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Showing posts with label correlation. Show all posts
Showing posts with label correlation. Show all posts

The New Kosher


Back in our Lord’s day, Israel was under the Law, which included strict dietary laws handed down by the Designer of the human digestive system. Then the Designer Himself came down to correct how folks were interpreting those laws and their importance. He made a point of saying that “it isn’t what goes into a mouth that causes real problems, it is the state of the person’s heart and what that causes folks to spew out of their mouths.” (paraphrase) Matthew shares the event in full in chapter 15:

Then some Pharisees and teachers of the law came to Jesus from Jerusalem and asked, “Why do your disciples break the tradition of the elders? They don’t wash their hands before they eat!”
Jesus replied, “And why do you break the command of God for the sake of your tradition? For God said, ‘Honor your father and mother’ and ‘Anyone who curses their father or mother is to be put to death.’ But you say that if anyone declares that what might have been used to help their father or mother is ‘devoted to God,’ they are not to ‘honor their father or mother’ with it. Thus you nullify the word of God for the sake of your tradition. You hypocrites! Isaiah was right when he prophesied about you:
“‘These people honor me with their lips,
but their hearts are far from me.
They worship me in vain;
their teachings are merely human rules.’”
Jesus called the crowd to him and said, “Listen and understand. What goes into someone’s mouth does not defile them, but what comes out of their mouth, that is what defiles them.”
Then the disciples came to him and asked, “Do you know that the Pharisees were offended when they heard this?”
He replied, “Every plant that my heavenly Father has not planted will be pulled up by the roots. Leave them; they are blind guides. If the blind lead the blind, both will fall into a pit.”
Peter said, “Explain the parable to us.”
“Are you still so dull?” Jesus asked them. “Don’t you see that whatever enters the mouth goes into the stomach and then out of the body? But the things that come out of a person’s mouth come from the heart, and these defile them. For out of the heart come evil thoughts—murder, adultery, sexual immorality, theft, false testimony, slander. These are what defile a person; but eating with unwashed hands does not defile them.”

Fast forward about 1750 years. Some wise men sat around arguing over the laws of a new nation, and decided that giving everyone the right to verbally express their ignorance or intelligence without governmental reprisal was a good thing. Given that the “what you should eat” thing had largely been a settled issue for going on two millennia, they overlooked that part.

7. What Is Science?: Proof


Okay, we’ve made an observation, hypothesized as to the cause, and performed some experiments to test the hypothesis. At what point do we have a proof?

When you say something and someone says to you “Prove it,” what kind of proof is he or she looking for? Chances are that subconsciously he or she is expecting a scientific proof. Herein lies the problem. As you’ve probably guessed, it isn’t as simple as we would like. It turns out there are at least two kinds of proof that matter in day to day life—scientific and legal-historical (LH). (There are also mathematical and statistical proofs, but I’m lumping them in with scientific proof, as they relate less to daily life.)

Scientific proof can be loosely defined as follows: Every time A and B occur, C results. If C doesn’t happen, then something is different about A and B, but as long as only A and B occur, C will result. In other words, if you let go of your pen, it falls. In fact, every time you let go of your pen, it falls. As long as you are inside a reasonably effective gravitational field, that stupid pen falls towards the center of the field. If all of a sudden, all else being equal, it didn’t fall, you would know instantly that all else isn’t equal—one of your starting conditions has changed. Scientific proof is based on the repeatability of events. If you have the specified conditions, you can expect a specific result. If you get a different result, then the starting conditions had to have changed. A rather corny joke illustrates this principle:

A chemist, mathematician, and engineer all lived on the same street. One night, the mathematician’s house caught fire. In an effort to minimize the damage, he calculated exactly the correct amount of water to just put out the fire, and gave the result to the firefighters. Of course, it took so long to get the answer that the house burned to the ground.

A few nights later, the engineer’s house burned. Not wanting to repeat his neighbor’s mistake, and understanding the general principle that ‘close enough is good enough,’ he instructs the firefighters to put it out as quickly as possible. They dump water on the fire and put it out immediately. However, there was so much water damage it was still a complete loss.

Well, you know how these stories go. The very next week, fire erupted at the chemist’s house. {The real joke here is that it was the chemist’s house to burn last!} To his friends’ astonishment, he whips out a giant buret, fills it with water and opens the valve. The fire is quickly extinguished, and all of the water used was exactly vaporized by the dying embers. The house and contents were saved! The neighbors’ congratulations quickly changed to gasps of horror as the chemist pulled out a match and relit the fire.

”What are you doing?!,” they cried.

”Reproducibility,” was his calm answer.

In a sense, the repeatability of experimental results can be said to lead to a hypothesis that is proved {almost} “beyond a shadow of a doubt.”

In contrast, LH proof is designed for what we techie types call a ‘singularity’—a non-reproducible or once-in-the-universe event. It is, by definition, impossible to make scientific proofs about a singularity, but they can be studied and information learned. It requires a different standard of proof though. That’s where LH proof comes in. As the name suggests, it is primarily the domain of lawyers and historians. “Who was the first president of the United States?” “What happened at the grassy knoll?” We cannot repeat these events, but we can gather evidence of all kinds that can point toward one or more conclusions upon which reasonable people can agree.

We’ve all watched the crime dramas. At the big courtroom climax, the defense attorney is making his grandiose closing arguments, performing for the jury. Then, in a sudden change of pace, he leans over the jury rail, looks each member in the eye and says slowly, confidently, “Today, ladies and gentlemen of the jury, I have proven to you that my client is innocent beyond [say it with me!] a reasonable doubt.”

So we see that the difference between a scientific proof and an LH proof is based on the type of phenomenon being studied. It leads to a difference in the burden of proof required. If a hypothesis-experiment pair is sufficiently clear, well defined, and well performed, then we tend to look askance at naysayers. They are viewed as not being all there or as folks who choose to disbelieve in the face of overwhelming evidence. (Take, for example, the Flat Earth Society.)

Confusion arises when scientific tools and methods are used on a singularity. Let’s say that for grins you developed a passionate desire to learn what I had for breakfast this morning. How would you go about trying to solve this dire mystery?

You might start by asking me. Simple enough. {Although, one semester when I posed this question to one of my classes, a student piped up, “Cut you open!” I replied, with tongue in cheek, “Thank you. Here’s your ‘F’, and there’s the door.”} I respond with a straight face, “This morning I ate filet mignon, Russian caviar, champagne, and finished it off with a splendid Havana.” You seriously doubt this, especially after learning my university salary from an Open Records request. What might you do then? You simply have to know what I had for breakfast.

Ask the folks who ate with me. They confirm my story. You, being an Oliver Stone protégé, suspect a conspiracy to hide the truth of my morning’s meal. What now?

Time to pull a CSI. You sneak into my house, turn out all the lights, turn on a flashlight, and examine my trash, my refrigerator, my kitchen sink, et cetera. Ah, but I am one step ahead of you! I have taken out the trash and put it in a dumpster 10 miles away. I’ve done my dishes, burned any receipts, cleaned the fridge and bleached the disposal. This only reinforces your need to know. Time for desperate measures.

You arrest me, haul me to a hospital and apply scopes to one end or another. I object, but you ignore me. My gut is pumped from both ends, and the contents analyzed. I had a breakfast taco. Hold the presses!

In your efforts, were scientific tools used? Sure. At the very least, the analysis equipment at the end would be considered scientific tools. Have you scientifically proven what I had for breakfast this morning? No. The event, ‘breakfast this morning,’ is a singularity. It cannot be repeated. Therefore, you have made a legal-historical proof.

If you wanted to know what I have for breakfast as a rule, you can observe me for a period of time long enough to see what my meal patterns are and develop a statistical model of my breakfast habits—78.2% of the time I have nothing (proving intelligent people can make stupid choices), 10% of the time I have Slim-Fast™, 9.6% is a breakfast taco, and so on. Yet this is still not a scientific proof, because there is not a repeatable set of conditions. Yes, each time it is morning, but that isn’t the only variable that affects the outcome. This kind of proof, known as statistical proof was mentioned earlier. However, we will not cover it any deeper here.

In summary, it is important to understand what type of proof is appropriate to answer the given question. But does that mean that all of science leads to scientific proof? If only it were that simple! (But then, of course, you knew I’d say that.) Take astronomy, for instance. Can you reproduce a supernova? No. (Chances are that you wouldn’t want to either! I hope.) How then do we study supernovae? We study records of observations made by others, turn our telescopes to those areas of the sky to see what’s left, etc. If we are lucky enough to observe one, then we make those observations. Based on what is learned, we then look for other areas with similar properties and try to determine if one has happened in the past or if a given star is likely to undergo one in the future. This leads to a body of evidence that describes what we know about supernovae. Therefore, conclusions about them are based in a legal-historical type of investigation.

Granted, this is a very simplistic discussion of the concept of proof, but it is a good starting place.

SDG

6. What is Science?: Preventing Problems


Yesterday, we discussed the nature of the scientific method and the intrinsic bias to prove one’s hypotheses correct. Given that fallible and inherently biased humans do science, one mechanism used to help overcome this bias is to, whenever possible, design experiments to disprove one’s hypothesis. Typically, a hypothesis is based either on a limited number of specific observations or on a large number of general observations. Therefore, trying to disprove a hypothesis helps to determine under what conditions the hypothesis is true. The harder it is to disprove the hypothesis, the higher the chances it is a reasonably accurate model and therefore more “rugged.”

Another, related, reason for disproving a hypothesis is the ‘correlation versus causation’ problem. Let’s say that someone observes that when event B occurs, event C also occurs. A preliminary hypothesis might be “B causes C.” Further investigation shows that there is another event, A, that also occurs immediately prior to B and C. Ultimately, we discover that A causes B and C. Therefore, B doesn’t cause C but occurs under the same conditions as C. In scientific jargon, we say that B and C correlate with each other, but A causes them. It turns out that many mistakes in science have occurred because the scientist assumed that B causes C rather than correlating with C and both being caused by A.

One historic example of this is that of spoiled meat producing maggots. The belief since Greek times was that if you left meat out to spoil, it would spontaneously create life in the form of maggots. This idea, appropriately enough, was called ‘spontaneous generation.’ Italian biologist Francesco Redi in 1668 disproved this theory by putting gauze over the meat, which kept flies from landing on it and laying their eggs, which hatched into maggots. Meat with gauze had no maggots. Meat without gauze had maggots. Thus the spoiling of meat did not cause maggots. The laying of eggs by flies in meat caused maggots and also contributed to the spoiling of the meat. A 2000+ year understanding of nature was overturned by someone who understood the difference between causation and correlation and how to experimentally distinguish between the two.

To emphasize the point, let’s look at a whimsical example of choosing good hypotheses and designing good experiments. A string of strange disappearances has occurred near Waller Creek (which runs through the UT campus). Victims were either alone or with a group and would suddenly just vanish. One UT student, a fan of the paranormal, suggests the disappearances are due to a rare creature called a one-eyed, one-horned flying purple people eater. Of course, society laughs. His response, “Prove I’m wrong.” The budding conspiracy theorist has a point. Which is easier to prove, the existence of something or the nonexistence? To prove nonexistence, one must explore the height, width, breadth, and depth of the natural world and show that in no situation does the object exist. To prove existence, one must merely produce the goods. Not being able to produce the goods is not a disproof but a failure to prove. There is a difference.

In either case, the real problem is the statement of the hypothesis. A slightly better hypothesis might have to do with the existence of such a creature on modern planet Earth (though this is still potentially a tall order). In order to make the hypothesis workable, the student would need to also propose what sorts of evidence/tests would satisfactorily test or ‘falsify’ the hypothesis. So you can see that it is important to choose both an appropriate hypothesis and design an appropriate experiment for its testing.

A possible appropriate response to this student is that if he is to make a truth claim such as the disappearances are caused by a one-eyed, one-horned flying purple people eater, then the burden of proof is on him, the maker of the claim. To tell others to prove him wrong is irresponsible and not intellectually honest, especially as the request to disprove is impossible unless you are an omnipotent person with full knowledge of the universe past, present, and future. The trouble is that polemics tend to make better sound bites than truth:  it is a better sound bite to say “Prove me wrong” than it is to explain that it’s his job to prove his own point. His snappy response is that I’m blame shifting, when the truth is that he is doing the blame shifting, then accusing me of it when I try to shift it back.

The problem of good hypotheses and good experiments is why science has the process of peer review, as a check on bad science. It is not foolproof, but it is better than nothing.

SDG