"....that which is known about God is evident within them; for God made it evident to them...." Romans 1:19 NASB^{®}
What are the error bars on your faith?by Tom Crawford 6/23/2008
All these questions are related. Are you certain that what you believe is true? What is the probability that you are wrong? How would you know or quantify it? At this point, I’m going to be generic. In talking about faith, I want you to know that I could be talking about your faith in God, in a god, or that there is no god; your faith in evolution, the Big Bang, or a law of physics; your faith in the chair in which you are sitting or the bridge that you are driving across; or your faith in anything else that you believe to be true. Things that we believe to be true always have some level of uncertainty. The level of uncertainty we have in our faith is inversely proportional to our true knowledge of the thing in which we are placing our faith.
How do I quantify limits of uncertainty? What are error bars? What is my probability of being right or wrong? Example 1 – a political poll The USA is currently in a presidential election season (summer 2008). We hear a lot about political polls. A good poll is accompanied by a level of uncertainty or a set of error bars. For example, a poll might look like:
The margin of error or level of uncertainty in the poll (the poll's error bars) is dependent on the number of people the pollsters survey, and on how well the people they surveyed represent the general voting population. The plus or minus ( ±) value given for the margin of error is a standard deviation. If the polling model is a good representative model of the voting population, then the standard deviation is simply the square root of the number of people surveyed divided by the number of people surveyed ( √N / N ). Using the standard deviation means that the pollsters are confident that if the election were held today, the actual results would have a 68% chance of falling somewhere within the poll numbers plus or minus the margin of error. They have stated how much faith they can place in that poll. Example 2 – a lab experiment measuring the speed of light Suppose we are in a physics lab and are doing an experiment to measure the speed of light. (No – you have not died and woken up in hell  that's more like an English literature class. LOL.) To do this, we set up the experiment shown in the following schematic diagram.
After setting up the experiment we shoot one laser pulse through the experimental setup, measure the time between the reference and experimental pulses, and calculate the speed of light. We get a value of 3.1 * 10^{8} meters per second. We write up our experiment and hand our lab report to the professor, who promptly asks us, “Do you believe your answer? How much faith can you put into your value of the speed of light?” We tell him, “We set up the experiment and it worked. We obviously have shown that light travels at a finite speed.” He then asks, “Would you stake your life on this value? If we were to program this value into the ring laser gyroscopes and other guidance equipment on the next space shuttle, would you fly on that shuttle?” We don’t have an answer  so back to the lab. At the present time, we do not know how much confidence or faith we can place in our measurement. Back at the physics lab, we run into some other students who are in similar predicaments, and we decide to compare answers. One group measured the speed of light to be 2.95 * 10^{8} meters/second. Another, 3.2 * 10^{8} meters/second, another 3.5 * 10^{8} meters/second. Why are everyone’s calculations different? We all as a group decide to figure out why we have different answers. We start going through our experimental setup, to see what we discover.
OK – Well we now have tried to get rid of as many error sources as possible, and we are confident we can measure the speed of light accurately to three significant figures. (Maybe not enough for a trip on the space shuttle, but enough for an “A” in the class.) We decide to make 10 measurements, and if they all agree, we are done. We take 10 measurements, and we obtain the following distribution of measurement data.
Well they don’t agree, but they are all close to each other. We decide to plot these values on a plot called a histogram (mainly because we want to impress the professor). A histogram plots the number of times a particular measurement value occurs (actually the number of times it falls between two values) vs the actual value of the measurement. Our histogram of the ten measurements looks like the following diagram.
Using this histogram, we see the following:
Since we are now having fun in our physics lab (a few of us geeks really do think physics is fun); since we are starting to understand a little bit about uncertainty in making measurements; and since we really need a “A+” in this lab to help us make up for a bad midterm grade, we decide to take 100 measurements, and then draw a histogram of the results. Our new histogram looks like:
From this histogram, we see that again the most probable value for the speed of light is 3.000 * 10^{8} meters/sec, that the average (or mean) value is 3.0018*10^{8} meters/sec. We also note that the average value is closer to the most probable value. Someone in our group then remembers reading something about the standard deviation of a distribution, and says we should calculate that. We calculate both the mean and the standard deviation as shown in the following diagram: For our 100 measurements, we calculate the mean to be 3.0018 * 10^{8} meters/second, and the standard deviation to be 0.0072 * 10^{8} meters/second. We aren’t sure what we are really doing, so we decide to look up the significance of the standard deviation. We find out that the standard deviation is a value that allows us to have a level of confidence in our measurements. In other words, we are about 68% sure that the true value for the speed of light will fall within the interval of the mean plus or minus the standard deviation, or between 2.9946 * 10^{8} meters/second and 3.0090 * 10^{8} meters/second. We also read that we are 99.8% confident that the actual value of the speed of light falls somewhere in the interval of plus or minus three times the standard deviation around our mean value. We are now at the point that we can know how much faith to put in our observations of the speed of light. We have measured or quantified our doubt. Suppose we really need some extra credit and therefore decide to automate our speed of light experiment so that we could make millions of measurements instead of just 10 or 100. We would find our histograms would become a continuous function or a continuous probability distribution.
The more precisely we can make our measurements, the more faith we can put in the results of our measurements. Suppose we take even more pains to eliminate uncertainty sources in our experiments. As we remove uncertainty, the probability distribution for our measurement of the speed of light becomes narrower. This is illustrated in the following figure. If the red Gaussian resulted from our experiments, we would be more confident of our data then if either the violet or blue Gaussians resulted from our experiments. The error bars on our knowledge of the speed of light are smaller in the red Gaussian, so the error bars on our faith in the red Gaussian measurements are also smaller. The red Gaussian measurements are much closer to the truth than either the violet or the blue Gaussian measurements.
Another insight from this figure is that as we narrow the error bars on our knowledge, often we need to revise what we are placing our faith in. Suppose the vertical blue line at 3.01 * 10^{8} meters/second represents our original belief of the speed of light (the value we originally measured and had placed our faith in). When our knowledge had the error bars or uncertainty represented by the blue probability distribution, our original belief was a reasonable belief. But as we learned more and reduced the error bars on our knowledge, then our original belief was shown to be wrong, and we needed to revise what we were believing. For this value, our probability of being right went down and our probability of being wrong went up. If the red probability distribution represented our measurement, then we would be more than 99.99% confident that the speed of light is not 3.01 * 10^{8} meters/second. Instead we would believe that 3.00 * 10^{8} meters/second was a better value for the speed of light. How does this discussion apply to the error bars on our religious faith? So let’s revisit the questions I asked in the first paragraph:
The fact is, we all believe in many things – religiously, scientifically, politically, practically, … On some things, the error bars on what we believe can be wide with very little consequence, but on the important things of life, we must focus on getting as close to the truth as possible. If God exists and He is Who He says He is, then narrowing in on the truth about God is the most important pursuit we could be involved in, because our eternity is at stake. Maybe we cannot completely eliminate the error bars on our knowledge of God and our faith. But if God is God, I believe He would not leave us groping in the dark for the truth concerning Him, but instead He would have given us ample evidence for the truth about Him. He would not expect us to trust in Him using just “blind faith.” One of my purposes of this website is to explore and narrow in on the truth that we can know about God, and thereby narrow the error bars of our faith.
