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The Computron and the Selectron, antediluvian ancestors of solid-state integrated circuits, were vacuum-tube versions of the microprocessor and memory chip.
were falling into place. “Exactly when we started to forget the problems for which the machine was supposed to be built and started to work in earnest on a universal computer for all problems,” Rajchman recalled in 1970, “I can’t say.”13
because of lack of computational facilities far exceeds the number in progress,
“No amount of augmentation of the staff of human computers—then around 200—would suffice,” wrote (now Captain) Goldstine in a postwar report. “It was accordingly decided … to sponsor the development of a radically new machine, the ENIAC, which if it were successful would reduce the computational time
I think back in 1944, no one knew the war would end in 1945. So funding ENIAC was to help the current short term goal
RCA declined the contract but freely contributed their expertise.
atmosphere, of course, of great fervor for the war, and nobody worried about patents or priorities.”21
exhibits submitted as evidence in the Honeywell Inc. v. Sperry Rand Corp. patent dispute,
The ENIAC was programmed by setting banks of 10-position switches and connecting thousands of cables by hand.
Data and instructions were intermingled within the machine.
The ENIAC was limited by storage, not by speed. “Imagine that you take 20 people, lock them up in a room for 3 years, provide them with 20 desk multipliers, and institute this rule: during the entire proceedings all of them together may never have more than one page written full,
“but with the mathematical nature of the problem and mistakes of the mathematicians who had designed the problem for the machine.
funny how programmers were essentially mathematicians at this point
Mauchly described it, was that “the fast memory was not cheap and the cheap memory was not fast.
One thousand pulses, about a microsecond apart, could be stored in the millisecond it took an acoustic signal to travel the length of a 5-foot “
wow. so this is not really storage but more like boomeranging
memory rather than by setting cables and switches by hand. “The idea of the stored program, as we know it now, and which is a clear-cut way of achieving a universal computer,
Eckert and Mauchly left to form the Electronic Control Company
dated May 1, 1945. As Eckert later complained, “he sold all our ideas through the back door to IBM.
Von Neumann played the invitations against one another—and against those who resisted the construction of a computer at the Institute
worked on
At a meeting of the School of Mathematics called to discuss the proposal, the strongest dissenting voice was Albert Einstein, who, the minutes record, “emphasizes the dangers of secret war work” and “fears the emphasis on such projects will further ideas of ‘
important ones. Indeed they are by definition those which we do not recognize at present because they are farthest removed from … our present sphere.”66
Gödel made the first, tentative announcement of his incompleteness results.
show that the consistency of mathematics is unprovable,” only to find out, by return mail, that Gödel had got there first.12
so Von Neumanns path was from fundamentals of mathematics, and on to computing .
Gödel set the stage for the digital revolution, not only by redefining the powers of formal systems—and lining things up for their physical embodiment by Alan Turing—but by steering von Neumann’s interests from pure logic to applied.
so Turing used Gödel s work in his 1936 paper? And what was the most helpful result of Turing saying that roughly what is noted in a few lines of logic ( code), can represent many computations . ( I'm not stating this well )
whether provable statements can be distinguished from disprovable statements by strictly mechanical procedures in a finite amount of time
maybe the implication is that computation that computers end up doing is only possible if we allow us to know what statements will be finitely solvable and which not.
So these computers were aimed at very difficult problems. And not just hello world programs.
These computers were built to understand bomb blast radius, and inspired by calculating ballistic artillery projectile targeting.
Gödel assigned all expressions within the language of the given formal system unique identity numbers—or numerical addresses
“The sentence with Gödel number g cannot be proved,” where the details of the system are manipulated so that the Gödel number of G is g.
Proposed by George Cantor in 1877, and presented in 1900 as the first of Hilbert’s twenty-three unsolved problems, the continuum hypothesis states that the set of real numbers (the continuum) is the smallest infinity whose size is larger than the set of integers,
work on the continuum hypothesis, Gödel became preoccupied with two areas of research: cosmology, as a result of having discovered a solution to Einstein’s equations that implied a rotating universe;
memory architecture, envisioned as 40 Selectron tubes each storing 4,096 bits—reduced to 1,024
“There should be some means by which the computer can signal to the operator when a computation has been concluded, or when the computation has reached a previously determined point. Hence an order is needed which will tell the computer to stop and to flash a light or ring a bell.
the early decisions architecting control logic ! that's how program lines are run one at a time. like the first operating system.
In 1675 he wrote to Henry Oldenburg, secretary of the Royal Society and his go-between with Isaac Newton, that “the time will come, and come soon, in which we shall have a knowledge of God and mind that is not less certain than that of figures and numbers, and in which the invention of machines will be no more difficult than the construction of problems in geometry.
“one could carry out the description of a machine, no matter how complicated, in characters which would be merely the letters of the alphabet, and so provide the mind with a method of knowing the machine and all its parts.”44
digital computing “the human race will have a new kind of instrument which will increase the power of the mind much more than optical lenses strengthen the eyes.… Reason will be right beyond all doubt only when it is everywhere as clear and certain as only arithmetic has been until now.
means for storing a particular word in the Selectron memory,” Burks, Goldstine, and von Neumann explained.
The 40 Selectron tubes constituted a 32-by-32-by-40-bit matrix containing 1,024 40-bit strings of code, with each string assigned a unique identity number,
Gödel’s paper on undecidability
Leibniz’s belief in a universal digital coding embodied his principle of maximum diversity:
such creation than the origin of numbers as here represented, using only unity and zero or nothing,” he wrote to the Duke of Brunswick in 1697,
does this representation issue have anything to do with Kolomogoroff's discussion of the complexity of a string as being how long a program is required to encode it? Basically, where does encoding exist in the space of programmable computers
wrote to his mother in 1961. “The idea that everything in the world has meaning is, after all, precisely analogous to the principle that everything has a cause, on which the whole of science rests.
At the end of 1938, Bigelow left Sperry and joined IBM in Endicott, New York, as their first employee with the job title of electronic engineer. “At that time, IBM was a very mechanically oriented company,
antiaircraft fire-control problem: the most intractable targeting challenge of World War II.
Wiener’s mathematics in an automatic antiaircraft fire director—dubbed the “debomber”—that was never built.
The odds favored the pilot: in 1940 only one out of about 2,500 antiaircraft shells scored a hit.
between signal and noise. Similar ideas were formalized by Claude Shannon (working in consultation with Wiener) and Andrey Kolmogorov (working independently in the Soviet Union) at about the same time.
possible trajectories (equivalent to the space of possible messages in communications theory)
circuitry to communicate coded pulses, at high speeds across noisy channels between aircraft, now faced the same problem in building electronic digital computers: how to transmit coded pulses, thousands of times per second,
“I remember sitting in my classes,” he recalls, “sketching out adders rather than paying any attention to quantum mechanics.”29
Von Neumann wanted to know how everything worked, but he left it to the engineers to make it work.
piece of advice for us: not to originate anything.
