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Applications of Tetration
#5
Hej Andydude

Here is one application - a little bit far fetched- but I just composed it today- from physics of consciousness - if that is a true conjecture, than many things in the middle will require attention:

Please look at this article:"Dimensions of consciousness" http://www.pubmedcentral.nih.gov/article...id=1201004

Though I do not know exactly how fractal dimensions of phase space are obtained, so I have to be careful with interpretations,may be it is pure coincidence, but numerically they might make sense, especially this table from the article:

Table
Rankings of highest fractal dimensions obtained from the electroencephalographs of 11 species
SpeciesHighest fractal dimension
Human4.85
Dog4.63
Bullfrog3.71
Minnow3.09
Catfish2.50
Perch2.37
Crayfish1.65
Earthworm0
Moth larva0
Starfish0
Anemone0


If You look at value e^pi/2=4,810................ The coincidence is quite interesting. One would say that dimensionality e^pi/2 would be ideal, as it would mean perfect value h(e^pi/2) = - i . Could it be that this fractal dimension shows the result of starting with e.g -i and taking infinite roots of it - kind of opposite operation of infinite exponetiation?if we start with - i and If You achieve 4,81...- perfect. 4,85 is a slight overshoot. The same happens, if one start with i - only pure infinite tetration backwards leads to e^pi/2. Opposite conjugate values, the same consciousness- 2 sexes?

Or if we start with 4,85 and perform infinite tetration, the result will have both imaginary close to -i component and a small Real one.
In infinite tetration h(z) , if z>=4,85> 4,81...=e^pi/2, real part of h(z) becomes negative. So there is a clear phase transition division line between humans and the rest.

If z<4,81 ( dogs and the rest), real part of h(z) is POSITIVE, and becomes bigger while imaginary gets bigger as well as z gets smaller. I have attached a curves by Gottfried Helms /Andydude where it is clearly visible.

http://math.eretrandre.org/tetrationforu...php?aid=78
http://tetration.itgo.com/up/selfroot-real-zeros.png
http://go.helms-net.de/math/tetdocs/Real...emboss.png


As z gets smaller, we move to the right along the curve- at z =b=3 (Minnow) Real part of h(3) is already +0,24.

Interestingly, due to properties of infinite tetration, it converges ( h(b) imaginary part becomes 0) when b< e^(1/e) = 1,444668. So there is another phase transition- infinite tetration of numbers below that does not lead to emergence of imaginary component- so no consciousness. Crayfish has b=1,65, and after that everything is 0. No consciousness.

Other interesting conclusion from this exercise could be the meaning of numbers. Essentially, these numbers represent some dimensionality in phase space of some complex non-linear process - and not at all simple points on the real line.

I think the number of meaningful variables/dimensions involved is much bigger, since to reach i from 4,81 ... You need to perform infinite number of infinitesimal operations.

Here in this forum Gottfrieds Im(s)=0 for s>e^(1/e) and its variations are well known, so obviously there is much more in it, but at main value level things seem reasonable. Weaving the Web of life, I would call the full graph with branches, as it resembles a spider.


How could it be easily checked if there exist a relation between tetration and chaos dynamics, fractal dimensions authors mention in the text? Most likely there is connection, since tetration anyway is a missing operation, but probably not well known, these connections are.

Best regards,

Ivars Fabriciuss
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Messages In This Thread
Applications of Tetration - by andydude - 01/01/2008, 05:57 PM
RE: Applications of Tetration - by Ivars - 01/02/2008, 08:36 PM
RE: Applications of Tetration - by andydude - 01/03/2008, 09:25 AM
RE: Applications of Tetration - by Ivars - 01/03/2008, 11:55 AM
RE: Applications of Tetration - by Ivars - 01/12/2008, 11:48 PM
RE: Applications of Tetration - by bo198214 - 01/19/2008, 09:01 AM
RE: Applications of Tetration - by Ivars - 01/20/2008, 08:32 AM
RE: Applications of Tetration - by andydude - 01/20/2008, 09:40 AM
RE: Applications of Tetration - by andydude - 01/20/2008, 09:50 AM
RE: Applications of Tetration - by Gottfried - 01/20/2008, 01:35 PM
RE: Applications of Tetration - by GFR - 01/20/2008, 04:46 PM
RE: Applications of Tetration - by andydude - 01/22/2008, 05:02 AM
RE: Applications of Tetration - by GFR - 01/22/2008, 11:45 AM
RE: Applications of Tetration - by andydude - 01/22/2008, 07:19 PM
RE: Applications of Tetration - by GFR - 01/23/2008, 03:00 PM

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