Let's encapsulate our story. Life is searching for a mathematical partner that will be sensitive to her subtle immediacy. Probability's Data Set Mathematics with his big picture focus accurately captures the features of the general population. However, because of this specialty he doesn't have the tools to understand Life's immediacy. Needless to say, her relationship with Probability has proved disappointing. His constant focus on providing measures for her fixed data sets has provided stability, in that he has accurately characterized her permanent features – even making definitive predictions about her fixed nature. Yet, Probability’s style, while dependable, has frustrated Life.
To understand her subtle and immediate nature Life requires a mathematics of data streams. Her subtle character is more associated with the momentum of recent moments, than it is with fixed and permanent features. If she hears of her general tendencies one more time, she is going to scream. She almost feels that Probability is objectifying her, rather than appreciating her for who she is and the characteristics that make her special. He even trivializes her ongoing data streams by transforming them into fixed data sets. While Probability accurately characterizes these fixed data sets, Life wants a mathematics that is sensitive to her ongoing data streams.
But this new mathematics of data streams can’t be just any old data stream mathematics. This new mathematics must fulfill some stringent requirements, if it wants to be considered the Mathematics of Living Systems. Life is very particular about who she partners up with. To be sensitive to her needs, this mathematics must weight the current moment more heavily and provide ongoing predictive descriptors that pragmatically characterize the trajectories of the moment. Further, due to Life's inherently changeable nature, she requires suggestive predictors that incorporate a range of possibility. This relative imprecision is an asset, not a liability. Probability's definitive predictions are too exacting and general to be sensitive to Life's contextual spontaneity. Life does not want to be boxed in. She has felt suffocated by Probability's approach. To form a new mathematical relationship, Life is looking for a Data Stream Mathematics that is sensitive to the special meaning of the moment – in short, a Mathematics of the Moment.
Where is Life going to find this special mathematics? Certainly not at a singles bar. Are her requirements too strict? Is she doomed to mathematical isolation – her subtle immediacy unappreciated? For some preliminary answers to these questions, read the next article in the stream – The Living Algorithm System. To continue with the metaphorical perspective, read on.
Life reflects upon her search for a mathematical partner.
"I want a guide that will assist me on my Journey - perhaps provide some direction. I even remember spewing to a friend just a short time ago. "Matter has his math. I feel it only fair that I should also have a mathematics of my own – one that is sensitive to my needs - not just his. I won't mention any names, but one of my suitors actually ignorantly stated, "I'm convinced that Matter's Math will eventually be sufficient for both of you." Who did he think he was talking to – a lump of clay?
And then along came the Living Algorithm. I certainly wasn't impressed when I first met her. But I'd heard good things. One of my good friends had introduced us. We went out a few times. She came dressed as first the Creative Pulse and then the Triple Pulse. I came as different forms of Human Behavior - mostly related to sleep. We got along famously - agreeing on everything.
My hopes were rising, but my standards are high. I'm big on data streams; they're everything for me. Without the ability to digest data streams, I am nothing - dead, just like an inanimate piece of matter. So it stands to reason that if a mathematics is going to provide me with guidance, it must also be a specialist in my beloved data streams. In an earlier discussion with Alga, she provided evidence that her sole function is to digest data streams. I was so thrilled.
But then Probability, another suitor tried to horn in. "I also digest data streams. They are my specialty as well. Further, I am far more suited than the Living Algorithm to characterize your features." He then boasted, "Within my system I have a multiplicity of fancy methods of complex analysis. The simplistic Living Algorithm is all by herself. What guidance could she possibly provide that I couldn't do better? In fact, she is just a subset in my domain, a very small subset, at that. Actually, not statistically significant at all."
I had long since grown tired of Probability's obsession with my general features. But his words disturbed me. Was the Living Algorithm just an insignificant subset of Probability? Was Probability really the mathematics of my dreams? In my heart I didn't think so. Probability is just sooo rigid. Everything is either right or wrong - within some specific limits and such. Don't get me wrong, Probability’s boxes provide broad guidelines - boundaries of behavior and such. But something is missing in his approach - my individual special nature.
I hate to admit it, but what he said tweaked me a little – actually disturbed my meditation – probably because of his prestige. I decided to go to the Living Algorithm and confront her directly. She immediately began laughing. "Probability says I'm just an insignificant subset of his? Hah! Forgive his ignorance. He's a bit insecure about all the phenomena he can't address. For instance he couldn't recognize a Moment, even if it was part of his beloved sets. I am not subservient to him; we are complementary systems. We each have a unique purpose and field of action. Although we are both equally obsessed with data, he processes data sets, while I digest data streams. To analyze my data streams he kills them by transforming them into data sets - like capturing a wild animal to study it in a zoo. Not the same.
Alga: “The last article compared our respective approaches to baseball’s batting average. Probability is more effective in characterizing a baseball player’s entire season, while I am more effective in characterizing the player’s recent performance. Probability provides an estimate as to how well the player will do in his next season, while my predictive cloud provides an estimate as to how well the player will do in his next at-bat. The information that Probability provides is more useful to the baseball community when determining seasonal awards and annual salaries, while my predictive cloud has more utility to players, coaches and gamblers, when making immediate decisions on game day. This example shows that rather than being subservient to him, we are complementary systems. He specializes in general features of the data set, while I specialize in the individual moments of a data stream.
There might be some who still feel that I, the Living Algorithm, am but a subset of Probability. To sweep away any remaining confusion as to our relationship, read the next article in the stream – Mathematics of the Moment (vs. Probability). Some of my good friends wrote it. I think they did a pretty good job."
To remain in the metaphorical world, read on.
Life was relieved to find that the Living Algorithm's claims are true.
Life: "The Living Algorithm is not a subset of Probability, but a complementary system. Further, Alga's Predictive Cloud provides relevant information regarding individual moments, something that is very important to me. Could she be the mathematical system of my dreams? Is it possible that she could reveal some codes to my living matrix that will enable me to better actualize my potentials?"
This pleasant reverie was disturbed when she saw Probability striding confidently towards her – obviously with some purpose in mind. Life could sense from his jutting chin that he still had bones to pick over their last interaction.
After pleasantries were exchanged, Probabilty asked in a not-so-innocent fashion: "So how is your mathematical relationship developing with the Living Algorithm?"
With a twinge of the victor, Life: "Great. She is able to address aspects of my innate being that the rest of you have ignored."
Probability: "So we're not good enough for you anymore?"
Life: "Sorry. I didn't mean to be offensive. I love you all. I really appreciate the unique form of guidance that each of you provides. Physics really understands the dynamics of my matter, while you are a specialist on my general features. I'm especially excited about Alga right now because she specializes in my immediacy and my ability to choose. As complementary systems, each of you addresses a different side of my innate nature. Remember in our last encounter, we found that Alga is not a subset of your system, but that you are complementary systems instead."
Life could sense that she had pushed some buttons because the muscles in Probability's smile tightened up into a grimace.
Probability: “I accept the argument that the Living Algorithm is not my child. Despite our common obsession with Data, we have unique fields of action, mine data sets and hers data streams. Consequently the questions we ask and the answers we get involve unique, yet complementary, matrices of thought. She characterizes moments in the data stream, while I characterize entire sets. The Living Algorithm’s results are ever changing, while my results are permanent and never changing. I appreciate the pragmatic utility of the information that the Living Algorithm provides. However the transitory nature of this information combined with the individual nature of the data streams she is analyzing limits, if not eliminates, any scientific value of her analysis. In contrast, the permanent nature of my results combined with the general and fixed nature of my sets renders my analysis perfect for the scientific community. Because of my talents scientific endeavors confidently employ my computations and measures to establish the validity of their results. Look at how famous I am in the world of subatomic particles. What scientific efficacy does the Living Algorithm have, if her analysis is transitory and her data streams individual?"
Rattled and not really understanding, Life responded feebly, "But what about the Living Algorithm’s Predictive Cloud? It certainly provides a unique and pragmatic perspective regarding individual moments – something that even you can’t do.”
Probability derisively: “A Predictive Cloud!? What kind of predictions can be made with a cloud? Sounds ambiguous to me.”
Life uncertainly: “I might be wrong. But it seemed that the Author’s most recent article illustrated that the Living Algorithm's Predictive Cloud does a good job with the batting average – perhaps even better than you when it came to the ongoing games in a player's career."
With a sense of superiority Probability boasted, "Ptah! I'll grant you that the Living Algorithm's method of analyzing the batting average might be useful to gamblers or coaches, but it has no scientific value and hence no significance. Stick with me, if you want some definitive answers. Go to her, if you are happy with mere suggestions."
Life was confused again. Questions raced through her mind, over and over again like a broken record. "Are my data streams so transitory and individual that I must be content with a pragmatic mathematics that has no scientific value? And why is Probability so famous in the subatomic world? Plus, why doesn't baseball’s batting average have any scientific significance?
“This is all too confusing. To sort things out or, at least establish priorities, I’m going to meditate."
“Ommm? Whoa! Recently, I’ve been riding a rollercoaster of emotions – and all due to my budding relationship with the Living Algorithm. Maybe I should just remain single to eliminate these psychic disturbances. But that wouldn’t help. I seem to crave a mathematical partner. I had grown dissatisfied with other more traditional mathematical choices for constantly attempting to box me in - regulate my every move. I decided to look for an alternative – a mathematical guide that might help me to realize my potentials by unlocking the code to my matrix. Friends introduced me to the Living Algorithm, which led to a few successful interactions. Wanting to take our relationship to another level, I posed some requirements, which the Living Algorithm fulfilled. Everything was going perfectly. It even seemed that the Living Algorithm and Probability, as complementary systems, might be able to join together to provide me with a more comprehensive set of clues to my behavior.
"But then Probability challenged the Living Algorithm's scientific credentials," Life fretted. "Perhaps he was jealous of all the attention I was giving to the Living Algorithm. Perhaps he is right. Could the Living Algorithm just be a poseur - pretending to be a valid system, but without any real scientific foundation? If her insights have no basis, how can I trust the codes she reveals? What was it that Probability said? Oh right. The Living Algorithm's analysis, while pragmatic, is too transitory and individual for Science. And then when I brought up how much useful information the Living Algorithm provided in the batting average example, Probability just snorted derisively. 'The batting average has no scientific significance.' Does Probability have a valid point or is he just attempting to undermine my budding relationship with the Living Algorithm?"
To see how much validity Probability's critique has, read the next article in the stream – Living Algorithm Patterns. To continue in the metaphorical world read on.
Smiling cockily, Probability summarized the analysis: “My batting average has a proven pragmatic value, as evidenced by the fact that it is a factor in determining both strategy and salary. However, due to its individual nature, it can’t be compared to any other set with any kind of scientific certitude. Accordingly, the batting average has no scientific value. The same analysis applies to the Living Algorithm’s predictive cloud. Data streams are so individual and transient that it is impossible to achieve the certitude that Science requires. I must admit that her predictive cloud characterizes moments much better than I. Nevertheless, her descriptions of moments have no more scientific validity than my batting average for the same reason. It is impossible to generalize the results to other data sets due to the individual character of the data we are analyzing.
However, I, Probability, can generalize my analysis of one homogeneous matter set to another. Atomic particles, whether electrons, atoms, or molecules, are identical and obey the same universal laws in all times and places. Under the same circumstances, one electron behaves the same as another – no individuality whatsoever. Because of my ability generalize my analysis Science has admitted me to his exclusive Circle. While the Living Algorithm’s Predictive Cloud provides potentially pragmatic information regarding future moments, this alone will never get her into the Science Circle. Because she only deals with transitory moments in individual data streams there can be no certainty of her predictions. Due to this lack of certitude, the Living Algorithm analysis is of questionable value, at best. Accordingly Science ignores her analysis.
I, on the other hand, am famous in the scientific community. Anyone who has anything to do with science must have at least a rudimentary knowledge of my system. In the hard sciences I am world renowned for cracking the code to the electron's matrix. The soft sciences employ my skills to establish the validity and significance of their experimental studies. They all worship at my altar. I will eventually solve your code just like I resolved the code of the subatomic matrix. Your Living Algorithm is unnecessary."
Somewhat taken aback by Probability's arrogance, Life responded quietly, "So you are going to identify all my general characteristics and then claim that this is me?"
Understanding the subtext of my comment, Probability angrily blurted, "You just wait and see! I will be able to predict your behavior just like I do matter. After all, you are just a sack of atoms." After asserting his presumed dominance, he stormed out.
I relayed this story to the Living Algorithm in our next encounter. She laughed so merrily that I joined in. "Probability is getting desperate. He is overly attached to becoming your mathematics. He needs to detach a bit from these expectations. They create emotional chains that are disturbing his internal peace. He is already famous the world over for his achievements. Why does he feel a need to dominate human behavior? Perhaps it is a way of compensating for a sense of inadequacy over his inability to address the dynamic nature of existence.
Let me first address his claim that my method has no scientific value because of the transient and individual nature of the data streams that are my sole obsession. As evidenced in our batting average example, my predictive clouds supply an abundance of practical information when applied to living data streams. Experimental evidence suggests the likelihood that Life employs this pragmatic tool, my predictive clouds, for assessing environmental patterns to best determine the most appropriate response to ensure survival. If Life employs my predictive clouds, then Life is also subject to my information patterns. In Triple Pulse Studies, the first notebook in this series, we examined many examples of how Life has employed the Triple Pulse, one of my many information patterns, to organize human behavior associated with sleep. Accordingly my scientific value lies in my ability to reveal the underlying information patterns that motivate behavior. However I can't establish the scientific certitude of these connections on my own. I require Probability’s analytical talents to verify, or at least establish the limits on the correspondences between human behavior and my information patterns. Thank you Probability.
Life was relieved to find out that the Living Algorithm was not a poseur. Her method had scientific merit even though she had to rely on Probability's services to establish certitude. "What a great team you can be. Probability can provide helpful information about my general features and assist you in your quest to establish your scientific validity. You, on the other hand, can unlock the code to my personal dynamics, the matrix of my behavior."
Alga: "Exactly. We need each other to provide a comprehensive picture. Probability is helpless before your dynamic nature, as his specialty is static data sets, not dynamic systems. He can establish precise definitions, but no causal mechanisms. At best he can provide a rough map of the landscape. This is very useful because it reveals where you can go and where you can't. But the map reveals very little about inner motivations and potentials – the factors that influence and inspire your behavior. That is my specialty, as my sole focus is the dynamics of data streams."
"Ironically, the story of how Probability became famous as ruler of the subatomic world illustrates both his inherent strengths and weaknesses. Further it pertains to why my dynamic nature is ideally suited to determining causality, while his static nature is more suited to description. As with other aspects of our respective systems, these talents are mutually exclusive. Read on to see how Probability was able to patch up the gaps in the subatomic universe that were left by classical Mechanics, the star of Physics. In so doing, Probability became the new star - both technically and philosophically – for a while at least. Fame is always so fleeting."
To explore these issues, read the next article in the stream – Description vs. Causality; Static vs. Dynamics. To continue in the metaphorical world read Life yearns for Mathematics of Relationship.