Why do we put letters in some words which are silent in pronunciation? If they make no sound then why we waste space in words? For example:
"Knife"; 'K' is silent
"Doubt"; 'b' is silent etc.
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The answer is complicated and requires knowing the etymological and phonological history of English. Doubt for instance comes to English ultimately through the Latin verb dubitare (to hesitate), in which the "b" is not silent. But it first took a detour through the Old French word douter, which had lost the letter "b" and its sound. The OED notes that douter was the "normal" form through the 14th century. The dictionary finds the first use of doubt-with-a-b in 1398 (as a noun, in an obsolete usage meaning a difficulty), this "artificial" spelling effected by "the influence of Latin." The two forms coexist through the 16th century, with the OED giving, on the one hand, the example of the Great Bible of 1539, a project of King Henry VIII, which records Matthew 28:17
But some douted.
and on the other hand, Thomas Cranmer, the Archbishop of Canterbury under King Henry who writes in 1548 of church doctrines
wherefore it is not lawful to doubt at them.
Perhaps the motivation for the insertion of the silent "b" was that it made clear the link between doubt and related words like dubious, which came to English directly from the same Latin word, and which not having taken the French detour, kept the "b". By the 17th century, the "b" is entrenched in English. Interestingly, the opposite happened in French, which eventually abandoned the extra letter.