The Nature and Limits of Scientific Investigation

I've spent most of my spare time since my last post thinking about Problem #3, and trying, mostly unsuccessfully, to torture The Superhero with it as well. I'm happy to report that I now understand the jump between the fuzzy fog inside my head and the math laws that describe reality.

Today I'm going to explain the nature of how we understand our world and what limitations are in how we can describe it. I'm also going to try to explain this in a lay-person-accessible way; I like the challenge of explaining complicated things in ways that make sense to people not acquainted with the details of the problem, and it's a good test for how well I understand things.

First, let's recap the problem. Suppose you and I are trying to measure the length of a piece of string. We'd hold the string up against a yardstick and argue back and forth about how long it is. I think it's 19.4 inches, and you think it's 19.6 inches. We decide in order to break the tie we're going to get a yardstick with ticks every 1/4 of an inch, and measure again. It turns out it's a bit on the long side of 19.5 inches, so you're closer to the right answer. But suppose I'm difficult and insist that it's not 19.6 inches: I say it's 19.58 inches. You can see this could go on for a while, getting ever-more precise yardsticks and eventually requiring magnifying glasses and microscopes to tell who's right. Still we could go on and on forever, never agreeing on the exact length, until we get down to the molecular level and we'd start arguing where the "end" of the string is in on the frayed end of the string.

To state the problem succinctly, our perceptions are foggy, and subject to interpretation. When we observe something, you and I will not necessarily agree on the measurement. So how do we make laws about the world? When we say a toothbrush falls at a constant acceleration of 9.8m/s², what do we mean exactly, and how can we measure it in a way we can agree on?

So thinking about this, I the first thing I did was study myself looking at stuff, observing what the problems were that stop me from understanding what I'm seeing in a well-defined way that I can make rules about. I noticed 3 things:

1. My perceptions are incomplete. I see some things and not others. For instance, I don't see x-rays.
2. My perceptions are unreliable. That is, I perceive the same thing in two different ways if it happens to me twice. For instance, when I wake up, things are much brighter than when I come in from out in the sun
3. My perceptions are undefined. This means that the lower levels of my brain that take the stimulation from my eyeball and turn it into a meaningful picture for me present it to my higher-level consciousness don't present that picture in a way I can write down and communicate clearly. For instance, when I look at two pieces of art and one looks nice and one does not, I can't describe to you every detail of why I think that's so.

Incompleteness doesn't really cause us any problems, since I can extend my senses by inventing measurement tools. Everything that is real can be observed in some way, by definition. For instance, suppose I told you I had a little red monster sitting in the corner and you couldn't see it. Suppose you couldn't hear/smell/taste/feel it either, and furthermore there was nothing whatsoever that you could do to detect my little red monster. You wouldn't believe me! In order to be real, things have to be detectable in some way.

Unreliability can be gotten around as well. The unreliability in my perceptions can be gotten around by using measurement devices that start out in exactly the same state. I could build a reliable thermometer that will always report the same temperature in the same way.

The core problem with us agreeing on the how long the string is, is the fact that our perceptions come to us in a way that's not formally defined. We can never decide exactly where the end of the string is; we think it's about 19.5 inches, but we can't decide because we both have this estimation that's going on inside our heads that comes out slightly differently.

The key to understanding how this works clearly, is that our brains are also part of the physical world, and in this case are forming part of the experiment. On close examination, it's clear that I am making a direct and exact measurement of the physical world, but the measurement is not just a function of the string. It's a function of everything. It's a function of the psychological estimation procedure in which I guess the end of the string is about 4/10 of the way between the 19 inch line and the 20 inch line. It's also a function of how the gravitational attraction from between the string and my brain stretches the string toward my head. It's also a function of the tides of the Pacific Ocean and how that water is pulling the string. The measurement device, and everything else in the universe, contributes towards getting the number 19.4. However, 19.4 is completely function of the real world, not a concoction of some mystical "consciousness" that's actually just a configuration of atoms in my brain.

If you don't want to measure anything about your psychology, you can pass your brain information from the outside world in a way that doesn't need interpretation. That is, you can make a measurement device that has a little display that shows you numbers, or little blinking lights that lend themselves to a non-fuzzy interpretation. So if your thermometer says 8 degrees, you and I can look at that and agree exactly what it says. The measurement is still a function of not only the ambient temperature but also of the thermometer (for instance, how it rounds the temperature off to 8 degrees). It's also technically a function of your brain, since maybe the thermometer says 18 degrees and you just missed the 1. But assuming we can read the device without error, we'll all agree on what it says.

So far so good. Despite the 3 weaknesses of how information comes into my brain when I hold a banana and look at it, these can be overcome and I can get direct, well-defined measurements of the physical world that I can then get to work on making rules about. I can put out my digital thermometer, take periodic readings, and try to notice patterns in how the temperatures change with the seasons and make scientific discoveries. Furthermore, I can create any kind of coccamamy ideas in my head to explain it, and they're all equally good, provided that they predict my observations correctly.

However this does not totally answer the questions of how we can conduct science. Suppose I come up with some law that describes how the temperature changes with the seasons. This is only a description of what my thermometer read at various times and rules about how the readings relate to each other. When someone else tries to interpret that and reproduce my results, he'll come up with some experimental setup that looks kind of like mine, but isn't quite the same. And we'll be back in the same position we were in trying to measure the string; I can't describe exactly how to reproduce the conditions of my experiment so that the readings off the next guy's digital thermometer measure the exact same thing as mine did.

So in conclusion, we can say the following about the physical laws (rules) we make up to describe our world:

• All observations we make that somehow get translated into a well-defined thought are exact physical measurements about our world, including our brain. By constructing our measurements in clever ways, we can limit the impact that our brain and other irrelevant effects have on measuring, but results will always be a function of everything.
• The theories we invent to explain the world, exist solely within our brains. We might make predictions based on a theory of electrons, and an alien race might make identical predictions with no concept of electrons, and we can both be equally right. The only test of the theory is does it predict measurements properly.
• The interpretation of how to make the measurement to test against the theory is fundamentally dependent on human interpretation. There is no way to describe a theory in which two people will make measurements to test it in precisely the same way and never disagree. By describing measurement techniques you can get people to agree more often and measure in more similar ways; but you will never get them to agree 100% of the time.

Therefore if, someone passes us a string and asks us to measure it, we may come up with different answers. And we'll have to agree to disagree.

P.S. Through this train of thought I've come up with a much more important question. How on earth do we manage to have such success in the world by making judgements on perceptions that can't be tested for whether they follow rules? Unfortunately, this is a question for psychology and neuroscience to answer. You can't figure it out just by thinking.