Why Believe Science, Part 1

HS #25  2017.8.1

Why Believe Science, Part I

Last month some friends and I took the Pictured Rocks Boat Cruise in the Upper Peninsula.  When a passenger asked the captain how old the cliffs were, his prepared answer was, “It depends on what you believe.”  My interest piqued, I asked him, “You mean that the rocks are 500 million years old for me, but only 5000 years old for someone else on the boat?”

It reminded me of a discussion I once had at the stately Unitarian-Universalist church in downtown Burlington Vermont. I had attended a service in which two pastors gave opposing sermonettes on whether a personal creator God exists. Other parishioners voiced their belief in tarot cards and witchcraft. Everyone was amiable and agreeable. No challenges. 

After the service I started a discussion with several and remarked, “You operate the opposite of scientifically, don’t you?” “Really, why?” “Well, two scientists may disagree about something, but if so, then they at least AGREE that one of them is wrong.  You all seem to think that everyone can be right – or that truth doesn’t matter.”  Despite that exchange, they welcomed me to a hearty potluck lunch.

So before going further, let’s agree: There is a difference between what IS and what we BELIEVE. Hopefully there is a connection between them, but the connection is not guaranteed. More to the point, what we BELIEVE does not change what IS.  I may live my life without realizing that I am wrong and my false belief may do me no harm – it may even help me. But my belief doesn’t change reality.

I used to ask students in my senior seminar course at Hope College, “What’s the difference between saying, ‘It is raining outside’ and ‘I know that it is raining outside’?”  Notice the difference? The first is making a statement about what IS – about the weather. The second is making a statement about the state of my mind. I KNOW something.  Every time we make a statement like “It is raining outside” we are assuming that the connection between what IS and what we THINK is solid. But, we could be wrong.

Think I’m getting a bit silly? OK, read this sentence aloud:

“Finished files are the result of years of scientific study combined with the experience of many years.“

Now go back and count the “F”s in the sentence. Count them a couple of times to be sure - I’ll wait.

When I do this in class, most of the students successfully find three F’s. Did you as well? Then I tell them that they missed three.  Did you? Congrats if you found all six – you’re in the minority.

Did you get that one correct? Then answer this one: Suppose I lay a rope around the equator of the earth – a distance of 25,000 miles. How much more rope is needed if I want to raise the rope one foot above the earth along the entire equator?  Will it require more or less than 100 miles of added rope? Turns out that it takes less than seven feet. If the algebra weren’t so simple, I wouldn’t believe it.

If you got them both right, I’ll try once more: What happens to a helium balloon in your car (with windows closed so no breeze) when you accelerate forward or go around a corner?  Try it sometime. You’ll likely be surprised.

Given that we are often surprised and mistaken by reality, if we want to know the truth about our natural world, how do go about building a firm foundation of beliefs about the physical universe that we are confident are true?  Once we have a foundation, how can we build on it?

Francis Bacon, the 16^th century philosopher, gave an answer that changed the world.   He asserted that since we are easily mistaken, we should be skeptical of our beliefs and use experiments to test them.  This was the beginning of the scientific method and it ushered in the modern scientific age.

A guide at Bryce Canyon this summer likened the scientific method to a detective at a crime scene. It’s crucial to come to it with an open mind, to observe the evidence carefully, to form a coherent hypothesis that best fits the evidence, and then to test that hypothesis repeatedly, being willing to modify it as demanded by the results of the experiments.

This scientific method has been a powerful means for discovering truth about our natural world, but it has limitations.   Next month: What science can’t do.

Independence

HS #24  2017.7.4

Independence

Any student who takes a course in probability will learn – and often confuse – two important notions: independence and mutual exclusivity. Two events are said to be “mutually exclusive” if they both can’t be true.  One excludes the other. For example, “I am sitting in my lounge chair” and “I am sitting on my couch” are mutually exclusive.

Two things are independent if they have nothing to do with each other – they are totally unrelated. Knowing about one makes the other no more or less likely to be true. For example, “I am sitting in my lounge chair” and “It is snowing on Mount Everest” are independent events. Knowing that I am sitting in my lounge chair reveals nothing about the weather in Tibet, and vice versa.

Other things are neither mutually exclusive nor independent. For example, “I am sitting in my lounge chair” and “It is snowing outside.” They are not mutually exclusive because both could be true at the same time. They are not independent because if it was snowing outside, I would more likely be sitting in my lounge chair than if it was warm and sunny.  That is, the two things are related to some extent.  If one is true, it changes the probability that the other is true.

Try your hand at it. Are the following mutually exclusive, independent, or neither:

i) “I will play racquetball this afternoon.” and “I will spend all afternoon cleaning the house.” ii) “I will play racquetball this afternoon.” and “I didn’t take a shower this morning.” iii) “I will play racquetball this afternoon.” and “You have the TV on as you are reading this.” 

The first is mutually exclusive. The second is neither. (I sometimes wait to take my shower until after a work out.) The third is (most likely) independent.

Notice above that I did not give the option for two things to be BOTH independent AND mutually exclusive. That is because it can’t happen. Do you see why? If I am sitting in my lounge chair, you know for certain that I am not sitting on my couch. If I spend all afternoon cleaning my house, then you know for certain that I did not play racquetball in the afternoon. One being true certainly affects whether the other is true.  So if two things are mutually exclusive they are not independent, and vice versa.

Congrats for your diligent reading. Here (hopefully) is the reward. These two notions help us understand the societal/governmental differences between, say, the United States and France. Also (I think) we can better understand the intentions of our Founding Fathers.

As I understand the laws of France, French citizens are not allowed to wear religious headdresses or other identifying religious garments in the public schools. This is just one example of France’s attempt to keep religion and government (church and state) mutually exclusive. If a person is in school, they are not wearing religious garments. If they are wearing religious garments, they are not in school.

In contrast to that, although they didn’t use the word “independence” (at least in the mathematical sense), I think our Founders had this notion in mind regarding the relationship between religion and government.  They did not want church and state to be mutually exclusive. Instead, their ideal was for them to be independent of each other. One was to have no effect on the other.

In my opinion, this was brilliant. As opposed to France where religion and government have no choice but to push at and exclude each other, in the U.S., the two can coexist with minimal influence on each other.

I say “minimal” because real life is messier than the idealized world of mathematics. If a commencement ceremony of a public school wants to offer a prayer from just one religious point of view and there are objections from those of other religious beliefs, then the government must step in to adjudicate. Nor, unlike businesses and private homeowners, do churches need to pay property taxes. If there were true independence of church and state, churches would pay property taxes like everyone else.

But these are minor. In the grand scheme, our Constitution and legal history are founded on the premise that the church should not officially influence the state, and the state should not affect the church. The wisdom of this approach has led to religions peacefully coexisting together and  thriving unencumbered within our country.  

Independence promotes independence. What a great heritage.