Infinities, Large and Small

     Infinities are enigmas that hide in the formulae of theoretical physicists waiting to pop out near the end of lengthy calculations making their efforts meaningless. Infinities stymie our investigative efforts and poison our logic yet we  give them status by assigning them their own mathematical symbol and by giving them names like singularities and black holes to make their embarrassing snubs appear to be logical conclusions.
     My keyboard has no infinity symbol but we all know that it looks like a twisted circle creating an intersection of lines at its center. The symbol was supposedly chosen to point out the fact that when one reaches the end they are back at the beginning, an appropriate reprimand for mathematicians and physicists that have followed their symbols to a dead end.  The pursuits leading to infinities seems to have become a game played by theorists that is lost whenever one wins.
     There are many functions that lead to infinities. Some take a diminishing path to reach the absurdity while others take an expansive path. Are there, then, large and small infinities?

       comments welcomed, especially in mathematical form     

    

Gravity <=> Acceleration ///////// pq - qp = x ///////// f(x) = 1/x

      
     Until recently, we held these truths to be self evident:
              Gravity is the product of matter
              Acceleration is the result of changing the velocity or position of matter
              Time is a fourth dimension represented by the constant (t)
              The speed of light through space is a universal constant; +- 297,000 km/second
        
     We have observed:
              That there appears to be a lot more gravity than can be accounted for by visible matter or
              by a lack of equivalence between the centrifugal and centripetal forces in spinning
              galaxies
              That time becomes a variable in gravitational fields and during accelerated
              displacements
              That light can be deflected and slowed by gravitational fields.
              That the universe appears to be expanding at an accelerating rate

     We now suspect:
              That the 'ether' permeating space we have long denied may exist as energy fields far more
              powerful and pervasive than the visible matter we observe using the
              electromagnetic spectrum and high energy particles.
              That Newton, Einstein and Heisenberg may have all missed an essential piece of
              the puzzle

     And have concluded::
              That our investigative efforts to resolve the inconsistency of galactic rotational
              acceleration and an accelerating expansion of the universe should be focused on finding
              a mysterious dark matter and a dark energy.

    But what if the dilemma is not the result of new mysterious forces or of new states of matter but a misinterpretation of our observations due to one or more false assumptions that have become a part of our formulizations. Scientific advances are based on careful observations, carefully thought out theories and many experiments and observations to verify any new understanding, and these efforts build on each other over time. But this wouldn't be the first time long established scientific principles have been tripped up by a new observation nor would it be the first time new observations were proved unreliable.
     We can and should search for the newly implied dark matter and dark energy but we should also be looking for an error in our established formulization of cause and effects at macro scales where {t}, time, and (c), the speed of light, are determinant factors. Treating time as a mental construct added for convenience rather than as a quantitative constant, and by treating the speed of light as a universal variable dependent upon the expanded state of the universe, may create more acceptable perspectives.

Persistant Perceptions

      As you view and interpret the first word of this blog it slips into the past while you view and interpret the next word, and so on, until you get to a little dot that tells you to recall all the words in the sentence and form them into a connected whole of subjects predicates and conclusions. This synaptic exercise is then stored and compared to other stored synaptic groupings as a part of your expanding record of all your perceptions, everything you have ever experienced.
      We often confuse the duration of what we call the "present" with a collection of recently recorded perceptions, the time it has taken to read this far in this blog for example. The duration of the present is arbitrarily assigned by every living active awareness and to each new set of perceptions. In reality the present is much more fleeting. (see my blog, "Between the Past and the Future") What gives our thoughts continuity is the persistence of our perceptions as synaptic captures that gives them a temporary permanence that can be carried forward from one fleeting moment to the next.
     The material world around us, and of which our bodies, sensory organs and synaptic organs are made, also posses this ability to persist as the thin event horizon moves forward in tiny flickering jumps and gives us the illusion of permanence and of a wide present. In fact change occurs much more rapidly than our perception of permanence and although not obvious from our limited perspective alters everything around us at macro and micro scales at a dizzying pace.
     We have begun to recognize this gap between our perceptive limitations and the flickering reality between the past and the future as quantum effects and are struggling to reconcile the two by reconciling quantum mechanics and relativity.
      This effort to join the two most effective approaches to understanding the universe around us is beyond most of us conceptually but the concept that we live primarily in the immediate past and control the future only by fleeting synaptic choices and recorded perceptions is easier to comprehend. As you walk from one room to another you put one foot in front of the other with the direction of your travel dictated by a decision made in the recent past. As you transfer your weight from your left foot to your right as you walk your last step is now in the past and your next step in the future but we overcome the necessity of providing synaptic oversight and micro moments of perceptions to every step by creating the illusion of an extended present moment lasting from several steps at a time to the entire trip into the next room to the entire day, at our discretion.
      The practical world of our existence is created by our perceptions and their ability to transcend the transition of many flickering present moments. The past is gone forever as soon as the electrons in an atom change position or the Earth turns a fraction of an inch and the future state and position of all things would be predictable if the number of atoms, objects and interactive forces were not nearly infinite and if matter become animate had developed awareness and choice.
     We, and all living things, perceive permanence only because our perceptions, like this blog, are recorded and move into the next fleeting moment of reality, a thin slice between a past that is gone forever and a future that is yet to exist.

         See blog:  Between the Past and the Future
     

Vindication

     My interest in science and technology began in my youth and has persisted into my declining years. I have been fortunate to live during a period of great discoveries and technological advances. Being able to remember life before television and computers and before relativity and quantum mechanics were widely accepted has given me a before and after perspective.  There has been a dramatic shift in human relations, and our relationship to the Universe around us. Attempting to follow these advances as science and cosmology delved ever deeper into the secrets of nature has been a great adventure, but it has also been humbling.. As great minds introduced concepts and theories that I could only partially understand, presented in mathematical formulas that were beyond my abilities, I felt excluded from the joy of discovery and the true meaning of the secrets that the geniuses of the day were sharing with their peers. But as theory began to reach beyond experiment and experiments began to produce conflicting results, my reverence for the privileged few who understood began to diminish. Could it be that the long chain of theories and discoveries had weak links?. Could it be that my own thought experiments into the nature of space, time and matter might be as valid as those that now fill the text books?
     As great mathematicians and visionaries presented nature's truths as closing arguments to our search for a theory of everything, I wanted to be one of them but I was excluded by my lack of understanding; And then a miraculous thing happened. With the help of new observational tools our nearly perfected theories ran into an old nemesis; "gravity".
     We have been able to describe and measure gravitational effects in detail since Newton and have based most of our cosmological conclusions on an, assumed, understanding of gravity's relationship to visible matter and mass. But when careful measurements of the visible mass and rate of rotation of galaxies revealed that there wasn't enough visible mass to hold them together at observed rates of spin we couldn't, or wouldn't argue with the math. At the rate they were spinning the galaxies could only remain intact if there was much more gravity than the observable mass of the galaxy could provide. Unwilling to give up the dependent connection between mass and gravity scientists have begun a search for invisible matter in the form of ephemeral atomic particles and I feel vindicated.
     The great minds of our time never claimed omnificence but I assumed it, and now that I know it isn't true, I can continue my own thought experiments and continue to blog on such matters with less intimidation.