On Giving Too Much Legitimacy to the Inferior Position

You find an ant mound in your house. Would you call an exterminator to remove it? Or would you treat it with “dignity” and offer to fight it in a “fair” duel?

There is something fundamentally wrong with the way arguments and debate work in modern society. Whereas the common sense choice is simply to remove the ant mound as fast as possible, the politically correct choice is to hear “both sides” of the story, run smear campaigns against the ant mound while defending against verbal insults made on yourself, and then put the ultimate decision to a referendum of not-the-most-intelligent voters, hoping they side with you and not the swarm of ants.

Debates and arguments are more focused today on winning vs. losing, not on right vs wrong, or truth vs fiction, or reason vs insanity.

The Appeal to Image

An enormous problem with this style of debate is that it gives too much legitimacy to the inferior position. A debate should focus on drawing logical conclusions from facts, not on maintaining personal reputations. For nearly all publicized debates, winning is glorified and losing is stigmatized.

Yet in the scientific disciplines, losing happens all the time, and if the loser is able to admit it, he is the one who actually learns more from the debate by discarding his outdated or incorrect theory, and progressing forward with a better one.

To quote Carl Sagan:

In science it often happens that scientists say, ‘You know that’s a really good argument; my position is mistaken,’ and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn’t happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.

In math, it is even better. You only need to come up with a correct proof or disproof, and every reasonable mathematician will agree with the correct side. There is literally no legitimate argument for the other side, because logically, it cannot exist.

Consider the equation 0.999… = 1. There is no ambiguity of truth to this statement. It can be proved many, many ways, though even one way is enough. We cannot pass such a statement to a referendum for a popular vote, as it is conceivable that the majority of the population will vote that the statement is false, yet among mathematicians, the vote will be unanimous for truth.

The act of even putting “False” on the ballot in the first place would be misleading to a non-mathematical voter. If I didn’t know enough math to deduce the truth of the statement, and all I saw on the ballot were “True” and “False,” I would probably think: “Well, since these positions are even on the ballot in the first place, it probably means there are some mathematicians arguing for ‘True’ and some arguing for ‘False.’ That means I need to use my own math skill. Hmm, obviously 0.9 is less than 1, 0.99 is less than 1, 0.999 is less than 1, so 0.999… is less than 1. I vote ‘False.’ ”

Yet, no one goes around protesting that the “other side” of this argument should be taught in schools, as whether 0.999… = 1 is irrelevant to their beliefs. When it comes to biology though, it becomes different.

Probably the most ridiculous instance of giving too much legitimacy to the inferior position is the evolution vs creationism “debate.” Just as among mathematicians there is no debate as whether 0.999… = 1, there is no debate among biologists as to whether evolution or creation led to where we are. By no debate, we mean that at least 99.85% of scientists in the earth and life sciences agree with evolution. Although, from just looking at the media, one might not expect this to be the case. Same with huge wastes of time and money that shouldn’t have even existed. There’s a difference between teaching true controversy and the disgrace of “Teach the Controversy,” which is just “Teach the Idiocy.”

It is much worse in religious debates, as religion somehow has a magical spell protecting it from all criticism. You’re encouraged to disagree all you want about musical taste, food, fashion, and even politics, but the moment anything remotely close to religion is debated, it is “offensive” and “disrespectful.” Other than due to an unfortunate social norm, Why? Why is it acceptable for an uneducated person to vocally disagree with scientists about matters of science and have their own article about it in the news, yet it is unacceptable for even an intellectual to disagree regarding religion?

It’s almost like a self-fulfilling prophecy. Anything they say must be respected, so they can make intolerant statements such as saying all people who disagree with them are fools, and as an audience we’re supposed to respect that. Just why? If an ignorant person calls you a fool, you have no responsibility to respect that opinion.

The Freedom of Speech

But we have the freedom of speech, you might say. We can say whatever we want.

Indeed, I think free speech is one of the most important features of an advanced, civilized society. (The lack of free speech is one of the reasons I despise modern China.) But there’s a difference between having the right to say whatever you want and the right to force an ignorant belief onto other people. Free speech lets you say the Earth is flat without being arrested by the government. But it sure doesn’t let you force the Flat-Earth theory into textbooks in public education. Or astrology. Or slavery. Or the 2012 doomsday.

Dissent from oppression is imperative. Dissent from authority is necessary. But dissent from truth is blindness. No matter how much one might protest the truth, the truth stays put. It is we who must adapt to the truth, not adapt the truth for us. The Freedom of Speech is not the Freedom to Brainwash.

Even the act of having to write this post deeply upsets me. Ideally this should all be Common Sense, yet Thomas Paine seems to have been all but forgotten by the inhabitants of America.

Seems like it’s about time for another Enlightenment, another Age of Reason.

Quote Mismatched

Can you correctly match the following quotes with their authors?

  1. Those people who think they know everything are a great annoyance to those of us who do.
  2. The empires of the future are the empires of the mind.
  3. Those who can make you believe absurdities can make you commit atrocities.
  4. All art is quite useless.
  5. Faith, as such, is extremely detrimental to human life: it is the negation of reason.
  6. If the people cannot trust their government to do the job for which it exists – to protect them and to promote their common welfare – all else is lost.
  7. Capitalism has worked very well. Anyone who wants to move to North Korea is welcome.
  8. You can tell more about a person by what he says about others than you can by what others say about him.
  9. The word god is for me nothing more than the expression and product of human weaknesses, the Bible a collection of honourable, but still primitive legends which are nevertheless pretty childish.
  10. Men are moved by two levers only: fear and self interest.

The choices, each used exactly once, are:

  • Albert Einstein
  • Napoleon Bonaparte
  • Isaac Asimov
  • Bill Gates
  • Barack Obama
  • Oscar Wilde
  • Ayn Rand
  • Voltaire
  • Audrey Hepburn
  • Winston Churchill

The answer key is found here, but try it yourself first! If you really are bold, I dare you to write down your guesses in the comments and then check the solution.

How to (Theoretically) Win a 2-Party Presidential Election with Just 21.8% of the Popular Vote

In an extreme case, consider the following electoral map:

Of course, this is nonsensical as DC is red and Texas is blue, but let’s assume this happened for the sake of argument. Despite the map being overwhelmingly red, the red states win the electoral vote by only the slightest margin of 270 to 268.

Let us assume that every single state was nearly evenly split, something like 50.01% to 49.99%. Then even though the red states won the electoral vote, the blue states contain 56.4% of the population, thus the blue candidate actually wins the popular vote 56.4% to 43.6%, a huge lead.

Now, suppose the vote was nearly even in the red states, but let the blue candidate win 100% of the vote in all the blue states. Then the red candidate wins only 21.8% of the popular vote, yet still wins the election, despite 78.2% of the electorate voting against him.

List of states in our hypothetical model: Red – Wyoming, District of Columbia, Vermont, North Dakota, Alaska, Rhode Island, South Dakota, Delaware, New Hampshire, Montana, Maine, Hawaii, Nebraska, West Virginia, Idaho, New Mexico, Nevada, Utah, Kansas, Arkansas, Mississippi, Iowa, Connecticut, South Carolina, Minnesota, Alabama, Oklahoma, Kentucky, Oregon, Colorado, Washington, Louisiana, Wisconsin  Maryland, Tennessee, Arizona, Indiana, Massachusetts, Missouri, and North CarolinaBlue – Virginia, Michigan, New Jersey, Pennsylvania, Georgia, Ohio, Illinois, Florida, Texas, New York, and California.

Note: After I wrote this post, I googled the 21.8% and found a few cases where people used intense computer computation with exponential-time algorithms to figure this out.

I was shocked when I discovered these methods, as my own method was extraordinarily simple, taking all of two minutes in Excel, with otherwise no number-crunching: just list out the states in ascending order of population per electoral vote, and then go down the list until you get to 270 or more. The list I got started with Wyoming, and went all the way down to Georgia. However, this added up to 271, so I searched for any way to shave off 1 electoral vote. As it turns out, there was a way: I replaced Georgia (16 electoral votes) by North Carolina (15 electoral votes), which has a smaller population.

Bonus Round #1:

Now pretend there are more than 2 parties. Then it is possible to win 270 with an even smaller percentage of the popular vote. Let n be the number of parties. Then you can win with 43.6/n % of the popular vote. The 2-party example of 21.8% is just a special case of this. For example, with 3 parties the red candidate just needs to win a 33.34% vs 33.33% vs 33.33% plurality in each of the required states, so to win the presidency, he only needs to win 43.6/3 %, or 14.5%, of the popular vote.

Bonus Round #2:

Let’s go back to 2 parties. Someone on Facebook asked:

What if the electoral college reps were voted in based on district? The representatives are based on members of congress, right? So what if every state did what Maine and Nebraska does and allow their representatives to split? Two elected based on statewide votes, the rest by congressional district. Keeps the small states relevant to the campaign while making the electoral process more representative.

As it turns out, the answer doesn’t change if we let electors vote by district. Just let the red candidate win every single district in every single red state listed above by one vote. Then it’s still an electoral win with 21.8% of the popular vote.

The number does change, however, if we remove the two state votes from each state and have the vote counted purely by district. Then a candidate must win 23.2% of the popular vote (win the 219 smallest districts by a marginal amount, outright lose the other 217 districts).

Sources:

The Perfect Prediction

Many have heard of Nate Silver’s prediction of the 2012 presidential election. For those of you who haven’t seen it yet, here was his prediction for last Tuesday, which may seem uncannily familiar:

It seems familiar because it bears a striking resemblance the actual results:

In fact, that’s all 50 states correctly predicted.

Given two equally likely options for each states, the chance to predict all 50 states correctly is one in 2^{50}, or one in 1.126 quadrillion. Granted, we already knew which direction states like Texas or Vermont would vote for, so for the sake of simplicity let’s consider only the 9 “swing” states: Colorado, Florida, Iowa, Nevada, New Hampshire, North Carolina, Ohio, Virginia and Wisconsin. That’s still a one in 512 chance to guess all 9 states correctly from sheer luck.

How did he do it? The answer is high-caliber aggregate statistics. When you conduct a poll, you are going to have very high uncertainty if you poll only a few people. But if you poll a lot of people, your prediction gets more accurate. And one way to poll many people at once is to aggregate the data from many, many polls.

In 2008, Silver’s prediction was accurate in 49 of the 50 states, missing only Indiana.

Does Your Individual Vote Really Matter?

Everyone on Facebook seems to be talking about how they voted today, and why you should as well. To be a good citizen, they say, you must vote. “Go vote!” says every other status on my Facebook feed.

Yet there are plenty of reasons not to vote, and in fact, not voting has been historically a very powerful form of protest against a government. This article debunks many of the voting myths that attempt to place voting on the moral high-ground. I found the most significant part of the article to be number 5, which responds to the claim that your vote is your voice in the government:

In a democratic form of government it would be. In a democratic form of government, such as a direct or participatory democracy, people can vote on things like budgets, wars, and other important issues, and have a voice in government. In our representative government, people can only vote for representatives who may or may not listen to them or act in their interests, and who cannot be held accountable during their terms of office, which is the only time they hold power and are needed to represent the interests of their constituents. Waiting until somebody has killed a million people in a war based on lies, destroyed the economy, and taken away your civil rights, and then trying to elect somebody else, is much too late because by then much of the damage cannot be undone and your grandchildren will still be paying for it.

Indeed, the United States is not a true democracy (though the term “democracy” gets thrown around enough that it seems to be synonymous with anything moral).

There are two more main reasons why, for the majority of voters, your vote will be futile. Firstly, the electoral college system places all importance on the swing states such as Ohio. Unless you live in one of these states, your individual vote will have nearly zero chance of affecting the outcome of the election, as the vote of your state is already determined. Even if you do live in one of these states, one vote will not statistically make a difference. There has not ever been a case where a president has been decided by one vote, and basic probability tells you it will remain that way.

But what if everyone thinks like that, you might say. If everyone does this, then no one will vote, and the election will fail. The bad guy will be elected with just a handful of votes.

This is hardly a valid concern. We all agree that being a medical doctor is a good and respectable profession. However, if everyone thinks like that, then everyone will be doctors, and nobody will be there to grow crops, educate children, provide entertainment, forecast weather, write books, or produce art. This argument fails because even though one might respect doctors, one must not necessarily become one.

Secondly, if you really want to change the world, you’re not going to do it by casting a single ballot once and then posting once on Facebook that you voted and then never mention politics again. Suppose I had a button in front of me such that every time I pressed the button, it would add one vote randomly for Barack Obama or Mitt Romney in a random polling booth in the United States. Even if I pressed the button a thousand times it would have no statistical effect on the outcome.

If you want to change something, start a movement. Your government won’t listen to an insignificant statistic in a polling booth, but it sure as hell will listen to a provocative demonstration. The beauty of the United States is that you have the right to challenge the government, a right that is too often taken for granted, for in many countries, speaking out against the slightest flaw in your country could be a death sentence. So exercise this right! We the people control the government, yet we have allowed the government to control us.

So if you think that by voting, you have fulfilled your civic duty for the next four years, think again. If you really care about your country that much, you would do a lot more than broadcasting your vote on Facebook to a bunch of people you already know anyways.

All that said, in an age of technology and reason, I would be very unhappy if Romney were elected. It is important that the United States lead the world in advancing forward, not regressing back into an anti-intellectual dark age. If I were to choose between Romney and Obama, I would without the slightest hesitation pick President Obama. However, given that Ithaca, NY is guaranteed to vote Democrat (and the state of New York as a whole), and given that both major party candidates have been quiet about the environment in the weeks leading up to the election, my vote today went to Green Party candidate Jill Stein.

Blogging Year 3

Today is the 3rd birthday of my blog! It was a fairly light year, with only 42 posts published, but it received 52k views, thereby averaging 1238 views per new post (many of these views were on older posts, so it is not an accurate representation of views for a given post). In comparison, Year 1 averaged 1042 views per post and Year 2 averaged 1053 [data].

The most visited posts in the third year were:

  1. The Persistence of Memory – 18,465 views
  2. (Home page) – 4,030 views
  3. 10 Mind Blowing Mathematical Equations – 2,506 views
  4. Tumblr vs WordPress: Simplicity vs Power – 2,360 views
  5. The End of an Experiment – 2,206 views
  6. US Census 2010 Win – 1,699 views

The vast majority of the hits for #1 and #5 resulted from Google image searches, whereas the majority for #3 and #4 came from normal Google searches. Interesting.

Haven’t tracked followers in previous years, but as it stands, 62 of you are following this blog. Nice!

One final note: unlike in the past two years, I am not participating in Nanowrimo this year due to some very busy math classes, though I would gladly cheer on anyone who is. Good luck getting to 50,000. May the Force be with you.