ATON is a hopefully evolving classification theory. It aspires to unify knowledge around numbers and prefers naive methods. Some of the older posts are wrong but I'll keep them for the sake of continuity.

Tuesday, March 27, 2007

Time and pressure

Time displays thermodynamic aspects. Consider the triplets;

{Time, Matter, Space}
{Pressure, Temperature, Volume}

The P-T-V triplet are related to each other by the famous equation of ideal gas; PV = NkT, where N is the number of particles, k is the Boltzmann constant.

Time stops at the event horizon of a black hole. The entropy of a black hole is proportional to it's area; S = k(c^3)A / 4G(hb), where c is speed of light, hb is Planck's constant. This equation contains all the goodies. Black holes are the boundaries of space-matter-time, so they must contain it. It also includes the Boltzmann's constant k, and makes the link to thermodynamics pretty explicit. The great surprise of this equation was that the entropy is proportional to the area A. Time slows down in gravity, and eventually stops at the most intense gravity gradient; the even horizon of a black hole.

Gravity works as if space-time is squishing out it's contents towards less pressure, since space-time dilate in gravity. A gravity field is like a 3D hill's surface of a 4D volume (a normal hill's surface is 2D). We feel the squeeze down of gravity by the counter pressure of the earth. Thus space-time is has strong thermodynamic aspects. {Matter, Temperature} correspondence makes sense since matter is equivalent to energy. {Space, Volume} correspondence is obvious. Thus we get {Time, Pressure} correspondence implied. As we well know, pressure cookers shorten the time of cooking. Sounds funny I know, but I think this fact reflects the correspondence quite well, since pressure increases the event density in time.

Friday, March 09, 2007

What exactly is nothingness?

When I started this blog on nothingness (Nn), I had a vague idea of what Nn is, and I still am not totally clear on it, although clearer. I have come to believe that it is a trancendental and relative concept.

I have already given few examples of what it might be; water for taste, air for smell, space-time for matter and so on. I still think these examples are pretty close, but there is still a problem. Water by itself is not taste, although taste evolves out of water. The smallest amount of taste, as compared to water, corresponds to Nn. Therefore Nn is a relative concept like probability;

Nn0 = ,/,

At the limiting case Nn0, both numerator and denominator are equal in quantity. I use numerical concepts since ATON aspires to be based on numbers. It also relates to the word nothingness since it compares almost nothing to almost nothing. Through comparision to itself, "nothing" (N) gets lifted and becomes "nothingness" (Nn). Thus we seem to get a connection to the concept of equivalence class as well. I like to iterate on this later.

A connection to my Mirror Set is also made;

M(m,n) = m!n / n^m

Where m!n is the multifactorial of m to depth n. M(0,0) is undefined, or fuzzy and multivalued, as I imagined Nn to be.

Let me try another example from my cat Rupty. I adopted her when she was very little, maybe a week or two old. After I brought her to my place, the first thing she did was to inspect the room, starting from a wander around the outer perimeter of the room. She did not get out of the room until she was sure where she was, I gathered. After many hours, she started little trips out of the room to inspect the corridor. Every time she would come back running and excited. In this fashion she finished inspecting the house in a day or two. Then she did the backyard, the frontyard and the street in many days to come.

The way she was doing these inspections was seemingly random. She would pick a direction and time out of the blue and inspect it many times until she was confident. The randomness is also displayed in her switching of the sleeping place. One day, out of the blue, she would swithch the place and start sleeping somewhere else she inspected before. This also applied to her other favorite places where she did one of her numbers like having a nap or sitting and watching.

I concluded that her behavior pattern is a fuzzy and random ball, like nothingness. It changed and took shape over time, but the essential fuzziness remained. We humans are also like cats when we are not regulated too much. We like to slumber along in a fuzzy pattern.

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