Toward a Coupled Oscillator Model of the Mechanisms of Universal - - PowerPoint PPT Presentation
Toward a Coupled Oscillator Model of the Mechanisms of Universal Evolution and Development Georgi Georgiev Worcester Polytechnic Institute, Assumption College and Tufts University Work with Thanh Vu, from Assumption College and Atanu
Georgi Georgiev
Worcester Polytechnic Institute, Assumption College and Tufts University Work with Thanh Vu, from Assumption College and Atanu Chatterjee and Germano Iannacchione from WPI
By Carl Sagan
By Ray Kurzweil
By Eric Chaisson
By Eric Chaisson
By Ray Kurzweil
ij
ij dt
t1 t2
ij
ij nm
Q = Iij
ij nm
h
200 400 600 800 1000 1020 1040 1060 1080 10100
time Log(φ)
= e Q=Q e = e
t t t τ β δ
α α φ φ
Q
γ µ
α ηφ φ χ = =
2 4 6 8 10 12 14 x 10
810
410
510
610
710
810
910
1010
1110
12Time [sec] Flow
Quantity Quality α Q + + FERD +
11 12 13 21 22 23 31 32 33
= + Q + Q= + Q+ = + Q+ a a a a a a a a a α α φ α φ φ α φ ɺ ɺ ɺ
Φ
12 13 31 32
Q + = + Q a a a a φ α φ α ɺ ɺ
If α or φ stops increasing,
changes in the same direction.
Data for CPUs since 1971 (closed circles) and an exponential fit (solid line). The transition from single to multicore processors around time 109[sec], does not affect the trend. α and Q do not increase smoothly but in steps.
2 4 6 8 10 12 14 x 10
8
10
10
10
10
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10
Time [sec] Alpha
An edge in this system is defined to be one computation. To calculate α, the potential energy of the electrons was taken to be constant. The Lagrangian was then calculated using the kinetic energy. The data for Million Instructions Per Second (MIPS) for each processor was divided by the thermal design power and multiplied by the table value of the Planck’s constant, to solve for α.
2 4 6 8 10 12 14 x 10
8
10
32
10
33
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Time [sec] Total number of quanta
Data for α and Q (closed circles) and an power law fit (solid line) with variations around the average.
10
32
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36
10
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Alpha Total number of quanta
(FERD) as a function of t (time). The data are from 1982 starting with Intel 286, to 2012.
Data are filled circles and solid line is the fit. The data are from 1982 starting with Intel 286, to 2012, ending with Intel Core i7 3770k. There is a good agreement between the data and a power law fit.
Quantity Quality
α Q + +
+ N +
Number
200 400 600 800 1000 1020 1040 1060 1080 10100
time Log(N)
2 4 6 8 10 12 14 x 10
810
310
410
510
610
710
810
910
10Time [sec] Transistor count
= e Q=Q e = e = e
t t t t
N N
τ β δ ε
α α φ φ
N N N Q
γ λ ψ
α η φ ω σ = = =
Atoms Molecules Particles Organisms Civilization Future Time Ln(Interfunction) Exponential growth
Death – plastic limit Disease – elastic limit Fh
+
Fh
+
Fh
f2 f3 fn ……..
,
h j j H
H H
3 1 2
,0 , , ,0
c t c t c t h j j H j H j j j ct
0.0 2.0x10
8
4.0x10
8
6.0x10
8
8.0x10
8
1.0x10
9
1.2x10
9
1.4x10
9
Ln(Alpha) time (sec)
Logarized fit: y = A + B*t + ln(C*exp(M*t) + D*cos(G*t*exp(H*t) + K)) H ΔH A T
3 1 2
,0
c t c t c t j j
Amplitude (A) is increasing and frequency (f=1/T) is increasing. The max deviation from the dynamic equilibrium exponential line (Homeostasis) – is the limit of elasticity of those Interfunctions, i.e. the homeostatic Limits. If the interfunctions deviate more from their Homeostatic values, the system destabilizes and falls apart. H ΔH A T
By Kurzweil
Neural System. Phase plot. Network activity versus connectivity for
solution with infinite n, whereas the transition appears in finite systems at slightly higher values of the control parameter n and is smoothed out over a small interval.
http://journal.frontiersin.org/article/10.3389/fnsys.2014.00166/full
Benard Cells: Convective heat Flux as a function
From Meyer et al, 1991.
JFM13c_ThermBL(Zhou)
The Evolution of Nu with Ra at different conditions.
Kaddiri-ISRN-Thermodynamis-2012
http://thebrain.mcgill.ca/flash/capsules/outil_bleu09.html
Biology – punctuated equilibrium Cultural evolution Number of tools vs time: Cultural accumulation when innovations may alter subsistence strategy, increasing biological carrying capacity and leading to an increase in population size. Red: leap innovations; Orange: toolkit innovations. Blue dots indicate the occurrence of big innovations that alter the biological carrying capacity The curve shows the number of mutation events for a single
https://ideagenius.com/the-s-curve-pattern-of-innovation- http://psyberspace.walterlogeman.com/tag/kevin-kelly/
http://www.theequitykicker.com/2017/05/31/change-the-beguiling-nature-of-exponential-curves/ http://passionateaboutoss.com/oss-s-curves/