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This question is about a detail in the biography of one of the greatest scientists who ever lived, Henry Cavendish. The Wikipedia article about him states that
He communicated with his female servants only by notes.
It seems that this passage of the article is based upon the article Brownian motion, Loschmidt's number, and the laws of utter chaos, by Willy Ley (Galaxy Science Fiction, June 1966, pp. 94-106), where it is written that
Later in life he refused even to be in the same room with a woman and gave his instructions to his maids in writing.
I have known this for years, but lately I have been having doubts about how likely is this to be true. Were London maids able to read in the eighteenth century? Or is it possible that those notes were only meant to be read by his housekeeper?
I think the answer to the headline question is "not very, which is why everyone thought Cavendish was a bit weird" :-)
But focusing on the detailed question - from his entry in the revised 2004 Oxford Dictionary of National Biography:
Almost misanthropic in his reserve, Cavendish never received strangers at his residence, and ordered his dinner by leaving a note on the hall table. He seems to have had no other communication with any of his female domestic staff.
The original 1886 edition has it as:
He received no stranger at his residence, he ordered his dinner daily by a note left on the hall table, and from his morbid shyness he objected to any communication with his female domestics.
This seems to clarify it as "he wrote one note per day requesting his meals, and otherwise ignored his female staff". Which implies a bit less communication than the way Wikipedia (and Ley) phrase it, and certainly makes it likely that only the housekeeper would actually be expected to read the notes.
Having said that, literacy was not that uncommon even among the working classes, and it is not a particular stretch to assume the maids could read as well. By 1800, an estimated 40% of women in England and Wales could read and write (compared to 60% of men). These rates were higher in London than in the national average; in a 1760s sample of emigrating servants, the London group were about ten percentage points more likely to be literate than those from elsewhere in the country. It would presumably also be more likely among younger women than older, given the gradual increase in education rates.
So I think it is entirely plausible that the majority of his household staff would be able to read, especially if he had deliberately wanted to have a literate household - it wouldn't have been that difficult to hire qualified people - but in the case of this particular situation, it probably wasn't needed.
The body of your question and the title don't exactly match. It's unlikely that anyone (noble or not) that could speak would communicate solely by written means with people that were within hearing distance. Even today with our electronic devices providing a quick and easy means of communicating, if people are within hollering distance, we generally speak. But that doesn't prevent unlikely people from existing.
Your question is also a bit short-sighted, as you are assuming that a nobleman that was determined to communicate with his maids in writing, would not make reading and writing a job requirement and would just have to deal with whatever fate happened to give him.
But if we take fate as a given with an inability or unwillingness to either pay a premium or to simply keep looking until a suitable candidate was located… a quick google for literacy in the 1730's found this document with some estimates of the literacy rates in London in that time period: https://scholarworks.wm.edu/cgi/viewcontent.cgi?article=4171&context=etd
TL;DR summary: ~35% of females would be literate. In short, I find it completely believable that a moderate to extremely wealthy individual with this particular
kink eccentricity would find it quite easy to satisfy.