Friday, March 25, 2011

Absolute Maximum Temperature

Updated: April 19, 2011
Binary mechanics (BM)[1] predicted an absolute maximum temperature which would be found below maximum energy density defined as maximum bit density [2]. A pilot study supported this hypothesis [3]. The present report replicates and polishes these results using a different method. Instead of starting with maximum bit density as in the pilot study, the present report started with a near-zero bit density, slowly adding bits randomly in small perturbation increments in each BM simulator Tick.

Methods
Data collection was conducted with the BM simulator, HotSpot 1.26 which may be downloaded here.

The procedure started with a 48x48x48 simulated cube of space with about 0.001 initial bit density. With each simulator Tick (4 BM time units, one for each bit operation), a procedure increased bit density by about 0.001, until maximum bit density was obtained. Simulator Box mode was ON to "reflect" bits exiting the simulated space back into it.

To replicate this experiment with a different randomization sequence, click Cancel for the HotSpot input file dialog. At the first prompt, enter 48,21. At the second prompt, enter 15,0.0009,0. As the Tick 0 initial state display is printed on the screen, immediately press the 2 key, activating HotSpot Experiment 2 (Ex=2), which automates the protocol.

Results
Fig. 1: Temperature vs Bit Density
Fig. 1 plots the first temperature-related measure used in the pilot study as a function of proportion maximum bit density (zero to one) from the 48x48x48 spot cube data.

With the present perturbation method, the primary operational definition of temperature peaked at 0.682 at 0.602 of maximum bit density.

Fig. 2: pRMS vs Bit Density

The pRMS momentum values were derived from position changes per simulator Tick, sqr((p12 + p22 + p32)/3), where {p1, p2, p3} are the average position changes over the simulated space, comparing the present and previous Tick.

Below peak-temperature bit density, at least three waves of increased whole body motion (pRMS) were discernible, with peaks just below the 0.2, 0.4 and 0.6 bit density levels. The wavelength of these three peaks, then, might be expressed in bit density units and is about 0.2.

As in the pilot study, above peak temperature at proportion maximum density 0.6 (Fig. 1), while temperature is falling, another major pRMS peak occurred (Fig. 2).

Discussion
The present data confirms the pilot study report [3], again suggesting the existence of an absolute maximum temperature, per the operational definition of bit motion due to EM bit operations. Absolute maximum temperature occurred at a bit density of about 0.6 maximum density.

However, the pilot study found maximum temperature at about 0.346 maximum density. This difference between the present and pilot studies may be due to the different methods. The present 0.6 density estimate at which maximum temperature was observed used a density variation method which might be deemed opposite to that used in the pilot study. The present method started from near-zero density slowly incrementing it with the Box option ON, while the pilot study started from absolute maximum density and followed the decrease in density due to bits exiting the simulated cube of space with the Box option OFF.

This methodological difference may explain the different maximum temperature densities, namely the density at which maximum temperature occurs may depend on the content in the spatial volume. In simple terms, different materials may reach maximum temperature at different bit densities.

In any case, the present and previous pilot data suggest that the density at which maximum temperature is achieved is not a constant, but depends on some combination of methods used and content in the simulated volume.

Bit density is thought to relate to energy content [2]. If the existence of an absolute maximum temperature is correct, then the inverted U shape of the temperature curve (Fig. 1) states that quite different states and their energy levels can have the same temperature. A perhaps paradoxical result is that maximum energy is associated with absolute zero temperature, at which all the energy is potential with no kinetic energy.

References
[1] Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.
[2] Keene, J. J. "Captives in a binary mechanical universe" J. Bin. Mech. March, 2011.
[3] Keene, J. J. "Maximum temperature at half maximum bit density" J. Bin. Mech. March, 2011.
© 2011 James J Keene