I like the word fiddle, and I quite like the musical instrument too.
If you're fiddling with a device, it means you're trying to repair it. It might be tricky because of all the tiny bits and pieces involved, and it will probably require time, patience and a little luck before the object is in perfect working order.
Mothers who see their children making nervous, time-wasting movements will tell them to “stop fiddling” with their hair, pens, or nowadays, mobiles.
Then there's fiddlesticks, a minced oath if ever there was one, perfect for when you find yourself in polite or unfamiliar company. A fiddlestick on the other hand, is only another name for a violin bow.
1. But when did “fiddling taxes/expenses” mean to cheat or swindle?
From India Today
but the fact remains that given the peculiar structure of the tax system it is virtually impossible to keep one's head above water, let alone swim, without a considerable amount of fiddling on the side.
From the British Guardian
When an MP or someone in a position of authority is found fiddling their expenses there is usually a public outcry and calls for resignation. But according to a new survey, dodgy claims are a part of every day working life in the UK.
Most of those who admitted to a bit of fiddling here and there said it was a bit like an unofficial perk, while many saw it as a convenient way of boosting their salary.
and again from the Guardian
My brother-in-law is a really good bloke—at least, I thought he was until he boasted that he's fiddling his income tax. He's really generous when it comes to Christmas and birthdays, but then he can afford to be. Now I'm wondering if I'm the mug. Should I copy him or shop him?
There is also the noun: tax fiddle
2. Is ‘fiddling the taxes/the books’ related to playing the musical instrument, fixing an object or with fidgeting?
3. Do Americans fiddle their taxes? What's the American English slang for not paying taxes?