Notes on a Cosmology - Part 1, A Toolbox for Thinking

When we sit down to think about things in general, we have to use some kind of rules or guidelines to separate interesting and useful thoughts from useless or uninteresting thoughts. Note that we are not striving to attain anything so lofty as truth or proof; rather, we are simply looking for tools that we hope will get us to our chosen destination and help us to defeat the sea-monsters and other beasts we encounter along the voyage.

What does it mean for some thoughts to be interesting or uninteresting? "All cats are green, therefore all dogs are blue" is not an interesting or useful thought for our purposes, whether or not it is true. It might be interesting to the Mad Hatter. "The sky is blue, therefore, trees are green" is almost interesting but it is not useful because it is an abuse of the language construct in which it is framed - the implication. When we say things of the form, "X is such-and-such, therefore, Y is so-and-so", we mean to indicate that the first clause implies or entails the second clause. The study of these kinds of language constructs is the field of logic and is very ancient, present among the oldest surviving records of systematic philosophy. Today, we have the luxury of being able to lean on thousands of years of study of this subject and, in the digital age, the formal and informal meanings of logical language are so clear as to make any serious dispute about their proper use a matter for the pedants.

Much of Western philosophy centers around the problem of certainty. For example, Descartes used the specter of a trickster demon to raise the question of how we know anything at all - perhaps we have been fooled about every last aspect of reality, what we think we know. Descartes reasoned that no matter how much he doubts, he cannot doubt that he is doubting and, thus, "I think, therefore, I am." This, Descartes argued, is the first principle of philosophy. In this series, we will dispense with questions of certainty because, as I will show, uncertainty plays a key role in the world around us. In its place, we will use hypothetical reasoning. Hypothetical reasoning is the kind of reasoning that scientists use, although there is nothing restricting the use of hypothetical reasoning exclusively to the domain of science. For example, alternative histories ("What if the Allies lost World War II?") utilize a kind of hypothetical reasoning that is outside the domain of science. This is the kind of reasoning we will be utilizing most in this series.

What is a thinking tool? Philosopher Daniel Dennett has coined the term "intuition pump" to describe certain kinds of thinking tools that help us to understand new concepts through analogy and intuition. Let's look at some examples of thinking tools.

The first example of a thinking tool I want to consider is called, in Latin, ceteris paribus. The phrase translates to English as, "all else equal" or "others the same". The idea of ceteris paribus is that we imagine changing just one or a few things about our world (or our hypothetical world) but leave all others as they are. For example, we might say, "Let the sky be green. What would a nature painting of such a world look like, ceteris paribus?" We frequently use this thinking tool in day-to-day life. When adjusting the interior decor or rearranging the paintings in your living room, your ideas about specific changes are a chain of ceteris paribus conditions. This is a powerful thinking tool.

The second example of a thinking tool I want to consider is called, in German, the Gedankenexperiment. The phrase translates to English as, "thought-experiment". It contrasts with laboratory experiment. Any sentence that begins with the phrase, "Let's suppose that..." is the beginning of a thought-experiment. There are many kinds of thought-experiments. Some are very complex and specific to a given purpose, others are so commonly used that they are like reusable templates. Most of the thinking we do in this series will consist in a series of thought-experiments. In fact, I will argue that the distinction between a thought-experiment and a laboratory experiment is actually fuzzy and making too strong of a distinction between the data that arise from these types of experimentation leads to mistakes when reasoning about cosmology.

The third example of a thinking tool I want to consider is called, as a class, equivalence principles. Einstein's special and general theories of relativity are founded on an equivalence principle. The special theory of relativity draws an equivalence between mass and energy. The general theory of relativity draws an equivalence between gravity and acceleration. It is not at all obvious that mass and energy could be the same thing - a block of wood sitting on my desk is inert, it has no energy. A baseball bat striking the ball does not transfer mass, it transfers energy. Of course, Einstein's theories do not overthrow our day-to-day notions of mass and energy. Rather, by drawing a theoretical equivalence (or, at least, interchangeability) between the quantities of mass and energy, Einstein was able to establish a common basis for both.

The fourth example of a thinking tool I want to consider is called the principle of indifference, or identity of indiscernibles. This tool was used by Leibniz, though I'm not sure if he invented it. The principle of identity of indiscernibles is: if we can't tell the difference between two things then these things are, for our purposes, one and the same. The principle of indifference is virtually the same but has to do with choice, rather than measurement. The principle of indifference is this: if you do not care whether you receive A or B then A and B are, for your purposes, interchangeable. They are equally satisfying or useful to you.

These four tools are all examples of intuition pumps, of which there are far too many to list. Metaphors and analogies, for example, are among the most powerful ways to "prime the pump" of intuition in order to "get the idea across". The point in giving these few examples is to illustrate the idea of organizing our thinking without worrying about whether our thinking is conforming to some external standard of rigor, not because such standards are useless, but because they will slow us down. As long as we're careful in how we apply our tools, we can get away without wearing the "safety harness" of more rigorous methods. In summary - while there is a risk that, if I grab a tool from my toolbox, it may not be the perfect tool for the job - I don't care as long as it's "good enough".

But what is good enough? To answer this question, I'm going to turn to my field, computer engineering. In software, there are well-known, general-purpose principles of good programming. "Avoid using global variables." "Avoid using labels and GOTO statements." "Write comments explaining code which will be non-obvious to someone else reading your code." And so on. You do not have to know what these maxims of good programming mean, you only need to understand that software professionals tend to follow these maxims, and there are many of them. In addition to principles of good programming, there are also principles of programming style. Programming style refers to the overall structure of code, the templates and patterns by which code is organized and how programming problems are broken down for solution. Practicing good programming style is similar to a writer who follows principles of good English style when writing. Style is intangible and not easily defined but it adds "polish" to the work at hand.

I propose that we call the manner we use the tools in our toolbox "good enough" when we follow principles of good thinking and principles of good style. A well-chosen metaphor does not constitute a convincing proof but it may convey an idea in a concise and comprehensible manner not possible any other way.

Another principle that is sometimes used in software design is called, There Is More Than One Way To Do It; its acronym is TIMTOWTDI and is pronounced "Tim Toady". A competing principle is called There Is Only One Right Way To Do It (no acronym). The TIMTOWTDI principle is a reflection of the wider world. As the old saying goes, "There is more than one way to skin a cat." Overly ornate solutions to software problems are often a reflection of an overly rigid approach, requiring more thinking than necessary and more work than necessary. Rather than trying to find the One Right Way to think, we are looking for a toolbox brimming with lots of Good Enough Tools. To extend the software metaphor further, we are looking for a general purpose "standard library" of thinking tools, tools that are flexible enough to be used in many different ways to establish a particular conclusion, or rule it out.

In closing, consider one of the most powerful ways of creating thinking tools: avoiding what are called logical fallacies, that is, ways not to think. The power of this approach lies in its generality. For example, proof by contradiction proceeds by assuming that a given statement (proposition) is true, and then showing that this entails a contradiction. Since a contradiction is an error of logic, we know that the given statement cannot be consistent with the laws of logic. Thus, we must either choose to believe the laws of logic (consistency), or sacrifice these to believe the given statement; and statements that are not consistent with the laws of logic are not interesting for our purposes. This kind of argument is called a reductio ad absurdum and almost any fallacy can be used to construct a similar argument to show that a given proposition is false. Under the right conditions, we can even prove that a given proposition is true by proving that its opposite is false. The sheer number of logical fallacies shows just how large our toolbox for thinking really is. Armed with these tools, let us sail confidently into the dark, monster-filled waters of cosmology.

Next: Part 2, Physical Reasoning