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Now, the reason that we think computer science is about computers is pretty much the same reason that the Egyptians thought geometry was about surveying instruments. And that is, when some field is just getting started and you don't really understand it very well, it's very easy to confuse the essence of what you're doing with the tools that you use. And indeed, on some absolute scale of things, we probably know less about the essence of computer science than the ancient Egyptians really knew about geometry.

Well, what do I mean by the essence of computer science? What do I mean by the essence of geometry? See, it's certainly true that these Egyptians went off and used surveying instruments, but when we look back on them after a couple of thousand years, we say, gee, what they were doing, the important stuff they were doing, was to begin to formalize notions about space and time, to start a way of talking about mathematical truths formally.

What does it really mean they went off and used?

  • This is written in a casual tone. As far as I can report from my own experience with the colloquial use of “went off and” formations, it is meant to indicate a departure from some vague sense of strictness. In this case, it seems as though the author wants to convey that the Egyptians didn’t really care about the essential principles of geometry when they used surveying instruments—they just hauled off and used them. (“Hauled off and” is a similar construction that doesn’t apply quite as well here, but could still be interesting.) – Tyler James Young Jul 8 '14 at 20:19
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Note there are hundreds of ways to use the verb "go", and quite a few different ways to use "go off", both in American and British English, of which this is only one!

This is one of the American English colloquial uses of the phrasal verb "go off", which is probably best categorized as, "go off and do-something-that-is-not-typical". In your case, formed in the past tense as "went off and did-something-that-was-not-typical".

As a first approximation, it means they "left their current location" or traveled through some relatively significant combination of space and time, and then did something that was special (or at least not-typical):

Consider the following more simple example:

"Did you hear about Johnny?"
"No! What happened?"
"He went off and got himself married!"

Above is more simply stated, "He got married." The idiomatic phrasal verb conjures an image of Johnny getting up from somewhere, going somewhere, and getting married. That isn't always intended to be absolutely literal, but rather, figurative of the effort required and, equally important, that it was a surprise that he did so. Perhaps nobody (especially the speaker and the person being spoken to) thought Johnny would get married. It certainly isn't typical for Johnny to get married. There is usually a basis for considering that some distance was traveled as well.

Consider the following common use of the phrase, followed by removal of the idiomatic structures:

Why don't you go and get yourself a job?
Why don't you go and get a job?
Why don't you get a job?

In your case sentence, "These Egyptians" refers collectively to the Egyptians over a longer period of time. They developed the science of surveying and used the instruments for practical use. Such a development collectively required some non-trivial movement and effort.

See, it's certainly true that these Egyptians went off and used surveying instruments. (Original)

See, it's certainly true that the Egyptians expended time, energy, and travel to use surveying instruments in ways both practical and novel.

A somewhat better-worded, holistic transformation of the sentence from the vernacular to the formal could be,

Of course, the Egyptians used and developed the science of using surveying instruments.

Even better holistic wordings require greater context:

What is meant by "the essence" of something, such as computer science or geometry? In the case of the Egyptians, while they certainly did forward the advancement of the science of using surveying instruments, more fundamentally, they were formalizing notions about space, time, and mathematical truths.

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To Go and.. (in speech)

Definition 1)

To do something unwisely, unexpectedly inexplicably precipitously, with insufficient or forethought.

Examples:

  • He only had his first job for a week and he **went out and got a loan for a new car.*
  • The newspaper's readership has droppped just five percent and they've already gone and sacked their eight best journalists.

Definition 2)

To take an initiative, without waiting for official orders or consultation.

  • His father lad wanted him to help run the farm but as soon as he turned 18, he went off and enrolled in medical school.

  • With her manuscript rejected down by all the best editors, she went and funded her own publishing company.

  • +1 This makes a perfect complement to my answer. While I focused on "go off and do-something", you've pointed out that the more generic phrase is "go [on | off | out | Ø] and do-something". – CoolHandLouis Jul 9 '14 at 15:12
  • Are you referencing some dictionary? – CoolHandLouis Jul 9 '14 at 15:18
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In the most simple form of explanation the use of the words "went off" signifies someone going off which also means that someone went and did something. I feel that the use in the example you shared with us is in a colloquial sense where people refer to others going and doing something through "went off" that may not have been a predictable course of action.

Example:

Jack was given specific instructions to purchase a new saddle for his horse but he went off and bought a new car.

This may not be the most suitable answer but I feel it is adequate. I look forward to contrasting opinions on my view.

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