Consider the common pavement ant. This little creature at the tip of our toe measures about 1/8 of an inch or 3.175 millimeters (mm) given that 1 inch equals 25.4 millimeters (mm). In looking at a still picture of the pavement ant, I guess that its torso and general width cannot exceed half of its length. Since I want to calculate the volume of the internal space of a rectangular box which would comfortably house one such ant, I make the width and depth of that container to each measure 1/16 of an inch or 1.5875 mm. Since volume equals the length times the width times the depth of a rectangle (V = l w d), the volume of space housing our ant is:
3.175 mm (length) x 1.5875 mm (width) x 1.5875 mm (depth) or 8.001 mm3.
Not many will mind if I round down in this case to accepting that the comfortable containment space for one ant would be 8 mm3.
Consider, now, the comfortable containment space for one human male. I choose male over female because I can easily measure myself as I believe I am quite average. Standing a little less than six feet (five feet eleven or so), I shall make the height to be six feet. From shoulder to shoulder I measure about 18. 5 inches and the depth of my torso at its deepest is 12.5 inches. To keep the unit of measurement consistent I first convert feet to inches and therefore describe the comfortable containment space for an average male to be 72 inches x 18.5 inches x 12.5 inches. To begin to grasp the issue of scale as it pertains to the limits of our knowledge, I wish to compare the comfortable containment space of human to ant and, therefore need to convert inches into millimeters for consistency. Thus, the comfortable containment space for one average human male can be understood as:
1828.8 mm (length) x 469.9 mm (width) x 317.5 mm (depth) or 272,844,615.6 mm3.
Let us round this number up to the nearest mm3 to 272,844,616 mm3. We are in good standing to compare the scale of the human to the ant.
Human’s comfortable containment space = 272,844,616 mm3 .
Ant’s comfortable containment space = 8 mm3.
I, as an average human male, am 34,105,577 times larger than the common pavement ant.
We rule! In our everyday experience, it is obvious that we are far larger than the ant. Our world of experience is far, far, far greater than that of the ant. What human does not fully understand this obvious fact? So, why do the math? It is important to keep in the forefront of our mind, the undisputed grandeur of the human being over the ant when we now compare our comfortable containment space with that of the universe.
The comfortable containment space of The Universe = (∞2)3.
Human’s comfortable containment space = 272,844,616 mm3.
Converting millimeters to meters I conclude that:
Human’s comfortable containment space = .272844616 m3.
Rounding up we get a whopping .3 m3.
The Universe = (∞2)3; Me = .3 m3.
Infinities of Infinities and/or Fractals
What the ant is to the human is gargantuan compared to what the human is to the universe. Having taken some basic biology and anatomy classes, I have had the experience of viewing bacteria through microscopes. Within the limits of my human experience, I come to terms with the human scale compared to that of The Universe by understanding that we are at best on the scale of bacteria and are probably far smaller than that.
Do we believe that bacteria has consciousness? Why don’t they? They have no nervous system. They are bacteria for god’s sake! I can’t argue that bacteria have consciousness. I don’t intend to. Rather, I simply want to point out that, against the backdrop of The Universe, an organism such as ourselves, is tiny and insignificant yet we have consciousness. I find our possession of consciousness, given our tiny and insignificant size, to be a wonder to behold. Arrogance, by the way, is an error in comprehending scale, and being a wonder of The Universe might lead us to believe that we are bigger and more significant than we really are. However, it is precisely our relative insignificance and size that makes us a wonder. The arrogant individual perceives himself or herself as larger than he or she really is. My studies in classical Greek literature exposed me to lessons regarding hubris, Greek tragedy and Apollo’s enlightened advice: “Man know thyself.” These are lessons, I believe, that humans are still struggling to learn.
The ant may be far less in stature than we are, but Bert Holldobler and Edward O. Wilson in their book, the ANTS, dedicate 71 pages (Chapter 7) to the “Communication” system of ants. It is quite apparent to me from reading this chapter that this organism which we have dubbed “insect” has a remarkable (if not marvelous) communication system given its relative stature within the realm of human experience.
Holldobler and Wilson observe on page 252 of their text:
For two reasons ants can be intuitively expected to practice economy in the evolution of their communication systems, that is, to use a small number of relatively simple signals derived from a limited number of ancestral structures and movements. First, the small brain and short life span of ant workers limit the amount of information these insects can process and store. Second, the tendency toward signal evolution through ritualization restricts the range of potential evolutionary pathways.
Reflect now upon the scale of the human to the ant and then on The Universe to the human. Jump now into the realm of fantasy and imagine an organism functioning within The Universe as we function within our earthly environment. Imagine that this “intelligent” creature is recording observations of the ant-like creature called humans. How similar would such a recorded observation be to the one recorded above by Holldobler and Wilson? For the scientific empiricists who cringe and shake their heads in utter distain and dismissal at such flights of fancy, I recall Jacob Bronowski’s reflections upon Niels Bohr to make my modifications thusly: When it comes to describing entities macrocosmically beyond human experience, I am not so much concerned with describing facts as I am with creating images. Having wrestled with the issue of scale, I focus upon the Holldobler and Wilson observation: “…the small brain and short life span of ant workers limit the amount of information these insects can process and store.” Relatively speaking on the scale of The Universe to the human, how big is the human brain and how long is the human life span? Given these two restrictions or parameters, how much pertinent information of the universe can humans process and store?
When considering the limits of human knowledge, it is all too obvious and convenient to state that humans cannot know more than humans are capable of knowing. So, the question is: What is the capacity of human knowledge? Is the correct answer a quantifier? (We get a number.) Or is the answer a qualifier? (We get a condition or state of being.) I understand the capacity of human knowledge as a qualified state of being because of the issues of scale. That human knowledge is based upon the human condition is a certainty. That the human condition (in comparison to that of The Universe) is minuscule is a certainty. That human knowledge is limited is a certainty. Quantum Mechanics’ principle of uncertainty, as well as Chaos theory’s nonlinear elements and “sensitive dependence on initial conditions” are scientific descriptions of the limits of scientific predictability of outcome. Perceiving knowledge as being embedded in language sets allows the following comparison of what is known and what is unknown.
Statement 1: I know this to be true: Statement 2: I perceive this to be true:
Statement 1 is a prelude to the verbalization of an absolute. The originator of statement 1 demonstrates little knowledge of the limits of human knowledge. Statement 2 is a prelude to the possibility that the perception is not an absolute (though it might be) and therefore demonstrates an awareness of the limits of human knowledge. Are we not now in a position to decide which of these two statements is a more accurate description of what can be known? Additionally, it must also be allowed that there are absolutes that permeate the Universe even though we may not be able to recognize or perceive them. Just because we do not perceive them, does not mean that absolutes do not exists. Absolutes just might exist in spite of our human science and inability to perceive all that exists.