Suppose that a Thing starts as not understood but can become understood, and that each Thing has a definition, which is a specific collection of Things. In order to understand a Thing you must understand at least one of the Things in its definition; if a Thing has no Things in its definition, it is not understood (naturally). Do you see the problem? With this arrangement of rules understanding seems entirely impossible because each definition invariably leads to more definitions. But all is not lost.
Suppose that there is a property called self evident, which is the very special occurrence of a Thing that is in its own definition; a self evident Thing is understood by default. With the inclusion of self evidence defined Things become understandable.
What is an example of a self evident Thing? Pick a number, any number!
Foundationalist philosophers seem like proto-mathematicians--a consequence of not recognizing that self evidence doesn't need to be proven, as it is enough to simply assume for the sake of argument. In an axiomatic system, the axioms are always assumed to be true. This is not done in order to answer the questions that the axiom might pose ("do parallel lines ever cross?"), but in order to derive many more interesting implications. The geometry that most people are familiar with is Euclidean geometry, and every single fact in Euclidean geometry can be proven to be a consequence of five axioms:
- Two different points can be connected by one and only one line.
- A line segment can be extended to produce an infinitely long line.
- A circle can be described with a point and a radius.
- All right angles are equal to one another.
- The parallel postulate: If a line segment intersects two lines forming interior angles that sums less than two right angles, then the two lines will intersect on that side of the segment.
The applicability of mathematics to reality is regarded as a great mystery. However, in terms of the rules above the applicability of mathematics to reality makes sense; indeed, how else might we know the universe? If there were no people around, it would be clear that reality isn't expressed in words. What we have come to know is that our experience of reality is the reception and translation of numbers and mathematical structure. When I suggest the color yellow, the thought of yellow occurs, maybe yellowish things: sunflowers, dandelions, etc, but yellow isn't defined by yellow things. What we've named yellow is actually photons oscillating with a wavelength around 570 nanometers--colors are by definition numerical, despite our experience of them as a visual cognitive phenomenon.
The case of colors is particularly interesting, because without the use of science to establish a self evident, or experimentally verifiable, numerical fact (wavelength) it is impossible to define color. There is an idea called qualia, which refers to some kind of purely subjective experience; for instance, even though most people will call a primary color by the same name, there is no guarantee that we experience the same thing. In other words, I might experience roses as what you see for the blue wavelength, but since Roses Are Red and everything I see that's called red is the same color as roses, my blue is your red. We will still agree on what items are red and what aren't, despite the fact that my subjective experience is not what you'd describe as red based on your subjective experience of light. Consider the following questions: What does pain feel like? What does a violin sound like? What does sweetness taste like? Qualia can be regarded as a word for the confusion and difficulty that comes with trying to answer these questions, particularly evident if these questions come from someone that doesn't possess the sense in concern, and thus can't gain understanding on the basis of related sensations. Qualia is still fiercely debated, and I'm not much surprised; behind every big debate there is a very ill posed question, but this doesn't imply that our experience is unquantifiable.
Consider the humble computer desktop: without a monitor, the modern desktop is apparently nothing more than a metal box that uses a lot energy in the form of electricity to warm the air. Without special tools, the only indication of activity is a light that's on when the machine is blowing out warm air, and a light that blinks at apparently random intervals when the first light is on. If this headless desktop were an alien instrument, deciphering its function would be extremely difficult. Even looking deep into the hottest part of the machine there would be perplexity abound, and a robust overwhelming with the realization that each of the over 2 billion elements might change state more than a billion times every second. Measuring the states of all of these elements at every step would be difficult given that each feature is smaller than the shortest wavelength of visible light. Even if that problem was solved, making sense of 1 second worth of data would require analyzing around 2*10^18 binary elements, which would require over 227,373 terabytes, or 222 petabytes. Even Then, the bits zooming around a CPU and patterns of gates give essentially no indication of what a computer is used for. Binary is just another way of representing quantity or number; we use decimal, which is base 10, which is kind of like saying we represent numbers with 10 different inherently meaningless symbols: 0 1 2 3 4 5 6 7 8 9. Binary is base 2, the only symbols are 0 and 1, but those symbols are equally sufficient to represent integer quantities. Thus, were you to look at the innermost workings of a CPU, what you'd see is voltages passing through a grid, sometimes changing and sometimes not. The problem is that seeing these voltages as decimal numbers wouldn't bring a modicum of sense to the madness. Even deciphering the relatively simple outbound digital video signal would be an uncanny feat; it would require a leap of imagination something like listening to Morse code and thinking that what you were hearing was actually triplets of values for a large array of photon emitters, plus whatever communication is part of the digital video standard. Some standards require two way connections, which means that before you could even draw the principal signal you'd have to have a precisely correct conversation with the machine that you're trying to figure out in the first place.
Consider the humble human being... I bet you see where this is going. Without motor function, the modern human is apparently nothing more than an elongated tube that uses water and a lot of energy in the form of food to warm the air and make fertilizer. Without special tools, the only indication of activity is from autonomic nervous function. If this were an alien instrument, deciphering its function would be extremely difficult. Even looking deep into the hottest part of the machine there would be perplexity abound, and a robust overwhelming with the realization that each of up to 100 billion elements might change state as many as 100 times every second. Assuming only full action potentials matter, and that this results in a binary signal, making sense of 1 second worth of data would require analyzing around 10^13 binary elements, which would require over 1 terabyte to store. Even Then, the bits zooming around a brain and patterns of neurons give essentially no indication of what a brain is used for. Were you to look at the innermost workings of a brain, what you'd see is voltages passing through a grid, sometimes changing and sometimes not. The problem is that seeing these voltages as decimal numbers wouldn't bring a modicum of sense to the madness. Even deciphering the relatively simple outbound analog audio signal would be an uncanny feat; it would require a leap of imagination something like looking at a continuous squiggly wave and thinking that what you were seeing was actually combinations of patterns for an abstract representation of physical phenomenon, plus whatever communication is part of the social standard. Some standards require two way connections, which means that before you could even draw the principal signal you'd have to have a precisely correct conversation with the machine that you're trying to figure out in the first place.
Is it possible to quantify the chemical senses of smell and taste? There are multiple ways on multiple scales, the most obvious: scents and flavors are particular molecules which are specific arrangements of atoms. Every atom is defined by quantities (mass, charge, etc), and the specific spatial arrangement of atoms that defines a molecule can also described mathematically... so even chemical sensation is merely an interpretation of numerical and mathematical structure. It may seem as though the mathematical definition of chocolate cake wouldn't make for much of a treat, but I'm suggesting that the mathematical definition is in fact the tasty part; there is no such thing as chocolate cake, only a variety of mathematical structures that are referred to as chocolate cake. If someone were to condense the sophisticated structure of chocolate cake down to a few succinct mathematical theorems written on a page, you wouldn't call the page chocolate cake, you'd call it a recipe; the recipe is a way to translate and understand chocolate cake, but without the quantization of the cake in some form, memorized, written, or otherwise recorded, there would be no cake. This comes across as very absurd, but consider the fact that there is no such Thing as chocolate cake; because "chocolate cake" can be interpreted as an exceedingly large range of Things, there is no objectively consistent Thing that is chocolate cake. This is different from self evident Things, which are objectively consistent; light with a wavelength of 570 nm will be light with a wavelength of 570 nm, even if you name it chocolate cake. Without a numerical level of specificity there is little assurance that everybody can and will interpret correctly.
|We may never know...|
- What is the meaning of rock?
- What is the meaning of light?
- What is the color of life?
- What is the interpretation of life?
- What is the sound of a vacuum?
On an almost entirely unrelated note, I was pleased to find that Google had the wisdom to include the ability to search for images free for re-use, which made it very easy to produce the above image without fear of accidentally stealing the intellectual property of some profitably litigious organization. Lately I've seen this practice of open and alternative licensing (Creative Commons, GNU General Public License, etc.) referred to as copyleft. What that means I amn't certain, but regardless this free functionality provided by Google offers me a modicum of comfort given that the FBI is apparently more concerned with copyright violation than identity theft and missing persons, as noted on /. recently. As usual the law is really too complicated for "free for re-use" to make much sense; for example the fair use doctrine, which may or may not save one's ass in court if it comes to that.