A Fractal Topology of Time

 

 A Fractal Topology of Time

Implications for Cosmology and Consciousness Kerri Welch  

 

Topology

Subjective Time Topological Dimension = 1 Fractal Dimension = 1.238… Non-differentiable -> unpredictable at every level of scale Objective Time Topological Dimension = 1 Linear  Topological Dimension = 1  

Non-differentiable at 0, 0 Slope is undefined

 

 

Weierstrass function: fractal, continuous everywhere,

 

differentiable nowhere

 

 

Koch curve, Fractal Dimension Fractal dimension D = log n = log 4 =1.261 =1.2619 9

log s

log 3

n = number of iterations, the pattern is reiterated 4x s = scaling factor, the t he pattern is 3x smaller at the next deeper layer 

 

Logarithms make the exponential linear  Log10 1 = 0 100 = 1 Log10 10 = 1 101 = 10 Log10 100 = 2 102 = 100 ….

LODs LO Ds = Le Leve vels ls of of De Descr scrii tion tion  

Fractal Dimension = Temporal Density D = log n = # reps = learning, remembering   log s scaling factor amount memory is compressed Temporal density = repetition x attention While fractals condense information perfectly, we are subject to error in our data com compression. pression. We compress compress data based on what we remember. The less we pay attention to the smaller the memory is condensed. The greater the compression the greater the information loss. The closer the compression is to 1, the more accurate the information retention.  

 

Susie Vrobel’s Fractal Time • Fractal Dimension = Temporal Density • Temporal Depth = # of LODs • recollecting, reflecting, and learning rearranges the past within the present thereby increasing the number of levels of description, LODs, or temporal depth  • The more LODs we are juggling, juggling, the greater the depth of time, the richer the experience, and the faster time t ime seems to go • Ex. Class reunion • Information Condensation or zooming in toward the “prime” creates the progression of time  

 

Prime, Timelessness • Smallest level pattern in a fractal, lowest limiting scale • Undividable and therefore timeless • I suggest that the pattern itself, at every level of scale is timeless. • The largest pattern is the present moment and the smallest is the photon. • Time emerges from, and deepens into, timelessness.

 

 

Photon timelessness

 

 

Insight • Vrobel aligns the prime to Penrose’s concept of insight • Insight is contact with Plato’s timeless realm of ideas, the “Ah Ha!” • the gestalt, recognizing a pattern, or relating one pattern to another from the perspective of an extra dimension – timelessness. • Gödel’s theorem shows shows that there are truths that are unprovable.. For Penrose and Nottale, this is fractals and unprovable quantum mechanics • Penrose - Consciousness must use some noncomputational process to access timelessness  

 

Mandelbrot Set  

  c² + c = c 2  c22 + c2 = c3  c32 + c3 = c4 … http://www.youtube.com/watch?v=9G6uO7ZHtK8   http://www.youtube.com/watch?v=9G6uO7ZHtK8

 

Nottale’s Fractal Spacetime • 1-D macroscopic spacetime path takes on a 2-D fractal dimension microscopically • There are infinitely many fractal geodesic paths between any two points in spacetime (ST) •  A particle chooses on only ly one of the paths. • Like the boundary of the Mandelbrot set, these paths are infinitely intertwined making it is impossible to determine which path a particle chooses without measuring it. • The properties of this family of paths defines the particle’s wave function • Hence, uncertainty, uncertaint y, wave particle/duality particle/dua lity etc.  

 

Microscopic temporal reversibility

 

(Nottale 1993)

 

Penrose and Hameroff’s quantum consciousness

(Hameroff 2009b)   

 

 

Reproduced by permission of Stuart Hameroff, “What is Consciousness,” Fig. 25

Fig. 25

 

Body Temperature and Time • Higher internal body temperature -> perception of slowed time (Hoagland 1981) • Modeled with Arrhenius temp -> increased rate ofequation: chemicalIncreased interactions • Rate of memory decay modeled / same eqn. • Pyrogenic drugs often induce alteration in temporal perception (amphetamines, cocaine, LSD and MDMA)

 

 

Dopamine as Clock Watcher  • Dopamine increases rate of looping through basal ganglia’s neural circuit, regulates entrainment with frequencies frequencie s of the external world • Dopamine decreases with time age: slowing internal clock, perceived increase in ext. • Dopamine deficit - (time estimation impairment) - ADHD, lack of entrainment, Ritalin boosts dopamine -from schizophrenia and amphetamine intoxication benefit blocking Dopamine   - Parkinsons, catatonia - experience of timelessness

 

 

Expanded Moment

 

 

Dopamine says Pay Attention! •  Attentio  Attention n as entra entrainment inment

 

 

Intention • desired time is inversely proportional to experienced time • Dopamine/Prolactin Dopamine/Prolactin - mutually inhibitive   desire/satisfaction   time/timelessness

 

 

• Time savoring vs. time saving techniques • Omnigenetic temporality

 

 

References •

Hameroff, Stuart. 2009b. What is consciousness? www.quantumconsciousness.org/ www.quantumconsciousness.org/presentations/whatisconsciousness.html presentations/whatisconsciousness.html (accessed Feb. 3, 2009).

•

Nottale, 1993. Fractal spacetime and microphysics: Towards a theory ofLaurent. scale relativity. New relativity.  New Jersey: World Scientific.

•

Penrose, R. 1989. Emperor’s new mind: Concerning computers, minds, and the laws of physics. New York: Oxford University Press.

•

Penrose, R. 1994. Shadows 1994. Shadows of the mind: A search for the missing science of consciousness. New York: Oxford University Press.

•

Vrobel, Susie. 1998. Fractal time. Houston, time. Houston, Texas: The Institute for  Advanced Interdisciplinary Interdisciplinary Research.