Why don't we define “imaginary” numbers for every “impossibility”? (2012)

Re:Why don't we define “imaginary” numbers for every “imposs... by syzarian on Monday April 10, 2023 @06:47PM (#35518322)

How does your pedantry contribute meaningfully?

If something doesn’t behave like 0 in a ring or other algebraic structure then using that label is confusing and simply not done. You are free to use any symbol you want but mathematics is a human endeavor and as such communication is important. Using the symbol 0 signifies something to those with mathematical training. Zero can’t have an multiplicative inverse because anything you call 0 that has an multiplicative inverse makes it behave like something other than zero. So no one would use 0 to describe such an element. In a ring, or abelian group, the symbol 0 is reserved for the additive identity element.

Similarly, I could say snkwoo is what most people call a chair. A grammarian would say there is no word snkwoo even though I just defined it.

Your original comment was wrong and bad. Instead of just admitting it or moving on you’ve decided to double down and make another bad comment.

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Re:Why don't we define “imaginary” numbers for every “imposs... by thaumasiotes on Monday April 10, 2023 @08:03PM (#35518972)

I'm having trouble following the argument from your premise "it is a stupid question to ask why I referred to a chair as a chair instead of a snkwoo" to your conclusion "it is not a stupid question to ask why, when we have no answer to a question, we don't just say that we do have one".

The answer (to both of those questions!) is, of course, that we could do that, but it wouldn't accomplish anything. Asking the question just means you have no idea what you're saying. Or in other words, it's a stupid question.

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[dead]

Re:Why don't we define “imaginary” numbers for every “imposs... by thaumasiotes on Monday April 10, 2023 @10:43PM (#35520114)

> Please don’t become a teacher.

I've been one!

Interestingly, the most consistent comment I got, from both students and school administration, was "you're so patient with the students".

Try humoring me. Did I describe your premise accurately? Did I describe your conclusion accurately? How do you get from one to the other?

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Re:Why don't we define “imaginary” numbers for every “imposs... by syzarian on Monday April 10, 2023 @11:51PM (#35520583)

A child asked her mother, “Can I put my hand in the fire?”. The mother responded, “That’s a stupid question. Of course you can.”. The child put her hand in the fire and got severe burns on her hand. She learned then that instead asking “Can I…” she should have asked, “Is it advisable…”. Unfortunately for her she lived in a society in which people frequently say things like, “You have to file taxes on or before April 15.” when they mean, “You can file taxes after April 15 but you may incur fees and penalties if you do so.”. She later became a teacher and was very patient with her students.

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Re:Why don't we define “imaginary” numbers for every “imposs... by scubbo on Monday April 10, 2023 @08:58PM (#35519337)

> Asking the question just means you have no idea what you're saying. Or in other words, it's a stupid question.

So, to be clear, you're saying that the only kind of question that isn't stupid is the one where the querent already has perfect knowledge of the discipline?

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Re:Why don't we define “imaginary” numbers for every “imposs... by thaumasiotes on Monday April 10, 2023 @10:48PM (#35520138)

I'm saying that to avoid asking a stupid question, you need to know the meaning of your own question. Stringing words together at random isn't going to get you there.

Compare the famous anecdote from Charles Babbage:

On two occasions I have been asked, -- "Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?" [...] I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.

Is it necessary to have perfect knowledge of the workings of the Difference Engine to avoid asking that question? Of course not. Any knowledge at all would do the trick. If you put gravel into a water mill instead of grain, will you still get flour out of it?

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