Showing posts with label 1/f. Show all posts
Showing posts with label 1/f. Show all posts

14 Jun 2009

Even While Men’s Minds are Wild?; Bostrom and Sandberg's Brain Emulation, Examined and Critiqued. Section 5


by Corry Shores
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[The following is tentative material for my presentation at the Society for Philosophy & Technology Conference this summer.]




Corry Shores


Do Posthumanists Dream of Pixilated Sheep?

Bostrom and Sandberg's Brain Emulation,

Examined and Critiqued


Section 5:


Even While Men’s Minds are Wild?



Neural noise can result from external interferences like magnetic fields. Or internal random fluctuations might make the signals unpredictable. (Ward 116-117) In both cases, chance & chaos reign our brains. According to Steven Rose, our brain is an “uncertain” system on account of “random, indeterminate, and probabilistic” events that are essential to its functioning (Rose 93). Alex Pouget and his research team recently found that the mind's ability to compute complex calculations has much to do with its noise. The word noise is misleading, he says, because it implies something goes wrong. But these unpredictable irregularities are the mind’s way of running at optimum performance. Our mind produces noisy signals to represent the uncertainty of the world around us. Pouget explains,

if we want to do something, such as jump over a stream, we need to extract data that is not inherently part of that information. We need to process all the variables we see, including how wide the stream appears, what the consequences of falling in might be, and how far we know we can jump.

In this way, the brain is flooded with countless variables. And the neurons transmit various signal patterns for the same stimulus. This allows us to estimate margins of error. We then use a probabilistic inference to make what is most likely to be the best decision. (Pouget, interview with Science Daily) So we might jump the stream, if probably we can cross it, even though we can never be certain about such matters.

Some also theorize that noise is essential to the human brain’s creativity. Johnson-Laird claims that creative mental processes are never predictable. (Johnson-Laird, The Computer and the Mind 256) He hypothesizes that we could make a machine creative by programming it to alter its own functioning according to generated random variations. (Human and Machine Thinking, 119-120) This would produce what Ben Goertzel refers to as “a complex combination of random chance with strict, deterministic rules.” (Goertzel 119) And according to Daniel Dennett, this indeterminism is precisely what endows us with what we call free will. (Dennett 295, cited in Dartnall 37) Likewise, Bostrom & Sandberg suggest we introduce random noise into our simulation by using pseudo-random number generators. They are not truly random, because eventually the pattern will repeat. But if it takes a very long time before the repetitions appear, then probably it would be sufficiently close to real randomness (Bostrom & Sandberg 38-39). Also, there might be random variations that are hidden to our observations, and thus would not be properly represented in the simulation. They recognize the profound difficulty in incorporating true randomness or hidden variables into the simulation. Yet they believe these sorts of randoms most likely will be unnecessary for whole brain emulation.

But perhaps there is more to consider. Lawrence Ward reviews findings that demonstrate neural noise is pink noise, or what is called 1/f noise. (Ward 145-153, citing research by Lundström and McQueen, and Novikov, Shannonhoff-Khalsa, Schwartz, and Wright) On account of its fractal nature, 1/f noises are always parts of similar larger-orders of variation happening on much longer time-scales. We might have to wait weeks or months to see larger-scale variations that were varying the randomness of the more local noisy events. (Anderson & Mandell 78-79) These are what Gregory Bateson calls metarandom variables. They are hidden to us, because we never see the whole picture (Bateson Steps to an Ecology 418). It’s why live lobsters never notice their cooking water gradually increase to boil (Mind and Nature 109). They only notices alterations on a local level, so nothing really seems to be changing. In a similar way, if all we are observing is randomness on a smaller scale, we might be missing the larger scale variations. It would be like randomly adjusting a radio to pick up different bands of radio static. If all we knew was the randomness of radio static at each moment, we might not also notice the higher order randomness that varies the lower one that we are listening-to. Because these uncontrollable unpredictabilities are essential to all the random changes happening around us, Bateson calls them wild variables. (Mind and Nature 49-50)

Perhaps it is for similar reasons that Benoit Mandelbrot classifies 1/f noise under what he terms “wild randomness” and “wild variation.” (Mandelbrot The (mis)Behavior of Markets 39-41) This sort of random might not be so easily simulated. Mandelbrot gives two reasons for this.

1) In wild randomness, there are events that defy the normal random distribution of the bell curve. He cites a number of stock market events that are astronomically improbable. But such events in fact happen quite frequently in natural systems despite their seeming impossibility. There is no way to predict when they will happen or how drastic they will be. (The (mis)Behavior of Markets 4)

2) Each event is random and yet it is not independent from the rest, like each toss of a coin is. One seemingly small anomalous event will echo like reverberations at unpredictable intervals into the future. (The (mis)Behavior of Markets 181-185)

For these reasons, he considers wild variation to be a qualitatively different state of indeterminism than the usual mild variations we encounter at the casino. For, there is infinite variance in the distributions of wild randomness. Anything can happen at any time (Mandelbrot, Fractals and Scaling 128). He says, “the fluctuation from one value to the next is limitless and frightening.” (Mandelbrot (mis)Behavior of Markets 39-41) This is the wildness of our brains.

Paul Shepard considers our minds to be wild in an even more literal sense: we are wild animals. He distinguishes tameness from domestication. Cows are domesticated. They have been bred to suit our needs. And now their genes would probably not prepare them to live in the wild without human protections. But the human species has merely been tamed by culture and not domesticated like cows. Genetically, we are still the same wild creatures who hunted the Pleistocene savannas. So to emulate the human brain is to simulate the workings not of a rational machine, but of a wild animal. (Shepard 132-133) He writes, “The savage mind is ours! ... as a species we have in us the call of the wild.” (143)

Shepard’s characterizes the wild, like Bateson and Mandelbrot do, as being too complex for any simulation. But he offers his own theory to explain why. He notes the fractal nature of reality. Within every scale is another smaller scale, and so on to infinity. He says that every layer of complexity operates according to deterministic principles. But, there is no lowest level of complexity. Hence there is no way to get to the bottom of what is happening now. It’s turtles all the way down. Thus there is no way to fully understand why things are the way they are now. And thus we can never know how things will be in the future. (146-147)


But let’s suppose that the brain’s wild randomness can be adequately simulated. Will brain emulation still attain its fullest success of perfectly replicating a specific person’s own identity? Bostrom & Sandberg recognize that neural noise will prevent precise one-to-one emulation. However, they think that the noise will not prevent the simulation from producing meaningful brain states (
Bostrom & Sandberg 7). But to pursue further the personal identity question, let’s imagine that we want to emulate a certain slot machine. A relevant property is its unpredictability. Consider these two possibilities. 1) We set the original and the simulation to the same starting position. We give both handles a number of pulls. Each time, they both show the same outcomes, because we replicated the mechanics perfectly. But then, we cannot say that we have preserved its relevant essential property of being unpredictable. For, we can just run the simulator by itself and that will predict the original’s future outcomes. Or, 2) instead the emulation produced its own different random series of outcomes. Then in fact we would be replicating the original’s property of unpredictability.

The problem is that the brain’s 1/f noise is wildly random. So suppose we emulate some person’s brain perfectly. And suppose further that the original person and her emulation have an identity merger where each one thinks they are talking to their very own selves when really they are talking to the other. They confuse themselves with one another. They are completely aware of what is in the other’s mind at that first moment, because they can tell it is the same as what is in their own mind. And suppose further that the original person loses her fear of death, knowing that something she cannot distinguish from himself will carry on after her body dies. But if both minds are subject to wild variations, then their consciousness and identity might come to differ more than just slightly. They could veer-off wildly. The original person and her emulation might become so mistrustful of each other, that they want to end the other’s existence.

So we might need to emulate this wild neural randomness. But that seems to remove the possibility that the emulation will continue on as the original person. Perhaps our very effort to emulate a specific human brain results in our producing an entirely different brain altogether.


[Next entry in this series.]


Anderson, Carl M. & Arnold J. Mandell. Fractal Time and the Foundations of Consciousness: Vertical Convergence of 1/fPhenomena from Ion Channels to Behavior States. in Fractals of Brain, Fractals of Mind. Ed. Earl Mac Cormac & Maxim I. Stamenov. Amsterdam: John Benjamins Publishing Company, 1996. More information and limited preview available at: http://books.google.be/books?id=WdERazd7Ik4C&hl=en


Bateson, Gregory. "Effects of Conscious Purpose on Human Adaptation." in Steps to an Ecology of Mind. London: Granada Publishing, 1972. . More information and limited preview available at: http://books.google.be/books?id=FQvfqk31zFQC&hl=en


Bateson, Gregory. Mind and Nature: A Necessary Unity. London: Fontana, 1979. More information available at: http://books.google.be/books?id=aQtHAAAAMAAJ&hl=en&pgis=1


Sandberg, A. & Bostrom, N. (2008): Whole Brain Emulation: A Roadmap, Technical Report #20083, Future of Humanity Institute, Oxford University. Available online at:http://www.fhi.ox.ac.uk/Reports/2008-3.pdf


Dartnall, Terry. "Introduction: On Having a Mind of Your Own." in Artificial Intelligence and Creativity: An Interdisciplinary Approach. Ed. Terry Dartnall. Dordrecht: Kluwer Academic Publishers, 1994. More information and limited preview available at: http://books.google.be/books?id=4phC9RwvC8YC&hl=en


Dennett, Daniel. Brainstorms. Hassocks: Harvester Press, 1978. More information available at: http://books.google.be/books?id=s3V-AAAAMAAJ&hl=en&pgis=1


Goertzel, Ben. Chaotic Logic: Language, Thought, and Reality from the Perspective of Complex Systems Science. London: Plenum Press, 1994. More information and limited preview available at: http://books.google.be/books?id=zVOWoXDunp8C&hl=en

Johnson-Laird, R. N. The Computer and the Mind: An Introduction to Cognitive Science. Cambridge: Harvard University Press, 1988. More information and limited preview available at: http://books.google.be/books?id=Tf5gRFgVuegC&hl=en


Johnson-Laird, Philip. Human and Machine Thinking. London: Lawrence Erlbaum Associates, Publishers, 1993. More information and limited preview available at: http://books.google.be/books?id=sPbdQjtkIhkC&hl=en


Mandelbrot, Benoit B., & Richard L. Hudson. The (mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward. New York: Basic Books, 2004. More information available at: http://books.google.be/books?id=DPwBTj99a7UC&hl=en


Science Daily. "Mysterious 'Neural Noise' Actually Primes Brain For Peak Performance." Nov. 13, 2006. Available online at: http://www.sciencedaily.com/releases/2006/11/061112094812.htm


Shepard, Paul. Coming Home to the Pleistocene. Washington, D.C.: Island Press, 1998. More information and limited preview available at: http://books.google.be/books?id=5b18NqLB8LMC&hl=en


Ward, Lawrence M. Dynamical Cognitive Science. London: MIT Press, 2002. More information and limited preview available at: http://books.google.be/books?id=g1ZMAoWGYesC&hl=en


Also mentioned:

(Lundström and McQueen, 1974, "A proposed 1/f noise mechanism in nerve cell membranes," Journal of Theoretical Biology, 45, 405-409).


(Novikov E., A. Novikov, Shannonhoff-Khalsa, Schwartz, and Wright, 1997, "Scale-similar activity in the brain," Physical Review E, 56, R2387-R2389,)



12 May 2009

1/f Noise Characterized and Long-term Fractal Layers Described, in Anderson & Mandell, in Fractals of Brain, Fractals of Mind


by Corry Shores
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1/f Noise Characterized and Long-term Fractal Layers Described


Anderson & Mandell

Fractal Time and the Foundations of Consciousness

in

Fractals of Brain, Fractals of Mind


In 1/f noise,

Big events are less frequent than little events. "Twice as big occurs half as often." In general, 1/f noise is fractal with respect to time, because the same process "[...] pshsh, ktshs, pdk, kshsh [...]" occurring on one timescale, say microseconds, is identical to a "[...] pshsh, ktshs, pdk, kshsh [...]" occurring on another timescale of say minutes. Press (1978) describes these bunched clustering, correlated patterns as manifesting a primitive form of memory:
[there is] indirect evidence that the flicker noise in a carbon resistor, say, gives rise to fluctuations [in atomic clocks] coherent over times as long as 10^6 seconds. This is quite fantastic! How does the resistor remember over a period of weeks or months that it is in an 'up' fluctuation? (Press 1978:109)
(Anderson & Mandell 78-79)


Anderson, Carl M. & Arnold J. Mandell. Fractal Time and the Foundations of Consciousness: Vertical Convergence of 1/f Phenomena from Ion Channels to Behavior States. in Fractals of Brain, Fractals of Mind. Ed. Earl Mac Cormac & Maxim I. Stamenov. Amsterdam: John Benjamins Publishing Company, 1996.


Wild Random 1/f Noise in the Human Brain, in Ward, Dynamical Cognitive Science


by Corry Shores
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Wild Random Brain Noise



Lawrence M. Ward

Dynamical Cognitive Science


We previously noted that for Benoit Mandelbrot, there is a certain kind of noise pattern, 1/f, that he classifies as "wild randomness." It is wild, because "anomalous" erratic events in fact are frequent yet still totally unpredictable. We now discuss research that suggests our brains function in accordance with such wild 1/f noise.


Ch 15
Colored Noise


[1/f Noise has a -1 line (down one, over one).]

Noise with this spectral "shape" is called "pink noise" because it is dominated by relatively low frequencies, but has some higher frequencies in it — just as light that appears pink to human eyes is dominated by low-frequency (long-wavelength) photons in it. As the supposed signature of a very interesting type of dynamical system called a "complex system," pink noise has proved notoriously difficult to explain. I will have more to say about complex systems, but for now it suffices to point out that, wherever pink noise appears, it is reasonable to look for other exotic phenomena, even in some cases the one called "chaos." (126b-c)


Ch. 16
1/f Noise in the Brain


The neuron's instantaneous rate of firing (i.e., of generating action potentials) is the dimension usually considered to encode the information, but more recently the time interval between successive pulses has also been suggested as an encoding dimension (e.g, Singer, W., 1999, "Neuronal Synchrony: A versatile code for the definition of relations?" Neuron, 24, 49-65.) Also, synchrony between the firing rates of several neurons in a network is supposed to be important, possibly as a solution to the "binding problem" of cognitive neuroscience. Of course because it will be affected by the ever present noise, the transmission of information by neurons cannot be completely precise. The noise will manifest itself in changes in the rate with which action potentials are generated by the neuron, and possibly in changes in the speed with which each one propagates down the axon. The noise arises from sources such as fluctuations in the ionic concentrations inside and outside the axon and other "channel noise" (White, Rubenstein and Kay, 2000, "Channel noise in neurons." Trends in Neuroscience, 21, 131-137.), fluctuations in the temperature of the surrounding fluids, and the decaying effects of previous action potentials received by the neuron. Some channel noise has been shown to be 1/f, probably arising from the vibration of hydrocarbon chains in the lipids in the nerve cell membrane affecting conductance of potassium ions through the membrane (Lundström and McQueen, 1974, "A proposed 1/f noise mechanism in nerve cell membranes," Journal of Theoretical Biology, 45, 405-409). The effect of previous action potentials is perhaps the most interesting in the present context, however, because it resembles a memory or relaxation process source for 1/f noise. After each action potential is generated, the neuron experiences an absolute refractory period of about 1 msec, during which no new action potentials can be generated, and an exponentially decreasing relative refractory period of an additional several msec, during which the probability of generating new action potential gradually increases. Thus the generation of a particular action potential affects the probability of generating another one for quite some time afterwards; the neuron "remembers" its previous activity and that memory is combined with current inputs to yield current activity. (145-146c)

Musha (1981, "1/f fluctuations in biological systems," In P.H.E. Meijer, R.D. Mountain, and R.J. Soulen, Jr., eds., Sixth International Conference on Noise in Physical Systems, 1473-146. Washington, DC: U.S. Department of Commerce and National Bureau of Standards) did some provocative experiments on the effects of previous action potentials on the time encoding of information by the giant axons of the squid, the easiest of all axons to work with, extensively studied since they were discovered by J.Z. Young. First, by exciting successive actions potentials with an electrical pulse, Musha showed that the refractory period also decreases the speed of transmission of the action potential in the axon, dropping from near 25m/sec for the first excitation to near 10 m/sec for later ones. Clearly, this would affect the encoding of information, whether the instantaneous rate of firing or the inter-action potential interval were the encoding dimension. After stimulating the axon with sequences of random electrical pulses (white noise), Musha recorded time series of the fluctuations in the time density (the inverse of transmission speed) of action potentials traveling down tthe axon. The power spectra for several such time series of density fluctuations are show in figure 17.1


along with the power spectrum of the electrical pulses that stimulated the action potentials (at the bottom of the graph). Below about 10 Hz, the action potential power spectra are approximately 1/f, whereas the spectrum of the stimulating pulses in that frequency region is white (flat). Thus the neurons, the basic building blocks of the brain, themselves display 1/f noise in the foundational mechanism of information transmission, the conduction of action potentials along the axon. Interesting, Musha and Higuchi (Muscha, 1981) had demonstrated the resemblance of the fluctuations of action potential speed to fluctuations of the speed of automobiles in traffic. The 1/f fluctuations in the traffic model are attributed to the "bunching" of the cars as they are forced to slow down by their proximity to other cars, a property of a more general statistical queueing theory approach to 1/f noise first described by Bell (1960, Electrical Noise. London: Van Nostrand.) (146c-147c)

From the perspective of physics, the brain is a system with strong interactions of many degrees of freedom. It consists of perhaps 100 billion neurons, each with up to 10, 000 connections to other neurons. These connections form hierarchical (and nonhierarchical) groups, from small groups of tens of neurons to large groups consisting of entire sensory, cognitive, or motor processing areas, such as the visual cortex, with many millions of neurons. In physics, such systems are usually described by a "similarity regime," in which similar behavior is observed at several scales. Under certain conditions, a 1/f power spectrum of temporal fluctuations can arise from such a similarity regime. Novikov et al. (Novikov E., A. Novikov, Shannonhoff-Khalsa, Schwartz, and Wright, 1997, "Scale-similar activity in the brain," Physical Review E, 56, R2387-R2389,) recorded the magnetoencephalogram to establish the existence of such a regime in the human brain. (148c)

[Chart shows peaks of specific brain wave frequencies.]

More interesting are the average slopes of these power spectra, represented by the straight lines in the graphs. These lines have slopes of -1.03 and -1.19, respectively over the range 0.4 to 40 Hz, very near the -1 expected for 1/f fluctuations. Power spectra for other sensors were very similar. Moreover, taking the difference between pairs of sensors usually eliminated the peaks and yielded even more stable 1/f spectra. ... Further analyses of the data established that the scale similarity implied by the 1/f spectra was relatively "local," meaning that it extended over only limited brain areas, probably related to the shared function of those areas. Thus the spontaneous activity of functionally related chunks of the human brain exhibits 1/f noise. This finding supports the assumptions made in chapter 16 regarding the origin of the 1/f spectra in human cognition. (150 a-b)

Not only is the evoked activity of the brain 1/f, but also the noise in which the evoked activity is embedded — and which possibly characterizes the process generating that evoked activity — is also 1/f. It is clear that the human brain is characterized by 1/f noise in many activity regimes, from ion flow in neurons to activity evoked by external stimuli. The challenge now is to discover the functional implications of this fact. (153c)



Ward, Lawrence M. Dynamical Cognitive Science. London: MIT Press, 2002.
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