Archive for the ‘EARTH, OTHER WORLDS, AND BEYOND’ Category



I don’t have the answers but I can’t help thinking about “infinity” and its reciprocal twin “infinitesimal”. This is dangerous to my mental health. The mathematician Cantor went mad while studying “infinity”.  However, I don’t think the risk to me is THAT large – I will never know enough to endanger  myself.

Ancient natural philosophers, as shown in the historical record, were asking how small can pieces of a “thing” be made by successive halving of pieces of the original “thing”. A little thought and one arrives at the conclusion pieces of the “thing” can never be reduced to a size smaller than the half of the piece last cut. Cut again and one still has half of the piece last cut. This is the line of reasoning which led to the first “atomic theory of matter”.  The ancients concluded “matter”is composed of “atoms” that are indivisible. They had no idea what these “atoms” were. This discussion illustrates the line of reasoning used to ponder the world of big and small. For instance, one can get a sense of “infinity” by first imagining a sum of successive numbers, starting at zero, suming out to as far as you care to. Have we arrived at “infinity”? No! It is obvious I can add to your sum one more number and thus create a number larger than your “infinity”. It is equally obvious this game can continue forever without reaching a final value for “infinity”. The definition of “infinity” is ” be without bound”. As an aside, note the concept of  “time going on forever”  is now part of the discussion. Poor Dr. Cantor!

An ancient natural philosopher named Zeno advanced a motion paradox which is still giving fits to theorists today. It is useful to use this paradox as a way to gain a little insight into the concept of the “infinitesimal”. Also known as “the very small”. The Zeno paradox, loosely interpreted, states: (1) a body, set in motion at point A toward point B, will never arrive at point B, (2) experience demonstrates  a body set in motion at point A will arrive at point B. (3) this is an obvious paradox. What is Zeno’s reasoning?

Zeno reasoned the moving body will reach half the distance to point B within a definite time. He further reasoned the body will reach half the remaining distance within a different definite time. Zeno continues this reasoning until the conclusion the body will never reach point B is reached. The body always has half the remaining distance to go. I just got back from filling my coffee cup and thus demonstrated point B will be reached in reality. Thus the paradox.

Now the insight part. As the time of the motion increases, the remaining distance traveled (half of the previous half, etc., etc.) will become smaller and smaller, ie. become infinitesimal. This “infinitesimal” is closely related to the “infinite” because the division of any number by a very small number is a very large result. In fact, if division by zero is attempted, the resulting quantity is defined to be without bound, ie, infinite. Mathematicians punted this problem long ago by declaring division by zero is not allowed. Issac Newton, the man who gave us “Newton’s Equations” of motion and the first explanation of how the Solar system uses Gravitational attraction to maintain orbital motion, was faced with the Zeno paradox and all that is associated with it. His solution to these difficulties was the invention of what is known today as ” The Calculus” mathematics. If you have studied “The Calculus” then you know about “taking the limit”, ie, division by a number arbitrarily close to zero, but, never allowed to be zero. ( Historians will point out that Leibnitz  shares credit for the invention of “The Calculus”.)

A  contemporary problem of long standing involves the most successful pair of thoeries yet devised to “explain” how matter works. The “General Theory Of Relativity” by Albert Einstein has been verified to high accuracy many times over using astronomical observations and very precise measurements of changes in time, length, and mass predicted to occur as the relative velocity between observers change. The second of these theories is the “Standard Model” of atomic particle physics. This theory has been verified to high accuracy using the results of many high energy particle collision experiments such as those now being conducted at CERN in Europe. At the energy levels of matter in our normal everyday existence,  four fundamental forces are observed. The first is predicted by the “General Theory Of  Relativity”; it is known as the Gravitational Force. The remaining three forces are the Weak force, the Strong Force, and the Electro-magnetic Force. The latter three forces have been shown to unify into a single force at very high energy levels. Many theorists expect further unification to occur at even higher energy levels.

The contemporary problem alluded to above is the expectation by theorists of one force and one theory. The problem arises upon attempts by theorists  to combine the two successful theories into a single theory. It does not work! Such combined theories yield nonsense results. The combined theory requires what essentially is division by zero. The results are described as being rife with infinities. So I’m told; the calculations are way beyond my pay grade. A. Einstein spent the rest of his life in an unsuccessful effort to crack this nut and failed. Unification work continues using a new approach  known as “String Theory”. The advantage of “String Theory” is the avoidance of division by zero. Good luck on that.

The “Big Bang Theory”  followed the announcement by Edwin Hubble about 1922 that the Universe was not static; it was expanding! It was quickly realized if the Universe is expanding, it must have a beginning. The “Big Bang Theory” was the result. The pondering of the implications of “The Big Bang Theory” quickly lead to questions about the size of  the Universe. Is it finite in extent? If so, what lies beyond? Is that infinite? If our Universe is not finite it must be infinite in extent. Does an infinite Universe mean somewhere in our Universe there is another “OLD MACHINIST” typing his Post?  Was all of the energy in our Universe crammed into an infinitesimal volume? Was it zero volume? How do we deal with the concept of all the energy in the Universe in zero volume when we can not understand our ordinary everyday infinities? Small wonder Dr. Cantor went mad.



The English language is said to have one million words within its lexicon. This large number of words within this lexicon allows the communication of ideas to be both nuanced and precise. This is why English is widely used all over the World. However, English has within its lexicon words that are not easily pinned down as to precise meaning. One such word is the noun form of “nothing”. I have been trying to pin down its meaning since I started wondering about “The Big Bang” and what came before the event. As in:”Before the event there was nothing”. I must add, my time spent wondering about the beginning of the Universe has not produced much in the way of insight.

My deluxe edition of “Webster’s Collegiate Dictionary” gives as the definitions of “nothing”: “something that does not exist”, and,”the absence of all magnitude or quantity”. These offerings by my dictionary seems to be feeble at best. The first offering equates “nothing” with “something”. This is nonsense. It is no help to add that the “something” does not exist! The first offering is a bust as a springboard to greater insight (at least for me). The second offering is a little better in that it uses the word “absence”. However, the word “absence” seems to imply an entity is merely missing. I tend to think of “nothing” as if entities (1)never were, (2)are not now, (3)never will be- there. Note the problem with the word “there”. The word “there” implies “nothing” has a place. But to have a “place”, or location requires a frame of reference. If “nothing” is to be nothing, it cannot even have a frame of reference; Spacetime is not allowed! Now that the confusion index has been elevated to a new level, its appropriate to now examine the rest of the second offering.

The words “magnitude” and “quantity”, as I understand them, are parameters used to describe an entity. They are not the entity itself. Furthermore, it is possible to envision an entity which does not have magnitude and quantity. I offer the example of Human consciousness. It exists without magnitude and quantity. Human consciousness also cannot be permitted within the concept of “nothing”. The confusion index has been elevated even more I fear.

I have concluded there are no words within the English language lexicon that are up to the task of defining the noun “nothing”. The root problem is all words stand for “things” or “abstractions” that are within the Human experience. The reality of “nothing” has not been within Human experience nor has it been imagined by the Human brain. No words exist to define “nothing”. That is my conclusion.



I occasionally find myself musing about the conceptual meaning of the word ‘SELF”. It is a word that I use in many different ways in normal everyday discourse.Some examples are: myself, yourself, selfless, selfish, self-conscious, self-sacrifice, self-awareness, etc., etc.. I usually don’t think about the conceptual meaning of these words as I use them, except as required by the context of the discourse. So, we use it; what does it represent or mean?  My dictionary gives a definition for “SELF” as “the union of elements (as body, emotions, thoughts, and sensations) that join the individuality and identity of a person”.   This definition is one of several given but this will serve as a starting point for further musing.

My concept of “SELF” starts with the idea that it is primary, indivisible, ie, without parts. So I have a problem with the first phrase of the dictionary definition.  This phrase,”union of elements”, clearly is in contradiction to my concept of “SELF” in that it implies “SELF” has “elements” or parts.  Furthermore,  the examples of “elements” have their own conceptual difficulties.   My concept includes the need that the “SELF” have zero mass.  The “body” has mass thus it cannot be the “SELF”.  My objection to “emotions” is based on my belief  that  emotions are a class of output signals which the “SELF” uses to reveal its state and that these are conveyed by the mechanisms of the body and  not the “SELF”.  In a similar way, I can argue that “sensations” are a class of input signals to the “SELF”,  which tell the “SELF” of the non-“SELF” world and thus influence the state of the “SELF”.  I view “thought” as the process which the “SELF” uses to extract meaning from input and create output. This view, I believe, negates the possibility of “thought” being the “SELF” even though, it being a process, has zero mass.  A further examination of the given definition begs for an exploration of  “individualty”as it relates to the “SELF”.  The word “individuality” implies differences exist between the members of the group.  For the purpose of my musing,  I assert that the perceived differences between “SELF”s ,that are observed when comparing the reaction of different “body”s confronted with similar circumstances, are due to differences in the process used by each “SELF” to produce action based on the “body”s sensory input.

I further assert that all “self”s are alike; all of them!  I take as my model, for the assertion  above, the example of the Electron.  The Electron is what is  known as a fundamental particle, ie, it has no internal structure, no smaller parts.   All Electrons are the same and can be freely interchanged without effect.  As a parallel to my assertion above, Electrons can be made to “act” differently when subjected to different processes;  they remain identical Electrons however.  It is not known what an Electron “is”.  However it is possible to study the Electron and define its properties without this knowledge.  In a similar way we can study the “SELF”without knowing what it “is”.

There are many interesting facets to the subject of the “SELF”.  For instance, when in the time period of a Human life, defined as starting at conception and ending at death, does the”SELF” become the “SELF”?  Does the nascent “SELF” develop gradually as a fetus does or does it pop into existence when the growth of the “body” reaches a threshold for the “SELF” to exist?  If the “SELF”s are identical and the perceived differences between people are due to differences in “process”s, how are these differences developed?  What happens at death? The seeking of answers to these “SELF” questions has much to offer in the quest for greater insight into the subject of Life on Earth.  I plan to keep up the musing.  It is better than television for exercising the brain – so  I’m told.



Are mathematicians discoverers or inventors? This question has been in my mind for a long while and the answer still has not been revealed to me. I suspect this question has been asked by many people, many times, over many years and remains unanswered to this day. So, why trouble myself with it if I believe there is little hope for an answer within my lifetime? Because, I answer, I am enamored with issues such as this which are related to the larger subject: The Nature of Reality. I find it impossible to cease wondering.

Humans, being capable of cognition, use their ability to observe what is around them to construct their perceived “reality”. For instance, most people when asked to describe the rock they have been handed would reply: it is a heavy red solid object with a hard surface. That is their “reality” as constructed from their sensory inputs. However, the rock is composed of atoms and the empty space between the atoms. Atoms are very small, in fact, so small that the rock is mostly empty space. This constitutes a different “reality” for the rock. Taking this example a step further, one wonders what the rock’s “reality” is when there are no living things to construct a “reality” for the rock.

As an aside, the “heaviness” of the rock is due to the mutual gravitational attraction between the mass of the rock and the mass of our planet, Earth. The rock looks “red” because the atoms of the rock absorb the non-red part of the incident light and reflects the red part. The rock is “hard and solid” due to the interaction between the electromagnetic forces that hold the atoms of the hand, and rock, in place.

Using the example of the rock’s “reality” as a kind of template, let us return to the mathematics question. Sir Issac Newton is remembered both for his insight-full motion and gravity equations as well as the mathematics required to understand the equations. It is noted that today Newton’s equations have been observed to apply everywhere in the visible Universe. We ask this question: Does “The Universe” operate according to its own “rules”, the effects of which Newton observed and then invented equations which provided much needed insight into these “rules”of the Universe, or, does “The Universe” operate without “rules” at all and thus any hope of for discovery of the “rules” is just another Human folly? It seems to me to be the latter. I believe any hope expressed of finding the “rules” that govern the operation of “The Universe” is the product of collective human hubris and any effort to do so is doomed to failure. However, I believe also that humankind is well served in many ways by the collective effort to better understand the “rules” of “The Universe” and we must keep trying in spite of it being thought folly. Is there a better way to have fun? Oh, by the way, I believe the whole body of mathematics enjoyed by Humankind was invented by Humans and the Universe just “IS”.

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