A wit is someone given to being witty. If sarcasm is often referred to as the lowest form of wit, it’s because wit requires a more etymological basis for its humor than sarcasm, which relies instead upon delivery. Sarcasm might distract you from being able to guess which cup the penny’s under, but wit will actually make the penny disappear. In order to best the purveyor of sarcasm, one has to keep one’s wits about them, has to retain their mental acuity.
The lovely thing about a mongrel language such as English is that a singular word can contain within it many shades of meaning, all related. Wit comes to us from the Old English witt, meaning understanding, intellect, knowledge, and consciousness. Thus is can refer to both the brain, the mind and thought. The phrase “to wit” means to know, and has become a shorthand form by which to introduce facts; things that can be accepted as being irrefutably known.
To know — to wit — in the past tense, is to wist. To have wist. Wistfully. The singular form is to wot, or to wost. (To wast, on the other hand, is “to be,” making for an interesting homophonic link that appears to confirm Descartes’ assertion “I think, therefore I am. I wost, ergo I wast. It’s perhaps a witty version of cogito ergo sum, suggesting that Old English is a funnier tongue than Latin.)
The actual grammar of the word wot is a bit scary-sounding: it’s a preterite-present verb. Things can get quite complicated when one roots around the roots of a word. Today you don’t hear much about wit, and you certainly won’t hear it described as wot. The way you DO hear the word “wot” is in a wholly different, but related, context.
Contemporary wits employ the word “wot” instead of “what” (and in turn, “that”) in order to deliberately sound uneducated, in the manner of someone who has no use for the rules of everyday grammar. Hence the popularity of the phrase “that thing wot I did,” which has started to infiltrate the idiom. Just as certain derogatory names can only be employed by those to whom they might apply, the use of “wot” can only really be used by those smart enough to know they are trying to be humble.
In an age where the internet and social media insists that in order to keep up we must all become self-promoters, one can be pretty sure that if something is introduced by the invitation to come look at “some thing wot I did / wrote / said / drew” etc., the author is very proud of it. It is an example of humor being employed to imply seriousness — the very heart of wit.