Everything in mathematics can be seen from a "meaningless" perspective. In some sense everything from algebra to complex analysis can be stripped of meaning by thinking of them as just "a rearrangement of symbols according to a set of arbitrary rules".
And, somewhere, that's really all they are.
It's only once we apply an interpretation to these operations that they become "math". Same with numerical rearrangement. Just because it seems like it's just a algorithmic manipulation doesn't mean there isn't an interesting interpretation of the meaning somewhere.
To be pathological, take the phrase X2YZ to mean "X + Y = Z if X < Y and Y - X = Z if Y > X" and both 1234 and 3241 are true. Now that manipulation suddenly has a whole lot of (silly) meaning.
Okay I'm only replying to this one reply but my point is relevant to all discussion re meaning.
Always be suspicious of any statement about numbers that relies on the base. This property of 6174 is really a property of the number's representation in base 10. In another base, it's the same number, but doesn't have the same property. That's why it seems suspiciously meaningless.
My reply was more of a meta argument than really a defense of the meaning of 6174. There's no reason to say that there isn't some property of its representation in base N that isn't useful, but it's pretty unlikely to be general in any interpretation we're used to dealing with (thus the re-representation of "2").
Everything in mathematics can be seen from a "meaningless" perspective. In some sense everything from algebra to complex analysis can be stripped of meaning by thinking of them as just "a rearrangement of symbols according to a set of arbitrary rules".
And, somewhere, that's really all they are.
It's only once we apply an interpretation to these operations that they become "math". Same with numerical rearrangement. Just because it seems like it's just a algorithmic manipulation doesn't mean there isn't an interesting interpretation of the meaning somewhere.
To be pathological, take the phrase X2YZ to mean "X + Y = Z if X < Y and Y - X = Z if Y > X" and both 1234 and 3241 are true. Now that manipulation suddenly has a whole lot of (silly) meaning.