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The Hixon Symposium – 1948

• This was symposium on cognitive science – not computer architecture

• So, why are we reading it?– We’re reading it due to the stature of John von

Neumann in the computer architecture arena– We’re 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 Neumann’s 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 Neumann’s Goal

• von Neumann’s 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 preferable…now 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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• First large-scale electronic digital computer

ENIAC

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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 one’s 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

• Didn’t believe that speed was an issue since neurons are relatively slow compared to vacuum tubes (and today’s 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 don’t 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 won’t 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 don’t know how to do it!• McCulloch-Pitts tied Turing’s 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

Read/WriteState

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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!