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The Hixon Symposium

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Title: The Hixon Symposium


1
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

2
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

3
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

4
What is Artificial Automata?
  • Artificial Automata Computing Machine
  • Long chain of events within a computing machine
    Program

5
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

6
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

7
Differential Analyzer
  • MIT 1930s Vannevar Bush
  • First well integrated analog computer
  • Rods and wheels
  • Solved differential equations

8
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)

9
ENIAC
  • First large-scale electronic digital computer

10
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

11
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

12
Vacuum Tubes(for those too young to remember)
  • Vacuum Tube
  • Nixie Tube



13
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

14
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.

15
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.

16
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

17
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

18
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

19
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

20
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

21
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

22
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?

23
Limiting Factors on Artificial Automata
  • Conclusion
  • McCulloch-Pitts work is important but does not
    get us to an intelligent machine

24
The Turing Machine
  • The ultimate computer architecture

25
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

26
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!
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