Registered: Feb 2004
Posts: 4

Astonishingly, in NKS neither the ultimate size of the single cell of a cellular automaton nor the optimal velocity of the wave travelling within an automaton are a theme. On the background of experimental data from neurophysiology and psychometrics we have come to the conclusion that both size and velocity have to be a function of planck length and golden mean, see http://www.volkmar-weiss.de/chaos.html or the online-version of our publication:
H. Weiss and V. Weiss: The golden mean as clock cycle of brain waves. Chaos, Solitons and Fractals 18 (2003) 643-652 (also found in the bibliography, citing NKS, see http://www.wolframscience.com/refer...bliography.html ).
Behind the definition of the second is the velocity of light, which is the constant on which size all other physical constants depend upon and hence represents the inherent speed limit that any particle information pattern is able to achieve. In this system of present-day constants the Planck length has the value 1.6160 x 10-35 m (standard uncertainty 0.0012 x 10-35 m). If we fix instead the Planck length at the value of the golden mean at 1.6180 x 10-35 m and recalculate consequently all other physical variables, a major step in our understanding of the universe may be done, opening the possibility of unifying the theories by Ashtekar, El Naschie (see the latest review of his infinity theory in: Chaos, Solitons and Fractals 19 (2004) 209-236) and others. We should not quantize and not merely discretize, but discretize transfinitely, this is the message.
The universal cellular automaton seems to be capable of updating its entire memory in a single clock cycle, which according to Occam’s razor could be nothing else than the Planck time as the relation between the velocity of light and the Planck length, the latter fixed at the value of the golden mean. If we, for example, look into NKS we see that Wolfram’s Model 3 and Model 4 automata are full of Pascal triangles. We all know that behind such a triangle are always the Fibonaccis and hence the golden mean. That means that by encoding and decoding the information of such and any automaton or system no other wave could be more optimal than a wavelet containing the golden mean itself.

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Registered: Aug 2003
Posts: 712

Um, and there should be a relation between the natural planck length and the completely arbitrary and conventional length of a meter why? With 35 (why 35?) powers of - why exactly 10? - in between.

Sorry, this doesn't make any sense. There might be ratios between physical constants that have real meaning or that arise for underlying detailed reasons, particularly in a discrete ultimate theory. But every time you see 1.6 something in some system of units, it does not mean the same underlying whatever is going on.

Not when the units, and the bases, and the orders of magnitude, are all completely arbitrary. The same ratio is 1.3425 times 2 to the minus 116th power if I just change the base from an arbitrary 10 to a "perhaps natural" 2. Still in meters. In feet it'll be something else, and in cubits something else again.

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Registered: Feb 2004
Posts: 4

Jason,
your reply seems to be plainly evident. Too plainly. What the planck length concerns, the idea is not a new one that this length could or should be a fundamental constant. An open question is whether the numerical sequence of this constant has any deeper meaning or is only a man-made artefact. The definition of the meter has been made in relation to cosmic parameters. This relationship is independent of any scaling; however, its numerical value depends upon the Hausdorff dimension. And if you change the base and the orders of magnitude, the golden mean always remains the golden mean.
In calculation of physics the velocity of light is often set to 1, in order to make calculations easier. In a similar way we could replace the planck length by the golden mean, but the result of such an identity is not easiness of calculation but a firework of possibilites for any automaton running the world.
To be not misunderstood: The results of our scientific work , see http://www.volkmar-weiss.de/chaos.html , mentioned above in my first posting, are quite independent of such a hypothetical relationship between planck length and golden mean. But we had the additional idea, that behind the scaling-invariant relationship between planck length, golden mean and Hausdorff dimension could be more than mere coincidence.

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Registered: Aug 2003
Posts: 712

Between two naturally occuring constants, the ratio can be meaningful. But the meter is not one of them. Yes, the meter is presently defined in relation to specific physical measurements. But the coefficients in those definitions were chosen simply to keep the meaning the same as the original definition, which was a fixed fraction of the distance between the earth's north pole and equator.

"The meter was originally defined in 1791 by the French Academy of Sciences as 1/10,000,000 of the distance along the Earth's surface from the North Pole to the Equator along the meridian of Paris and on April 7, 1795 France adopted the meter as its official unit of length. Uncertainty in the measurement of that distance led the International Bureau of Weights and Measures in 1889 to redefine the meter as the distance between two lines on a standard bar of platinum-iridium kept at Sevres.

"In 1960, as lasers had become available, the 11th General Conference on Weights and Measures changed the definition of meter to be the length of 1,650,763.73 wavelengths in vacuum of the orange-red emission line in the spectrum of krypton-86. In 1983 the General Conference on Weights and Measures defined the meter as the distance traveled by light in a vacuum in 1/299,792,458 of a second (that is, the speed of light in a vacuum was defined to be 299,792,458 meters per second). Since the speed of light in vacuum is believed to be the same everywhere, this definition is easier to maintain and more consistent than a measurement based on the circumference of the Earth or the length of a specific metal bar. Thus, should the bar be destroyed or lost, the standard meter can still be easily recreated in any laboratory. It also has the advantage that it can (at least in theory) be measured with far greater precision than the circumference of the earth or the distance between two lines."

The values "1650.76373" and "299792458" (leaving aside "second") were arrived at purely to match the previous definition, and reflect no underlying real relationship. Any numerical relation seen between a unit so defined and the planck length is coincidence. You might look at scaling laws in a base two digit sequence of a dimensionless parameter, and perhaps talk about some inherent structure. You can even find structure in random conventional data in some base, like the frequency of digit A rather than B and whether it changes for leading as opposed to later digits. But just a leading 1.6xx in conventional units is meaningless.

There are plenty of better places to investigate natural instances of numbers like the golden ratio, in dimensionless parameters or with units that arise from the phenomena itself - in the forms of spirals, in tilings, in sequences and substitution systems.

http://mathworld.wolfram.com/GoldenRatio.html

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