[כאשר אין בחינה של רקורסיה, אין מקום לחלק בין ההשראה בסקלה
המרחבית של הכלל לבין הסמכות של הפרט. רקורסיה עובד כאשר יש פרטים שפועלים
באותו סקלה, והקישוריות שלהם והשפעות ההדדיות שלהם יוצרות משהו בסקלה
שונה. בדוגמא שלנו שני הסמכויות פועלות באותו סקלה ויוצרת אחת את
השני]
כאשר
אני מניח רצון למערכת (בקלוסטרים הכלל שלי הוא שהמערכת ישכח כמה שפחות --
מינימום איבוד אינפורמציה), זה נותן השארה למערכת, וכל פרט במערכת פועל לפי חוק
פרטי, מקומי, להתחבר לשכן הקרוב. הפרט יודע את החוק הפרטי המקומי ואינו יודע
את ההשראה לחוק. האם זה בפשטות ׳הכוונה׳, כלומר יש סיבה (מרצון על) קאוסטי,
למסובב (לפרטים). או יש מקום לחלק בין הכוונה להשראה? שהרי כל פרט
פועל עצמי לפי חוק מקומי ואינו מודע להכוונה?
In my article 'an agglomerative method for on-line clustering of non-stationary data' I describe the phase transitions that occur as a function of scale.
A phase transition is an identification of an emergent entity. It requires a metric, the measure of emergence of an entity. Each level-order-Makom that emerges is recognizable with the metric that jumps.
The properties necessary for emergence in my paper are:
1. multiple scales, the number of centroids relative to the number of data points defines the scale. This is similar to temperature in water
2. a metric, the number of centroids utilized (i.e. representing more than 1% of the data). In water the metric is viscosity.
3. a local rule that is tied to a high-degree of connectivity, merging the two closest centroids when a new data observation enters the entire system. The local rule is that two local centroids are merged, but a high degree of connectivity is needed to a) determine that a new observation arrived b) determine that the two are the closest, i.e. the relative distance between each and every centroid.
I wonder if the new observation is Hasgaha that creates the Makom!
It would be fun to re-write my algorithm in network language with connectivity properties.
What is the third (3) property of water? In what way is there global connectivity? diffusion for sure exists.
So water molecules:
1. the scale is defined by temperature (centroids) relative to pressure (data points)
2. viscosity can be measure
3. water molecules constantly bind to each other with each new observation.
When the temperature drops, this is analogous to a reduced resolution, less centroids, hence there is a limited resource (centroids) and in water what is that limited resource? binding energy?
Each new observation: In water there are constantly new observations as the molecules constantly expand their diffusion and reach out to affect each other.
So, each new observation puts a strain on the limited resource, which forces a merge, a sharing of the resource.
The higher the level of connectivity the more pressure on the limited resource the more likely a merge will occur.
What is the limited resource in a water molecule? (temperature/pressure related -- binding energy/surface tension)
What is the limited resource in a pasuk of Torah?
So the Torah:
1. the scale is defined by the relationship between the number of pesukim and the number of concepts
2. the number of interpretations defines a measure (inverse of Information)
3. the connectivity (local and global) is created by the Limud.
The fewer pesukim, the lower resolution, the less possible to differentiate between the clusters. The amount of Information is low, the number of interpretations high.
As the resolution increases, more pesukim are added, the global network increases and forces a local merge of access to the limited resource.
The limited resource is the MDL, the compressed representation of the concept. Since I want to have as few concepts as possible, with highest Information content and hence minimal number of interpretations.
The more connections between the particles (the pesukim) the more pressure on the limited resource, since more people are sharing it.
