New Math Blog

I started up a math blog yesterday called Epic Math:

The reason for doing this is that some of the higher-level topics in math that I want to write about are just too advanced for a general audience. In this earlier post, I debated what direction this blog was headed. And I felt it was important to always keep the audience in mind.

My decision is largely due to how theoretical some of my classes are becoming. It would simply make no sense for me to write posts about theorems in topology or abstract algebra or even combinatorics, alongside posts about politics or religion or philosophy. It would be a rather awkward combination.

Thus, I am splitting off mathematical topics into the new blog. The old math posts already on this blog shall remain. Anyways, the new blog will contain more topics, most likely based on what classes I am taking.

Happy Halloween! (Seems like I haven’t posted on a major holiday in a while.)

The Rise of Non-Religion as a Political Movement

After decades of stagnation, non-religion in America is finally on the move. See this recent report by the Pew Research Center.

In the past, America stood firm by the belief in God, while Europe become more and more secularized. Gallup poll results show that for the last nearly 40 years, the belief in God in America has remained at least 94% until the last few decade:

The corresponding numbers for Europe are different. From the 2005 Eurobarometer poll: in the United Kingdom, 20% do not believe in a god or universal spirit; in Germany, 25%; and in France, 33%. The United States of America, at 8%, has a long way to go.

There is yet hope, as religious affiliation declines drastically the younger the age group. Roughly one-third of Americans between 18 and 29 do not affiliate with a religion:

What I found the most insightful in the Pew report is the precise connection between non-religion and political affiliation:

So not only has non-religion increased in number, but it has become increasingly leaning towards the Democratic party. This trend may change with the results of the upcoming election; however, it is almost certain to lean Democrat with a significant majority.

Finally, the non-religious movement has also a similar leaning on many issues. Of these, it is strongly opinionated on abortion:

And on same-sex marriage:

Interestingly, the Atheist/Agnostic vote supporting abortion and same-sex marriage is more one-sided than even the Christian evangelical vote against them. And yet, there are still those who claim that religion is the absolute source of morals!

Non-religion is on the rise. Following the Civil Rights, feminist, and LGBT movements, the secularist movement will surely be next.

Orwell, Chomsky, and the Power of Twisting Language

Choosing the right word is very important, but I’ve recently found it to be far more important than I previously thought. Influences: George Orwell, Noam Chomsky.

An Experiment

Consider the 1974 Loftus and Palmer experiment [1][2][3]. Participants were shown identical short videos of car crashes, and were then asked one of the questions:

  1. About how fast were the cars going when they smashed into each other?
  2. About how fast were the cars going when they collided into each other?
  3. About how fast were the cars going when they bumped into each other?
  4. About how fast were the cars going when they hit each other?
  5. About how fast were the cars going when they contacted each other?

The only difference is the wording. Yet it was able to produce a statistically significant result:

People will believe what they hear.

Framing the Question: Politics and Religion

There are many issues today in America that suffer similar biases from wording.

Take immigration for example. Most people would probably be against illegal aliens, but would probably be more sympathetic towards undocumented workers. With this phrasing, the same person might support giving rights to undocumented workers, yet might vote the opposite way when the media or a political party calls them illegal aliens. Even though they are referring to the same people, one term focuses to the illegality, while the other focuses on their work. Of course when you call them illegal aliens, you’re going to have a biased discussion.

Abortion falls to the same bias. It is the termination of pregnancy, yet those who are opposed label it as bad as killing babies.

Or if you are not a Muslim, you are a non-Muslim; however, Islamist extremists label you as an infidel.

And don’t think Christianity gets off the hook here. A non-Christian is similarly labeled by extremists as a blasphemer (or infidel or heretic as well). And since one can’t be both Muslim and Christian at the same time, every person on Earth is an infidel or a blasphemer. That’s just the logical truth.

Framing the Question: Science and Religion

The power of twisting language is nowhere more important than in the evolution vs creationism “debate.” The reason I put the word “debate” in quotes is that it’s really not a debate where both sides use logic, reason, and facts. Yet, as long as the creationists manage to convince people there is still “debate” by labeling the whole thing as a “debate,” then they are winning their “debate.”

So far, every debate I’ve seen between evolution and creationism, and between logic and religion in general, is more of a lecture to a stubborn adolescent who still believes in fairy tales. The power of language is so strong that in labeling the conflict as a “debate” in the first place, the creationists are creating the false presumption that there even is a debate.

They use completely wrong and misleading words to describe the theory of evolution. Even calling it a theory or hypothesis in the first place is misleading, because the word theory in everyday speech strongly focuses on the possibility of being uncertain or wrong (if I said “My theory about why the grades were lower on this test…”), whereas the word theory in science implies strong logical mechanisms and the possibility to confirm or deny through evidence (such as the theory of gravity).

To adapt this “debate” to everyday speech, we should really call it the fact of evolution. One is of course allowed to call it a theory, but only seriously if one actually understands it scientifically. Most of those who claim “it’s just a theory” don’t actually understand it at all.

A debate would imply both sides are using reason. That is hardly the case. It is really more of a clearing of misunderstandings than the use of any higher cognitive skills.

The following words are extremely well misunderstood: random, chance, selection, adapt, and purpose. Consider the following dialog, which more or less actually happened (I am putting quotes around the word “Evolutionist” as it is really just a label that shouldn’t have to exist, just as you don’t have to call people who believe the world is round “Round-Earthers”):

Creationist: It’s hard to believe that the eye happened by accident.

“Evolutionist”: Evolution doesn’t say it happened by accident.

Creationist: Then it has to have a purpose.

What’s going on here is not a debate at all, but an abuse of language. The eye does not have any intrinsic purpose, but it is also not an accident. Creationists often create this false dichotomy of purpose vs accident. And when they show it is preposterous for life to have developed by accident, they think they have shown it must have been done on purpose.

Randomness does not imply either purpose or accident. Why is a cheetah fast? Because in a larger pool of animals in an ecosystem, if it were slower, it wouldn’t be able to catch its prey, and it would die off, and that would have happened millions of years ago, so we wouldn’t see it today. That’s the simple logic. No accident or purpose is implied.

So many other words—good, evil, salvation, sin, faith, and I’m sure I’m missing a ton more—are all heavily loaded, ill-defined, ambiguous concepts that are twisted around by religion to suit its needs depending on the situation. This is Orwellian Doublespeak at its strongest.

Words and the Future

It is imperative that the American public understand how loaded words are affecting its choices and decisions. The election process should be dependent on the rational discussion of real issues, not by a massive popularity contest shrouded by mutual insults and loaded words oversimplifying the situation and vilifying the other party. News should be news, not political indoctrination. Language should be the way we voice our concerns to the government, not the way political parties usher us like pawns to certain death.

In addition to math and science education, which should most certainly be improved, we really do need to keep our English and history classes in able hands. But, in English classes, instead of teaching only books written long in the past, they should occasionally make students read current news articles and critically think about them. Then maybe people will realize that English is not all pointless. And once this happens, the government will be afraid, and it will be forced to listen to the educated American people, as history perhaps once intended.

How Do You Define Obvious?

Mathematical Obviousness

Mathematicians often say things like “It is obvious that…” or “It can be easily shown that…” when the desired result is relatively easy. But to a normal person, what they are saying is not obvious at all. Other fields often have similar situations. An economist might consider a particular problem trivial, yet even a bright student might not understand it at all.

Consider the following:

1 + 1 = 2

That was obvious, right? Then what about this:

\frac{1}{2} = \frac{3}{6}

You probably thought that was obvious as well. Even though the two numbers are written differently, they are the same number.

Okay, one more statement. The question is, as always: obvious or not obvious?

0.999... = 1

There are three types of people on this issue:

  1. Those who think it is true and find it obvious.
  2. Those who think it is true and find it not obvious.
  3. Those who think it is false.

My opinion, which belongs to that of the first group, is no doubt influenced by the fact that I am studying math. For me, this is the same as saying 1 + 1 = 2 or saying 1/2 = 3/6. The two expressions on the left and right sides of the equals sign are written differently, but as the math shows, they exactly equal. Yet many people cannot accept this truth, and are bent on believing 0.999… is not equal to 1.

True Story

Last year I took Math 6120, or graduate Complex Analysis. One day Professor John Hubbard was proving Jensen’s Theorem. I do not remember where in the proof it happened, but at some point, there was a small detail that Hubbard could not immediately prove.

As it turns out, the book he was using left out this particular part of the proof. When Hubbard prepared his notes, he assumed that any small detail the author left out would be “obvious,” and that he would be able to derive it quickly during the lecture.

So he writes the statement on the board and asks, “Why is this obvious?” Nobody in the room has any idea.

It took a while to figure out why that little “obvious” statement was true. And even then, Hubbard had to re-explain, as there were grad students who still did not understand it. Then we found that our justification for why it was “obvious” did not work in general, but luckily did work for this specific problem. When it was all over, this “obvious” result took about 15 minutes of our time.