In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In perturbation theory, the solution is expressed as a power series in a small parameter . The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of
usually become smaller. An approximate 'perturbation solution' is
obtained by truncating the series, usually by keeping only the first two
terms, the solution to the known problem and the 'first order'
perturbation correction.
Perturbation theory is used in a wide range of fields, and reaches its most sophisticated and advanced forms in quantum field theory. Perturbation theory (quantum mechanics) describes the use of this method in quantum mechanics. The field in general remains actively and heavily researched across multiple disciplines.
Description
Perturbation theory develops an expression for the desired solution in terms of a formal power series known as a perturbation series
in some "small" parameter, that quantifies the deviation from the
exactly solvable problem. The leading term in this power series is the
solution of the exactly solvable problem, while further terms describe
the deviation in the solution, due to the deviation from the initial
problem. Formally, we have for the approximation to the full solution a series in the small parameter (here called ε), like the following:
In this example, would be the known solution to the exactly solvable initial problem, and the terms represent the first-order, second-order, third-order, and higher-order terms, which may be found iteratively by a mechanistic but increasingly difficult procedure. For small
these higher-order terms in the series generally (but not always)
become successively smaller. An approximate "perturbative solution" is
obtained by truncating the series, often by keeping only the first two
terms, expressing the final solution as a sum of the initial (exact)
solution and the "first-order" perturbative correction
Some authors use big O notation to indicate the order of the error in the approximate solution:
If the power series in converges with a nonzero radius of convergence, the perturbation problem is called a regular perturbation problem. In regular perturbation problems, the asymptotic solution smoothly approaches the exact solution.
However, the perturbation series can also diverge, and the truncated
series can still be a good approximation to the true solution if it is
truncated at a point at which its elements are minimum. This is called
an asymptotic series.
If the perturbation series is divergent or not a power series (for
example, if the asymptotic expansion must include non-integer powers or negative powers ) then the perturbation problem is called a singular perturbation problem. Many special techniques in perturbation theory have been developed to analyze singular perturbation problems.
Prototypical example
The earliest use of what would now be called perturbation theory was to deal with the otherwise unsolvable mathematical problems of celestial mechanics: for example the orbit of the Moon, which moves noticeably differently from a simple Keplerian ellipse because of the competing gravitation of the Earth and the Sun.
Perturbation methods start with a simplified form of the original problem, which is simple enough to be solved exactly. In celestial mechanics, this is usually a Keplerian ellipse. Under Newtonian gravity, an ellipse is exactly correct when there are only two gravitating bodies (say, the Earth and the Moon) but not quite correct when there are three or more objects (say, the Earth, Moon, Sun, and the rest of the Solar System) and not quite correct when the gravitational interaction is stated using formulations from general relativity.
Perturbative expansion
Keeping the above example in mind, one follows a general recipe to obtain the perturbation series. The perturbative expansion
is created by adding successive corrections to the simplified problem.
The corrections are obtained by forcing consistency between the
unperturbed solution, and the equations describing the system in full.
Write for this collection of equations; that is, let the symbol stand in for the problem to be solved. Quite often, these are differential equations, thus, the letter "D".
The process is generally mechanical, if laborious. One begins by writing the equations so that they split into two parts: some collection of equations which can be solved exactly, and some additional remaining part for some small . The solution (to ) is known, and one seeks the general solution to .
Next the approximation is inserted into . This results in an equation for , which, in the general case, can be written in closed form as a sum over integrals over . Thus, one has obtained the first-order correction and thus is a good approximation to . It is a good approximation, precisely because the parts that were ignored were of size . The process can then be repeated, to obtain corrections , and so on.
In practice, this process rapidly explodes into a profusion of terms, which become extremely hard to manage by hand. Isaac Newton is reported to have said, regarding the problem of the Moon's orbit, that "It causeth my head to ache."
This unmanageability has forced perturbation theory to develop into a
high art of managing and writing out these higher order terms. One of
the fundamental breakthroughs for controlling the expansion are the Feynman diagrams, which allow perturbation series to be written down diagrammatically.
Examples of the kinds of solutions that are found perturbatively include the solution of the equation of motion (e.g., the trajectory of a particle), the statistical average of some physical quantity (e.g., average magnetization), the ground state energy of a quantum mechanical problem.
Examples of exactly solvable problems that can be used as starting points include linear equations, including linear equations of motion (harmonic oscillator, linear wave equation),
statistical or quantum-mechanical systems of non-interacting particles
(or in general, Hamiltonians or free energies containing only terms
quadratic in all degrees of freedom).
Examples of systems that can be solved with perturbations include
systems with nonlinear contributions to the equations of motion, interactions between particles, terms of higher powers in the Hamiltonian/free energy.
For physical problems involving interactions between particles,
the terms of the perturbation series may be displayed (and manipulated)
using Feynman diagrams.
History
Perturbation theory was first devised to solve otherwise intractable problems in the calculation of the motions of planets in the solar system. For instance, Newton's law of universal gravitation
explained the gravitation between two astronomical bodies, but when a
third body is added, the problem was, "How does each body pull on each?"
Newton's equation only allowed the mass of two bodies to be analyzed.
The gradually increasing accuracy of astronomical observations
led to incremental demands in the accuracy of solutions to Newton's
gravitational equations, which led several notable 18th and 19th century
mathematicians, such as Lagrange and Laplace, to extend and generalize the methods of perturbation theory.
These well-developed perturbation methods were adopted and adapted to solve new problems arising during the development of quantum mechanics in 20th century atomic and subatomic physics. Paul Dirac
developed quantum perturbation theory in 1927 to evaluate when a
particle would be emitted in radioactive elements. This was later named Fermi's golden rule. Perturbation theory in quantum mechanics is fairly accessible, as the
quantum notation allows expressions to be written in fairly compact
form, thus making them easier to comprehend. This resulted in an
explosion of applications, ranging from the Zeeman effect to the hyperfine splitting in the hydrogen atom.
Despite the simpler notation, perturbation theory applied to quantum field theory still easily gets out of hand. Richard Feynman developed the celebrated Feynman diagrams
by observing that many terms repeat in a regular fashion. These terms
can be replaced by dots, lines, squiggles and similar marks, each
standing for a term, a denominator, an integral, and so on; thus complex
integrals can be written as simple diagrams, with absolutely no
ambiguity as to what they mean. The one-to-one correspondence between
the diagrams, and specific integrals is what gives them their power.
Although originally developed for quantum field theory, it turns out the
diagrammatic technique is broadly applicable to all perturbative series
(although, perhaps, not always so useful).
In the second half of the 20th century, as chaos theory developed, it became clear that unperturbed systems were in general completely integrable systems, while the perturbed systems were not. This promptly lead to the study of "nearly integrable systems", of which the KAM torus is the canonical example. At the same time, it was also discovered that many (rather special) non-linear systems,
which were previously approachable only through perturbation theory,
are in fact completely integrable. This discovery was quite dramatic, as
it allowed exact solutions to be given. This, in turn, helped clarify
the meaning of the perturbative series, as one could now compare the
results of the series to the exact solutions.
The improved understanding of dynamical systems coming from chaos theory helped shed light on what was termed the small denominator problem or small divisor problem. It was observed in the 19th century (by Poincaré,
and perhaps earlier), that sometimes 2nd and higher order terms in the
perturbative series have "small denominators". That is, they have the
general form where , and are some complicated expressions pertinent to the problem to be solved, and and are real numbers; very often they are the energy of normal modes. The small divisor problem arises when the difference
is small, causing the perturbative correction to blow up, becoming as
large or maybe larger than the zeroth order term. This situation signals
a breakdown of perturbation theory: it stops working at this point, and
cannot be expanded or summed any further. In formal terms, the
perturbative series is a asymptotic series:
a useful approximation for a few terms, but ultimately inexact. The
breakthrough from chaos theory was an explanation of why this happened:
the small divisors occur whenever perturbation theory is applied to a
chaotic system. The one signals the presence of the other.
Beginnings in the study of planetary motion
Since
the planets are very remote from each other, and since their mass is
small as compared to the mass of the Sun, the gravitational forces
between the planets can be neglected, and the planetary motion is
considered, to a first approximation, as taking place along Kepler's
orbits, which are defined by the equations of the two-body problem, the two bodies being the planet and the Sun.
Since astronomic data came to be known with much greater
accuracy, it became necessary to consider how the motion of a planet
around the Sun is affected by other planets. This was the origin of the three-body problem; thus, in studying the system Moon–Earth–Sun the mass ratio between the Moon and the Earth was chosen as the small parameter. Lagrange and Laplace
were the first to advance the view that the constants which describe
the motion of a planet around the Sun are "perturbed", as it were, by
the motion of other planets and vary as a function of time; hence the
name "perturbation theory".
Perturbation theory was investigated by the classical scholars—Laplace, Poisson, Gauss—as a result of which the computations could be performed with a very high accuracy. The discovery of the planet Neptune in 1848 by Urbain Le Verrier, based on the deviations in motion of the planet Uranus (he sent the coordinates to Johann Gottfried Galle who successfully observed Neptune through his telescope), represented a triumph of perturbation theory.
Perturbation orders
The
standard exposition of perturbation theory is given in terms of the
order to which the perturbation is carried out: first-order perturbation
theory or second-order perturbation theory, and whether the perturbed
states are degenerate, which requires singular perturbation. In the singular case extra care must be taken, and the theory is slightly more elaborate.
In chemistry
Many of the ab initio quantum chemistry methods use perturbation theory directly or are closely related methods. Implicit perturbation theory works with the complete Hamiltonian from the very beginning and never specifies a perturbation operator as such. Møller–Plesset perturbation theory uses the difference between the Hartree–Fock
Hamiltonian and the exact non-relativistic Hamiltonian as the
perturbation. The zero-order energy is the sum of orbital energies. The
first-order energy is the Hartree–Fock energy and electron correlation
is included at second-order or higher. Calculations to second, third or
fourth order are very common and the code is included in most ab initio quantum chemistry programs. A related but more accurate method is the coupled cluster method.
Shell-crossing
A shell-crossing (sc) occurs in perturbation theory when matter trajectories intersect, forming a singularity. This limits the predictive power of physical simulations at small scales.
The Haskalah, often termed as the Jewish Enlightenment (Hebrew: הַשְׂכָּלָה; literally, "wisdom", "erudition" or "education"), was an intellectual movement among the Jews of Central and Eastern Europe, with a certain influence on those in Western Europe and the Muslim world. It arose as a defined ideological worldview during the 1770s, and its last stage ended around 1881, with the rise of Jewish nationalism.
The Haskalah pursued two complementary aims. It sought to
preserve the Jews as a separate, unique collective, and it pursued a set
of projects of cultural and moral renewal, including a revival of Hebrew for use in secular life, which resulted in an increase in Hebrew
found in print. Concurrently, it strove for an optimal integration in
surrounding societies. Practitioners promoted the study of exogenous
culture, style, and vernacular, and the adoption of modern values. At
the same time, economic production, and the taking up of new occupations
was pursued. The Haskalah promoted rationalism, liberalism, freedom of thought, and enquiry, and is largely perceived as the Jewish variant of the general Age of Enlightenment.
The movement encompassed a wide spectrum ranging from moderates, who
hoped for maximal compromise, to radicals, who sought sweeping changes.
In its various changes, the Haskalah fulfilled an important, though limited, part in the modernization of Central and Eastern European Jews. Its activists, the Maskilim,
exhorted and implemented communal, educational and cultural reforms in
both the public and the private spheres. Owing to its dual policies, it
collided both with the traditionalist rabbinic elite, which attempted to preserve old Jewish values and norms in their entirety, and with the radical assimilationists who wished to eliminate or minimize the existence of the Jews as a defined collective.
Definitions
Literary circle
The Haskalah was multifaceted, with many loci which rose and dwindled at different times and across vast territories. The name Haskalah became a standard self-appellation in 1860, when it was taken as the motto of the Odessa-based newspaper Ha-Melitz, but derivatives and the title Maskil for activists were already common in the first edition of Ha-Meassef from 1 October 1783: its publishers described themselves as Maskilim.[1]
While Maskilic centres sometimes had loose institutions around which
their members operated, the movement as a whole lacked any such.
In spite of that diversity, the Maskilim shared a sense of
common identity and self-consciousness. They were anchored in the
existence of a shared literary canon, which began to be formulated in
the very first Maskilic locus at Berlin. Its members, like Moses Mendelssohn, Naphtali Hirz Wessely, Isaac Satanow and Isaac Euchel,
authored tracts in various genres that were further disseminated and
re-read among other Maskilim. Each generation, in turn, elaborated and
added its own works to the growing body. The emergence of the Maskilic
canon reflected the movement's central and defining enterprise, the
revival of Hebrew as a literary language for secular purposes (its restoration as a spoken tongue
occurred only much later). The Maskilim researched and standardized
grammar, minted countless neologisms and composed poetry, magazines,
theatrical works and literature of all sorts in Hebrew. Historians
described the movement largely as a Republic of Letters, an intellectual community based on printing houses and reading societies.
The Maskilim's attitude toward Hebrew, as noted by Moses Pelli,
was derived from Enlightenment perceptions of language as reflecting
both individual and collective character. To them, a corrupt tongue
mirrored the inadequate condition of the Jews which they sought to
ameliorate. They turned to Hebrew as their primary creative medium. The
Maskilim inherited the Medieval Grammarians' – such as Jonah ibn Janah and Judah ben David Hayyuj – distaste of Mishnaic Hebrew and preference of the Biblical one as pristine and correct. They turned to the Bible as a source and standard, emphatically advocating what they termed "Pure Hebrew Tongue" (S'fat E'ver tzacha) and lambasting the Rabbinic style of letters, which mixed it with Aramaic as a single "Holy Tongue"
and often employed loanwords from other languages. Some activists,
however, were not averse to using Mishnaic and Rabbinic forms. They also
preferred the Sephardi pronunciation, considered more prestigious, to the Ashkenazi one, which was linked with the Jews of Poland,
who were deemed backward. The movement's literary canon is defined by a
grandiloquent, archaic register copying the Biblical one and often
combining lengthy allusions or direct quotes from verses in the prose.
During a century of activity, the Maskilim produced a massive contribution, forming the first phase of modern Hebrew literature. In 1755, Moses Mendelssohn began publishing Qohelet Musar
"The Moralist", regarded as the beginning of modern writing in Hebrew
and the very first journal in the language. Between 1789 and his death, Naphtali Hirz Wessely compiled Shirei Tif'eret "Poems of Glory", an eighteen-part epic cycle concerning Moses that exerted influence on all neo-Hebraic poets in the following generations. Joseph ha-Efrati Troplowitz [he] was the Haskalah's pioneering playwright, best known for his 1794 epic drama Melukhat Sha'ul "Reign of Saul", which was printed in twelve editions by 1888. Judah Leib Ben-Ze'ev
was the first modern Hebrew grammarian, and beginning with his 1796
manual of the language, he authored books which explored it and were
vital reading material for young Maskilim until the end of the 19th
century. Solomon Löwisohn was the first to translate Shakespeare into Hebrew, and an abridged form of the "Are at this hour asleep!" monologue in Henry IV, Part 2 was included in his 1816 lyrical compilation Melitzat Yeshurun (Eloquence of Jeshurun).
Joseph Perl pioneered satirist writings in his biting, mocking critique of Hasidic Judaism, Megaleh Tmirin "Revealer of Secrets" from 1819. Avraham Dov Ber Lebensohn was primarily a leading metricist, with his 1842 Shirei S'fat haQodesh "Verses in the Holy Tongue" considered a milestone in Hebrew poetry, and also authored biblical exegesis and educational handbooks. Abraham Mapu authored the first Hebrew full-length novel, Ahavat Zion "Love of Zion", which was published in 1853 after twenty-three years of work. Judah Leib Gordon was the most eminent poet of his generation and arguably of the Haskalah in its entirety. His most famous work was the 1876 epic Qotzo shel Yodh (Tittle of a Jot). Mendele Mocher Sforim was during his youth a Maskilic writer but from his 1886 B-Sether Ra'am
(Hidden in Thunder), he abandoned its strict conventions in favour of a
mixed, facile and common style. His career marked the end of the
Maskilic period in Hebrew literature and the beginning of the Era of Renaissance.
The writers of the latter period lambasted their Maskilic predecessors
for their didactic and florid style, more or less paralleling the
Romantics' criticism of Enlightenment literature.
The central platforms of the Maskilic "Republic of Letters" were
its great periodicals, each serving as a locus for contributors and
readers during the time it was published. The first was the Königsberg (and later Berlin)-based Ha-Meassef, launched by Isaac Abraham Euchel
in 1783 and printed with growing intervals until 1797. The magazine had
several dozen writers and 272 subscribers at its zenith, from Shklow in the east to London in the west, making it the sounding board of the Berlin Haskalah. The movement lacked an equivalent until the appearance of Bikurei ha-I'tim in Vienna between 1820 until 1831, serving the Moravian and GalicianHaskalah. That function was later fulfilled by the Prague-based Kerem Hemed from 1834 to 1857, and to a lesser degree by Kokhvei Yizhak, published in the same city from 1845 to 1870. The Russian Haskalah was robust enough to lack any single platform. Its members published several large magazines, including the Vilnius-based Ha-Karmel (1860–1880), Ha-Tsefirah in Warsaw and more, though the probably most influential of them all was Ha-Melitz, launched in 1860 at Odessa by Aleksander Zederbaum.
Reforming movement
While the partisans of the Haskalah
were much immersed in the study of sciences and Hebrew grammar, this
was not a profoundly new phenomenon, and their creativity was a
continuation of a long, centuries-old trend among educated Jews. What
truly marked the movement was the challenge it laid to the monopoly of
the rabbinic elite over the intellectual sphere of Jewish life,
contesting its role as spiritual leadership. In his 1782 circular Divrei Shalom v'Emeth (Words of Peace and Truth), Hartwig Wessely, one of the most traditional and moderate maskilim, quoted the passage from Leviticus Rabbah stating that a Torah scholar
who lacked wisdom was inferior to an animal's carcass. He called upon
the Jews to introduce general subjects, like science and vernacular
language, into their children's curriculum; this "Teaching of Man" was
necessarily linked with the "Teaching (Torah) of God", and the latter, though superior, could not be pursued and was useless without the former.
Historian Shmuel Feiner discerned that Wessely insinuated
(consciously or not) a direct challenge to the supremacy of sacred
teachings, comparing them with general subjects and implying the latter
had an intrinsic rather than merely instrumental value. He therefore
also contested the authority of the rabbinical establishment, which
stemmed from its function as interpreters of the holy teachings and
their status as the only truly worthy field of study. Though secular
subjects could be and were easily tolerated, their elevation to the same
level as sacred ones was a severe threat, and indeed mobilized the
rabbis against the nascent Haskalah. The potential of "Words of
Peace and Truth" was fully realized later, by the second generation of
the movement in Berlin and other radical maskilim, who openly and
vehemently denounced the traditional authorities. The appropriate
intellectual and moral leadership needed by the Jewish public in modern
times was, according to the maskilim, that of their own. Feiner
noted that in their usurpation of the title of spiritual elite,
unprecedented in Jewish history since the dawn of Rabbinic Judaism
(various contestants before the Enlightened were branded as schismatics
and cast out), they very much emulated the manner in which secular
intellectuals dethroned and replaced the Church from the same status
among Christians. Thus the maskilim generated an upheaval which –
though by no means alone – broke the sway held by the rabbis and the
traditional values over Jewish society. Combined with many other
factors, they laid the path to all modern Jewish movements and
philosophies, either those critical, hostile or supportive to
themselves.
The maskilim sought to replace the framework of values held by the Ashkenazim
of Central and Eastern Europe with their own philosophy, which embraced
the liberal, rationalistic notions of the 18th and 19th centuries and
cast them in their own particular mold. This intellectual upheaval was
accompanied by the desire to practically change Jewish society. Even the
moderate maskilim viewed the contemporary state of Jews as
deplorable and in dire need of rejuvenation, whether in matters of
morals, cultural creativity or economic productivity. They argued that
such conditions were rightfully scorned by others and untenable from
both practical and idealistic perspectives. It was to be remedied by the
shedding of the base and corrupt elements of Jewish existence and
retention of only the true, positive ones; indeed, the question what
those were, exactly, loomed as the greatest challenge of Jewish
modernity.
The more extreme and ideologically bent came close to the universalist aspirations of the radical Enlightenment,
of a world freed of superstition and backwardness in which all humans
will come together under the liberating influence of reason and
progress. The reconstituted Jews, these radical maskilim
believed, would be able to take their place as equals in an enlightened
world. But all, including the moderate and disillusioned, stated that
adjustment to the changing world was both unavoidable and positive in
itself.
Haskalah ideals were converted into practical steps via
numerous reform programs initiated locally and independently by its
activists, acting in small groups or even alone at every time and area.
Members of the movement sought to acquaint their people with European
culture, have them adopt the vernacular
language of their lands, and integrate them into larger society. They
opposed Jewish reclusiveness and self-segregation, called upon Jews to
discard traditional dress
in favour of the prevalent one, and preached patriotism and loyalty to
the new centralized governments. They acted to weaken and limit the
jurisdiction of traditional community institutions – the rabbinic courts,
empowered to rule on numerous civic matters, and the board of elders,
which served as lay leadership. The maskilim perceived those as remnants
of medieval discrimination. They criticized various traits of Jewish
society, such as child marriage
– traumatized memories from unions entered at the age of thirteen or
fourteen are a common theme in Haskalah literature – the use of anathema to enforce community will and the concentration on virtually only religious studies.
Maskilic reforms included educational efforts. In 1778, partisans
of the movement were among the founders of the Berlin Jewish Free
School, or Hevrat Hinuch Ne'arim (Society for the Education of
Boys), the first institution in Ashkenazi Jewry that taught general
studies in addition to the reformulated and reduced traditional
curriculum. This model, with different stresses, was applied elsewhere. Joseph Perl opened the first modern Jewish school in Galicia at Tarnopol in 1813, and Eastern European maskilim opened similar institutes in the Pale of Settlement and Congress Poland. They all abandoned the received methods of Ashkenazi education: study of the Pentateuch with the archaic I'vri-Taitsch (medieval Yiddish) translation and an exclusive focus on the Talmud as a subject of higher learning, all presided over by old-school tutors, melamdim,
who were particularly reviled in maskilic circles. Those were replaced
by teachers trained in modern methods, among others in the spirit of
German philanthropinism,
who sought to acquaint their pupils with refined Hebrew so they may
understand the Pentateuch and prayers and thus better identify with
their heritage; ignorance of Hebrew was often lamented by maskilim
as breeding apathy towards Judaism. Far less Talmud, considered
cumbersome and ill-suited for children, was taught; elements considered
superstitious, like midrashim,
were also removed. Matters of faith were taught in rationalistic
spirit, and in radical circles also in a sanitized manner. On the other
hand, the curriculum was augmented by general studies like math,
vernacular language, and so forth.
In the linguistic field, the maskilim wished to replace the dualism which characterized the traditional Ashkenazi community, which spoke Judaeo-German
and its formal literary language was Hebrew, with another: a refined
Hebrew for internal usage and the local vernacular for external ones.
They almost universally abhorred Judaeo-German, regarding it as a
corrupt dialect and another symptom of Jewish destitution – the movement
pioneered the negative attitude to Yiddish which persisted many years
later among the educated – though often its activists had to resort to
it for lack of better medium to address the masses. Aaron Halle-Wolfssohn, for example, authored the first modern Judaeo-German play, Leichtsinn und Frömmelei (Rashness and Sanctimony) in 1796. On the economic front, the maskilim
preached productivization and abandonment of traditional Jewish
occupations in favour of agriculture, trades and liberal professions.
In matters of faith (which were being cordoned off into a
distinct sphere of "religion" by modernization pressures) the movement's
partisans, from moderates to radicals, lacked any uniform coherent
agenda. The main standard through which they judged Judaism was that of
rationalism. Their most important contribution was the revival of Jewish philosophy, rather dormant since the Italian Renaissance, as an alternative to mysticist Kabbalah
which served as almost the sole system of thought among Ashkenazim and
an explanatory system for observance. Rather than complex allegorical exegesis, the Haskalah sought a literal understanding of scripture and sacred literature. The rejection of Kabbalah, often accompanied with attempts to refute the ancientness of the Zohar, were extremely controversial in traditional society; apart from that, the maskilim
had little in common. On the right-wing were conservative members of
the rabbinic elite who merely wanted a rationalist approach, and on the
extreme left some ventured far beyond the pale of orthodoxy towards Deism.
Another aspect was the movement's attitude to gender relations. Many of the maskilim
were raised in the rabbinic elite, in which (unlike among the poor
Jewish masses or the rich communal wardens) the males were immersed in
traditional studies and their wives supported them financially, mostly
by running business. Many of the Jewish enlightened were traumatized by
their own experiences, either of assertive mothers or early marriage,
often conducted at the age of thirteen. Bitter memories from those are a
common theme in maskilic autobiographies. Having imbibed the
image of European bourgeoisie family values, many of them sought to
challenge the semi-matriarchal order of rabbinic families – which
combined a lack of Jewish education for women with granting them the
status of providers – early marriage, and rigid modesty. Instead, they
insisted that men become economically productive while confining their
wives to the home environment but also granting them proper religious
education, a reversal of what was customary among Jews, copying
Christian attitudes at the time.
Transitory phenomena
The Haskalah
was also mainly a movement of transformation, straddling both the
declining traditional Jewish society of autonomous community and
cultural seclusion and the beginnings of a modern Jewish public. As
noted by Feiner, everything connected with the Haskalah was
dualistic in nature. The Jewish Enlighteners pursued two parallel
agendas: they exhorted the Jews to acculturate and harmonize with the
modern state, and demanded that the Jews remain a distinct group with
its own culture and identity. Theirs was a middle position between
Jewish community and surrounding society, received mores and modernity.
Sliding away from this precarious equilibrium, in any direction,
signified also one's break with the Jewish Enlightenment.
Virtually all maskilim received old-style, secluded
education, and were young Torah scholars before they were first exposed
to outside knowledge (from a gender perspective, the movement was almost
totally male-dominated; women did not receive sufficient tutoring to
master Hebrew). For generations, Mendelssohn's Bible translation to
German was employed by such young initiates to bridge the linguistic gap
and learn a foreign language, having been raised on Hebrew and Yiddish
only. The experience of abandoning one's sheltered community and
struggle with tradition was a ubiquitous trait of maskilic
biographies. The children of these activists almost never followed their
parents; they rather went forward in the path of acculturation and
assimilation. While their fathers learned the vernaculars late and still
consumed much Hebrew literature, the little available material in the
language did not attract their offspring, who often lacked a grasp of
Hebrew due to not sharing their parents' traditional education. Haskalah was, by and large, a unigenerational experience.
In the linguistic field, this transitory nature was well
attested. The traditional Jewish community in Europe inhabited two
separate spheres of communication: one internal, where Hebrew served as
written high language and Yiddish as vernacular for the masses, and one
external, where Latin and the like were used for apologetic and
intercessory purposes toward the Christian world. A tiny minority of
writers was concerned with the latter. The Haskalah sought to
introduce a different bilingualism: renovated, refined Hebrew for
internal matters, while Yiddish was to be eliminated; and national
vernaculars, to be taught to all Jews, for external ones. However, they
insisted on the maintenance of both spheres. When acculturation far
exceeded the movement's plans, Central European Jews turned almost
solely to the vernacular. David Sorkin demonstrated this with the two great journals of German Jewry: the maskilic Ha-Me'assef was written in Hebrew and supported the study of German; the post-maskilic Sulamith (published since 1806) was written almost entirely in German, befitting its editors' agenda of linguistic assimilation. Likewise, upon the demise of Jewish Enlightenment in Eastern Europe, authors abandoned the maskilic paradigm not toward assimilation but in favour of exclusive use of Hebrew and Yiddish.
The political vision of the Haskalah was predicated on a
similar approach. It opposed the reclusive community of the past but
sought a maintenance of a strong Jewish framework (with themselves as
leaders and intercessors with the state authorities); the Enlightened
were not even fully agreeable to civic emancipation, and many of them
viewed it with reserve, sometimes anxiety. In their writings, they drew a
sharp line between themselves and whom they termed "pseudo-maskilim"
– those who embraced the Enlightenment values and secular knowledge but
did not seek to balance these with their Jewishness, but rather strove
for full assimilation. Such elements, whether the radical universalists
who broke off the late Berlin Haskalah or the Russified
intelligentsia in Eastern Europe a century later, were castigated and
derided no less than the old rabbinic authorities which the movement
confronted. It was not uncommon for its partisans to become a
conservative element, combating against further dilution of tradition:
in Vilnius, Samuel Joseph Fuenn turned from a progressive into an adversary of more radical elements within a generation. In the Maghreb, the few local maskilim
were more concerned with the rapid assimilation of local Jews into the
colonial French culture than with the ills of traditional society.
Likewise, those who abandoned the optimistic, liberal vision of
the Jews (albeit as a cohesive community) integrating into wider society
in favour of full-blown Jewish nationalism or radical, revolutionary
ideologies which strove to uproot the established order like Socialism, also broke with the Haskalah. The Jewish national movements of Eastern Europe, founded by disillusioned maskilim,
derisively regarded it – in a manner similar to other
romantic-nationalist movements' understanding of the general
Enlightenment – as a naive, liberal and assimilationist ideology which
induced foreign cultural influences, gnawed at the Jewish national
consciousness and promised false hopes of equality in exchange for
spiritual enslavement. This hostile view was promulgated by nationalist
thinkers and historians, from Peretz Smolenskin, Ahad Ha'am, Simon Dubnow and onwards. It was once common in Israeli historiography.
A major factor which always characterized the movement was its
weakness and its dependence of much more powerful elements. Its
partisans were mostly impoverished intellectuals, who eked out a living
as private tutors and the like; few had a stable financial base, and
they required patrons, whether affluent Jews or the state's
institutions. This triplice – the authorities, the Jewish communal
elite, and the maskilim – was united only in the ambition of
thoroughly reforming Jewish society. The government had no interest in
the visions of renaissance which the Enlightened so fervently cherished.
It demanded the Jews to turn into productive, loyal subjects with
rudimentary secular education, and no more. The rich Jews were sometimes
open to the movement's agenda, but mostly practical, hoping for a
betterment of their people that would result in emancipation and equal
rights. Indeed, the great cultural transformation which occurred among
the Parnassim (affluent communal wardens) class – they were
always more open to outside society, and had to tutor their children in
secular subjects, thus inviting general Enlightenment influences – was a
precondition of Haskalah. The state and the elite required the maskilim
as interlocutors and specialists in their efforts for reform,
especially as educators, and the latter used this as leverage to benefit
their ideology. However, the activists were much more dependent on the
former than vice versa; frustration from one's inability to further the maskilic
agenda and being surrounded by apathetic Jews, either conservative
"fanatics" or parvenu "assimilationists", is a common theme in the
movement's literature.
The term Haskalah became synonymous, among friends and foes alike and in much of early Jewish historiography,
with the sweeping changes that engulfed Jewish society (mostly in
Europe) from the late 18th century to the late 19th century. It was
depicted by its partisans, adversaries and historians like Heinrich Graetz as a major factor in those; Feiner noted that "every modern Jew was identified as a maskil and every change in traditional religious patterns was dubbed Haskalah". Later research greatly narrowed the scope of the phenomenon and limited its importance: while Haskalah
undoubtedly played a part, the contemporary historical consensus
portrays it as much humbler. Other transformation agents, from
state-imposed schools to new economic opportunities, were demonstrated
to have rivaled or overshadowed the movement completely in propelling
such processes as acculturation, secularization, religious reform from
moderate to extreme, adoption of native patriotism and so forth. In many
regions the Haskalah had no effect at all.
Origins
As long as the Jews lived in segregated communities, and as long as all social interaction with their gentile neighbors was limited, the rabbi
was the most influential member of the Jewish community. In addition to
being a religious scholar and "clergy", a rabbi also acted as a civil
judge in all cases in which both parties were Jews. Rabbis sometimes had
other important administrative powers, together with the community
elders. The rabbinate was the highest aim of many Jewish boys, and the
study of the Talmud was the means of obtaining that coveted position, or
one of many other important communal distinctions. Haskalah followers
advocated "coming out of the ghetto", not just physically but also mentally and spiritually, in order to assimilate among gentile nations.
The example of Moses Mendelssohn (1729–86), a Prussian Jew, served to lead this movement, which was also shaped by Aaron Halle-Wolfssohn (1754–1835) and Joseph Perl (1773–1839). Mendelssohn's extraordinary success as a popular philosopher and man of letters
revealed hitherto unsuspected possibilities of integration and
acceptance of Jews among non-Jews. Mendelssohn also provided methods for
Jews to enter the general society of Germany. A good knowledge of the
German language was necessary to secure entrance into cultured German
circles, and an excellent means of acquiring it was provided by
Mendelssohn in his German translation of the Torah. This work became a bridge over which ambitious young Jews could pass to the great world of secular knowledge. The Biur,
or grammatical commentary, prepared under Mendelssohn's supervision,
was designed to counteract the influence of traditional rabbinical
methods of exegesis. Together with the translation, it became, as it were, the primer of Haskalah.
Language played a key role in the haskalah movement, as
Mendelssohn and others called for a revival of Hebrew and a reduction in
the use of Yiddish. The result was an outpouring of new, secular literature, as well as critical studies of religious texts. Julius Fürst
along with other German-Jewish scholars compiled Hebrew and Aramaic
dictionaries and grammars. Jews also began to study and communicate in
the languages of the countries in which they settled, providing another
gateway for integration.
Berlin was the city of origin for the movement. The capital city of Prussia and, later, the German Empire,
Berlin became known as a secular, multi-cultural and multi-ethnic
center, a fertile environment for conversations and radical movements.
This move by the Maskilim away from religious study, into much more
critical and worldly studies was made possible by this German city of
modern and progressive thought. It was a city in which the rising middle
class Jews and intellectual elites not only lived among, but were
exposed to previous age of enlightenment thinkers such as Voltaire, Diderot, and Rousseau. The movement is often referred to as the Berlin Haskalah.
Reference to Berlin in relation to the Haskalah movement is necessary
because it provides context for this episode of Jewish history.
Subsequently, having left Germany and spreading across Eastern Europe,
the Berlin Haskalah influenced multiple Jewish communities who
were interested in non-religious scholarly texts and insight to worlds
beyond their Jewish enclaves.
Spread
Haskalah did not stay restricted to Germany, however, and the movement quickly spread throughout Europe. Poland–Lithuania was the heartland of Rabbinic Judaism, with its two streams of Misnagdic Talmudism centred in Lithuania and other regions, and Hasidic
mysticism popular in Ukraine, Poland, Hungary and Russia. In the 19th
century, Haskalah sought dissemination and transformation of traditional
education and inward pious life in Eastern Europe. It adapted its
message to these different environments, working with the Russian
government of the Pale of Settlement to influence secular educational methods, while its writers satirised Hasidic mysticism, in favour of solely Rationalist interpretation of Judaism. Isaac Baer Levinsohn (1788–1860) became known as the "Russian Mendelssohn". Joseph Perl's
(1773–1839) satire of the Hasidic movement, "Revealer of Secrets"
(Megalleh Temirim), is said to be the first modern novel in Hebrew. It
was published in Vienna in 1819 under the pseudonym "Obadiah ben
Pethahiah". The Haskalah's message of integration into non-Jewish
society was subsequently counteracted by alternative secular Jewish political movements
advocating Folkish, Socialist or Nationalist secular Jewish identities
in Eastern Europe. While Haskalah advocated Hebrew and sought to remove
Yiddish, these subsequent developments advocated Yiddish Renaissance among Maskilim. Writers of Yiddish literature variously satirised or sentimentalised Hasidic mysticism.
Effects
The Haskalah also resulted in the creation of a secular Jewish culture, with an emphasis on Jewish history and Jewish identity,
rather than on religion. This, in turn, resulted in the political
engagement of Jews in a variety of competing ways within the countries
where they lived on issues that included
later (in the face of continued persecutions in late nineteenth-century Europe), the development of Zionism.
One commentator describes these effects as "The emancipation of the
Jews brought forth two opposed movements: the cultural assimilation,
begun by Moses Mendelssohn, and Zionism, founded by Theodor Herzl in 1896."
One facet of the Haskalah was a widespread cultural adaptation,
as those Jews who participated in the enlightenment began, in varying
degrees, to participate in the cultural practices of the surrounding
gentile population. Connected with this was the birth of the Reform movement, whose founders (such as Israel Jacobson and Leopold Zunz)
rejected the continuing observance of those aspects of Jewish law which
they classified as ritual—as opposed to moral or ethical. Even within
orthodoxy, the Haskalah was felt through the appearance, in response, of
the Mussar Movement in Lithuania, and Torah im Derech Eretz
in Germany. "Enlightened" Jews sided with gentile governments, in plans
to increase secular education and assimilation among the Jewish masses,
which brought them into acute conflict with the orthodox, who believed
this threatened the traditional Jewish lifestyle – which had up until that point been maintained through segregation from their gentile neighbors – and Jewish identity itself.
The spread of Haskalah affected Judaism, as a religion, because
of the degree to which different sects desired to be integrated, and in
turn, integrate their religious traditions. The effects of the
Enlightenment were already present in Jewish religious music, and in
opinion on the tension between traditionalist and modernist tendencies.
Groups of Reform Jews, including the Society of the Friends of Reform and the Association for the Reform of Judaism
were formed, because such groups wanted, and actively advocated for, a
change in Jewish tradition, in particular, regarding rituals like
circumcision.
Another non-Orthodox group was the Conservative Jews, who emphasized
the importance of traditions but viewed with a historical perspective.
The Orthodox Jews were actively against these reformers because they
viewed changing Jewish tradition as an insult to God and believed that
fulfillment in life could be found in serving God and keeping his
commandments.
The effect of Haskalah was that it gave a voice to plurality of views,
while the orthodoxy preserved the tradition, even to the point of
insisting on dividing between sects.
Another important facet of the Haskalah was its interest in
non-Jewish religions, and for some the desire to synchronize or
appreciate Christian and Islamic traditions and history. Moses
Mendelssohn criticized some aspects of Christianity, but depicted Jesus
as a Torah-observant rabbi, who was loyal to traditional Judaism.
Mendelssohn explicitly linked positive Jewish views of Jesus with the
issues of Emancipation and Jewish-Christian reconciliation. Similar
revisionist views were expressed by Rabbi Isaac Ber Levinsohn and other
traditional representatives of the Haskalah movement.
Aleksander Zederbaum (1816–1893) was a Polish-Russian Jewish journalist. He was founder and editor of Ha-Meliẓ, and other periodicals published in Russian and Yiddish; he wrote in Hebrew.
Avrom Ber Gotlober
(1811–1899) was a Jewish writer, poet, playwright, historian,
journalist and educator. He mostly wrote in Hebrew, but also wrote
poetry and dramas in Yiddish. His first collection was published in
1835.
David Friesenhausen (1756–1828), was a Hungarian maskil, mathematician, and rabbi.
Ephraim Deinard
(1846–1930) was one of the greatest Hebrew 'bookmen' of all time. He
was a bookseller, bibliographer, publicist, polemicist, historian,
memoirist, author, editor and publisher.
Gotthold Ephraim Lessing
(1729–1781) was a German philosopher, dramatist, publicist and art
critic, and a representative of the Enlightenment era; considered by
theatre historians to have been the first dramaturg. Author of works
attempting to reconcile the Abrahamic faiths, such as Nathan der Weise, Nathan the Wise.
Isaac Bär Levinsohn
(1788-1860), also known as the Ribal; Jewish scholar of Hebrew, a
satirist, a writer and Haskalah leader. He has been called "the
Mendelssohn of Russia."
Moses Mendelssohn (1729-1786) philosopher and theologian, one of the central founders of Haskalah (noted in Haskalah article)
Joseph Perl (1773-1839) (noted in Haskalah article)
Isaac ben Jacob Benjacob
(1801–1863) was a Russian bibliographer, author, and publisher. His
parents moved to Vilnius when he was still a child, and there he
received instruction in Hebrew grammar and rabbinical lore.
Kalman Schulman (1819–1899) was a Jewish writer who translated various volumes and novels into Hebrew.
Leopold Zunz
(1794–1886) was the German Jewish founder of academic Judaic Studies
(Wissenschaft des Judentums), the critical investigation of Jewish
literature, hymnology and ritual.