When did Kalidasa live?

The most popular theory is that Kalidasa flourished during the reign of Chandragupta II, and therefore lived around 4th-5th century CE. Several Western scholars have supported this theory, since the days of William Jones and A. B. Keith. Many Indian scholars, such as Vasudev Vishnu Mirashi and Ram Gupta, also place Kalidasa in this period. According to this theory, his career might have extended to the reign of Kumaragupta I (r. 414 – 455 CE), and possibly, to that of Skandagupta (r. 455 – 467 CE).

Kālidāsa

Kālidāsa was a Classical Sanskrit writer, widely regarded as the greatest poet and dramatist in the Sanskrit language of India. His plays and poetry are primarily based on the Vedas, the Mahabharata and the Puranas.

Much about his life is unknown, only what can be inferred from his poetry and plays. His works cannot be dated with precision, but they were most likely authored within the 4th-5th century CE.

Scholars have speculated that Kalidasa may have lived near the Himalayas, in the vicinity of Ujjain, and in Kalinga. This hypothesis is based on Kalidasa's detailed description of the Himalayas in his "Kumārasambhava", the display of his love for Ujjain in "Meghadūta", and his highly eulogistic descriptions of Kalingan emperor Hemāngada in "Raghuvaṃśa" (sixth "sarga").

Lakshmi Dhar Kalla (1891-1953), a Sanskrit scholar and a Kashmiri Pandit, wrote a book titled "The birth-place of Kalidasa" (1926), which tries to trace the birthplace of Kalidasa based on his writings. He concluded that Kalidasa was born in Kashmir, but moved southwards, and sought the patronage of local rulers to prosper. The evidence cited by him from Kalidasa's writings includes:According to folklore, once a scholarly princess decided to find a suitable groom by testing men in her kingdom for their intelligence. When no man could pass the test, the frustrated citizens decided to send Kalidasa, an unintelligent man, for an interview with the princess. Kalidasa fared poorly, and was greatly humiliated by the princess. Challenged by the princess, he visited a Kali temple, and was inspired to learn Sanskrit; he studied the Puranas and other ancient texts, and become a great poet. He then wrote three epics starting with the words of his insult: "अस्ति कश्चित् वाग्विशेश?".

Another legend is that he visited Kumaradasa, the king of Sri Lanka formerly known as Ceylon and, because of some treachery, Kalidasa was murdered there.

Several ancient and medieval books state that Kalidasa was a court poet of a king named Vikramaditya. A legendary king named Vikramāditya is said to have ruled from Ujjain around 1st century BCE. A section of scholars believe that this legendary Vikramaditya is not a historical figure at all. There are other kings who ruled from Ujjain and adopted the title "Vikramaditya", the most notable ones being Chandragupta II (r. 380 CE – 415 CE) and Yasodharman (6th century CE).

The earliest paleographical evidence of Kalidasa is found in a Sanskrit inscription dated c. 473 CE, found at Mandsaur's Sun temple, with some verses that appear to imitate Meghaduta Purva, 66; and the Ritusamhara V, 2-3, although Kalidasa is not named. His name, along with that of the poet Bharavi, is also mentioned in a stone inscription dated 634 C.E. found at Aihole, located in present-day Karnataka.

Some scholars, including M. Srinivasachariar and T. S. Narayana Sastri, believe that all the works attributed to "Kalidasa" are not by a single person. According to Srinivasachariar, writers from 8th and 9th centuries hint at the existence of three noted literary figures that share the name Kalidasa. These writers include Devendra (author of "Kavi-Kalpa-Lata"), Rajashekhara and Abhinanda. Sastri lists the works of these three Kalidasas as follows:Sastri goes on to mention six other literary figures known by the name "Kalidasa": Parimala Kalidasa alias Padmagupta (author of "Navasahasanka Charita"), Kalidasa alias Yamakakavi (author of "Nalodaya"), Nava Kalidasa (author of "Champu Bhagavata"), Akbariya Kalidasa (author of several "samasya"s or riddles), Kalidasa VIII (author of "Lambodara Prahasana"), and Abhinava Kalidasa alias Madhava (author of "Sankshepa-Sankara-Vijayam").

According to K. Krishnamoorthy, "Vikramaditya" and "Kalidasa" were used as common nouns to describe any patron king and any court poet respectively.

Kālidāsa wrote three plays. Among them, "Abhijñānaśākuntalam" ("Of Shakuntala recognised by a token") is generally regarded as a masterpiece. It was among the first Sanskrit works to be translated into English, and has since been translated into many languages.

Kālidāsa is the author of two epic poems, "Raghuvaṃśa" ("Dynasty of Raghu") and "Kumārasambhava" (Birth of 'Kumara' or Subrahmanya).Kālidāsa also wrote two "khandakavyas" (minor poems):Montgomery Schuyler, Jr. published a bibliography of the editions and translations of the drama Shakuntala while preparing his work "Bibliography of the Sanskrit Drama". Schuyler later completed his bibliography series of the dramatic works of Kālidāsa by compiling bibliographies of the editions and translations of Vikramorvaçī and Mālavikāgnimitra. Sir William Jones published English translation of "Sakuntala" in 1791 C.E. and "Rtusamhara" was published by him in original text during 1792 C.E.

Many scholars have written commentaries on the works of Kālidāsa. Among the most studied commentaries are those by Kolāchala Mallinātha Suri, which were written in the 15th century during the reign of the Vijayanagar king, Deva Rāya II. The earliest surviving commentaries appear to be those of the 10th-century Kashmirian scholar Vallabhadeva. Eminent Sanskrit poets like Bāṇabhaṭṭa, Jayadeva and Rajasekhara have lavished praise on Kālidāsa in their tributes. A well-known Sanskrit verse ("Upamā Kālidāsasya...") praises his skill at "upamā", or similes. Anandavardhana, a highly revered critic, considered Kālidāsa to be one of the greatest Sanskrit poets ever. Of the hundreds of pre-modern Sanskrit commentaries on Kālidāsa's works, only a fraction have been contemporarily published. Such commentaries show signs of Kālidāsa's poetry being changed from its original state through centuries of manual copying, and possibly through competing oral traditions which ran alongside the written tradition.

Kālidāsa's "Abhijñānaśākuntalam" was one of the first works of Indian literature to become known in Europe. It was first translated to English and then from English to German, where it was received with wonder and fascination by a group of eminent poets, which included Herder and Goethe.

Kālidāsa's work continued to evoke inspiration among the artistic circles of Europe during the late 19th century and early 20th century, as evidenced by Camille Claudel's sculpture "Shakuntala".

Koodiyattam artist and Natya Shastra scholar Māni Mādhava Chākyār (1899–1990) choreographed and performed popular Kālidāsā plays including Abhijñānaśākuntala, Vikramorvaśīya and Mālavikāgnimitra.

The Kannada films "Mahakavi Kalidasa" (1955), featuring Honnappa Bagavatar, B. Sarojadevi and later "Kaviratna Kalidasa" (1983), featuring Rajkumar and Jayaprada, were based on the life of Kālidāsa. "Kaviratna Kalidasa" also used Kālidāsa's Shakuntala as a sub-plot in the movie.V. Shantaram made the Hindi movie "Stree" (1961) based on Kālidāsa's Shakuntala. R.R. Chandran made the Tamil movie "Mahakavi Kalidas" (1966) based on Kālidāsa's life. Chevalier Nadigar Thilagam Sivaji Ganesan played the part of the poet himself. "Mahakavi Kalidasu" (Telugu, 1960) featuring Akkineni Nageswara Rao was similarly based on Kālidāsa's life and work.

Surendra Verma's Hindi play "Athavan Sarga", published in 1976, is based on the legend that Kālidāsa could not complete his epic "Kumārasambhava" because he was cursed by the goddess Parvati, for obscene descriptions of her conjugal life with Lord Shiva in the eighth canto. The play depicts Kālidāsa as a court poet of Chandragupta who faces a trial on the insistence of a priest and some other moralists of his time.

"Asti Kashchid Vagarthiyam" is a five-act Sanskrit play written by Krishna Kumar in 1984. The story is a variation of the popular legend that Kālidāsa was mentally challenged at one time and that his wife was responsible for his transformation. Kālidāsā, a mentally challenged shepherd, is married to Vidyottamā, a learned princess, through a conspiracy. On discovering that she has been tricked, Vidyottamā banishes Kālidāsa, asking him to acquire scholarship and fame if he desires to continue their relationship. She further stipulates that on his return he will have to answer the question, "Asti Kashchid Vāgarthah"" ("Is there anything special in expression?"), to her satisfaction. In due course, Kālidāsa attains knowledge and fame as a poet. Kālidāsa begins Kumārsambhava, Raghuvaṃśa and Meghaduta with the words "Asti" ("there is"), "Kashchit" ("something") and "Vāgarthah" ("spoken word and its meaning").

Bishnupada Bhattacharya's "Kalidas o Robindronath" is a comparative study of Kalidasa and the Bengali poet Rabindranath Tagore.

"Ashadh Ka Ek Din" is a play based on fictionalized elements of Kalidasa life.

Kalidasa has had great influence on several Sanskrit works, on all Indian literature. He also had a great impact on Rabindranath Tagore. The Meghadutam's romanticism is found in Tagore's poems on the monsoons. Sanskrit plays by Kalidasa influenced late eighteenth and early nineteenth-century European literature. According to Dale Carnegie, Father of Modern Medicine Sir William Osler always kept on his desk a poem written by Kalidasa.

Mahakavi Kalidasa () is 1955 Indian Kannada film directed by K. R. Seetharama Sastry, in his debut direction.The movie is based on the legends of the poet Kālidāsa. It stars Honnappa Bhagavatar as Kālidāsa, a Sanskrit poet who lived during the 4th and 5th Century CE. It tells the story about how he, aristocratic young man cursed by his guru with ignorance, goes on to become a great poet. B. Raghavendra Rao, Narasimharaju and B. Saroja Devi, in her first film, feature in supporting roles.

Mahakavi Kalidasa

It was remade in Telugu in 1960 as "Mahakavi Kalidasu" starring Akkineni Nageswara Rao and in Tamil in 1966 as "Mahakavi Kalidas" starring Sivaji Ganesan.

At the 3rd National Film Awards, the film won the award for Best Feature Film in Kannada. The film is seen as a landmark in Kannada cinema.


What is the number one cause of Broca's aphasia?

Broca's (expressive) aphasia is a type of non-fluent aphasia in which an individual’s speech is halting and effortful. Misarticulations or distortions of consonants and vowels, namely phonetic dissolution, are common. Individuals with expressive aphasia may only produce single words, or words in groups of two or three. Long pauses between words are common and multi-syllabic words may be produced one syllable at a time with pauses between each syllable. The prosody of a person with Broca's aphasia is compromised by shortened length of utterances and the presence of self-repairs and disfluencies. Intonation and stress patterns are also deficient.

Expressive aphasia

Expressive aphasia, also known as Broca's aphasia, is a type of aphasia characterized by partial loss of the ability to produce language (spoken, manual, or written), although comprehension generally remains intact. A person with expressive aphasia will exhibit effortful speech. Speech generally includes important content words, but leaves out function words that have only grammatical significance and not real-world meaning, such as prepositions and articles. This is known as "telegraphic speech". The person's intended message may still be understood but his or her sentence will not be grammatically correct. In very severe forms of expressive aphasia, a person may only speak using single word utterances. Typically, comprehension is mildly to moderately impaired in expressive aphasia due to difficulty understanding complex grammar.

It is caused by acquired damage to the anterior regions of the brain, such as the left posterior inferior frontal gyrus or inferior frontal operculum, also described as Broca's area (Brodmann area 44 and Brodmann area 45). It is one subset of a larger family of disorders known collectively as aphasia. Expressive aphasia contrasts with receptive aphasia, in which patients are able to speak in grammatical sentences that lack semantic significance, and generally also have trouble with comprehension. Expressive aphasia differs from dysarthria, which is typified by a patient's inability to properly move the muscles of the tongue and mouth to produce speech. Expressive aphasia also differs from apraxia of speech which is a motor disorder characterized by an inability to create and sequence motor plans for speech.

For example, in the following passage, a patient with Broca's aphasia is trying to explain how he came to the hospital for dental surgery and it may look like this:Yes... ah... Monday... er... Dad and Peter H... (his own name), and Dad... er... hospital... and ah... Wednesday... Wednesday, nine o'clock... and oh... Thursday... ten o'clock, ah doctors... two... an' doctors... and er... teeth... yah.The speech of a person with expressive aphasia contains mostly content words such as nouns, verbs, and some adjectives. However, function words like conjunctions, articles, and prepositions are rarely used except for “and” which is prevalent in the speech of most patients with aphasia. The omission of function words makes the person's speech agrammatic. A communication partner of a person with aphasia may say that the person's speech sounds telegraphic due to poor sentence construction and disjointed words. For example, a person with expressive aphasia might say "Smart... university... smart... good... good..."

Self-monitoring is typically well preserved in patients with Broca's aphasia. They are usually aware of their communication deficits, and are more prone to depression and outbursts from frustration than are patients with other forms of aphasia.

In general, word comprehension is preserved, allowing patients to have functional receptive language skills. Individuals with Broca's aphasia understand most of the everyday conversation around them, but higher-level deficits in receptive language can occur. Because comprehension is substantially impaired for more complex sentences, it is better to use simple language when speaking with an individual with expressive aphasia. This is exemplified by the difficulty to understand phrases or sentences with unusual structure. A typical patient with Broca's aphasia will misinterpret "the man is bitten by the dog" by switching the subject and object to “the dog is bitten by the man.”

Typically, people with expressive aphasia can understand speech and read better than they can produce speech and write. The person's writing will resemble his or her speech and will be effortful, lacking cohesion, and containing mostly content words. Letters will likely be formed clumsily and distorted and some may even be omitted. Although listening and reading are generally intact, subtle deficits in both reading and listening comprehension are almost always present during assessment of aphasia.

Because Broca's area is anterior to the primary motor cortex which is responsible for movement of the face, hands, and arms, a lesion affecting Broca's areas may also result in hemiparesis (weakness of both limbs on the same side of the body) or hemiplegia (paralysis of both limbs on the same side of the body). The brain is wired contralaterally, which means the limbs on right side of the body are controlled by the left hemisphere and vice versa. Therefore, when Broca's area or surrounding areas in the left hemisphere are damaged, hemiplegia or hemiparesis often occurs on the right side of the body in individuals with Broca's aphasia.

Severity of expressive aphasia varies among patients. Some people may only have mild deficits and detecting problems with their language may be difficult. In the most extreme cases, patients may be able to produce only a single word. Even in such cases, over-learned and rote-learned speech patterns may be retained- for instance, some patients can count from one to ten, but cannot produce the same numbers in novel conversation.

In deaf patients who use manual language (such as American Sign Language), damage to the left hemisphere of the brain leads to disruptions in their signing ability. Paraphasic errors similar to spoken language have been observed; whereas in spoken language a phonemic substitution would occur (e.g. "tagle" instead of "table"), in ASL case studies errors in movement, hand position, and morphology have been noted. Agrammatism, or the lack of grammatical morphemes in sentence production, has also been observed in lifelong users of American Sign Language who have left hemisphere damage. The lack of syntactic accuracy shows that the errors in signing are not due to damage to the motor cortex, but rather are a manifestation of the damage to the language-producing area of the brain. Similar symptoms have been seen in a patient with left hemisphere damage whose first language was British Sign Language, further showing that damage to the left hemisphere primarily hinders linguistic ability, not motor ability. In contrast, patients who have damage to non-linguistic areas on the left hemisphere have been shown to be fluent in signing, but are unable to comprehend written language.

In addition to difficulty expressing oneself, individuals with expressive aphasia are also noted to commonly have trouble with comprehension in certain linguistic areas. This agrammatism overlaps with receptive aphasia, but can be seen in patients who have expressive aphasia without being diagnosed as having receptive aphasia. The most well-noted of these are object-relative clauses, object Wh- questions, and topicalized structures (placing the topic at the beginning of the sentence). These three concepts all share phrasal movement, which can cause words to lose their thematic roles when they change order in the sentence. This is often not an issue for people without agrammatic aphasias, but many people with aphasia rely heavily on word order to understand roles that words play within the sentence.
The most common cause of expressive aphasia is stroke. A stroke is caused by hypoperfusion (lack of oxygen) to an area of the brain, which is commonly caused by thrombosis or embolism. Some form of aphasia occurs in 34 to 38% of stroke patients. Expressive aphasia occurs in approximately 12% of new cases of aphasia caused by stroke.

In most cases, expressive aphasia is caused by a stroke in Broca's area or the surrounding vicinity. Broca's area is in the lower part of the premotor cortex in the language dominant hemisphere and is responsible for planning motor speech movements. However, cases of expressive aphasia have been seen in patients with strokes in other areas of the brain. Patients with classic symptoms of expressive aphasia in general have more acute brain lesions, whereas patients with larger, widespread lesions exhibit a variety of symptoms that may be classified as global aphasia or left unclassified.

Expressive aphasia can also be caused by trauma to the brain, tumor, and cerebral hemorrhage by extradural hematoma.

Understanding lateralization of brain function is important for understanding which areas of the brain cause expressive aphasia when damaged. In the past, it has been believed that the area for language production differs between left and right-handed individuals. If this were true, damage to the homologous region of Broca's area in the right hemisphere should cause aphasia in a left-handed individual. More recent studies have shown that even left-handed individuals typically have language functions only in the left hemisphere. However, left-handed individuals are more likely to have a dominance of language in the right hemisphere.

Less common causes of expressive aphasia include primary autoimmune phenomenon and autoimmune phenomenon that are secondary to cancer (as a paraneoplastic syndrome) have been listed as the primary hypothesis for several cases of aphasia, especially when presenting with other psychiatric disturbances and focal neurological deficits. Many case reports exist describing paraneoplastic aphasia, and the reports that are specific tend to describe expressive aphasia. Although most cases attempt to exclude micrometastasis, it is likely that some cases of paraneoplastic aphasia are actually extremely small metastasis to the vocal motor regions.

Neurdegenerative diseases may present with aphasia. Alzheimer's Disease may present with either fluent aphasia or expressive aphasia. There are case reports of Creutzfeldt-Jakob disease presenting with expressive aphasia.

Expressive aphasia is classified as non-fluent aphasia, as opposed to fluent aphasia. Diagnosis is done on a case by case basis, as lesions often affect the surrounding cortex and deficits are highly variable among patients with aphasia.

A physician is typically the first person to recognize aphasia in a patient who is being treated for damage to the brain. Routine processes for determining the presence and location of lesion in the brain include Magnetic Resonance Imaging (MRI) and Computed Tomography (CT) scans. The physician will complete a brief assessment of the patient's ability to understand and produce language. For further diagnostic testing, the physician will refer the patient to a speech-language pathologist, who will complete a comprehensive evaluation.

In order to diagnose a patient who is suffering from Broca’s aphasia, there are certain commonly used tests and procedures. The Western Aphasia Battery (WAB) classifies individuals based on their scores on the subtests; spontaneous speech, auditory comprehension, repetition, and naming. The Boston Diagnostic Aphasia Examination (BDAE) can inform users what specific type of aphasia they may have, infer the location of lesion, and assess current language abilities. The Porch Index of Communication Ability (PICA) can predict potential recovery outcomes of the patients with aphasia. Quality of life measurement is also an important assessment tool. Tests such as the Assessment for Living with Aphasia (ALA) and the Satisfaction with Life Scale (SWLS) allow for therapists to target skills that are important and meaningful for the individual.

In addition to formal assessments, patient and family interviews are valid and important sources of information. The patient’s previous hobbies, interests, personality, and occupation are all factors that will not only impact therapy but may motivate them throughout the recovery process. Patient interviews and observations allow professionals to learn the priorities of the patient and family and determine what the patient hopes to regain in therapy. Observations of the patient may also be beneficial to determine where to begin treatment. The current behaviors and interactions of the patient will provide the therapist with more insight about the client and his or her individual needs. Other information about the patient can be retrieved from medical records, patient referrals from physicians, and the nursing staff.

In non-speaking patients who use manual languages, diagnosis is often based on interviews from the patient's acquaintances, noting the differences in sign production pre- and post- damage to the brain. Many of these patients will also begin to rely on non-linguistic gestures to communicate, rather than signing since their language production is hindered.

Currently, there is no standard treatment for expressive aphasia. Most aphasia treatment is individualized based on a patient's condition and needs as assessed by a speech language pathologist. Patients go through a period of spontaneous recovery following brain injury in which they regain a great deal of language function.

In the months following injury or stroke, most patients receive traditional treatment for a few hours per day. Among other exercises, patients practice the repetition of words and phrases. Mechanisms are also taught in traditional treatment to compensate for lost language function such as drawing and using phrases that are easier to pronounce.

Emphasis is placed on establishing a basis for communication with family and caregivers in everyday life. Treatment is individualized based on the patient's own priorities, along with the family's input.

A patient may have the option of individual or group treatment. Although less common, group treatment has been shown to have advantageous outcomes. Some types of group treatments include family counseling, maintenance groups, support groups and treatment groups.

Melodic intonation therapy was inspired by the observation that individuals with non-fluent aphasia sometimes can sing words or phrases that they normally cannot speak. "Melodic Intonation Therapy was begun as an attempt to use the intact melodic/prosodic processing skills of the right hemisphere in those with aphasia to help cue retrieval words and expressive language." It is believed that this is because singing capabilities are stored in the right hemisphere of the brain, which is likely to remain unaffected after a stroke in the left hemisphere. However, recent evidence demonstrates that the capability of individuals with aphasia to sing entire pieces of text may actually result from rhythmic features and the familiarity with the lyrics.

The goal of Melodic Intonation Therapy is to utilize singing to access the language-capable regions in the right hemisphere and use these regions to compensate for lost function in the left hemisphere. The natural musical component of speech was used to engage the patients' ability to produce phrases. A clinical study revealed that singing and rhythmic speech may be similarly effective in the treatment of non-fluent aphasia and apraxia of speech. Moreover, evidence from randomized controlled trials is still needed to confirm that Melodic Intonation Therapy is suitable to improve propositional utterances and speech intelligibility in individuals with (chronic) non-fluent aphasia and apraxia of speech.

Melodic Intonation Therapy appears to work particularly well in patients who have had a unilateral, left hemisphere stroke, show poor articulation, are non-fluent or have severely restricted speech output, have moderately preserved auditory comprehension, and show good motivation. MIT therapy on average lasts for 1.5 hours per day for five days per week. At the lowest level of therapy, simple words and phrases (such as "water" and "I love you") are broken down into a series of high- and low-pitch syllables. With increased treatment, longer phrases are taught and less support is provided by the therapist. Patients are taught to say phrases using the natural melodic component of speaking and continuous voicing is emphasized. The patient is also instructed to use the left hand to tap the syllables of the phrase while the phrases are spoken. Tapping is assumed to trigger the rhythmic component of speaking to utilize the right hemisphere.

FMRI studies have shown that Melodic Intonation Therapy (MIT) uses both sides of the brain to recover lost function, as opposed to traditional therapies that utilize only the left hemisphere. In MIT, individuals with small lesions in the left hemisphere seem to recover by activation of the left hemisphere perilesional cortex. Meanwhile, individuals with larger left-hemisphere lesions show a recruitment of the use of language-capable regions in the right hemisphere. The interpretation of these results is still a matter of debate. For example, it remains unclear whether changes in neural activity in the right hemisphere result from singing or from the intensive use of common phrases, such as "thank you", "how are you?" or "I am fine." This type of phrases falls into the category of formulaic language and is known to be supported by neural networks of the intact right hemisphere.

A pilot study reported positive results when comparing the efficacy of a modified form of MIT to no treatment in people with nonfluent aphasia with damage to their left-brain. A randomized controlled trial was conducted and the study reported benefits of utilizing modified MIT treatment early in the recovery phase for people with nonfluent aphasia.

Melodic Intonation Therapy is used by music therapists, board-certified professionals that use music as a therapeutic tool to effect certain non-musical outcomes in their patients. Speech language pathologists can also use this therapy for individuals who have had a left hemisphere stroke and non-fluent aphasias such as Broca’s or even apraxia of speech.

Constraint-induced aphasia therapy (CIAT) is based on similar principles as constraint-induced movement therapy developed by Dr. Edward Taub at the University of Alabama at Birmingham. Constraint-induced movement therapy is based on the idea that a person with an impairment (physical or communicative) develops a "learned nonuse" by compensating for the lost function with other means such as using an unaffected limb by a paralyzed individual or drawing by a patient with aphasia. In constraint-induced movement therapy, the alternative limb is constrained with a glove or sling and the patient is forced to use the affected limb. In constraint-induced aphasia therapy the interaction is guided by communicative need in a language game context, picture cards, barriers making it impossible to see other players' cards, and other materials, so that patients are encouraged ("constrained") to use the remaining verbal abilities to succeed in the communication game.

Two important principles of constraint-induced aphasia therapy are that treatment is very intense, with sessions lasting for up to 6 hours over the course of 10 days and that language is used in a communication context in which it is closely linked to (nonverbal) actions. These principles are motivated by neuroscience insights about learning at the level of nerve cells (synaptic plasticity) and the coupling between cortical systems for language and action in the human brain. Constraint-induced therapy contrasts sharply with traditional therapy by the strong belief that mechanisms to compensate for lost language function, such as gesturing or writing, should not be used unless absolutely necessary, even in everyday life.

It is believed that CIAT works by the mechanism of increased neuroplasticity. By constraining an individual to use only speech, it is believed that the brain is more likely to reestablish old neural pathways and recruit new neural pathways to compensate for lost function.

The strongest results of CIAT have been seen in patients with chronic aphasia (lasting over 6 months). Studies of CIAT have confirmed that further improvement is possible even after a patient has reached a "plateau" period of recovery. It has also been proven that the benefits of CIAT are retained long term. However, improvements only seem to be made while a patient is undergoing intense therapy. Recent work has investigated combining constraint-induced aphasia therapy with drug treatment, which led to an amplification of therapy benefits.

In addition to active speech therapy, pharmaceuticals have also been considered as a useful treatment for expressive aphasia. This area of study is relatively new and much research continues to be conducted.

The following drugs have been suggested for use in treating aphasia and their efficacy has been studied in control studies.The most effect has been shown by piracetam and amphetamine, which may increase cerebral plasticity and result in an increased capability to improve language function. It has been seen that piracetam is most effective when treatment is begun immediately following stroke. When used in chronic cases it has been much less efficient.

Bromocriptine has been shown by some studies to increase verbal fluency and word retrieval with therapy than with just therapy alone. Furthermore, its use seems to be restricted to non-fluent aphasia.

Donepezil has shown a potential for helping chronic aphasia.

No study has established irrefutable evidence that any drug is an effective treatment for aphasia therapy. Furthermore, no study has shown any drug to be specific for language recovery. Comparison between the recovery of language function and other motor function using any drug has shown that improvement is due to a global increase plasticity of neural networks.

In transcranial magnetic stimulation (TMS), magnetic fields are used to create electrical currents in specified cortical regions. The procedure is a painless and noninvasive method of stimulating the cortex. TMS works by suppressing the inhibition process in certain areas of the brain. By suppressing the inhibition of neurons by external factors, the targeted area of the brain may be reactivated and thereby recruited to compensate for lost function. Research has shown that patients can demonstrate increased object naming ability with regular transcranial magnetic stimulation than patients not receiving TMS. Furthermore, research suggests this improvement is sustained upon the completion of TMS therapy. However, some patients fail to show any significant improvement from TMS which indicates the need for further research of this treatment.

Described as the linguistic approach to the treatment of expressive aphasia, treatment begins by emphasizing and educating patients on the thematic roles of words within sentences. Sentences that are usually problematic will be reworded into active-voiced, declarative phrasings of their non-canonical counterparts. The simpler sentence phrasings are then transformed into variations that are more difficult to interpret. For example, many individuals who have expressive aphasia struggle with Wh- sentences. "What" and "who" questions are problematic sentences that this treatment method attempts to improve, and they are also two interrogative particles that are strongly related to each other because they reorder arguments from the declarative counterparts. For instance, therapists have used sentences like, "Who is the boy helping?" and "What is the boy fixing?" because both verbs are transitive- they require two arguments in the form of a subject and a direct object, but not necessarily an indirect object. In addition, certain question particles are linked together based on how the reworded sentence is formed. Training "who" sentences increased the generalizations of non-trained "who" sentences as well as untrained "what" sentences, and vice versa. Likewise, "where" and "when" question types are very closely linked. "What" and "who" questions alter placement of arguments, and "where" and "when" sentences move adjunct phrases. Training is in the style of: "The man parked the car in the driveway. What did the man park in the driveway?" Sentence training goes on in this manner for more domains, such as clefts and sentence voice.

Results: Patients’ use of sentence types used in the TUF treatment will improve, subjects will generalize sentences of similar category to those used for treatment in TUF, and results are applied to real-world conversations with others. Generalization of sentence types used can be improved when the treatment progresses in the order of more complex sentences to more elementary sentences. Treatment has been shown to affect on-line (real-time) processing of trained sentences and these results can be tracked using fMRI mappings. Training of Wh- sentences has led improvements in three main areas of discourse for aphasics: increased average length of utterances, higher proportions of grammatical sentences, and larger ratios of numbers of verbs to nouns produced. Patients also showed improvements in verb argument structure productions and assigned thematic roles to words in utterances with more accuracy. In terms of on-line sentence processing, patients having undergone this treatment discriminate between anomalous and non-anomalous sentences with more accuracy than control groups and are closer to levels of normalcy than patients not having participated in this treatment.

Mechanisms for recovery differ from patient to patient. Some mechanisms for recovery occur spontaneously after damage to the brain, whereas others are caused by the effects of language therapy. FMRI studies have shown that recovery can be partially attributed to the activation of tissue around the damaged area and the recruitment of new neurons in these areas to compensate for the lost function. Recovery may also be caused in very acute lesions by a return of blood flow and function to damaged tissue that has not died around an injured area. It has been stated by some researchers that the recruitment and recovery of neurons in the left hemisphere opposed to the recruitment of similar neurons in the right hemisphere is superior for long-term recovery and continued rehabilitation. It is thought that, because the right hemisphere is not intended for full language function, using the right hemisphere as a mechanism of recovery is effectively a "dead-end" and can lead only to partial recovery.

It has been proven that, among all types of therapies, one of the most important factors and best predictors for a successful outcome is the intensity of the therapy. By comparing the length and intensity of various methods of therapies, it was proven that intensity is a better predictor of recovery than the method of therapy used.

In most individuals with expressive aphasia, the majority of recovery is seen within the first year following a stroke or injury. The majority of this improvement is seen in the first four weeks in therapy following a stroke and slows thereafter. However, this timeline will vary depending upon the type of stroke experienced by the patient. Patients who experienced an ischemic stroke may recover in the days and weeks following the stroke, and then experience a plateau and gradual slowing of recovery. On the contrary, patients who experienced a hemorrhagic stroke experience a slower recovery in the first 4–8 weeks, followed by a faster recovery which eventually stabilizes.

Numerous factors impact the recovery process and outcomes. Site and extent of lesion greatly impacts recovery. Other factors that may affect prognosis are age, education, gender, and motivation. Occupation, handedness, personality, and emotional state may also be associated with recovery outcomes.

Studies have also found that prognosis of expressive aphasia correlates strongly with the initial severity of impairment. However, it has been seen that continued recovery is possible years after a stroke with effective treatment. Timing and intensity of treatment is another factor that impacts outcomes. Research suggests that even in later stages of recovery, intervention is effective at improving function, as well as, preventing loss of function.

Unlike receptive aphasia, patients with expressive aphasia are aware of their errors in language production. This may further motivate a person with expressive aphasia to progress in treatment, which would affect treatment outcomes. On the other hand, awareness of impairment may lead to higher levels of frustration, depression, anxiety, or social withdrawal, which have been proven to negatively affect a person's chance of recovery.

Expressive aphasia was first identified by the French neurologist Paul Broca. By examining the brains of deceased individuals having acquired expressive aphasia in life, he concluded that language ability is localized in the ventroposterior region of the frontal lobe. One of the most important aspects of Paul Broca's discovery was the observation that the loss of proper speech in expressive aphasia is due to the brain's loss of ability to produce language, as opposed to the mouth's loss of ability to produce words.

The discoveries of Paul Broca were made during the same period of time as the German Neurologist Carl Wernicke, who was also studying brains of aphasiacs post-mortem and identified the region now known as Wernicke's area. Discoveries of both men contributed to the concept of localization, which states that specific brain functions are all localized to a specific area of the brain. While both men made significant contributions to the field of aphasia, it was Carl Wernicke who realized the difference between patients with aphasia that could not produce language and those that could not comprehend language (the essential difference between expressive and receptive aphasia).

Expressive aphasia

Self-monitoring is typically well preserved in patients with Broca's aphasia. They are usually aware of their communication deficits, and are more prone to depression and outbursts from frustration than are patients with other forms of aphasia.

Typically, people with expressive aphasia can understand speech and read better than they can produce speech and write. The person's writing will resemble his or her speech and will be effortful, lacking cohesion, and containing mostly content words. Letters will likely be formed clumsily and distorted and some may even be omitted. Although listening and reading are generally intact, subtle deficits in both reading and listening comprehension are almost always present during assessment of aphasia.

Severity of expressive aphasia varies among patients. Some people may only have mild deficits and detecting problems with their language may be difficult. In the most extreme cases, patients may be able to produce only a single word. Even in such cases, over-learned and rote-learned speech patterns may be retained- for instance, some patients can count from one to ten, but cannot produce the same numbers in novel conversation.

Expressive aphasia can also be caused by trauma to the brain, tumor, and cerebral hemorrhage by extradural hematoma.

Neurdegenerative diseases may present with aphasia. Alzheimer's Disease may present with either fluent aphasia or expressive aphasia. There are case reports of Creutzfeldt-Jakob disease presenting with expressive aphasia.

Expressive aphasia is classified as non-fluent aphasia, as opposed to fluent aphasia. Diagnosis is done on a case by case basis, as lesions often affect the surrounding cortex and deficits are highly variable among patients with aphasia.

In non-speaking patients who use manual languages, diagnosis is often based on interviews from the patient's acquaintances, noting the differences in sign production pre- and post- damage to the brain. Many of these patients will also begin to rely on non-linguistic gestures to communicate, rather than signing since their language production is hindered.

Currently, there is no standard treatment for expressive aphasia. Most aphasia treatment is individualized based on a patient's condition and needs as assessed by a speech language pathologist. Patients go through a period of spontaneous recovery following brain injury in which they regain a great deal of language function.

In the months following injury or stroke, most patients receive traditional treatment for a few hours per day. Among other exercises, patients practice the repetition of words and phrases. Mechanisms are also taught in traditional treatment to compensate for lost language function such as drawing and using phrases that are easier to pronounce.

Emphasis is placed on establishing a basis for communication with family and caregivers in everyday life. Treatment is individualized based on the patient's own priorities, along with the family's input.

A patient may have the option of individual or group treatment. Although less common, group treatment has been shown to have advantageous outcomes. Some types of group treatments include family counseling, maintenance groups, support groups and treatment groups.

A pilot study reported positive results when comparing the efficacy of a modified form of MIT to no treatment in people with nonfluent aphasia with damage to their left-brain. A randomized controlled trial was conducted and the study reported benefits of utilizing modified MIT treatment early in the recovery phase for people with nonfluent aphasia.

Melodic Intonation Therapy is used by music therapists, board-certified professionals that use music as a therapeutic tool to effect certain non-musical outcomes in their patients. Speech language pathologists can also use this therapy for individuals who have had a left hemisphere stroke and non-fluent aphasias such as Broca’s or even apraxia of speech.

It is believed that CIAT works by the mechanism of increased neuroplasticity. By constraining an individual to use only speech, it is believed that the brain is more likely to reestablish old neural pathways and recruit new neural pathways to compensate for lost function.

In addition to active speech therapy, pharmaceuticals have also been considered as a useful treatment for expressive aphasia. This area of study is relatively new and much research continues to be conducted.

The following drugs have been suggested for use in treating aphasia and their efficacy has been studied in control studies.The most effect has been shown by piracetam and amphetamine, which may increase cerebral plasticity and result in an increased capability to improve language function. It has been seen that piracetam is most effective when treatment is begun immediately following stroke. When used in chronic cases it has been much less efficient.

Bromocriptine has been shown by some studies to increase verbal fluency and word retrieval with therapy than with just therapy alone. Furthermore, its use seems to be restricted to non-fluent aphasia.

Donepezil has shown a potential for helping chronic aphasia.

No study has established irrefutable evidence that any drug is an effective treatment for aphasia therapy. Furthermore, no study has shown any drug to be specific for language recovery. Comparison between the recovery of language function and other motor function using any drug has shown that improvement is due to a global increase plasticity of neural networks.

It has been proven that, among all types of therapies, one of the most important factors and best predictors for a successful outcome is the intensity of the therapy. By comparing the length and intensity of various methods of therapies, it was proven that intensity is a better predictor of recovery than the method of therapy used.

Numerous factors impact the recovery process and outcomes. Site and extent of lesion greatly impacts recovery. Other factors that may affect prognosis are age, education, gender, and motivation. Occupation, handedness, personality, and emotional state may also be associated with recovery outcomes.

Studies have also found that prognosis of expressive aphasia correlates strongly with the initial severity of impairment. However, it has been seen that continued recovery is possible years after a stroke with effective treatment. Timing and intensity of treatment is another factor that impacts outcomes. Research suggests that even in later stages of recovery, intervention is effective at improving function, as well as, preventing loss of function.

Unlike receptive aphasia, patients with expressive aphasia are aware of their errors in language production. This may further motivate a person with expressive aphasia to progress in treatment, which would affect treatment outcomes. On the other hand, awareness of impairment may lead to higher levels of frustration, depression, anxiety, or social withdrawal, which have been proven to negatively affect a person's chance of recovery.

Expressive aphasia was first identified by the French neurologist Paul Broca. By examining the brains of deceased individuals having acquired expressive aphasia in life, he concluded that language ability is localized in the ventroposterior region of the frontal lobe. One of the most important aspects of Paul Broca's discovery was the observation that the loss of proper speech in expressive aphasia is due to the brain's loss of ability to produce language, as opposed to the mouth's loss of ability to produce words.

Broca's aphasia is a specific type of expressive aphasia and is so named due to the aphasia that results from damage or lesions to the Broca's area of the brain, that exists most commonly in the left inferior frontal hemisphere. Thus, the aphasia that develops from the lack of functioning of the Broca's area is an expressive and non-fluent aphasia. It is called 'non-fluent' due the issues that arise because Broca's area is critical for language pronunciation and production. The area controls some motor aspects of speech production and articulation of thoughts to words and as such lesions to the area result in the specific non-fluent aphasia.

Lateralization of brain function

The lateralization of brain function is the tendency for some neural functions or cognitive processes to be specialized to one side of the brain or the other. The medial longitudinal fissure separates the human brain into two distinct cerebral hemispheres, connected by the corpus callosum. Although the macrostructure of the two hemispheres appears to be almost identical, different composition of neuronal networks allows for specialized function that is different in each hemisphere.
Lateralization of brain structures is based on general trends expressed in healthy patients; however, there are numerous counterexamples to each generalization. Each human's brain develops differently leading to unique lateralization in individuals. This is different from specialization as lateralization refers only to the function of one structure divided between two hemispheres. Specialization is much easier to observe as a trend since it has a stronger anthropological history. The best example of an established lateralization is that of Broca's and Wernicke's areas where both are often found exclusively on the left hemisphere. These areas frequently correspond to handedness, however, meaning that the localization of these areas is regularly found on the hemisphere corresponding to the dominant hand (anatomically on the opposite side). Function lateralization such as semantics, intonation, accentuation, prosody, etc. has since been called into question and largely been found to have a neuronal basis in both hemispheres. Another example is that each hemisphere in the brain tends to represent one side of the body. In the cerebellum this is the same bodyside, but in the forebrain this is predominantly the contralateral side.

Language functions such as grammar, vocabulary and literal meaning are typically lateralized to the left hemisphere, especially in right handed individuals. While language production is left-lateralized in up to 90% of right-handers, it is more bilateral, or even right-lateralized, in approximately 50% of left-handers.

Broca's area and Wernicke's area, two areas associated with the production of speech, are located in the left cerebral hemisphere for about 95% of right-handers, but about 70% of left-handers.

The processing of visual and auditory stimuli, spatial manipulation, facial perception, and artistic ability are represented bilaterally. Numerical estimation, comparison and online calculation depend on bilateral parietal regions while exact calculation and fact retrieval are associated with left parietal regions, perhaps due to their ties to linguistic processing.

Depression is linked with a hyperactive right hemisphere, with evidence of selective involvement in "processing negative emotions, pessimistic thoughts and unconstructive thinking styles", as well as vigilance, arousal and self-reflection, and a relatively hypoactive left hemisphere, "specifically involved in processing pleasurable experiences" and "relatively more involved in decision-making processes". Additionally, "left hemisphere lesions result in an omissive response bias or error pattern whereas right hemisphere lesions result in a commissive response bias or error pattern." The delusional misidentification syndromes, reduplicative paramnesia and Capgras delusion are also often the result of right hemisphere lesions.

Damage to either the right or left hemisphere, and its resulting deficits provide insight into the function of the damaged area. Left hemisphere damage has many effects on language production and perception. Damage or lesions to the right hemisphere can result in a lack of emotional prosody or intonation when speaking. Right hemisphere damage also has grave effects on understanding discourse. People with damage to the right hemisphere have a reduced ability to generate inferences, comprehend and produce main concepts, and a reduced ability to manage alternative meanings. Furthermore, people with right hemisphere damage often exhibit discourse that is abrupt and perfunctory or verbose and excessive. They can also have pragmatic deficits in situations of turn taking, topic maintenance and shared knowledge.

Lateral brain damage can also affect visual perceptual spatial resolution. People with left hemisphere damage may have impaired perception of high resolution, or detailed, aspects of an image. People with right hemisphere damage may have impaired perception of low resolution, or big picture, aspects of an image.

If a specific region of the brain, or even an entire hemisphere, is injured or destroyed, its functions can sometimes be assumed by a neighboring region in the same hemisphere or the corresponding region in the other hemisphere, depending upon the area damaged and the patient's age. When injury interferes with pathways from one area to another, alternative (indirect) connections may develop to communicate information with detached areas, despite the inefficiencies.

Wernicke's aphasia is the result of damage to the area of the brain that is commonly in the left hemisphere above the sylvian fissure. Damage to this area causes primarily a deficit in language comprehension. While the ability to speak fluently with normal melodic intonation is spared, the language produced by a person with Wernicke's aphasia is riddled with semantic errors, and may sound nonsensical to the listener. Wernicke's aphasia is characterized by phonemic paraphasias, neologism or jargon. Another characteristic of a person with Wernicke's aphasia is that they are unconcerned by the mistakes that they are making.

Terence Hines states that the research on brain lateralization is valid as a research program, though commercial promoters have applied it to promote subjects and products far outside the implications of the research. For example, the implications of the research have no bearing on psychological interventions such as EMDR and neurolinguistic programming, brain-training equipment, or management training.

Some popularizations oversimplify the science about lateralization, by presenting the functional differences between hemispheres as being more absolute than is actually the case.

In the 19th century and to a lesser extent the 20th, it was thought that each side of the brain was associated with a specific gender: the left corresponding with masculinity and the right with femininity and each half could function independently. The right side of the brain was seen as the inferior and thought to be prominent in women, savages, children, criminals, and the insane. A prime example of this in fictional literature can be seen in Robert Louis Stevenson's "Strange Case of Dr. Jekyll and Mr. Hyde".

The widespread lateralization of many vertebrate animals indicates an evolutionary advantage associated with the specialization of each hemisphere.

One of the first indications of brain function lateralization resulted from the research of French physician Pierre Paul Broca, in 1861. His research involved the male patient nicknamed "Tan", who suffered a speech deficit (aphasia); "tan" was one of the few words he could articulate, hence his nickname. In Tan's autopsy, Broca determined he had a syphilitic lesion in the left cerebral hemisphere. This left frontal lobe brain area (Broca's area) is an important speech production region. The motor aspects of speech production deficits caused by damage to Broca's area are known as expressive aphasia. In clinical assessment of this aphasia, it is noted that the patient cannot clearly articulate the language being employed.

German physician Karl Wernicke continued in the vein of Broca's research by studying language deficits unlike expressive aphasia. Wernicke noted that not every deficit was in speech production; some were linguistic. He found that damage to the left posterior, superior temporal gyrus (Wernicke's area) caused language comprehension deficits rather than speech production deficits, a syndrome known as receptive aphasia.

These seminal works on hemispheric specialization were done on patients or postmortem brains, raising questions about the potential impact of pathology on the research findings. New methods permit the "in vivo" comparison of the hemispheres in healthy subjects. Particularly, magnetic resonance imaging (MRI) and positron emission tomography (PET) are important because of their high spatial resolution and ability to image subcortical brain structures.

In the 1940s, neurosurgeon Wilder Penfield and his neurologist colleague Herbert Jasper developed a technique of brain mapping to help reduce side effects caused by surgery to treat epilepsy. They stimulated motor and somatosensory cortices of the brain with small electrical currents to activate discrete brain regions. They found that stimulation of one hemisphere's motor cortex produces muscle contraction on the opposite side of the body. Furthermore, the functional map of the motor and sensory cortices is fairly consistent from person to person; Penfield and Jasper's famous pictures of the motor and sensory homunculi were the result.

Research by Michael Gazzaniga and Roger Wolcott Sperry in the 1960s on split-brain patients led to an even greater understanding of functional laterality. Split-brain patients are patients who have undergone corpus callosotomy (usually as a treatment for severe epilepsy), a severing of a large part of the corpus callosum. The corpus callosum connects the two hemispheres of the brain and allows them to communicate. When these connections are cut, the two halves of the brain have a reduced capacity to communicate with each other. This led to many interesting behavioral phenomena that allowed Gazzaniga and Sperry to study the contributions of each hemisphere to various cognitive and perceptual processes. One of their main findings was that the right hemisphere was capable of rudimentary language processing, but often has no lexical or grammatical abilities. Eran Zaidel also studied such patients and found some evidence for the right hemisphere having at least some syntactic ability.

Language is primarily localized in the left hemisphere. One of the experiments carried out by Gazzaniga involved a split-brain male patient sitting in front of a computer screen while having words and images presented on either side of the screen and the visual stimuli would go to either the right or left visual field, and thus the left or right brain, respectively. It was observed that if the patient was presented with an image to his left visual field (right brain), he would report not seeing anything. If he was able to feel around for certain objects, he could accurately pick out the correct object, despite not having the ability to verbalize what he saw. This led to confirmation that the left brain is localized for language whereas the right brain does not have this capability, and when the corpus callosum is cut, the two hemispheres cannot communicate in order for situation-pertinent speech to be produced.


When was the Arabic numeral system introduced in Europe?

From India, the thriving trade between Islamic sultans and Africa carried the concept to Cairo. Arabic mathematicians extended the system to include decimal fractions, and Muḥammad ibn Mūsā al-Ḵwārizmī wrote an important work about it in the 9th  century. The modern Arabic numerals were introduced to Europe with the translation of this work in the 12th century in Spain and Leonardo of Pisa's "Liber Abaci" of 1201. In Europe, the complete Indian system with the zero was derived from the Arabs in the 12th century.

Numerical digit

A numerical digit is a single symbol (such as "2" or "5") used alone, or in combinations (such as "25"), to represent numbers (such as the number 25) according to some positional numeral systems. The single digits (as one-digit-numerals) and their combinations (such as "25") are the numerals of the numeral system they belong to. The name "digit" comes from the fact that the ten digits (Latin "digiti" meaning fingers) of the hands correspond to the ten symbols of the common base 10 numeral system, i.e. the decimal (ancient Latin adjective "decem" meaning ten) digits.

For a given numeral system with an integer base, the number of digits required to express arbitrary numbers is given by the absolute value of the base. For example, the decimal system (base 10) requires ten digits (0 through to 9), whereas the binary system (base 2) has two digits (e.g.: 0 and 1).

In a basic digital system, a numeral is a sequence of digits, which may be of arbitrary length. Each position in the sequence has a place value, and each digit has a value. The value of the numeral is computed by multiplying each digit in the sequence by its place value, and summing the results.

Each digit in a number system represents an integer. For example, in decimal the digit "1" represents the integer one, and in the hexadecimal system, the letter "A" represents the number ten. A positional number system has one unique digit for each integer from zero up to, but not including, the radix of the number system.

Thus in the positional decimal system, the numbers 0 to 9 can be expressed using their respective numerals "0" to "9" in the rightmost "units" position. The number 12 can be expressed with the numeral "2" in the units position, and with the numeral "1" in the "tens" position, to the left of the "2" while the number 312 can be expressed by three numerals: "3" in the "hundreds" position, "1" in the "tens" position, and "2" in the "units" position.

The Hindu–Arabic numeral system (or the Hindu numeral system) uses a decimal separator, commonly a period in English, or a comma in other European languages, to denote the "ones place" or "units place", which has a place value one. Each successive place to the left of this has a place value equal to the place value of the previous digit times the base. Similarly, each successive place to the right of the separator has a place value equal to the place value of the previous digit divided by the base. For example, in the numeral 10.34 (written in base 10),

The total value of the number is 1 ten, 0 ones, 3 tenths, and 4 hundredths. Note that the zero, which contributes no value to the number, indicates that the 1 is in the tens place rather than the ones place.

The place value of any given digit in a numeral can be given by a simple calculation, which in itself is a compliment to the logic behind numeral systems. The calculation involves the multiplication of the given digit by the base raised by the exponent, where "n" represents the position of the digit from the separator; the value of "n" is positive (+), but this is only if the digit is to the left of the separator. And to the right, the digit is multiplied by the base raised by a negative (−) "n". For example, in the number 10.34 (written in base 10),

The first true written positional numeral system is considered to be the Hindu–Arabic numeral system. This system was established by the 7th century in India, but was not yet in its modern form because the use of the digit zero had not yet been widely accepted. Instead of a zero sometimes the digits were marked with dots to indicate their significance, or a space was used as a placeholder. The first widely acknowledged use of zero was in 876. The original numerals were very similar to the modern ones, even down to the glyphs used to represent digits.
By the 13th century, Western Arabic numerals were accepted in European mathematical circles (Fibonacci used them in his "Liber Abaci"). They began to enter common use in the 15th century. By the end of the 20th century virtually all non-computerized calculations in the world were done with Arabic numerals, which have replaced native numeral systems in most cultures.

The exact age of the Maya numerals is unclear, but it is possible that it is older than the Hindu–Arabic system. The system was vigesimal (base 20), so it has twenty digits. The Mayas used a shell symbol to represent zero. Numerals were written vertically, with the ones place at the bottom. The Mayas had no equivalent of the modern decimal separator, so their system could not represent fractions.

The Thai numeral system is identical to the Hindu–Arabic numeral system except for the symbols used to represent digits. The use of these digits is less common in Thailand than it once was, but they are still used alongside Arabic numerals.

The rod numerals, the written forms of counting rods once used by Chinese and Japanese mathematicians, are a decimal positional system able to represent not only zero but also negative numbers. Counting rods themselves predate the Hindu–Arabic numeral system. The Suzhou numerals are variants of rod numerals.

The binary (base 2), octal (base 8), and hexadecimal (base 16) systems, extensively used in computer science, all follow the conventions of the Hindu–Arabic numeral system. The binary system uses only the digits "0" and "1", while the octal system uses the digits from "0" through "7". The hexadecimal system uses all the digits from the decimal system, plus the letters "A" through "F", which represent the numbers 10 to 15 respectively.

The ternary and balanced ternary systems have sometimes been used. They are both base 3 systems.

Balanced ternary is unusual in having the digit values 1, 0 and –1. Balanced ternary turns out to have some useful properties and the system has been used in the experimental Russian Setun computers.

Several authors in the last 300 years have noted a facility of positional notation that amounts to a "modified" decimal representation. Some advantages are cited for use of numerical digits that represent negative values. In 1840 Augustin-Louis Cauchy advocated use of signed-digit representation of numbers, and in 1928 Florian Cajori presented his collection of references for negative numerals. The concept of signed-digit representation has also been taken up in computer design.

Despite the essential role of digits in describing numbers, they are relatively unimportant to modern mathematics. Nevertheless, there are a few important mathematical concepts that make use of the representation of a number as a sequence of digits.

The digital root is the single-digit number obtained by summing the digits of a given number, then summing the digits of the result, and so on until a single-digit number is obtained.

Casting out nines is a procedure for checking arithmetic done by hand. To describe it, let formula_5 represent the digital root of formula_6, as described above. Casting out nines makes use of the fact that if formula_7, then formula_8. In the process of casting out nines, both sides of the latter equation are computed, and if they are not equal the original addition must have been faulty.

Repunits are integers that are represented with only the digit 1. For example, 1111 (one thousand, one hundred and eleven) is a repunit. Repdigits are a generalization of repunits; they are integers represented by repeated instances of the same digit. For example, 333 is a repdigit. The primality of repunits is of interest to mathematicians.

Palindromic numbers are numbers that read the same when their digits are reversed. A Lychrel number is a positive integer that never yields a palindromic number when subjected to the iterative process of being added to itself with digits reversed. The question of whether there are any Lychrel numbers in base 10 is an open problem in recreational mathematics; the smallest candidate is 196.

Counting aids, especially the use of body parts (counting on fingers), were certainly used in prehistoric times as today. There are many variations. Besides counting ten fingers, some cultures have counted knuckles, the space between fingers, and toes as well as fingers. The Oksapmin culture of New Guinea uses a system of 27 upper body locations to represent numbers.

To preserve numerical information, tallies carved in wood, bone, and stone have been used since prehistoric times. Stone age cultures, including ancient indigenous American groups, used tallies for gambling, personal services, and trade-goods.

A method of preserving numeric information in clay was invented by the Sumerians between 8000 and 3500 BC. This was done with small clay tokens of various shapes that were strung like beads on a string. Beginning about 3500 BC, clay tokens were gradually replaced by number signs impressed with a round stylus at different angles in clay tablets (originally containers for tokens) which were then baked. About 3100  BC, written numbers were dissociated from the things being counted and became abstract numerals.

Between 2700 and 2000 BC, in Sumer, the round stylus was gradually replaced by a reed stylus that was used to press wedge-shaped cuneiform signs in clay. These cuneiform number signs resembled the round number signs they replaced and retained the additive sign-value notation of the round number signs. These systems gradually converged on a common sexagesimal number system; this was a place-value system consisting of only two impressed marks, the vertical wedge and the chevron, which could also represent fractions. This sexagesimal number system was fully developed at the beginning of the Old Babylonia period (about 1950 BC) and became standard in Babylonia.

Sexagesimal numerals were a mixed radix system that retained the alternating base 10 and base 6 in a sequence of cuneiform vertical wedges and chevrons. By 1950 BC, this was a positional notation system. Sexagesimal numerals came to be widely used in commerce, but were also used in astronomical and other calculations. This system was exported from Babylonia and used throughout Mesopotamia, and by every Mediterranean nation that used standard Babylonian units of measure and counting, including the Greeks, Romans and Egyptians. Babylonian-style sexagesimal numeration is still used in modern societies to measure time (minutes per hour) and angles (degrees).

In China, armies and provisions were counted using modular tallies of prime numbers. Unique numbers of troops and measures of rice appear as unique combinations of these tallies. A great convenience of modular arithmetic is that it is easy to multiply, though quite difficult to add. This makes use of modular arithmetic for provisions especially attractive. Conventional tallies are quite difficult to multiply and divide. In modern times modular arithmetic is sometimes used in digital signal processing.

The oldest Greek system was that of the Attic numerals, but in the 4th century BC they began to use a quasidecimal alphabetic system (see Greek numerals). Jews began using a similar system (Hebrew numerals), with the oldest examples known being coins from around 100 BC.

The Roman empire used tallies written on wax, papyrus and stone, and roughly followed the Greek custom of assigning letters to various numbers. The Roman numerals system remained in common use in Europe until positional notation came into common use in the 16th century.

The Maya of Central America used a mixed base 18 and base 20 system, possibly inherited from the Olmec, including advanced features such as positional notation and a zero. They used this system to make advanced astronomical calculations, including highly accurate calculations of the length of the solar year and the orbit of Venus.

The Incan Empire ran a large command economy using quipu, tallies made by knotting colored fibers. Knowledge of the encodings of the knots and colors was suppressed by the Spanish conquistadors in the 16th century, and has not survived although simple quipu-like recording devices are still used in the Andean region.

Some authorities believe that positional arithmetic began with the wide use of counting rods in China. The earliest written positional records seem to be rod calculus results in China around 400. In particular, zero was correctly described by Chinese mathematicians around 932.

The modern positional Arabic numeral system was developed by mathematicians in India, and passed on to Muslim mathematicians, along with astronomical tables brought to Baghdad by an Indian ambassador around 773.

The binary system (base 2), was propagated in the 17th century by Gottfried Leibniz. Leibniz had developed the concept early in his career, and had revisited it when he reviewed a copy of the I ching from China. Binary numbers came into common use in the 20th century because of computer applications.

Adelard of Bath (; 1080 1152 AD) was a 12th-century English natural philosopher. He is known both for his original works and for translating many important Arabic and Greek scientific works of astrology, astronomy, philosophy and mathematics into Latin from Arabic versions, which were then introduced to Western Europe. He is known as one of the first to introduce the Arabic numeral system to Europe. He stands at the convergence of three intellectual schools: the traditional learning of French schools, the Greek culture of Southern Italy, and the Arabic science of the East.

Adelard of Bath

Given the period when he was alive, Adelard's biography is incomplete in places and leaves some aspects open to interpretation. As a result, much of what is ascribed to Adelard is a product of his own testimony. As his name suggests, he was born in the Roman English city of Bath but how he lived is not entirely known. Despite his extensive travels, by the end of his life he had returned to Bath, where he died. Scholars are hesitant to ascribe definitive parents to the philosopher but Fastred, a tenant of the Bishop of Wells, is mostly plausibly identified as this figure. His name (Adelard) is of Anglo-Saxon origin, which would have placed him in the subordinate class, status wise, in 11th-century England. It is believed that he left England toward the end of the 11th century for Tours, likely on the advice of Bishop John de Villula, who had moved the seat of his bishopric from Wells to Bath in 1090. During his studies in Tours, an anonymous "wise man of Tours" inspired Adelard with his interest in astronomy to study the science. Adelard later taught for a time at Laon, leaving Laon for travel no later than 1109. After leaving Laon, he travelled to Southern Italy and Sicily no later than 1116.

Adelard also travelled extensively throughout the "lands of the Crusades": Greece, West Asia, Sicily, Spain, Tarsus, Antioch and potentially Palestine. The time spent in these areas would help explain his fascination with mathematics and his access to Arabic scholars. By 1126, Adelard returned to the West with the intention of spreading the knowledge he had gained about Arab astronomy and geometry to the Latin world. One aspect of particular interest with respect to Adelard, his teachings, and the time period he grew up, was the relation to the Crusades. This time of remarkable transition marked an opportunity for someone to gain valuable influence over the evolution of human history. While the Crusades offered little in the way of a victor, Adelard's non-discriminatory scholarly work inspired him to bring back to England many ancient texts and new questions that would later give rise to an English Renaissance. Again, given the 11th-century time period that Adelard was alive, it was understandably difficult for Adelard to have achieved his educational pursuits. In the absence of a printing press and given the weak public literacy rate, books were rare items in medieval Europe—generally held only by royal courts or Catholic monastic communities (Kraye, "et al." 1987). Fittingly, Adelard studied with monks at the Benedictine Monastery at Bath Cathedral.

Among Adelard of Bath's original works is a trio of dialogues, written to mimic the Platonic style, or correspondences with his nephew. The earliest of these is "De Eodem et Diverso (On the Same and the Different)". It is written in the style of a protreptic, or an exhortation to the study of philosophy. The work is modelled on Boethius' "Consolation of Philosophy", evident in Adelard's vocabulary and phraseology. It is believed to have been written near Tours after he had already travelled, though there is no indication that he had travelled past Southern Italy and Sicily at the time of writing. The work takes the form of a dramatic dialogue between Philocosmia, who advocates worldly pleasures, and Philosophia, whose defence of scholarship leads into a summary of the seven liberal arts. Underlining the entire work is the contrast between Philocosmia's "res" (perceptible reality), and Philosophia's "verba" (mental concepts). Each section of the liberal arts is divided into two parts. Presented first is a description of the allegorical figure representing the art, in which the importance of that art is indicated, followed by a summary of the doctrines of that art, as told by the allegorical figure who is presented as the founder or main proponent of the particular art.

The second of this trio, and arguably Adelard's most significant contribution, was his "Questiones Naturales" or "Questions on Natural Science". It can be dated between 1107 and 1133 as, in the text, Adelard himself mentions that seven years have passed since his lecturing in schools at Laon. He chooses to present this work as a forum for Arabic learning, referring often to his experiences in Antioch. He sets out seventy-six questions, in the form of a Platonic dialogue about meteorology and natural science. It was used heavily in schools into and beyond the 13th century but the teaching on natural things would ultimately be superseded by Aristotle's writing. The text is broken up into three parts: "On Plants and Brute Animals", "On Man" and "On Earth, Water, Air, and Fire". Two of the more specific features associated with this text are (1) a preference for reason over authority in matters of science and nature (in other words, seeking solutions via reason and logic rather than through faith) and (2) the use of the literary device of invoking Arab teachings when presenting very controversial topics (i.e. that brute animals may possess knowledge and souls) Adelard didn't think that the use of reason to seek knowledge was in any way contradictory with Christian faith in God. The soul is a large part of the dialogue in this text as "On Man" discusses a corporeal soul in man, while the final section elaborates on the incorporeal soul of elements and animals. "Questiones Naturales" appears to have been an immediate success as it was copied on both sides of the English Channel and was even presented in a "pocket-book" format, suggesting that it was meant to be carried around.

The final section in his trilogy is a treatise on hawking called "De Avibus Tractatus (Treatise on Birds)". It is a medical text that addresses disease from head-to-toe. While it has been argued that this treatise was not widely distributed, an investigation of later Latin and French treatises reveals a number of excerpts from Adelard's work.

The remainder of Adelard's original works did not involve the persona of his nephew. He wrote a treatise on the use of the abacus called "Regulae Abaci", which was likely written very early in his career because it shows no trace of Arab influence. This treatise is believed to be proof that Adelard was connected to the Exchequer table that was used for monetary calculations in the medieval period. Further evidence for this can be found in the Pipe Roll of Henry I, which shows that he had received a discharge from the murder fine (a fine levied on inhabitants of a certain area based on the murder of a Norman that occurred in a generally accessible field in that same area) levied on the community of Wiltshire in 1130, though there is no other proof for this fact. The work that Adelard of Bath is known for in the Latin world is his translation of the astronomical tables of al-Khwarizmi, the first widely accessible Latin translation of the Islamic ideas about algebra. In the Middle Ages he was known for his rediscovery and teaching of geometry, earning his reputation when he made the first full translation of Euclid's ""Elements"" and began the process of interpreting the text for a Western audience.

When Adelard's influence on the study of philosophy is considered, it is clear that his ideas most notably manifested in the later works of Robert Grosseteste and Roger Bacon. While his work in natural philosophy is probably overshadowed by Aristotle, it still helped lay the foundations for much of the progress that was made in the later centuries. His work surrounding Euclid's "Elements", for example, was of great help in providing training that would help future scholars understand the relationships between demonstrative and geometrical proofs. While his original writings demonstrate that he had a sincere passion for the seven liberal arts (grammar, rhetoric, logic, mathematics, geometry, music, and astronomy), his work in "Quaestiones naturales" illustrated a more encompassing dedication to subjects such as physics, the natural sciences, and possibly even metaphysics. His influence is also evident in "De philosophia mundi" by William of Conches, Hugh of Saint Victor, and Isaac of Stella's "Letters to Alcher on the Soul". He introduced algebra to the Latin world and his commentaries in Version III of Euclid's "Elements" were extremely influential in the 13th century. Adelard also displays original thought of a scientific bent, raising the question of the shape of the Earth (he believed it round) and the question of how it remains stationary in space, and also the interesting question of how far a rock would fall if a hole were drilled through the Earth and a rock dropped through it, see center of gravity.
Campanus of Novara probably had access to Adelard's translation of "Elements", and it is Campanus' edition that was first published in Venice in 1482 after the invention of the printing press. It became the chief textbook of the mathematical schools of Western Europe until the 16th century.

The first mentions of the numerals in the West are found in the "Codex Vigilanus" of 976.

Arabic numerals

Arabic numerals are the ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; or numerals written using them in the Hindu–Arabic numeral system (where the position of a digit indicates the power of 10 to multiply it by). It is the most common system for the symbolic representation of numbers in the world today.

The Hindu-Arabic numeral system was developed by Indian mathematicians around AD 500 using quite different forms of the numerals. From India, the system was adopted by Arabic mathematicians in Baghdad and passed on to the Arabs farther west. The current form of the numerals developed in North Africa. It was in the North African city of Bejaia that the Italian scholar Fibonacci first encountered the numerals; his work was crucial in making them known throughout Europe. The use of Arabic numerals spread around the world through European trade, books and colonialism.

The term "Arabic numerals" is ambiguous, it may also be intended to mean the numerals used by Arabs, in which case it generally refers to the Eastern Arabic numerals. Although the phrase "Arabic numeral" is frequently capitalized, it is sometimes written in lower case: for instance in its entry in the "Oxford English Dictionary", which helps to distinguish it from "Arabic numerals" as the Eastern Arabic numerals.

Alternative names are Western Arabic numerals, Western numerals, Hindu–Arabic numerals, and Unicode calls them digits.

The decimal Hindu–Arabic numeral system with zero was developed in India by around AD 700. The development was gradual, spanning several centuries, but the decisive step was probably provided by Brahmagupta's formulation of zero as a number in AD 628. The system was revolutionary by including zero in positional notation, thereby limiting the number of individual digits to ten. It is considered an important milestone in the development of mathematics. One may distinguish between this positional "system", which is identical throughout the family, and the precise glyphs used to write the numerals, which varied regionally.

The first universally accepted inscription containing the use of the 0 glyph in India is first recorded in the 9th century, in an inscription at Gwalior in Central India dated to 870. Numerous Indian documents on copper plates exist, with the same symbol for zero in them, dated back as far as the 6th century AD, but their dates are uncertain. Inscriptions in Indonesia and Cambodia dating to AD 683 have also been found.

The numeral system came to be known to the court of Baghdad, where mathematicians such as the Persian Al-Khwarizmi, whose book "On the Calculation with Hindu Numerals" was written about 825 in Arabic, and the Arab mathematician Al-Kindi, who wrote four volumes, "On the Use of the Indian Numerals" ("Ketab fi Isti'mal al-'Adad al-Hindi") about 830, propagated it in the Arab world. Their work was principally responsible for the diffusion of the Indian system of numeration in the Middle East and the West.

In the 10th century, Middle-Eastern mathematicians extended the decimal numeral system to include fractions, as recorded in a treatise by Syrian mathematician Abu'l-Hasan al-Uqlidisi in 952–953. The decimal point notation was introduced by Sind ibn Ali, who also wrote the earliest treatise on Arabic numerals.

A distinctive West Arabic variant of the symbols begins to emerge around the 10th century in the Maghreb and Al-Andalus (sometimes called "ghubar" numerals, though the term is not always accepted), which are the direct ancestor of the modern "Arabic numerals" used throughout the world.
Woepecke has proposed that the Western Arabic numerals were already in use in Spain before the arrival of the Moors, purportedly received via Alexandria, but this theory is not accepted by scholars.

Some popular myths have argued that the original forms of these symbols indicated their numeric value through the number of angles they contained, but no evidence exists of any such origin.

In 825 Al-Khwārizmī wrote a treatise in Arabic, "On the Calculation with Hindu Numerals", which survives only as the 12th-century Latin translation, "Algoritmi de numero Indorum". "Algoritmi", the translator's rendition of the author's name, gave rise to the word "algorithm".

From the 980s, Gerbert of Aurillac (later, Pope Sylvester II) used his position to spread knowledge of the numerals in Europe. Gerbert studied in Barcelona in his youth. He was known to have requested mathematical treatises concerning the astrolabe from Lupitus of Barcelona after he had returned to France.

Leonardo Fibonacci (Leonardo of Pisa), a mathematician born in the Republic of Pisa who had studied in Béjaïa (Bougie), Algeria, promoted the Indian numeral system in Europe with his 1202 book "Liber Abaci":

When my father, who had been appointed by his country as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him while I was still a child, and having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting. There, when I had been introduced to the art of the Indians' nine symbols through remarkable teaching, knowledge of the art very soon pleased me above all else and I came to understand it.

The numerals are arranged with their lowest value digit to the right, with higher value positions added to the left. This arrangement is the same in Arabic as well as the Indo-European languages.

The reason the digits are more commonly known as "Arabic numerals" in Europe and the Americas is that they were introduced to Europe in the 10th century by Arabic-speakers of North Africa, who were then using the digits from Libya to Morocco. Arabs, on the other hand, call the base-10 system (not just these digits) "Hindu numerals", referring to their origin in India. This is not to be confused with what the Arabs call the "Hindi numerals", namely the Eastern Arabic numerals ( - - - - - - - - - ) used in the Middle East, or any of the numerals currently used in Indian languages (e.g. Devanagari: ).

The European acceptance of the numerals was accelerated by the invention of the printing press, and they became widely known during the 15th century. Early evidence of their use in Britain includes: an equal hour horary quadrant from 1396, in England, a 1445 inscription on the tower of Heathfield Church, Sussex; a 1448 inscription on a wooden lych-gate of Bray Church, Berkshire; and a 1487 inscription on the belfry door at Piddletrenthide church, Dorset; and in Scotland a 1470 inscription on the tomb of the first Earl of Huntly in Elgin Cathedral. (See G.F. Hill, "The Development of Arabic Numerals in Europe" for more examples.) In central Europe, the King of Hungary Ladislaus the Posthumous, started the use of Arabic numerals, which appear for the first time in a royal document of 1456. By the mid-16th century, they were in common use in most of Europe. Roman numerals remained in use mostly for the notation of anno Domini years, and for numbers on clockfaces.

Today, Roman numerals are still used for enumeration of lists (as an alternative to alphabetical enumeration), for sequential volumes, to differentiate monarchs or family members with the same first names, and (in lower case) to number pages in prefatory material in books.

Cyrillic numerals were a numbering system derived from the Cyrillic alphabet, used by South and East Slavic peoples. The system was used in Russia as late as the early 18th century when Peter the Great replaced it with Arabic numerals.

Arabic numerals were introduced to China during the Yuan Dynasty (1271–1368) by the Muslim Hui people. In the early 17th century, European-style Arabic numerals were introduced by Spanish and Portuguese Jesuits.

The numeral system employed, known as algorism, is positional decimal notation. Various symbol sets are used to represent numbers in the Hindu–Arabic numeral system, potentially including both symbols that evolved from the Brahmi numerals, and symbols that developed independently. The symbols used to represent the system have split into various typographical variants since the Middle Ages:The evolution of the numerals in early Europe is shown here in a table created by the French scholar Jean-Étienne Montucla in his "Histoire de la Mathematique", which was published in 1757:

The Arabic numerals 0–9 are encoded in ASCII at positions 0x30 to 0x39. Masking to the lower 4 binary bits (or taking the last hexadecimal digit) gives the value of the digit, a great help in converting text to numbers on early computers. These positions were inherited in Unicode and in virtually all other encodings based in any way on ASCII. EBCDIC used different values, but also had the lower 4 bits equal to the digit value.