• WordNet 3.6
    • adj irrational not consistent with or using reason "irrational fears","irrational animals"
    • adj irrational real but not expressible as the quotient of two integers "irrational numbers"
    • n irrational a real number that cannot be expressed as a rational number
    • ***
Webster's Revised Unabridged Dictionary
  • Interesting fact: In the 19th century, craftsmen who made hats were known to be excitable and irrational, as well as to tremble with palsy and mix up their words. Such behavior gave rise to the familiar expression "mad as a hatter". The disorder, called hatter's shakes, was caused by chronic mercury poisoning from the solution used to treat the felt. Attacking the central nervous system, the toxin led to behavioral symptoms.
    • irrational Not according to reason; having no rational basis; clearly contrary to reason; easily disproved by reasoning; absurd; -- of assertions and beliefs. "It seemed utterly irrational any longer to maintain it."
    • irrational (Math) Not capable of being exactly expressed by an integral number, nor by a ratio of integral numbers; surd; -- said especially of roots. See Surd.
    • irrational Not rational; void of reason or understanding; as, brutes are irrational animals.
    • ***
Century Dictionary and Cyclopedia
    • irrational Not rational; without the faculty of reason; void of understanding; unreasoning.
    • irrational Without the quality of reason; contrary to reason; illogical; unreasonable: as, irrational motives; an irrational project.
    • irrational In mathematics: In arithmetic, not capable of being exactly expressed by a vulgar fraction, proper or improper; surd. In mathematics irrational is a translation of Greek α%27λογον, inexpressible (by a fraction), opposed to ρ\ητόν. (See surd.) Every irrational quantity can, however, be conceived as expressed by an infinite continued fraction or interminate decimal.
    • irrational In translations of Euclid, and cognate writings, at once incommensurable with the assumed unit and not having its square commensurable with that of the unit. This is the peculiar meaning given by Euclid to α%27λογος, though Plato uses it in sense , above.
    • irrational In algebra, noting a quantity involving a variable raised to a fractional power; or. in a wider sense, noting a quantity not rational, not a sum of products of constants and of variables into one another or into themselves.
    • irrational In Greek prosody, incapable of measurement in terms of the fundamental or primary time or metrical unit.
    • n irrational That which is devoid of reason, as one of the lower animals.
    • n irrational A prime number.
    • n irrational In mathematics, an irrational number, that is, the mark of a cut which separates all rational numbers into two classes, the first having no greatest number, the second no least.
    • ***
Chambers's Twentieth Century Dictionary
    • adj Irrational ir-rash′un-al void of reason or understanding: absurd
    • ***


  • Friedrich Nietzsche
    “The irrationality of a thing is no argument against its existence, rather a condition of it.”
  • Gunther Grass
    Gunther Grass
    “Art is so wonderfully irrational, exuberantly pointless, but necessary all the same. Pointless and yet necessary, that's hard for a puritan to understand.”
  • A. N. Wilson
    A. N. Wilson
    “The fact that logic cannot satisfy us awakens an almost insatiable hunger for the irrational.”
  • Lisa Hoffman
    Lisa Hoffman
    “Love is like pi -- natural, irrational, and very important.”
  • Cyril Connolly
    “As repressed sadists are supposed to become policemen or butchers so those with an irrational fear of life become publishers.”
  • George Santayana
    “The irrational in the human has something about it altogether repulsive and terrible, as we see in the maniac, the miser, the drunkard or the ape.”


Webster's Revised Unabridged Dictionary
L. irrationalis,: cf. F. irrationnel,. See In- not, and Rational


In literature:

Immortality, unbelief in, irrational, 247.
"The Ascent of the Soul" by Amory H. Bradford
That was irrational, and Jack MacRae knew it was irrational.
"Poor Man's Rock" by Bertrand W. Sinclair
The hero is not he who feels no fear, for that were brutal and irrational.
"The Lee Shore" by Rose Macaulay
As a matter of fact, the ratio is irrational.
"Amusements in Mathematics" by Henry Ernest Dudeney
It was a moment full of bitterness, and of a quite irrational indignation against Rupert Gunning.
"All on the Irish Shore" by E. Somerville and Martin Ross
In this combination, I maintain, it is the rational optimist who fails, the irrational optimist who succeeds.
"Orthodoxy" by G. K. Chesterton
So also would light be no irrational thought.
"Probabilities" by Martin Farquhar Tupper
The power of caste is as irrational as it is unbounded; and it works almost unmixed evil.
"Two Old Faiths" by J. Murray Mitchell and William Muir
If so, how irrational!
"Theodicy" by G. W. Leibniz
It is admitted that this is not in the least irrational.
"Is Life Worth Living?" by William Hurrell Mallock

In poetry:

Like the buzzing of an insect,
Still, irrational, persistent . . .
I must listen, listen, listen
In a passion of attention;
"Nocturn" by William Ernest Henley

In news:

I put in time at night or on weekends to meet her irrational deadlines.
Irrational fears explain alarming return of whooping cough.
Don't try to fight irrationality with rationality.
What's your experience with understanding — and embracing — irrationality in your organization.
The horrible tragedy in Aurora, Colorado during The Dark Knight Rises movie got me thinking about my irrational fears, and sometimes — movie theaters are one of them.
The EPA's Irrational , Anti-Coal Mercury Regulations.
The other side of irrational fans.
Mexican official calls cartel violence ' irrational '.
Well, because his worst nightmare has come true or should I say irrational fear.
I'm Not " Irrational and Overprotective" With Second Baby.
Fear of flying is irrational , but pack a teddy bear.
Irrationality is not the same as madness.
How Irrational Beliefs Keep Us Sane.
USDA?bows to irrational BPI critics.
Mars budget cuts ' irrational ' says former NASA science chief.

In science:

When r is such that ψ(pr (y )) is irrational, then using (i) we have that ypr (y ) is the strong∗ limit of yps(y ) as s tends to r through rational numbers.
Invariant subspaces of Voiculescu's circular operator
We will assume that θ is irrational; then it was proved in that two modules having the same K -theory class are isomorphic.
Gauge theories on noncommutative spaces
For z irrational there are infinite possibilities for Xn+1 .
Exact solutions to chaotic and stochastic systems
For z irrational, all the row sequences are quasiperiodic and different.
Exact solutions to chaotic and stochastic systems
This irrational z does not have to be a large number.
Exact solutions to chaotic and stochastic systems