In your otherwise beautiful poem one verse reads,
Every moment dies a man,
Every moment one is born
If this were true the population of the world would be at a standstill. In truth, the rate of birth is slightly in excess of that of death. I would suggest that the next edition of your poem should read:
Every moment dies a man
Every moment 1 1/16 is born
Strictly speaking the actual figure is so long I cannot get it into a line, but I believe the figure 1 1/16 will be sufficiently accurate for poetry.
I can't help smiling at this because it illustrates the great difficulty persons of great computational ability (which I shall refer to as nerds) have in overlooking small matters of inaccuracy. It's not uncommon to see computer folk arguing over fine points of semantics or mathematics, or deliberately playing with words and puns, or laughing about the minutiae of some program, machine or situation.
This comes about because nerds spend all their time worrying about details. Computers are exceedingly finnicky things. They do precisely what they are told (with heavy emphasis on precisely). Thus anyone who works with them (and by that I mean anyone who actually deals with computers rather than mere users) ends up training themselves to spot minute details that are incorrect or out of place.
Unfortunately, that attention to tiny detail seems to change the brain so that it is searched for everywhere. I think that's because it takes great mental effort to hold in your head the details of any computer system and be able to spot problems. Often you are looking for the tiniest needle in an enormous haystack of information.
By the time Babbage wrote that letter he had spent 20 years on his calculating/computing engines often working 11 hour days. It is no wonder that Tennyson's error stood out to him. I have seen Babbage's letter described as insulting, humorous and over-zealous. To me it is none of these things. Tennyson was a great supporter of 19th century science and Babbage was merely pointing out a technical inaccuracy.
PS Sadly I have not been able to find in any of Alfred, Lord Tennyson's letters a reply to Babbage.