AskDefine | Define discrepancy

Dictionary Definition

discrepancy

Noun

1 a difference between conflicting facts or claims or opinions; "a growing divergence of opinion" [syn: disagreement, divergence, variance]
2 an event that departs from expectations [syn: variance, variant]

User Contributed Dictionary

English

Pronunciation

  • /dɪsˈkrɛpənsi/ (RP)

Noun

  1. An inconsistency between facts or sentiments.
    They found a discrepancy between the first set of test results and the second, and they're still trying to figure out why.
  2. The state or quality of being discrepant.

Quotations

  • 1841 — Edgar Allan Poe, Three Sundays in a Week
    The fact is, some trivial discrepancy did exist, just then, between what I said and what I had not the courage to say—between what I did and what I had half a mind to do.
  • 1873 — James Clerk Maxwell, A Treatise on Electricity and Magnetism, Preface
    I was aware that there was supposed to be a difference between Faraday's way of conceiving phenomena and that of the mathematicians, so that neither he nor they were satisfied with each other's language. I had also the conviction that this discrepancy did not arise from either party being wrong
  • 1889 — Mark Twain, A Connecticut Yankee in King Arthur's Court, Ch XXVIII
    Sire, as between clothes and countenance, you are all right, there is no discrepancy; but as between your clothes and your bearing, you are all wrong, there is a most noticeable discrepancy.
  • 1911 — Algernon Blackwood, The Centaur, XXX
    The discrepancies--the omissions in his written account especially--were simply due, I feel, to the fact that his skill in words was not equal to the depth and brilliance of the emotions that he experienced.
  • 1923 — H. P. Lovecraft, The Horror at Martin's Beach
    Despite the large number of witnesses, no two accounts agree; and the testimony taken by local authorities contains the most amazing discrepancies.
  • 1946 — Paramahansa Yogananda, Autobiography of a Yogi, Ch 44
    One day the public treasurer, Kasturabai, could not account for a disbursement of four rupees. Gandhi duly published an auditing in which he inexorably pointed out his wife's four rupee discrepancy.
  • 1978 — Chicago Statement on Biblical Inerrancy, Art XIV
    We deny that alleged errors and discrepancies that have not yet been resolved violate the truth claims of the Bible.
  • 1980 — NASA/ASEE, Advanced Automation for Space Missions, Ch 5.2
    A machine can compare the stored description of itself with the description obtained by inspection, and note the discrepancies.

Translations

inconsistency
discrepant state

Extensive Definition

In mathematics, discrepancy theory describes the deviation of a situation from the state one would like it to be. It is also called theory of irregularities of distribution. This refers to the theme of classical discrepancy theory, namely distributing points in some space such that they are evenly distributed with respect to some (mostly geometrically defined) subsets. The discrepancy (irregularity) measures how far a given distribution deviates from an ideal one.
Discrepancy theory can be described as the study of inevitable irregularities of distributions, in measure-theoretic and combinatorial settings. Just as Ramsey theory elucidates the impossibility of total disorder, discrepancy theory studies the deviations from total uniformity.

History

Classic theorems

  • Axis-parallel rectangles in the plane (Roth, Schmidt)
  • Discrepancy of half-planes (Alexander, Matousek)
  • Arithmetic progressions (Roth, Sarkozy, Beck, Matousek & Spencer)
  • Beck-Fiala theorem
  • Six Standard Deviations Suffice (Spencer)

Major open problems

  • Axis-parallel rectangles in dimensions three and higher (Folklore)
  • Komlos conjecture
  • The three permutations problem (Beck)
  • Homogeneous arithmetic progressions (Erdos, $500)

Applications

See also

References

  • Irregularities of Distribution (Beck & Chen)
  • Geometric Discrepancy (Matousek)
  • The Discrepancy Method (Chazelle)
discrepancy in German: Diskrepanz
discrepancy in Serbian: Дискрепанција

Synonyms, Antonyms and Related Words

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