Energy’s Behavior: Work, Kinetic, Potential, Entropy
Numerical Energy: Work, Kinetic, Potential, Entropy
Logarithmic Decay: Numerical Energy ≈ Radioactive Energy
Relevance: Attention’s Mental Energy ≈ LA’s Numerical Energy
Numerical energy is certainly a curious concept. How can numbers have energy? Isn’t a number just a symbol – a representative of something else – a pure abstraction without any substance? If numbers are not linked to the material world of atoms and molecules, numerical energy must also be symbolic.
Solitary numbers, standing alone, obviously don’t possess any energy. Is it possible that numbers could behave as if they had energy, if they interacted with other numbers? But numbers don’t tend to interact with other numbers. They seem to be a bit standoffish, presumably preferring to be by themselves. In fact, our entire computer world is based upon isolated 1s and 0s.
As solitary mental abstractions, how can numbers even exhibit behavior? We tend to think in terms of the behavior of things, for instance galaxies, humans, horses, protons, or electrons. Of course, we can also talk about the behavior of energy, such as fire, lightening and electricity. Yet the behavior of energy is generally either expressed in physical terms, or in relationships to the material world. Further, these energetic interactions somehow occur in the space-time continuum.
Numbers are usually a symbolic representation of some feature of quantifiable reality. Existing only in our mind, they don’t really persist through time and move through space. Devoid of these essential features, how can numbers behave?
Despite this standard perception, numbers certainly exert a powerful emotional influence upon our lives. We follow the numbers associated with our financial assets, for instance savings accounts and stocks. We become anxious when these numbers drop and experience happiness when they rise. Fans attend to the statistics of their favorite teams and players. Athletes regularly attempt to surpass the highest numbers ever recorded. The Guinness World Book of Records is a testament to the power of numbers. Students follow their grades; dieters their weight; the list goes on and on. Although they are merely symbolic, numbers exert a powerful effect upon our lives. Where does this power derive from?
Let us suppose that numbers can behave as if they had energy. What does it even mean to behave like energy? How does energy behave?
In its most basic form, energy works to change the system it belongs to. For instance, energy heats a room and moves our cars. Energy can also be stored. For instance, oil, coal and natural gas are all forms of stored energy that we employ to power our world. Kinetic energy is the name scientists have given to active working energy and potential energy is stored energy.
Physicists have developed and defined the notions of kinetic and potential energy with mathematical equations. Engineers have employed these equations to create engines that convert the potential energy of gasoline to the kinetic energy that moves our cars down the road. An understanding of the mathematics of energy has allowed the scientific community to precisely describe the behavior of physical systems, whether mechanical, electrical, or gravitational. In fact, the concept of energy binds these diverse material systems together into one unified package.
Energy has a specific and definable relationship to work and power. Kinetic energy is employed to do work and potential energy is stored for a later date, like a savings account. Power is how quickly work is accomplished.
Energy is also associated with entropy. Closed systems tend to seek equilibrium. This process is entropic in nature. Shannon connected entropy with information. This connection provided organization with a version of energy. Energy organizes, while entropy disorganizes. It takes energy from outside the system to reverse the tendency towards entropy.
In the material world, energy is also conserved. It never disappears or is consumed. It is merely converted from one form to another.
If a number exhibited these features, then it could be said to behave as if it had energy.
The Living Algorithm’s (LA’s) computational process produces data stream derivatives by relating present data to input from the past. This relating process generates a dynamical system that seems to include numerical energy. Let’s examine the LA’s System through the energy filter.
The LA operates upon data streams (DS). The computational process generates the data stream’s central measures, a.k.a. DS Derivatives. The ongoing measures are part of a mathematical system.
The Living Average is the most basic of these central measures. As the name indicates, it can be likened to the data stream’s running average – its ongoing mean. The Living Average indicates the state of the LA System, somewhat akin to its temperature.
Upon entry into the LA System, each number could be said to consist entirely of potential energy, i.e. filled with potentiality. The LA’s computational process converts a portion of the number’s potential energy into kinetic energy. With each subsequent iteration, a portion of the remaining potential energy is converted into kinetic energy.
Eventually, i.e. after sufficient iterations, virtually all of the original potential energy is converted to kinetic energy. The LA System has completely consumed the numerical energy. Put another way, the total amount of kinetic energy that does work is equal to the original energy that entered the System.
What kind of work is accomplished with a number’s kinetic energy? The numerical energy acts to change or maintain the Living Average, i.e. the System’s state (temperature). The numerical energy attempts to change the System to its state. For instance, a ‘1’ attempts to change the Living Average to ‘1’. Similarly, when hot air enters a cold room, the heat raises the temperature.
However, these changes are far from permanent. In fact, change is the only constant. There are innate entropic mechanisms in the computational process that inevitably draw all the data stream derivatives to 0 unless new numerical energy enters the System. It could be said that the numerical energy acts as an organizing force, while the computational process acts as an entropic force.
It is evident from this brief description that numbers behave as if they have energy after they enter the Living Algorithm System. As with material systems, numerical energy can do work as kinetic energy or stored as potential energy. A number’s kinetic energy does work to raise the System’s state (temperature). A number’s potential energy is gradually converted into kinetic energy with each iteration of the LA’s computational process.
Further there are innate entropic forces at work that are inherent to the computational process. These forces draw the System’s state (temperature) back to zero (equilibrium) unless new numerical energy enters the LA System. In similar fashion, material systems move to equilibrium unless new energy enters the system. It is evident from this analysis that the logics of material and numerical energy have much in common.
LA’s Numerical Energy ≈ Material Energy
The LA’s mathematical system also behaves in a similar fashion to radioactive systems. For instance, the original numerical energy decays in a logarithmic fashion just like radioactive substances. Let’s examine the process in more detail.
Upon entrance into the system, a number consists entirely of potential energy. With each iteration of the LA process, the potential energy goes through logarithmic decay, emitting an equal amount of kinetic energy. Each repetition of the computational process transforms a proportion of the remaining potential energy into kinetic energy. This kinetic energy exerts an effect upon the LA environment. In similar fashion, Uranium’s potential energy goes through logarithmic decay, emitting an equivalent amount of kinetic energy that changes the physical environment.
The following table illustrates the differences in the rate of decay with a variety of Decay Factors. The top row indicates the Decay Factor, while the left column indicates the percentage of the total potential energy that remains after the number of iterations listed in the table.
For instance, if the Decay Factor is 12, the remaining potential energy is about 10% of the original energy after 26 iterations and .01%, i.e. 1/10,000th, after 113 iterations. If only .01% of the original energy is left, there is no potential energy remaining for all practical purposes.
Radioactive uranium also decays in a logarithmic fashion. Like uranium, numbers also have a half-life: indicated by the 50% row. There is one major difference. While uranium decays continuously, numbers decay in a step-like fashion.
Iterations, Decay Factors & Rate of Decay |
|||||||||
% of Total |
2 |
3 |
5 |
10 |
12 |
15 |
20 |
30 |
50 |
50% |
1 |
2 |
3 |
7 |
8 |
12 |
13 |
20 |
34 |
25% |
2 |
4 |
6 |
13 |
16 |
20 |
27 |
41 |
69 |
10% |
3 |
6 |
10 |
21 |
26 |
33 |
45 |
68 |
114 |
1% |
6 |
11 |
20 |
44 |
53 |
67 |
90 |
136 |
228 |
0.10% |
10 |
17 |
31 |
66 |
79 |
100 |
135 |
205 |
344 |
0.01% |
14 |
26 |
44 |
93 |
113 |
144 |
193 |
292 |
490 |
It seems that numerical energy has many parallels with physical energy: potential, kinetic and radioactive energy.
Is LA’s numerical energy just a mathematical oddity? Or does it have some practical applications? If numerical energy is a purely mathematical construct, then it is just an interesting curiosity, with no relevance.
However, the LA system is not confined solely to the mathematical realm. We have presented evidence indicating that LA is Attention’s computational tool. Operating under this perspective, Attention issues a quantum of mental energy with each iteration of the LA’s process. We have exhibited that Attention’s Mental Energy behaves in similar fashion to the LA’s Numerical Energy. Put another way, there seems to be logical symmetry between the two systems of energy.
Attention’s Mental Energy ≈ LA’s Numerical Energy
Is this symmetry between mental energy and numerical energy just an interesting factoid or does it have any relevance to our day-to-day lives? Does this symmetrical relationship provide any useful insights into our behavior? Understanding physical energy has certainly transformed our material existence. Could an understanding of mental energy transform our immaterial existence? Could this knowledge assist our self-actualization process? Definitely. Understanding underlying causes enables us to get better control of the factors that exert an almost unconscious control over our lives.