The Hixon Symposium

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The Hixon Symposium 1948

• This was symposium on cognitive science not
  computer architecture
• So, why are we reading it?
• Were reading it due to the stature of John von
  Neumann in the computer architecture arena
• Were reading it because we must understand
  something about computation if we are to
  understand computer architecture
• The human brain is the best computer architecture
  around yet the least well understood

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Why von Neumann?

• von Neumanns presence was many-fold
• Interest/expertise in artificial automata
  (computing machines) and the similarity to the
  brain
• Interest in self-replicating systems
• He hoped to gain an understanding of the human
  brain to drive the direction of computer
  architecture development
• He hoped that through the study of artificial
  automata new insights could be gained regarding
  the structure/operation of the human brain

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von Neumanns Goal

• von Neumanns goal was to draw an analogy between
  artificial automata and natural organisms through
  the eyes of a mathematician
• His approach is that of divide-and conquer
  understand the elementary units then understand
  how the function as a whole
• He then proceeded to write off the elementary
  units and accept them as black-boxes that
  receive an input and deterministically produce an
  output The Axiomatic Procedure

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What is Artificial Automata?

• Artificial Automata Computing Machine
• Long chain of events within a computing machine
  Program

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Fixation on Multiplication

• Multiplication as the gauge
• Use of a computing machine was determined by the
  number of multiplications required by the
  computation computers are only justified for
  problems requiring one million or more
  multiplications
• Difference between organic systems and artificial
  automata is that organic systems can be inexact
  yet still arrive at a correct answer. Artificial
  automata must perform every step flawlessly or
  errors may occur
• Consider what happens if an LSB is flipped
• Consider what happens if an MSB is flipped

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Two Types of Computers

• Analogy (analog)
• Either electrical or mechanical (rotating discs
  with angle of rotation representing the analog
  value)
• Inherently inaccurate (noisey) (The Analogy
  Principle)
• Use statistics to gain accuracy/reduce the
  effects of noise (improve signal-to-noise ratio
  where noise are error-prone calculations)
• Consider averaging noisy samples
• Noise is reduced as the square root of the number
  samples averaged mathematical proof exists

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Differential Analyzer

• MIT 1930s Vannevar Bush
• First well integrated analog computer
• Rods and wheels
• Solved differential equations

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Two Types of Computers

• Digital
• At the time machines were decimal all digital
  machines built to date operate in this system
• Prediction the binary (base 2) system will, in
  the end, prove preferablenow under construction
• ENIAC was completed in 1945 mathematical table
  generator based on decimal data
• EDVAC came afterwards programmable machine
  based on binary data
• Perfectly accurate so long as components work as
  designed (The Digital Principle)

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ENIAC

• First large-scale electronic digital computer

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Two Types of Computers

• Digital
• Inaccuracies arise due to limitations of word
  size similar to those of the analogy principle
• Use more bits to gain accuracy/reduce the effects
  of noise (improve signal-to-noise ratio where
  noise is round-off error)
• This is why digital computation may be considered
  more powerful than analog
• Clearly depends on ones definition of powerful

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Artificial Automata vs. Organic Processing

• Organic contains both digital and analog
  processing
• Neuron firings (outputs) are all-or-none
  computations (threshold)
• Technically speaking they are analog but when
  viewed as a black-box they act digital
• Internal to the neuron is a chemical humoral
  (analog) process
• Artificial automata are purely digital (although
  analog machines existed von Neumann did not
  consider them in this context)
• Technically speaking the vacuum tubes of the day
  (and the ICs of today) are analog but when viewed
  as a black-box they act digital

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Vacuum Tubes(for those too young to remember)

• Vacuum Tube

• Nixie Tube

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Artificial Automata vs. Organic Processors

• The digital nature of the both the neuron and the
  vacuum tube/IC is a form of Abstraction (which is
  good for us Computer Scientists)
• Both use switching organs
• Analog ? neuron
• Digital ? mechanical relay or vacuum tube

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Some Predictions

• It is quite possible that computing machines
  will not always be primarily aggregates of
  switching organs, but such a development is as
  yet quite far in the future.
• A development which may lie much closer is that
  the vacuum tubes may be displaced from their role
  of switch organs in computing machines. This,
  too, however, will probably not take place for a
  few years yet.

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Some Factual Statements

• To sum up, about 104 switching organs seem to be
  the proper order of magnitude for a computing
  machine. In contrast to this, the number of
  neurons in the central nervous system has been
  variously estimated as something of the order of
  1010.
• The implication being that the number of
  switching organs is the primary drawback but we
  know that algorithms (or lack thereof) are
  another sticky wicket.

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Some Beliefs

• Didnt believe that speed was an issue since
  neurons are relatively slow compared to vacuum
  tubes (and todays ICs.)
• Physical comparisons between the ENIAC and the
  human brain
• 30 tons vs. 1 pound
• Regenerative nature of the organic systems (able
  to repair themselves.)
• Inability of artificial automata to do so

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Conclusion

• Inferiority of materials used in artificial
  automata is the primary culprit.
• If we had better raw materials to work with then
  we could build an artificial automata that could
  mimic the behaviors of organic processors

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Limiting Factors on Artificial Automata

• Complication of organic systems
• We dont fully understand them
• We can physically build anything nearly as
  complex
• Available materials and knowledge of how to use
  them

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Limiting Factors on Artificial Automata

• Lack of a logical theory of automata
• Turing proved that anything that can be described
  algorithmically can be computed in a finite
  number of steps
• But, current machines wont work because of
  component failures
• Algorithms must be made fault tolerant (ref.
  signal-to-noise discussion, above)
• Nature does this by making the effect of the
  failure unimportant (distributed representation)
• Artificial automata must deal with the failure
  immediately

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Limiting Factors on Artificial Automata

• Method of data representation
• Organic systems tend to represent data as a
  temporal form e.g. counting over time
• Artificial automata tend to represent data as a
  spatial form e.g. the binary number system

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Limiting Factors on Artificial Automata

• Fault tolerance
• Organic systems tend to minimize the importance
  of isolated errors
• In many cases they are self-correcting
• Artificial automata tend to be hindered by
  isolated errors and disabled by multiple errors
• They must be detected as soon as they occur so as
  to not adversely affect later results

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Limiting Factors on Artificial Automata

• Intellectual inadequacy we just dont know how
  to do it!
• McCulloch-Pitts tied Turings work to artificial
  neural networks
• That is, if you can describe it, we can implement
  it with Artificial Neural Networks (formal
  neural networks)
• The underlying problem is the specification of
  the algorithm!!!
• von Neumann alludes to training a pattern
  recognizer through the phrase complete
  catalogue but admits the size is prohibitive
• Does this contradict the definition of computer
  that says the answers are not stored in the
  system?

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Limiting Factors on Artificial Automata

• Conclusion
• McCulloch-Pitts work is important but does not
  get us to an intelligent machine

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The Turing Machine

• The ultimate computer architecture

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Self Replicating Machines

• von Neumann then proceeds to discuss machines
  that can create copies of themselves as a means
  for discussing complexity
• Must the building machine be more complex than
  the one being built?
• His goal was to further the study of automata

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So, Why was von Neumann at a Conference on
Cerebral Processing?

• reflects merely the present, imperfect state of
  our technology a state that will presumably
  improve with time
• This is why we study computer architecture.
• To come up with an artificial automata that will
  get us closer to that of an organic processor!