Sampling

Here's how we make a computer play sound. We take "samples" of a signal, store them in the computer, then play them back one at a time at a constant rate. If we take enough samples of the sound, when we connect the samples back together, the result is close enough to the original that our ears don't detect the difference. The black lines represent the original waveform and sample points. The red line shows the reconstruction of the waveform. 

Sampled Saveform

 

But look at this:

Sampled Waveform

In this second version the number of samples for each period of the waveform have been reduced to one-third the original number and the waveform is now quite a bit different from the original. Interestingly, at high pitches, the ear will still hear the sound much the same as the original, but at lower pitches there will be quite a bit of difference in sound. Even so, the frequency of the two sounds is still the same and we hear the same pitch between the original and the sample sound. But look what happens if we continue to reduce the number of samples until we are taking less than two samples for each period of the waveform.

Sampling error

Ooops. At this point we have a serious problem (shown by the brackets above and below the figure). Not only did we lose the original wiggles in the waveform, the frequency of the waveform (where it crosses zero) is now less than the original. It won't sound at the same pitch anymore! This is an interesting phenomenon called "foldover" and is a critical consideration when creating sounds with a computer. We have to take more than two samples per period of a sound if we want to accurately represent the pitch.

So, here's the point. If you don't have enough data samples you can seriously misrepresent something. Even people who are fairly intelligent and well-meaning can fall prey to this little factoid. It's something that I have noticed in many areas of life (and have written about before). When we only have a small amount of information to go on, it is very easy to just "fill-in" the missing pieces based on some assumptions and presumptions and make it look like we know something important when we really don't.

I see this problem show up in many places. One recent example is a book I have been reading by a well-known atheist who is very skeptical of religion. He gives numerous examples of how bad religion is, and someone reading only his book would easily get the idea that everyone who believes in God is some kind of nutcase. It's a perfect example of sampling too-few data points to get any kind of a meaningful result. It looks impressive, but is actually just tedious and inane. Amazingly, the inside cover of the book is filled with accolades from reviewers. Apparently they aren't too concerned with the truth; only with promoting an atheist agenda.

But I'm not trying to pick on the atheists here, because it's not just some loudmouthed atheists that have this problem. You get the same problem with the nightly television news, Internet blogs, and gossip around the coffee machine at work. The really bad news is that a lot of Christian preachers don't seem to understand either. They pick and choose a few verses of scripture and try and build a doctrine on those alone. The result is a distortion of what the Bible really says. In hermeneutics (i.e., Bible interpretation) we say that they didn't take the context into account.

That's what we mean by "context" in Bible interpretation and why it is so important. Trying to base some doctrine on a mere one or two verses will almost always result in error (aka heresy). We have to take into account the broader scope of the writings in the Bible and understand the language and historical period so we can recognize figures of speech.

"You have heard that it was said, 'An eye for an eye and a tooth for a tooth.' But I say to you, do not resist the evildoer. But whoever strikes you on the right cheek, turn the other to him as well. (Mat 5:38-39)

So, what about that? Does that mean that Christians are to be punching bags for anyone who comes along? Or, does that mean that Jesus repudiated the law? No and no. Jesus had already said:

"Do not think that I have come to abolish the law or the prophets. I have not come to abolish these things but to fulfill them. I tell you the truth, until heaven and earth pass away not the smallest letter or stroke of a letter will pass from the law until everything takes place. (Mat 5:17-18)

So, the "law" of "an eye for an eye and a tooth for a tooth" is not being abolished by what Jesus said. Instead, Jesus is taking it to a higher level. To make a comparison, Jesus is "up-sampling" the data – providing more data points so that we get an even better representation of what the law meant. The typical human response to assault is to return the assault to the other. That's a very literal response to "an eye for an eye" and is probably how most people think of it. But if you take things to a higher level, "an eye for an eye" represents the principle of justice. Justice requires balance, and if something is taken from one place something has to taken from somewhere else to balance things out. Since someone harms me, it seems only just that a recompense is made. But what about all the unjust things I have done to others, even those done unintentionally? Well, if I demand retribution against others for their attack on me, then I automatically declare a willingness for retribution to be taken against me for any wrongs I have done. Ooops.

"Do not judge so that you will not be judged. For by the standard you judge you will be judged, and the measure you use will be the measure you receive." (Mat 7:1-2)

OK. There's the point made in summary of the preceding verses, the full context in other words. If you judge that others are to be condemned you have judged yourself as well. If you forgive wrongs done to you, you have set the standard for yourself as well. That's the way God does things. Most people want vengeance for the wrongs of others because they are ignorant of their own wrongs. God is not ignorant, however, and if you demand retribution for all wrongs, God will probably oblige you.

When you take a full sampling of the actions of human beings, you are going to find that "all have sinned" and all are judged guilty. It's very easy to limit our samplings to the weakness of others; much more difficult to take a full measure of things and recognize our own weaknesses as well.

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