Quotes & Sayings About Irrational Numbers

[T]he superstitions to be feared in the present day are much less religious than political; and of all the forms of idolatry I know none more irrational and ignoble than this blind worship of mere numbers. - William Lecky, Democracy and Liberty — Bryan Caplan

When I first learned of the existence of pi, I knew immediately that we had something in common. We share a parallel path. Certainly there are many times when I too have been considered irrational. Often when alone in my room, I silently ponder the equation for the area of a circle. Area (A) equals R-squared (RR) times the constant pi (C). Then I thought, by assigning the designation (K) and assuming there was an nth or final numeric digit to pi, it all might somehow become rational. The random rolling numbers that could at some point define that ultimate integer, passed through my mind. To me they were like the consecutive series of episodes that define my life. It seemed that it was more than a coincidence that when I took the variables and the constants from the equation and put them all together, A-R-R-C-K, it spells my name. That is why I need to get to the truth. — John Lack

Our enemies may be irrational, even outright insane, driven by nationalism, religion, ethnicity or ideology. They do not fear the United States for its diplomatic skills or the number of automobiles and software programs it produces. They respect only the firepower of our tanks, planes and helicopter gunships. — Ronald Reagan

Arithmetic starts with the integers and proceeds by successively enlarging the number system by rational and negative numbers, irrational numbers, etc ... But the next quite logical step after the reals, namely the introduction of infinitesimals, has simply been omitted. I think, in coming centuries it will be considered a great oddity in the history of mathematics that the first exact theory of infinitesimals was developed 300 years after the invention of the differential calculus. — Abraham Robinson

In newsreels or news-photos, the Arab is always shown in large numbers. No individuality, no personal characteristics or experiences. Most of the pictures represent mass rage and misery, or irrational (hence hopelessly eccentric) gestures. Lurking behind all of these images is the menace of jihad. Consequence: a fear that the Muslims (or Arabs) will take over the world. — Edward W. Said

Highly complex numbers like the Comma of Pythagoras, Pi and Phi (sometimes called the Golden Proportion), are known as irrational numbers. They lie deep in the structure of the physical universe, and were seen by the Egyptians as the principles controlling creation, the principles by which matter is precipitated from the cosmic mind.

Today scientists recognize the Comma of Pythagoras, Pi and the Golden Proportion as well as the closely related Fibonacci sequence are universal constants that describe complex patterns in astronomy, music and physics. ...

To the Egyptians these numbers were also the secret harmonies of the cosmos and they incorporated them as rhythms and proportions in the construction of their pyramids and temples. — Jonathan Black

The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers. — Georg Cantor

I chose the name Pi because it's an irrational number (one with no discernable pattern). Yet scientists use this irrational number to come to a "rational" understanding of the universe. To me, religion is a bit like that, "irrational" yet with it we come together we come to a sound understanding of the universe. — Yann Martel

God has given us the fascination and mystery of irrational numbers, as one aspect of a rich world — Vern Poythress

Just as the introduction of the irrational numbers ... is a convenient myth [which] simplifies the laws of arithmetic ... so physical objects are postulated entities which round out and simplify our account of the flux of existence ... The conceptional scheme of physical objects is [likewise] a convenient myth, simpler than the literal truth and yet containing that literal truth as a scattered part. — Willard Van Orman Quine

A canny reader here may object that there's some kind of Zenoid sleight of hand going on in the above proof, and might ask why a similar hankie procedure and series couldn't be applied to the irrational numbers to quote-unquote prove that the total % of Line-space taken up by the irrationals is also 2*(Infinitesimally small symbol). The reason such a proof can't work is that, no matter how infinitely or even (Infinity to the Infinity symbol) ly many red hankies you drape, there will always be more irrational numbers than hankies. Always. Cantor proved this, too. — David Foster Wallace

The thing that struck me was his intensity. Whatever he was interested in he would generally carry to an irrational extreme." Jobs had honed his trick of using stares and silences to master other people. " One of his numbers was to stare at the person he was talking to. He would stare into their fucking eyeballs, ask some question, and would want a response without the other person averting their eyes. — Walter Isaacson

I believe in numbers. The ones you can see and the ones you can't. The real and the imaginary, the rational and the irrational, and every point on lines that go on forever. Numbers have never let me down. They don't waffle. They don't lie. They don't pretend to be what they're not. They're timeless. — Amy Harmon

predecessor of Isaac Newton at Cambridge University, maintained that irrational numbers have no meaning independent of geometric lengths. — Morris Kline

It is shown that the golden ratio plays a prominent role in the dimensions of all objects which exhibit five-fold symmetry. It is also showed that among the irrational numbers, the golden ratio is the most irrational and, as a result, has unique applications in number theory, search algorithms, the minimization of functions, network theory, the atomic structure of certain materials and the growth of biological organisms. — Richard A. Dunlap

When numbers are substituted for morality, and no individual can claim a right, but any gang can assert any desire whatever, when compromise is the only policy expected of those in power, and the preservation of the moment's "stability," of peace at any price, is their only goal - the winner, necessarily, is whoever presents the most unjust and irrational demands; the system serves as an open invitation to do so. — Ayn Rand

I think that a society cannot live without a certain number of irrational beliefs. They are protected from criticism and analysis because they are irrational. — Claude Levi-Strauss

What good your beautiful proof on the transcendence of Pi: Why investigate such problems, given that irrational numbers do not even exist? — Leopold Kronecker

The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly disimilar to, and I might even say in priciple the same as, my method described above of introducing trasfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite. — Georg Cantor

I understand and sympathize with the reasonable needs of a reasonable number of people on a finite continent. All life depends upon other life. But what is happening today, in North America, is not rational use but irrational massacre. Man the Pest, multiplied to the swarming stage, is attacking the remaining forests like a plague of locusts on a field of grain. — Edward Abbey