@RegDwight's answer, which I upvoted, is very well-written–as always–and unbiased; it allows visitors to make up their own minds by showing both sides of the argument.
Is there a difference in meaning?
If one expects to find the difference in meaning between cannot and can not in a dictionary, they will be sorely disappointed. Dictionaries either state there is no difference in meaning or avoid mentioning it altogether
Cannot is sometimes also spelled can not. The one-word spelling is by far the more common:
- Interest rates simply cannot continue at their present level.
The contraction can't is most common in speech and informal writing.
Cambridge Dictionary says simply that cannot is the negative form of the verb "can" and under its American definition says: can not; to be unable or not allowed to. Oxford Learner's Dictionary, Macmillan Dictionary, Collins Dictionary do not add anything new to that essential definition. Wiktionary has a little more detail
- Can not (am/is/are unable to)
- Am/are/is forbidden or not permitted to
The American Heritage Dictionary, on the other hand, has this lengthy usage note, worth quoting in full.
The negative form of can.
Usage Note: The idiomatic phrase cannot but has sometimes been criticized as a double negative, perhaps because it has been confused with can but. The but of cannot but, however, means "except," as it does in phrases such as no one but, while the but of can but has the sense only, as it does in the sentence We had but a single bullet left.
Both cannot but and can but are established as standard expressions.
The construction cannot help is used with a present participle to roughly the same effect as a verb form ending in -ing in a sentence such as We cannot help admiring his courage. This construction usually implies that a person is unable to affect an outcome normally under his or her control. Thus, saying We could not help laughing at such a remark would imply that one could not suppress one's laughter.
The construction cannot help but probably arose as a blend of cannot help and cannot but; it has the meaning of the first and the syntax of the second: We cannot help but admire his courage. The construction has sometimes been criticized as a redundancy, but it has been around for more than a century and appears in the writing of many distinguished authors.
The expression cannot (or can't) seem to has occasionally been criticized as illogical, and so it is. Brian can't seem to get angry does not mean "Brian is incapable of appearing to get angry," as its syntax would seem to dictate; rather, it means "Brian appears to be unable to get angry." But the idiom serves a useful purpose, since the syntax of English does not allow a logical equivalent like Brian seems to cannot get angry; and the cannot seem to construction is so widely used that it would be pedantic to object to it.
No mention whatsoever that cannot and can not have overtly or subtly different meanings.
I am of the opinion that if someone tells me
You can not / cannot park there
the meaning is absolutely identical, i.e. I am not allowed to park there.
Why is “cannot” spelled as one word?
Evidence suggests that compound words – when two or more words express a single idea – often start life as two separate words, a hyphen is later added, and as usage becomes increasingly familiar the two words fuse and become permanently bonded.
For example, the original salutation (1400) “God be with thee” was shortened to the more familiar compound word “Good by” around 1700 which eventually led to following spelling variants: “good-by(e)” and to its now solid form “goodbye”.
The construction cannot, in my view, is an example of a compound verb.