# divergence

## Definitions

• WordNet 3.6
• n divergence the act of moving away in different direction from a common point "an angle is formed by the divergence of two straight lines"
• n divergence a difference between conflicting facts or claims or opinions "a growing divergence of opinion"
• n divergence an infinite series that has no limit
• n divergence a variation that deviates from the standard or norm "the deviation from the mean"
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Webster's Revised Unabridged Dictionary
• Divergence A receding from each other in moving from a common center; the state of being divergent; as, an angle is made by the divergence of straight lines. "Rays come to the eye in a state of divergency ."
• Divergence Disagreement; difference. "Related with some divergence by other writers."
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Century Dictionary and Cyclopedia
• n divergence The act or state of diverging, or moving or pointing in different directions (not directly opposed) from a common point; a receding one from another: opposed to convergence: as, the divergence of lines.
• n divergence Departure from a course or standard; differentiation in action or character; deviation: as, the divergence of religious sects; divergence from rectitude.
• n divergence In mathematics, the negative of the scalar part of the result of operating with the Hamiltonian operator upon a vector function. It is so called because if the vector function represents displacements of the parts of a fluid, the divergence represents the decrement of density at any point due to this displacement.
• n divergence In botany, gradual separation during the process of lengthening, as in the pods of Asclepias.
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Chambers's Twentieth Century Dictionary
• Divergence a tendency to recede from one point
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## Quotations

• Robert Frost
“Two roads diverge in a wood, and I took the one less traveled by, and that has made all the difference.”

## Etymology

Webster's Revised Unabridged Dictionary
Cf. F. divergence,
Chambers's Twentieth Century Dictionary
L. dis, asunder, vergĕre, to incline.

## Usage

### In literature:

Only thus can we forecast the probable course and consequences of the free social intercourse of widely divergent races.
"Evolution Of The Japanese, Social And Psychic" by Sidney L. Gulick
And yet all the time she was wondering how she should break it to him that their ways must now diverge.
"The Divine Fire" by May Sinclair
Some divergence in view as to music is more easily condoned, on both sides, than in the other realms of the spirit.
"Mount Music" by E. Oe. Somerville and Martin Ross
A wedge of mountainous country separated these roads as they diverged from the neighbourhood of Montenotte.
"The Life of Napoleon I (Volumes, 1 and 2)" by John Holland Rose
Here, of course, the parallelism ends and the divergence begins.
"The Promise Of American Life" by Herbert David Croly
This death on the stage is the only point on which Mr. Browning diverges from historical truth.
"A Handbook to the Works of Browning (6th ed.)" by Mrs. Sutherland Orr
That such divergence of character has actually occurred we have some direct evidence.
"Darwinism (1889)" by Alfred Russel Wallace
They were wholly divergent, and divergence there spelt disaster.
"The Development of the European Nations, 1870-1914 (5th ed.)" by John Holland Rose
The chief effect of the violences and cruelties applied was to increase the divergency of feeling between the brute and his master.
"Around The Tea-Table" by T. De Witt Talmage
At this point the two systems diverge.
"Ten Great Religions" by James Freeman Clarke
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### In poetry:

From the common urges,
From the human highest
Far thy path diverges:
Following thou fliest…
"Time Without End" by Arthur Rimbaud
TWO travellers, worn with sun and rain
And gropings o'er dim paths unknown,
Meet where long separate ways have grown
To one, and then diverge again.
"Sundered Paths" by Mathilde Blind
Then from my heart will young petals diverge,
As rays of the sun from their focus;
I from the darkness of earth will emerge,
A happy and beautiful crocus.
"The Crocus's Soliloquy" by Hannah Flagg Gould
We've reached diverging paths, dear heart,
'Tis pity, but 'tis true, we part;
It may be thine, it may be mine;
But truly the fault seems thine.
But place it, dear, just where you will,
The fault, let it be mine.
"The Love That Would Not Keep" by Samuel Alfred Beadle
Still I passed on until I reached at length, not knowing
Whither the tangled and diverging paths might lead,
A land of baser men, whose coming and whose going
Were urged by fear, and hunger, and the curse of greed.
"The Land Of Pallas" by Archibald Lampman
Young life and young thought are alike barred,
And no unheralded noises jolt old nerves,
And old wheezy breaths
Pass around old thoughts, dry as snuff,
And there is no divergence and no friction
Because life is flattened and ground as by many mills.
"The Ghetto" by Lola Ridge

### In news:

Roads diverge, loop, merge and meander.
Michigan decommits take divergent paths -- one could lead back to Ann Arbor.
With many more members and increasingly diverging interests, a one-size Europe may no longer fit all.
Growing divergence in various model forecast tracks.
A diverging diamond with a flyover is part of Alternative 3 for the interchange at Interstate 75 and Collier Boulevard, according to the Florida Department of Transportation's project development and environment study.
Where are the divergent voices in these newsrooms that would present a more accurate picture of America.
That initial scene diverges into three main story arcs that come together in the second act.
BERLIN — The widely divergent paths that London and Berlin envision for the European Union came into stark relief on Tuesday, adding to a growing sense that a more deeply integrated Europe would be one with less participation from Britain.
The reasons for the divergent economic circumstances of the two towns have emerged as a focal point of the French presidential campaign.
I've bolded, in these translations, the bits that diverge from the above version you've seen dominating coverage of the controversy .
Jim Dickrell is the editor of Dairy Today and is based in Monticello, Minn. An Idaho cheese manufacturer and a dairy producer diverge over free market and market reality.
Divergent Views, Agency Infighting Slow White House Efforts to Address the Cause of Deadly Strike on Consulate in Libya.
U-M decommits take divergent paths -- one could lead back to Ann Arbor.
Two students, two high schools, two divergent paths to college.
Obama, Romney offer divergent closing arguments in key battlegrounds.
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### In science:

This allows us to trade off the divergent sum for a divergent integral, which may be computed using the standard results of dimensional regularization.
Power corrections in models with extra dimensions
For SF networks with γ ≤ 3, µ diverges as N → ∞, as a consequence of the divergence of hk2 i.
Self-avoiding walks on scale-free networks
Further, when we adopt KL-divergence divided by √n instead of normalized KL-divergence, the compressed data is different from the uniform random number.
Second order asymptotics in fixed-length source coding and intrinsic randomness
For comparison with Han’s result, we treat intrinsic randomness under another KL-divergence criterion, in which the input distributions of KL-divergence are exchanged.
Second order asymptotics in fixed-length source coding and intrinsic randomness
The divergence of the total number of paths is typical: average quantities as well as typical characteristics diverge near the transition point.
Kinetic Theory of Random Graphs
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