A Theory of Distribution

The relationship of clumps* to the reality of probabilities was the subject on a car trip from Florida to Kentucky. Clumps are a significant part of reality, and a clump is contained in a probability. As in, “Based on a study of 500 college students, it was found that 23.4 percent preferred real cigarettes to Vaping..”  Now that is just a fictitious example, but I’m sure we can all agree that probabilities are everywhere, from dietary recommendations, to politics.  Which candidate is the good guy for those of us who fear Global Warning, or Mercury in our fish? But here’s the clump angle. Suppose your statistical sample just happened to have a clump in it. A clump of smokers or fish eaters or Democrats who hate fat people. You see what I mean. A statistical sample is most likely a limited grouping of a much larger grouping. 
  Suppose for instance that I wanted to find out what percentage of Second Graders, on average, had been victims of child abuse. I could narrow the statistical grouping down to, between 1980 and 1985.  And I could narrow it down to public schools in the state of Wisconsin.  But how do I know that 1980 didn’t produce a clump of kids in Wisconsin who were abused for no other reason then that probabilities are a crap game? What is the law of probabilities after all other than the Universe’s version of a Random Number Generating Machine?

Clump. A clump of dirt. A bunch of stuff all bunched up. Well, a clump is tighter than a bunch. And it would have to be Bunched-up-ness because I’m looking for a thing. A Noun. 
I may have to invent my own new term.  Hmm.  A T.S.G.?  A tightly structured grouping? I’ll think on it. But, in the meantime. Here’s how I got to worrying this labeling to death. 

My wife and I were driving along the highway. We were going from New York to Kentucky, and she was driving because she likes to be in control, and she began musing about how the cars and trucks seem to gather in clumps, which slows down her speed-controlled cruising at 85mph. 
  Which led me to start thinking about clumps. So many things can be clumps. Galactic star forming regions are clumps… An iceberg can be a clump, and so can something that’s less a tightly structured grouping such as vegetable soup. With the soup it’s more contextual. I mean it’s loosely structured so in order to be a clump it would have to have containment. Therefore a soup is a loose clump. 
   Also, people; say, cops on the order of Officer Finnegan; (Catholic, Democrat, beer drinker, type O blood); or, belief systems, (which could break down into a clump of sub-systems), as in Marxist, Unitarian, Vegetarian, Astrologer, together or apart; pick one or reassemble.   
   To keep it simple though; lets assume that a tree is not a clump. It’s a bunch of cells that are interwoven, re-enforced, stuck, contained, could be a clump but that’s stretching it.  A tree is an organism.  Like a cell.  

To jump from vegetable to animal, a flock of ducks, by any other name, could be, I suppose, roughly considered a clump. Maybe more-so if they are not flying, but bobbing up and down in the water in close proximity of each other; but there are other better terms for those, such as brace, flock, raft, or you name it. Or how about lying inert, in a pile, having been shot by a hunter. A pile is a clump.  

Am I thinking more of a clot?  Like a blood clot? A blood clot is a very complicated thing. It involves something called the clotting cascade, which entails a knowledge of Organic Chemistry, a field way above most of our pay grades, I am assuming. 
  There is though, as you might expect, a place you can go to in cyberspace called Clotting For Dummies, which explains it thusly, and I’m not quoting directly;

Blood lives in a circulatory system, and clever stuff that it is, when there is a leak in said system, said system and surrounding systems put into affect a series of events designed for this emergency.  First, there is a conscious freakout, then a constriction of the blood vessels happens, which prompts our little platelets, whatever they are, to stick to the collagen fibers that are part of the walls of the vessels. Eventually they form a platelet plug, similar to what happens when you put oatmeal in the radiator of your old jalopy, assuming you’re old enough to remember what those are. The plug is just the beginning. When it accomplishes its mission, it triggers a chain of events that cause a clot. All these activities are catalyzed by enzymes called clotting factors, of which there are twelve. Twelve is a lot, and that’s why it’s called a cascade, and why there is a mnemonic to help medical students to remember all those chemicals; something similar to Every Good Boy Does Fine, which is for piano lessons, but that’s another story. Basically, as those of us who weren’t pre-med put it, the coagulation phase involves a series of enzyme activations that lead to the conversion of prothrombin to thrombin. Calcium is required for this reaction, which is why you must eat your cheeseburger; or at least some chicken bones. 
  Thrombin then “acts as an enzyme and causes fibrinogen, one of the two major plasma proteins, to form long fibrin threads." Fibrin threads entwine the platelet plug forming a mesh-like framework for a clot. Here I should quote; 
 

“The framework traps red blood cells that flow toward it, forming a clot. Because red blood cells are tangled in the mesh-work, clots appear to be red. As the red blood cells trapped on the outside dry out, the color turns a brownish red, and a scab forms.”*  So there you have it. Scabs. 

Which leads us to heap. “Heap much trouble, Kimo-sabe", as the Lone Ranger's trusty companion Tonto once said. (I bring up heap just to show that there is a reality after clumps.) A heap can be something that can easily be disseminated, or scattered, as in a heap of straw, or a heap of dust, or it can be a heap of mud or even something more noxious, any of various forms of sludge. 

 

An old heap is a car that is stuck together, but is it a clump?  Perhaps it is too complex for a clump, to many organized parts?  I would say that if you add diversified to those parts you could separate it from the complex organic thing called wholism; mud-flaps and fuzzy dice aren't necessarily part of any known whole. 

 
So I’ve established that clumps are accidental, but not accidental, which leads to paradox. They are random in a probability sense, but not without meanings and causes. Causes like stickiness, morphic resonance, environmental pressures such as weather, and a host influences of,  I might suggest, an infinite number. So let me proceed to the important question, which is how do clumps affect the subject at hand? (Our selfish selves.)
 

Here’s how. From the time we are born, [make that conceived], we are subject to clumping. Our parents belong to a social clump.  Sometimes they reproduce enough, six children say, or eight, ten or twelve, more common to be sure in the olden days, but it still happens, and when we go to school, if we are three close-in-age children from one family, we are a family clump in a larger clump known as a grade, which more often than not is the same one that we follow through time for the next eight to twelve years, after which we may go on to another set of clumpings, called College.

 

Which brings us to the late Prof. Williams:

 

“When one accepts the idea of biochemical individuality, he sees how this can be.  [In this case the diversity of clumpiness.] Getting a clear picture of the clotting mechanism in man would be like getting a clear picture of the branching of arteries from the aortic arch in man. It cannot be done. It should be possible to get a clear picture of the mechanism and the various factors that enter into the coagulation of my blood and of yours, but when one tries to include all human bloods, the picture gets confused. The blood chemistries of individuals vary - not just in trifling ways - enough  to make a picture which is accurate for one individual inaccurate for another.   

 

"The clotting of blood is, of course, intimately concerned with coronary heart attacks and also with “'strokes'” because in each case unwanted clotting causes stoppage of blood vessels. What Dr. T.P. Bond of the Medical School at Galveston found and published recently [sic.] is that exercise affects the clotting mechanisms of individuals un-uniformly. In some individuals exercise may cause the release into the blood of factors which make the blood clot less readily, whereas in others, exercise causes the release of clot-promoting factors. If these observations hold up, exercise should be discouraged in those whose blood clots more readily as a result of it, whereas exercise should be encouraged in those whose blood clots less readily as a result of the exertion. So doctors on both sides of the fence may be right - in appropriate cases. 
  "My intuition tells me that the situation will not prove quite this simple, but it also tells me most emphatically that the relationships between exercise and blood clotting will never clear up as long as the scientists who investigate the problem adhere tenaciously to the uniformity idea.” *

*  You Are Extraordinary; by Roger J. Williams, Random House, N.Y., 1967. 

*  Previously published in Dispatches,  

c.  Tonyprohaska@comcast.net