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incommensurable

Definitions

  • WordNet 3.6
    • adj incommensurable not having a common factor
    • adj incommensurable impossible to measure or compare in value or size or excellence
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Webster's Revised Unabridged Dictionary
    • a Incommensurable Not commensurable; having no common measure or standard of comparison; as, quantities are incommensurable when no third quantity can be found that is an aliquot part of both; the side and diagonal of a square are incommensurable with each other; the diameter and circumference of a circle are incommensurable. "They are quantities incommensurable ."
    • n Incommensurable One of two or more quantities which have no common measure.
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Century Dictionary and Cyclopedia
    • incommensurable Not commensurable; having no common measure: thus, two quantities are incommensurable when no third quantity can be found that is an aliquot part of both; in arithmetic, having no common divisor except unity. See commensurable.
    • n incommensurable One of two or more quantities which have no common measure.
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Chambers's Twentieth Century Dictionary
    • adj Incommensurable in-kom-en′sū-ra-bl having no common measure
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Etymology

Webster's Revised Unabridged Dictionary
Pref. in-, not + commensurable,: cf. F. incommensurable,

Usage

In literature:

The whole question seems to be incommensurate to our faculties.
"Thoughts on Man" by William Godwin
You shall not measure them; they are incommensurable: the one is death eternal to a man, the other is life eternal.
"Heroes and Hero Worship" by Thomas Carlyle
For us with the standard of good and evil given us by Christ, no human actions are incommensurable.
"War and Peace" by Leo Tolstoy
The two things are not merely different, they are incommensurable.
"Considerations on Representative Government" by John Stuart Mill
He compares incommensurables, and flies to ideal standpoints.
"America To-day, Observations and Reflections" by William Archer
And he comes, not merely in time, pretty close to Defoe, incommensurable as is the genius of the two.
"The English Novel" by George Saintsbury
We do not find fault with men for being born in positions that confer powers upon them incommensurate with their rights.
"The Atlantic Monthly, Vol. 13, No. 78, April, 1864" by Various
It was incommensurate with the terrible excitement of which one was talking.
"Orthodoxy" by G. K. Chesterton
The new gods thus far were not incommensurable with the old ones.
"The Religion of Numa" by Jesse Benedict Carter
How often magnified by little causes into an importance wholly incommensurate with the object desired!
"The Knickerbocker, or New-York Monthly Magazine, January 1844" by Various
The most barbaric tendencies in man come to life again in war, and for war's uses they are incommensurably good.
"Masterpieces of Negro Eloquence" by Various
The possible results of such an enterprise were incommensurate with the risk that must be incurred.
"As It Was in the Beginning" by Philip Verrill Mighels
Since the philosopher and the common man do not see alike, the terms of their experience are incommensurable.
"The Approach to Philosophy" by Ralph Barton Perry
The difference of two incommensurable mathematical quantities.
"The Sailor's Word-Book" by William Henry Smyth
I think it right to give the proof that the ratio of the circumference to the diameter is incommensurable.
"A Budget of Paradoxes, Volume II (of II)" by Augustus de Morgan
Our reasons are ludicrously incommensurate with the volume of our feeling, yet on the latter we unhesitatingly act.
"The Will to Believe" by William James
These differ from other forms of force in being incommensurate with extension.
"The Religious Sentiment" by Daniel G. Brinton
The influence of an incommensurably greater poet, of Wordsworth, is also to be traced in it.
"Life of John Keats" by Sidney Colvin
Incommensurables, 162 ff., 237.
"Our Knowledge of the External World as a Field for Scientific Method in Philosophy" by Bertrand Russell
His definitions hold for commensurable as well as for incommensurable quantities.
"Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6" by Various
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In news:

When faced with functional visual complaints incommensurate with a normal structural eye exam in an older patient (age 55 and older), your differential diagnosis should include possible dementia.
Swamp Things, Presocratic philosophy and Incommensurable interconnectivity are just a few of the discussion topics at the International Comics Art Forum.
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In science:

Up to this point, the observed sequence of phase transitions in strontium and the predicted sequence in calcium are identical: fcc → bcc → I41/amd → C2/c-12 (Sr-IV). The next higher-pressure phase of strontium, Sr-V, is an incommensurate host-guest structure.
Exotic behavior and crystal structures of calcium under pressure
Observation of the incommensurate barium-IV structure in strontium phase V.
Exotic behavior and crystal structures of calcium under pressure
The scans did not indicate additional intensity at other, e.g. incommensurate, positions.
Magnetism and superconductivity driven by identical 4$f$ states in a heavy-fermion metal
K where the CDW is incommensurate, the Ta4f spectrum shows a broad peak feature.
Femtosecond core level photoemision spectroscopy on 1T-TaS2 using 60 eV laser source
It was remarkable there that incommensurate SDW was confined inside the superconducting phase, meaning that here superconductivity is an essential ingredient for SDW to develop.
Field-Induced Spin-Exciton Condensation in dx2-y2-wave Superconducting CeCoIn5
There was found that low-temperature/high-field superconducting phase in CeCoIn5 is a coexisting phase of FFLO and incommensurate SDW orders.11 Also, there was pointed out12 the enhancement of nesting by superconductivity in the gap nodal direction.
Field-Induced Spin-Exciton Condensation in dx2-y2-wave Superconducting CeCoIn5
The dispersion shows15 a downward shape and an incommensurate ground state is expected.
Field-Induced Spin-Exciton Condensation in dx2-y2-wave Superconducting CeCoIn5
Alice and Bob share a catalyst state |φi, and there are incommensurate states |φ1 i and |φ2 i such that in the presence of the catalyst, |φ1 i can be converted to |φ2 i while retaining |φi.
Quantum Communication Complexity of Quantum Authentication Protocols
For each axis, Γi and αi exhibit a sign change (at low temperature) at the critical concentration xc ≃ 0.25, at which the incommensurate magnetic propagation vector changes.
Complex magneto-elastic properties in the frustrated kagome-staircase compounds (Co$_{1-x}$Ni$_x$)$_3$V$_2$O$_8$
At low temperature, a first-order phase transition occurs at the critical concentration xc, where the direction of the incommensurate propagation vector changes.8 Changes of signs in the thermal expansion and Gr¨uneisen coefficients are observed close to xc .
Complex magneto-elastic properties in the frustrated kagome-staircase compounds (Co$_{1-x}$Ni$_x$)$_3$V$_2$O$_8$
In addition, frustration brings incommensurability in the real-space spin correlation functions, the onset of which evolves smoothly from the J1 -J2 chain value to zero in the large-J⊥ limit.
Melting of a frustration-induced dimer crystal and incommensurability in the J_1-J_2 two-leg ladder
The onset of incommensurability in the spin structure-factor and in the dispersion relation is also analyzed.
Melting of a frustration-induced dimer crystal and incommensurability in the J_1-J_2 two-leg ladder
Here, we present an exhaustive study of the full phase diagram of the J1 -J2 ladder model of Fig. 1, motivated by several aspects such as the shape of the whole phase diagram, the nature of the excitations, and the evolution of the incommensurability upon increasing frustration.
Melting of a frustration-induced dimer crystal and incommensurability in the J_1-J_2 two-leg ladder
Numerical results are presented in section II where the nature of the quantum phase transition, low energy spectra and incommensurate correlations are studied.
Melting of a frustration-induced dimer crystal and incommensurability in the J_1-J_2 two-leg ladder
They account for the evolution of the spin gap and incommensurate wavevectors in the RS phase obtained by simulations.
Melting of a frustration-induced dimer crystal and incommensurability in the J_1-J_2 two-leg ladder
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