Hcfyk

Are these the same?

The image will be sheared such that the x-axis goes through (1,1).

The image will be sheared so that the x-axis goes through (1,1).

I think I have usually seen the former, I didn't even know that “so that” is allowed in English until I once saw it in a text from a (as I assume) native English speaker.

Simon

The sentences, while very similar, do have a subtle difference of meaning.

"Such that" is a description of HOW something is to be done:

The image will be sheared such that the x-axis goes through (1,1). -> The image will be sheared in such a way that the x-axis goes through (1,1).

"So that" is a description of WHY something is to be done:

The image will be sheared so that the x-axis goes through (1,1) -> The image will be sheared in order for the x-axis to go through (1,1). (Or, more obviously: Because the x-axis needs to pass through (1,1), the image will be sheared appropriately.)

This distinction criterion is very simple and always works: 'such that' expresses consequence, 'so that' purpose.

I think that 'such that' should refer to a subject noun or pronoun. It is often stretched these days like in example 1, where it is lost upon the reader that it is the image that is such that... at least a comma after 'sheared' could help.

Still, it would be good style to avoid 'such that' without clear subject, just like 'so that' would not be appropriate without a verb.

I would say “ The image will be sheared such that the x-axis goes through (1,1)” but, as indicated by Hellion, would keep the other construct to express some higher-level aim: “ The image will be sheared so that it is clearer”.

"Such that" is idiomatic mathematical jargon most often used in the definition of mathematical objects. The usage in your example is a bit atypical. The phrase is difficult to directly gloss, but one possible rendering for the phrase as it is used in definitions is "...for which it is true that..."

For example, we define a rational number as "any p/q such that p and q are integers and p≠0," we've established that if there are two integers that can be divided by one another to produce a given number, then that number is rational.

Your example is a bit different, because it isn't directly defining a mathematical object, but rather describing a transformation on a mathematical object. (Some branches of mathematics would allow you to define transformations as objects, but that isn't what's being done here.)

By contrast, the phrase "so that" is not mathematical jargon; it's a common-use phrase that indicates the intent or result of some action or condition. Consider the following examples:

• "I drank coffee so that I could stay awake."


• "I drank coffee such that I could stay awake."

These sentences are very different! The former sentence is saying that your reason for drinking coffee was to stay awake -- in order to stay awake, you drank coffee. The latter sentence is describing the coffee, not your action of drinking the coffee, saying that it's coffee that you drank before a period of time when you were able stay awake, and suggesting that the coffee had something in it that kept you awake.

Note also that the meaning of the sentence changes yet again when a comma is added as follows:

• "I drank coffee, such that I could stay awake."

In this case, the phrase "such that" is modifies the entire clause in a similar manner to "so that", except it describes the result of your action of drinking the coffee rather than your reason for drinking the coffee. For one reason or another, you drank coffee, and because you drank that coffee, you were able to stay awake. If you ever see the phrase "such that" used outside of mathematics, it will probably be used like this: following a clause, separated from that clause by a comma, and describing the result of whatever's happening in that clause. Your example seems to be using the phrase in this sense, such that the sentence should probably have a comma between "sheared" and "such that".

In particular, this usage often connotes extent, i.e., that the preceding clause is true to an extent that results in whatever's going on in the following clause -- you drank enough coffee to stay awake. This connotation is especially strong if the preceding clause uses some word or phrase that itself describes extent, as in "I drank lots of coffee, such that I could stay awake."