This is getting worse and more abstract. Maybe next time I’ll start writing down vocabulary and definitions. A concept word is hard to define, and I’m not finding anything that would do the job of explaining the concept words of Utd’mbts. Well, in the mean time, I’m still looking for interesting candidates for the grand analogy.
I’m trying to extend more analogies with physics in the description of human interaction. In previous posts** I made the analogy that the momentum towards an opinion or goal choice would change if an outside force (peer pressure-force) was applied. I was flipping through some physics books to see how the analogy could be extended. It is interesting how after a certain point they give up on going further with the force applied to a mass analysis.
It is possible to write out the math for a continuous variable force applied to an object. So then, they say that if you knew how the force varies with time by supplying an equation that describes it then you could solve the problem of what is the change in momentum for a given force. However, they say that in the real world, they don’t know and can’t describe how a particular variable force in a given problem changes with time. Usually it’s not constant and changes in a complicated way.
Because they had to abandon that approach for most problems, they came up with new approaches. They use what is accomplished (the the work done) or the change in energy. The force changes the work done or facilitates a transformation of energy of some kind. The human analogy I’d say would be the peer force effects the equivalent objects of Accomplishment(work) or Enthusiasm (energy).
For example, the principle is expressed this way:
“… the work of the resultant external force on a body is equal to the change in kinetic energy of the body.”
— Sears, F.W., and Zemansky, M.W 1960. College Physics. P. 129. Reading, Mass.: Addison-Wesley Publishing Co., Inc.
How does the force move the object? Don’t know… but the result is blah, blah. What’s a force? Don’t know. What’s energy? Something that does work…. Anyway so everything goes in circles and it’s all calculations.
[In the following where I haven’t made a picture, variables in bold face are vectors]
About the vicious circle of force:
The fundamental equation tells us that the force equals the rate of change of the momentum p given as F = dp/dt and if the force is known as a function of time, we want to know how when that continuously varying force is applied to a particle, what it does at every moment in
We want to know the sum of all these effects which is called integration symbolized by
The quantity on the right is given a new name, I, or impulse. so the new formulation according to Alonso and Finn2 is
“the change in momentum of the particle is equal to the impulse.
[and] a very strong force acting through a short time may produce the same change in momentum as a weaker force acting for a longer time…”
Replace momentum p by mv which is its definition:
mv – mv0 = I or v = v0 + 1/m I
and v = dr/dt, so
“However… [often] THE FORCE ON A PARTICLE IS NOT KNOWN AS A FUNCTION OF TIME BUT AS A FUNCTION OF POSITION [r] … HENCE WE CANNOT EVALUATE THE INTEGRAL and it’s a vicious circle
— 2 Alonso, M. and Finn, E. J. 1967. Fundamental University Physics. P. 196. Reading: Addison-Wesley.
** The Goal Space of Utd’mbts
The ancient language is a difficult thing to analyze, and I must resort to imperfect analogies written in our crude English to attempt a translation of the major features of its expression. Actually, I suppose what I’m calling “major features” are actually minor elements of the real manifestation that is purported to have existed. So anyway, I might propose a feature that I will call the “goal or opinion space” which I will begin to endeavor to be a cluster of meaningful concepts perhaps giving hints at the structure of the ancient language in its elementary form that was intended for children.
There is a tendency for a person to cling to an established goal or opinion, to only observe and remember that which would confirm that belief, and to ignore or distort that which would refute that belief or interfere with an important goal. This core goal or belief is indicated here as the Goal 0. There is a position vector R which designates a particular goal or opinion point on a path to be fulfilled. A peer pressure force (F) can alter the direction of travel towards a goal. I’ll come back to this later and add it as an edit here… [I’m going to look at what this looks like so far, and I suppose it’s best to post something before a crash or whatever… (I’ll be back here later)]
Where m = the number of people holding a particular opinion or goal, and
v = the velocity with which the people are moving towards that goal
(So maybe another approach to Utd’mbts)
I was looking for some more analogies to use for explanatory purposes. There are many paraphrases of Newton’s Laws, but let me put the first one this way: an object tends to stay in the same motion as it was unless an external force makes it change. So too, people tend to stay on their course towards the confirmation of their established opinion unless acted on by an external force. So loosely, we could say that an object has a mass, m, and the people have the masses. An object can accelerate (a) in velocity, and the masses of people can accelerate in their motion towards an opinion.
The value of the force necessary to change course is often given by that famous equation “F= ma“, where it can be seen that if an object does not continue as before along its merry way, but has a non-zero a (acceleration), meaning it’s continuously going faster or changing direction then a force must have been applied. If a force is applied, a mass of people may change the direction of their opinions.
But, of course, as always, this is the simplified version. It assumes the mass is a constant and is extracted from a more complicated version. The original is closer to saying that the force equals the mass times “the rate of change” (d/dt) of the momentum (mv) of the object: F = (d/dt) mv. Or with the momentum called “p”, F= (d/dt) p. In the case of people, the momentum towards an opinion changes if an outside force is applied.
I’ll come back to this later after I make a picture for the equation superscripts so that it’s neater, and I’ll make a picture for the opinion and motivation things. I forced myself to begin this essay even though it’s not complete because until this moment I was writing nothing. So maybe if I at least get started now at this moment, I’ll have the momentum to continue at an accelerated pace towards my goal later.