing the player to have no good choice).

The second is argument from authority. People shouldn’t believe in God just because other people said they should; they should find it on their own. Despite how silly this sounds to me, at least I find it more noble than blindly following the will of other people. In practice, however, it seems most people are led into Christianity through authority, from their parents or community when they are young and vulnerable.

I mean, if someone is nonreligious but suffers a crisis when they are 30, and chooses to accept a religion to cope with it, that is fine. In fact, hooking people up to mythical virtual realities is a valid method these days of dealing with trauma. The real world is too harsh, so they can more easily cope in a fantasy world. But if a kid is forced to accept a religion when they wouldn’t know better, that is an entirely different thing, and is just wrong. (I agree with Bill Nye’s take on this.)

This would be entirely opposite of the gravity case presented in the “Two Types of Agreeing” section. When a kid learns about gravity, if she is skeptical she can try to disprove it by throwing a ball so high into the air that it does not come down. But the more gravity works, the more accepting she becomes. Whether she thinks gravity is true is determined by her own experiences.

However, if she is skeptical of religion, there is nothing she can do to disprove it, since anything could be justified by some made-up explanation, and this is probably very confusing for a young mind. Whether she thinks religion is true is determined solely by the statements of others, i.e. authority figures.

If this forcing of views on a child concerned any subject other than religion, it would be called brainwashing. Yet when it’s religion, it’s not considered brainwashing, and—quite disturbingly—it’s actually considered by some to be education.

My writing of this section is inspired by Carl Sagan’s skeptical philosophy and Bill Nye’s recent video that was linked above.

Disagreeing and Agreeing

I’d rather someone disagree with me using the truth, rather than have someone agree with me based on a lie. Both in politics and religion, a shallow agreement based on lies is valueless, ridiculous, and devoid of morality.

This is often why there are such heated debates in both of these subjects on the Internet, where multiple people can chime in on both sides. The “Democrat” side of a forum thread might be extremely polarized within itself, and so is the “Republican” side. Thus, instead of there being a straight back-and-forth debate, there is a jumbled web of personal insults and baseless accusations. This would be avoided if people were actually knowledgeable and knew what they were talking about and as well as what other people are talking about. This is why knowledge and respect should be taught, not whatever is causing them to resort to insults.

In the case of religion, religious people generally don’t use logic, so even the terms “agree” and “disagree” begin to lose meaning. That’s why a religious debate usually never ends up being a peaceful debate. It always becomes derailed because logic itself is missing from one side, so it isn’t really a debate at all. It is a lecture where the student is willfully ignorant. At least that’s what happens in the case of an atheist vs theist debate. I can only imagine the horror of what a theist vs theist-of-a-different-religion debate on the Internet would be like, e.g. a Christian vs Muslim debate.

In the political system of the United States, I am somewhat hopeful. But I have almost no hope at all for the current education system. Until something like “Logic for First Graders” is taught—lies, misunderstandings, and ignorance will always be the face of our country.

The Daily Stumble #1: Slow Time

I’m starting a series where I take the 5th Stumble of the day and write a blog post about it. Why the 5th one? I don’t know, why not?

Today’s 5th stumble is: 20 Things that Are Way Better in Slow Motion – [link], from the site BuzzFeed.

Note: I’m going to take a screenshot of every page I stumble for this series, just in case the link breaks in the future. This way, someone reading my blog can still see what I am referring to.

This random stumble is very coincidental, considering my last blog post was about Light in Slow Motion. What are the chances?

Anyways, the site itself has a variety of interesting events happening in slow motion: the popping of popcorn, the impact of a bullet, the lighting of a match, and the hitting of a drum. But the most epic one on this site is definitely the lightning strike:

That just looks insane. When we look at things in slow motion, we see shapes and patterns that are otherwise never observe. We discover physical phenomena that seem impossible to our natural human-time intuition.

At this scale, things happen at time scales so short that that particles zap in and out of existence in billionths of a second. In just a blink of an eye, entire universes of particles have appeared and disappeared, entire realities created and destroyed.

Of course, even one billionth of a second is an eternity compared to events that are predicted to have occurred at the onset of the Big Bang. Such events occurred at 10^-34 of a second, or 0.0000000000000000000000000000000001 second.

It is indeed interesting to watch man-made objects such as bullets and golf balls in slow motion. But it is far more fascinating to watch nature, whether it is lightning, atomic collisions, and even light itself, move in slow time.

The list for The Daily Stumble series is found here.

Light in Slow Motion, and Curiosity’s Descent Video

That is light, recorded at a frame rate so high that a bullet would take a year to cross the screen. It is one of the most amazing videos I have watched this year, perhaps second only to the Curiosity landing video, both of which show that the impossible is always being achieved.

Why Math?

As a math major, I am often asked the question, “Why math?” In particular, why theoretical math, when it doesn’t seem to be related to anything?

I often have trouble coming up with a full and satisfying answer on the spot. Math is one of the subjects whose material and categorization can be confusing. It spans several fields that many have not even heard of. When I say “topology” or “analytic number theory,” it often draws blank stares; in fact, topology is often misunderstood as “topography,” the study of terrain.

Well, here is my more thought-out answer to why I study math.

Is It Relevant?

Take a good look at the following equation:

\displaystyle \sum_{n} \frac{1}{n^s} = \prod_{p} {\frac{1}{1 - \frac{1}{p^s}}}

Through the cryptic jumble of symbols, you might ask yourself, how is this useful?

An even more relevant question for most readers is, what does it even mean?

As it turns out, this particular equation has very little practical value. Yet it is one of the most fundamental equations in the field of analytic number theory, and it is a remarkable statement about the prime numbers.

It basically links the infinite set of natural numbers (1, 2, 3, 4, 5,…) with the infinite set of prime numbers (2, 3, 5, 7, 11,…). The proof is relatively simple, but I am not going to give it here. It is known as the Euler product formula.

There is virtually no “useful” information given by this highly abstract formula. It doesn’t help with daily finance. It doesn’t solve traffic congestion. It doesn’t even help in landing a rover on Mars. But it does is provide us with an insight into the fundamental truth of nature. In a way, this equation exceeds the known universe, as according to current theory, the universe is finite. The equation, by contrast, deals with the infinite.

In fact, modern mathematics is full of statements and theorems that have currently no practical use. There are entire branches and fields of study that are, in essence, useless. Sometimes, useless things have applications in the far future. Complex numbers, for example, were invented centuries ago, but didn’t really find any use until modern electronics and physics were developed.

Maybe everything we know today in math will be applied somehow. But this cannot happen forever. The universe is finite, after all, and knowledge is infinite. Sooner or later, or perhaps even now, we will have found knowledge that serves no use in our universe. This leads to the next question.

Is Knowledge Worth Seeking?

Should we seek knowledge for the sake of knowledge?

Is a culture with more knowledge inherently richer than one without?

Historically, knowledge in the form of technology had the power to save oneself, one’s family, and even one’s country. Entire civilizations were wiped out due to the technological superiority of the invaders. Knowledge has for a long time acted as a defense tool.

So perhaps we should embrace new knowledge for the sake of defending against a future alien force. But what about afterwards?

Assuming humans survive long enough to establish a galactic presence, and have enough technology to be virtually indestructible as a species, so that survivability is no longer an issue, what will be the point of further knowledge? What will be the point of knowledge for the sake of knowledge?

That picture above is the Mandelbrot set, a fractal generated by the fairly simple quadratic function

z \mapsto z^2 + c

where c is a complex number.

There could easily be no purpose to this fractal, yet it certainly holds some value. It is aesthetically pleasing, and the ability to zoom in on the image forever raises some old philosophical questions. In this sense, it is almost like art, only the rules are completely different.

In essence, knowledge for the sake of knowledge is what math is all about. There is no intrinsic need for math to apply to the real world, nor does any topic in mathematics need an analogy in real life. Math is knowledge at the abstract level.

Recently someone asked me what classes I was taking, and when I mentioned topology, he asked if that was a map making course. Topology and topography sound quite similar, I suppose.

In any case, topology is a great example of what pure math is about. It is the underlying foundation behind geometry. Geometry is highly applicable in real life, because shapes, sizes, and angles of things all affect the way they work. But in topology, sizes and angles do not matter. A line is the same thing as a curve, a square is really the same thing as a triangle or a hexagon, and a sphere is really the same thing as a cube or amoeba.

And a donut is really the same thing as a coffee mug.

These fields of math are totally alien to the math taught at the pre-college level. Geometry, basic algebra, and calculus are about sizes of things and comparing objects to determine their shapes, lengths, volumes, etc.

But when you get to the higher fields, such as analysis, number theory, abstract algebra, and topology, everything completely changes. They feel like entirely different subjects than the math taught in middle school and high school.

Previously, you were told that dividing by zero is impossible and that it is pointless to think of infinity. But in complex analysis, you can actually “cancel out” zeroes and infinities provided certain properties are counted, and you actually care about where functions hit infinity and how often they do so. And in set theory, you discover that there are actually different sizes of infinity. These facts are much more interesting than, say, the quadratic equation, which is taught in every high school algebra course.

The fact that zeros can actually cancel out infinities, or that there are different sizes of infinities, is much more interesting than such a formula.

This graph, showing a region of the gamma function, generalizes the notion of factorial (i.e., 5! = 5 * 4 * 3 * 2 * 1) to complex numbers.

The gamma function is also closely related to the equation at the very top of the page, with the natural numbers on one side and the prime numbers on the other. Those two expressions also define the Riemann zeta function.

You might be able to see some relation between the two images. It turns out that the trivial zeroes of the zeta function, which can be seen as the strange color mismatches on a line going from the center to the left, are the result of the poles of the gamma function, which are the vertical spikes in the other picture.

Basically, that is why I study math. The point is not to memorize formulas or to calculate quickly. It is to discover fundamental truths out of ridiculous-sounding things, and to make sense out of them. In a way, this is what people do in other academic fields as well. Sometimes math goes over the top and seems completely useless. This is bound to happen. But some things, like art and mathematics, don’t need a practical purpose to exist. Such things are valuable in their own right.

An International Readership

As an avid blogger, I often wondered where my readers come from. Well, a relatively new feature (as of February of this year) allows WordPress users to see exactly that!

The first page of countries for my blog is below, with data showing number of views since Feb 25, 2012:

As expected, the United States is in first by far, with a few more English-speaking countries as runner ups.

For the non-primarily English-speaking countries, the high positions of Korea, Brazil, and Germany are quite interesting. My blogging often includes intellectual topics, and these countries have some highly developed education systems.

The most populous nation in the world, China, is near the bottom with only 3 visits to the site, most likely due to their strict Internet censorship rules, which go against the philosophy of free thinking and free speech that I often advocate on this blog. On the other hand, Switzerland, with a relatively tiny population, has made 68 visits.

Thanks to all my readers, wherever you are!

Science Exaggeration in the Media

Recently, new scientific data showed that the Sun is rounder than previously thought. As readers of this blog probably know, I am a very fact-oriented person and I dislike exaggeration, especially regarding scientific data.

Let’s see how the media decided to label this discovery, just looking at the titles of a few articles…

Doing it right:

  • Huffington Post –  “Sun’s Shape: NASA Data Show Our Star More Round Than Previously Thought”
  • Complex Tech – “Scientists Discover the Sun is Rounder, Flatter Than Previously Thought”
  • Gizmodo (UK) – “Turns Out The Sun Is Rounder And Flatter Than We Thought”

Doing it wrong:

  • Gizmodo (US) – “We Were Totally Wrong About the Sun’s Shape Until Yesterday”
  • Yahoo! – “Astronomers continue to be baffled by Sun’s nearly perfect shape”
  • The Independent – “Sun is too round, say scientists”
  • Herald – “Mystery of our too-round sun”
  • The Christian Science Monitor – “Mystery continues: Why is the sun ‘too round’? New measurements show the shape of our sun is ‘too round’ to match the theories about the forces at work on the sun.”

Want to know the really interesting part?

The article in the Huffington Post link and The Christian Science Monitor link are the exact same article by Charles Q. Choi, frequent contributor to Scientific American. Funny how different news agencies manage to spin the same story with a different title.