In mathematics, the square root of -1.

There is no value in the real numbers which, when squared, gives -1. So mathematicians just invented another symbol to represent it, and called it a new number. It's happened before - there is no integer which, when multiplied by 2, gives 1 - so mathematicians invented a symbol for it, ½, which generalised into the whole concept of division and rational numbers. There is no natural number which, when added to 1, gives 0 - so mathematicians invented a symbol for it, -1, which generalised into the whole subtraction and negative numbers idea. iota is just another step on the ladder of expanding the expressiveness of mathematics, encompassing an ever-increasing set of values. iota itself generalises to give us a whole set of imaginary and complex numbers.

Iota, when written properly, does not have a dot over it - unlike the letter 'i'.

“We will not retreat one iota in our path to nuclear victory,” proclaimed the Iranian president.

“Not one iota of land has been returned on the basis of our inherent rights,” declared a tribal leader following the Australian High Court decision in the 2003 Yorta Yorta land use case.

“If I shared my view, and it happened to deviate one iota, one little inch, from what the President's doing . . . it would be terrible,” demurred George Bush the Elder, declining to state his own foreign policy views at a recent press conference.

For being such a small Greek letter, the word iota sure seems to get a lot of play in the modern press. As Webster defines it, the word simply means a “very small quantity or degree; a jot; a particle.” But the sense of the word goes beyond that meager designation, signifying instead an amount that, while small in absolute quantity, has significance extending beyond its literal measure.

Hence, you might see it appear in a sentence like “They didn’t change that awful screenplay for Joey one little bit, not one iota." The added significance here comes from the fact that iota, as used in this example, refers to that initial element of change, so that its absence necessarily demonstrates a complete lack of change.

Perhaps the best way to capture the essence of the word, then, would be to say that it means “a small quantity or degree, in its entirety.” The whole of a thing, or none at all.

But where did this rather sophisticated meaning come from? I mean, it’s really just a letter, after all. Why all the subtle shading?

Well, I’m glad you asked. Because while it’s a fairly simple question, the answer, it seems, is not so straightforward, and might even be . . . dare I say it . . . meaningful? To get to this answer, we must go back a bit in time. A long time. Over a millennium, actually, to the First Council of Nicaea, in 325 A.D.

Early Christianity was in a constant state of controversy and flux back then. Kind of like the crust of the Earth millions of years ago, when it was liquid and hot and easy to get burned.

There was at that time a smoldering controversy over the nature of Jesus Christ and his relationship to God. Was he divine? Was he human? Was he both?

One side, led by Alexandria presbyter Arius, preached the neoplatonist idea of the absolute oneness of the divinity. Because this was a unity that could not be shared, Arius reasoned, Jesus must have been a “lesser deity” called into existence by God.

Under this Arian view, Jesus was homoiousios (ηομοιουσιος), meaning “of a similar substance” of God. That is, of a similar nature to God, but not the same as, God.

The competing, and ultimately dominant, side, led by Athanasius, bishop of Alexandria, preached that Jesus was, in fact, homoousios (ηομοουσιος), meaning “of the same substance” as God.

Homoiousios, with an "i" . . . homoousios, without.

The furor caused by this debate, which, as you can see, revolves around a single iota’s difference between the two words, caused such conflict that Roman Emperor Constantine decreed that the matter be settled at what became the Council of Nicaea in 325.

In case you don't know already, Athanasius won. He and his cohorts walked out of the Council with a new name for their ideas and doctrine. It was called the Nicene Creed, and it's now repeated daily by millions of Catholics worldwide.

Arius walked out of the Council branded a heretic. That is, if he walked out at all. Being a heretic was a tough gig, from what I hear. The job had a pretty short lifespan.

So one little letter, one iota, changed the course of Christianity. In chaos theory, such small differences can bring about great changes because of the inherent instability of equilibria in complex systems.

In philosophical terms, such small differences bring about great change because such differences matter. God as well as the Devil is in the details, and those details cannot be ignored. The modern-day equivalent might be something like this.

The President is Commander-in-Chief.

The President as Commander-in-Chief.

One letter. A simple change that might be lost on the current Commander-in-Chief, and would no doubt escape the brain trust at Fox News, as well. But a change that makes a world of difference, nonetheless.

I*o"ta (?), n. [L., fr. Gr. . See Jot.]

1.

The ninth letter of the Greek alphabet (ι) corresponding with the English i.

2.

A very small quantity or degree; a jot; a particle.

<-- from iota being the smallest letter -->

They never depart an iota from the authentic formulas of tyranny and usurpation. Burke.

Iota subscript Gr. Gram., iota written beneath a preceding vowel, as a,, h,, w,, -- done when iota is silent.

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