Counting is the process of determining the number of elements of a finite set of objects; that is, determining the size of a set. The traditional way of counting consists of continually increasing a counter by a unit for every element of the set, in some order, while marking those elements to avoid visiting the same element more than once, until no unmarked elements are left; if the counter was set to one after the first object, the value after visiting the final object gives the desired number of elements. The related term enumeration refers to uniquely identifying the elements of a finite (combinatorial) set or infinite set by assigning a number to each element.

Just like the syllable-counting meters regulate the alternation of light and heavy syllables, the principal jtis regulate the alternation of syncopated and unsyncopated gaas that each consist of four moras. A syncopated gaa begins a prosodic foot (i.e., usually a heavy syllable, or the first of two light syllables) on the second mora; an unsycopated gaa begins a prosodic foot on the first mora. The shape  is always syncopated; the shapes , , and  are always unsyncopated. The shape  is syncopated when a word begins from the second mora (= syllable); otherwise it counts as unsyncopated.


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A japamala, jaap maala, or simply mala (Sanskrit: ; ml, meaning 'garland'[1]) is a loop of prayer beads commonly used in Indian religions such as Hinduism, Buddhism, Jainism, Sikhism, for counting recitations (japa) of mantras, prayers or other sacred phrases. It is also worn for warding off evil, for counting some other sadhana (spiritual practice) such as prostrating before a holy icon and as a symbol of religious identification.[2][3]

The specific origin of the mala is unknown, with the use of beads for counting being a widespread practice in ancient cultures.[4] No references to malas occur in Chinese literature before the introduction of Buddhism during the Han dynasty, suggesting that the practice spread from India to China and may have originated there.[4] No mention of a mala occurs in the Agamas or Pali Nikayas, generally regarded as the oldest Buddhist literature, and it is unclear if their use originated with Buddhists or with Brahmins, Jains, or another Indian religious community.[4]

In Buddhism in Japan, Buddhist prayer beads are known as ojuzu (, counting beads) or onenju (, thought beads), where the "o" is the honorific o-. Different Buddhist sects in Japan have different shaped prayer beads, and use them differently.

Jdo-sh is somewhat unusual because of the use of a double-ringed prayer beads, called nikka juzu (), which are used for counting nenbutsu recitations (i.e. recitation of the name of Amitabha Buddha): one ring contains single beads used to count a single recitation while the other ring is used to count full revolutions of the first ring. Additionally, other beads hang from the strings, which can count full revolutions of the second ring (flat beads), or full revolutions of the first string of beads. In all, it is possible to count up to 120,000 recitations using these beads. The design is credited to a follower of Hnen named Awanosuke.[18]

Mala may have extra beads hanging from the guru/mother bead or middle bead. These may be decorative elements, especially when unable to move along the cord because knots hold them in place. They may or may not have religious symbolism (for example, three beads representing the Buddhist Triple Gem of Buddha, Dharma and Sangha) but are not used for counting recitations in any way.[4]

In some more complex malas, three distinctive, often smaller, beads are placed so that, with the guru bead, they divide the regular beads into four sections of 27 beads each. They allow quick estimation of the fraction of a round completed. Their presence raises the number of beads (not counting the guru bead) to 111.

The main use of a mala is to repeat mantras or other important religious phrases and prayers (like the Pure Land Buddhist nianfo). Mantras are typically repeated hundreds or even thousands of times. The mala is used so that those who are trying to achieve an exact number of repetitions can focus on the meaning or sound of the mantra rather than counting its repetitions.[22]

In Buddhism, there are numerous ways of holding a mala and using it during recitation. This differs across traditions. It is commonly taught that the left hand is used to hold a mala.[2] However, sometimes both hands are involved in the recitation and counting process. In Chinese Buddhism it is common for monks to wear it around their necks when not in use. In other traditions, the mala is left on one's altar or placed in a pouch when not in use. In Tibetan Buddhism, malas used for esoteric (mantrayana) practices are often kept private and should not be shown to anyone.[23]

Tibetan Buddhists generally teach the use of the left hand for counting mantras.[11] Different methods of holding it and moving the beads are taught in Tibetan Buddhism, depending on the type of practice. For example, for peaceful deity practices, one moves the beads towards the body over the forefinger and one holds the mala at the heart. For increasing practices meanwhile, one moves the beads over the middle finger and holds the mala at the navel.[11]

A common taboo is that the guru bead is not used for counting repetitions; counting for each round begins and ends with either of the beads next to the guru bead. In the Hindu tradition and some Buddhist traditions, practitioners who undertake more than one round at a time will, rather than moving their fingers across the guru bead, turn the mala around so that the same bead which was used at the end of the previous round becomes the first bead use for the next round.[4][2]

Sri K Pattabhi Jois (1915-2009) counting through the Ashtanga Vinyasa Primary Series with the traditional Sanskrit counted method. Pattahbi Jois was an indian yoga teacher (fondly referred to as Guruji by his students) whole developed the popular vinyasa style of yoga, know as Ashtanga Yoga. In 1948 he set up the Ashtanga Yoga Research Institute in Mysore, India kpjayi.org which to this day continues to attract thousands of keen Ashtanga students a year from all over the world. 

I had a bad car crash earlier this year on one of the busiest highways in Dubai. To avoid being hit by another car, I smashed into the divider wall between lanes and completely damaged my car. Surprisingly my body had almost no damage, apart from a cut on my arm. As i stepped out of the car in the middle a highway to wait for help, my body almost instinctively retreated to the count. I started counting each breath in Sanskrit the same way I do when I practice or teach. Despite the chaos around me, uncertainty, fear and panic, I could retreat to that place inside of my being where stillness is. In our daily practice we create and re create states of fear, uncertainty and anxiety on our mats. The only way out of them is to focus, to breath through. Similarly I did the same off my mat after that accident. And when medical came and checked my pulse and BP, it was all actually lower than normal.

But the question is how to count result points? Because there is some conditions in counting: every question is Yes or No, and depending on question group those values can be 1 or 0. After the respondent finishes, his points should be summed up and multiplied by value which is individual to every question group.

The IPLL Language Certificate consists of a minimum of 15 credits from 201 or above. Double-dipping between HSL courses and certificate requirements is allowed. Students must maintain a 3.0 GPA in all courses counting toward the certificate. All courses must likewise be taken for a letter grade; CR/NC and Back Credits cannot count toward the certificate. A detailed description of the program requirements is available from the department office in Spalding 454.


Stphane Lamass (University Paris Panthon Sorbonne) et Olivier Mattoni (University Paris Panthon Sorbonne)

Computing and accounting in the 15th century


Grain was an essential commodity of the ancient world. Both administrative documents and mathematical texts refer to problems of grain management, which was often a state matter. What historical approaches can help us to understand grain accounting and the mathematical tools it required? 2351a5e196

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