To which they should cleverly reply, "Aha! You said 'first' centimeter, not 'zeroth' centimeter, thus defeating your own argument."

Someone I knew at university, who prefers starting at 0 (for mathematical, rather than computational, reasons) made the following argument/proposal.

"First" is an abbreviated form of "foremost". So if you start counting at 0, "first" corresponds to index 0. There's no real clash here yet; "first" and "one" are entirely separate terms.

"Second" is from Latin "secundus" meaning "following"; the second thing follows the first. So "second" corresponds to index 1. Again, no clash yet; "second" and "two" are basically unrelated.

"Third", though, actually derives from "three". So "third" has to correspond to index 3.

This leaves a gap, which might perhaps be filled by a new word "twifth", corresponding to index 2.

So now we have the cardinal numbers: zero, one, two, three. And the corresponding ordinals: first, second, twifth, third.

The hypothetical student's sarcastic answer isn't technically correct.

> you can just show them a ruler and > ask them where does the first centimeter start(s)

The question involves a nuance of the english language, the distinction between a measure of wholeness and the contents of that unit.

Length is a count of the completeness of a measure. The length of an interval must inherently include 0 as a unit to describe taking no units.

A 0 starting index is likewise also required to indicate skipping no storage cells.

Therefore an absolute index start must be zero based, and the Addition of duration must also include the option of zero as a means of describing a point at which to begin, but having not yet used any length.

The subtle trick is that is a point, an array of zero size; this is why the length, or alternately absolute stop point, for an array storing anything is one higher. It isn't actually zero indexed, it's a different property of measure (the size or stopping address).

A centimeter is also a wonderful example since it should graphically contain eight additional ticks for millimeter marks, and naught else, among it's inner span. This aligns wonderfully with explaining that there are targets spots for 8 bits of an octet within that single byte of indexed storage.

Doesn't that just demonstrate your (edit: the teacher's) point exactly?

The first centimeter starts at 0.

The first array element starts at 0.

No, that's the lower bound of the first array element.

It's the offset of the first array element from the start of the array. The first element is at the start of the array, so the offset is naturally zero—there are zero elements prior to the first element. Like the markings on a ruler, array indices are cardinal numerals (0, 1, 2, …) counting the distance from a reference point, not ordinal numerals (1st, 2nd, 3rd, …) representing rank in a sequential order.

If you're comparing arrays to centimeters on a ruler, the first element is at the center of the first cell; at zero, there's the left border of the first cell.

(Also please note that both this and my previous reply are tongue-in-cheek).

There's a difference between a cm being the thing that exists between the lines with 0 and 1 against them and the distance that is 1cm. Indexing is within the scope of the first definition. You might as well ask where the 0 or 1th element in an array starts and finishes.

Or give the example of birthdays; in your first (initial) year of life you are 0 years old.

And they'll see that rulers are broken too, they should start with 1 instead!

To which some of us older Americans would say, "Which one is the centimeter?" It's so hard for me to think in metric.

so the question is: what's worse - imperial or 1-based index?

Imperial, because of it's vagueness people use other measurements as well. Something is x stories high. Something is a "stones throw away".

Though i do appreciate Fahrenheit for how it scales with humans. 0 is really damn cold, 100 is really damn hot, while in Celcius 0 is kinda chilly and 100 is instant death.

>100 is really damn hot,

It's actually supposed to be the body temperature. Due to imprecise measurements, it's actually having a light fever. Flip note: C scales the same - 0 is the water freezing point, and then you have the same scaling as F but in 5s instead of 10s. [and you gotta remember: (f-2pow5)*5/9].

That's an old debate, yet if you are born/used to C, F is pretty horrific.

I forgot to mention that I'm Swedish and use C daily, I just think the F scale makes more sense for humans

100C isn't instant death, see sauna. Maybe you compare 0C air and 100C water so to be fair, 0C water is maybe death within dozen of minutes

Very nice, I'll steal that.