Allegory and Simile

Alchemists are people who study the science, alchemy. Taking something apart and putting it back together in a new form. So no it cannot be an allegory, which according to Incablue's description:

An Allegory is a form of extended metaphor, in which objects, persons, and actions in a narrative, are equated with the meanings that lie outside the narrative itself. The underlying meaning has moral, social, religious, or political significance, and characters are often personifications of abstract ideas as charity, greed, or envy.

Thus an allegory is a story with two meanings, a literal meaning and a symbolic meaning.

Examples

In illustrations, allegorical figures such as the Grim Reaper and Blind Justice represent the concepts of death and law, respectively.

In literature, a classic example is Herman Melville's Moby Dick, where the sea and the whale, and Ahab's actions, all represent elements of life and human behavior.

The use of "X times more" and "X times less" is a pernicious mathematical idiom; it diverts the meaning of "more" away from the concept of "additional" and the meaning of "times" away from the concept of counting. "3 times more" becomes unsupportably synonymous with "3 times as much" or "3 times the quantity." The X is unconsciously and artificially restricted (the number 1 is seemingly disallowed) and the results are ambiguous (compare "5 times less" and ".8 times less"). It's expeditious, but it's facile.

The answer to the question "how much" (how much more? how much less?) is not present in either expression. The only way to reach that answer is to perform the calculation that should have been made at the outset: addition or subtraction.

Multiplication is a shorthand method. The underlying concepts are counting and addition. One reason for the "fencepost" form of the off-by-one error (see Wikipedia) is that multiplication consists of X instances but only X-1 additions. (How many spaces are there between the five fingers on one hand?) So "3 times" consists of three instances, NOT three additions (unless the starting point of counting is considered to be zero). The upshot is that "times" and "more" both refer to addition, and "times more" should indicate both a multiplication and a further addition. For mathematical consistency, "3 times more" should indicate "4 times as much."

Using "times" to represent division muddles the elements used in THAT shorthand method. The basis for division is the counting of subtractions. Division expresses one quantity (the dividend) in units of another (the divisor). Confusion arises because in teaching division the quotient is stated as how many "times" the reference unit "goes into" the compared quantity. But in "3 times less," the division is performed using 3 as the divisor, not as the quotient. It isn't the reference unit, and it isn't a count of subtractions.

This idiom is responsible for misstatements of fact. Writers who rely on it have published claims such as "the price of oil is down 384%" and "a 24 MHz processor is 150% faster than a 16 MHz CPU." A doubling of insurance rates is mistakenly called a "200% increase." In these examples, the authors used the "times" expression and converted X to a percentage.

How often have you heard that a man fell eight floors to his death--from the eighth floor, where the ground level is the first floor? Hint: how many staircases do you climb to get to the eighth floor? This mistake happens because the eighth floor is assumed to be "8 times higher." (When the deceased fell from the eighth floor to a THIRD-floor balcony, reporters--and readers--do the math and get it right. No idiom, no mistake.)

Although one can find this phraseology in the works of educated and generally astute people, there is no way to determine how many others have recognized its incongruities and opted for more careful language. Besides, most occurrences don't provide empirical data and can't be evaluated. And if you can't evaluate it, why trust it?

Idiomatic and literal interpretation of this formulation can't coexist; they contradict one another. Most people aren't aware that it's an idiom and not a straightforward mathematical statement. It's often used in a simple declarative with no context provided. And it's a form of sensationalism, overstating something that could be said less dramatically.

In the absence of a concerted (and monumentally difficult) effort to eliminate this mathematical idiom, at a minimum its existence, parameters and effects should be made explicit at the middle- (primary-?) school level.