New Delhi: The Delhi police are India’s best in terms of staffing, infrastructure and use of budget, followed by Kerala and Maharashtra, a new study has revealed. Uttar Pradesh, Chhattisgarh and Bihar are the worst and most overworked among the 22 states analysed. 

These findings are based on a Police Adequacy Index, derived from national data, part of the ‘Status of Policing in India Report 2019’, released on August 27, 2019 by Common Cause and Lokniti–Centre for the Study Developing Societies, a nonprofit and a think tank, respectively, based in New Delhi. 

The study of 11,000 personnel in 22 states used available government data to analyse and rank the performance of state police on parameters of staffing, infrastructure and budget. Researchers also interviewed 11,834 police personnel across 105 locations in 21 states between February and April 2019. The survey covered the personnel’s opinions over adequacy of police infrastructure, their duties and their perception over several types of crimes and different sections of the society. You can IndiaSpend’s full coverage of the study, here and here.

The index

To derive indices, researchers used data from the Bureau of Police Research and Development and the National Crime Records Bureau for the following parameters:
 

1. Strength:
   1. Police strength as a percentage of sanctioned strength (2012-16 average)
2. Infrastructure
   1. Police stations having vehicles (2012-16 average)
   2. Police stations having telephones and wireless (2012-2016 average)
   3. Computers per police station (2012-2016 average)
3. Budget
   1. Police expenditure as a percentage of budget (2014-16 average)

These indicators are then used to derive index scores on each of the three heads: An index score of zero indicates the worst performing state and a score of one indicates the best performing state.

Overall, as of 2016, Indian police forces were working at 77.4% of their sanctioned capacity, the study said, leading to personnel being overworked. 

The study also pointed out the lack of diversity in the India police. About 86% states (19 of 22) did not fulfil their Scheduled Castes (SC) quota, 73% (16 of 22) did not fulfill their Scheduled Tribes (ST) quotas while 59% (13 of 22) failed to fulfil their Other Backward Classes (OBC) quotas, it said.

None of the states achieved the mandated 33% representation of women in the police force. Further, while 14.3% of all police personnel were officers in 2016–up from 11.6% in 2007, the proportion of officers among policewomen has declined from 11.4% in 2007 to 10.2% in 2016. 

While 41% personnel think women lack the “physical strength and aggressive behaviour” required for the job, 32% think “women police are incapable of handling high intensity crimes and cases”, and 51% think that, due to “inflexible working hours, it is not alright for women to work in the police force as they cannot attend to homely duties”, as IndiaSpend reported on August 29, 2019.

Further, 267 police stations across India had no telephones and 129 had no wireless communication devices as of January 2017, as IndiaSpend reported on August 24, 2019, citing the latest available data from the Bureau of Police Research and Development (BPRD).

There were eight vehicles for every 100 police personnel for responding to distress calls, patrolling and maintaining law and order in their jurisdictions.

Across the 22 states analysed in the study, police stations had, on average, six computers each. Delhi had the highest (16.5 computers per police station) and Bihar had the lowest (0.6). 

The utilisation of police forces’ modernisation budget was less than half (48%) of the funding available, according to an IndiaSpend analysis (cited above) of government data.

Nagaland, Kerala had best staffing, Delhi best infrastructure, Tamil Nadu spent best

Delhi police performs well on both infrastructure (1.03) and strength (0.70) parameters. 

Uttar Pradesh, the worst performer in the country, scored poorly on both the police strength (0.10) and the budget utilisation (0.05).
However, it scored well in Infrastructure indicators with an index value of 0.79. The overall index value of the state remained at 0.31, lower than the national overall index value of 0.42. 

Nagaland had the best score on police strength (0.80), followed by Kerala (0.71) and Delhi (0.70). Delhi had the best infrastructure (1.03), followed by Haryana (0.94) and Kerala (0.89). Tamil Nadu scored the highest on budget utilisation (0.09), followed by Maharashtra, Odisha, Rajasthan and Haryana (0.08).

Telangana (0.41), Andhra Pradesh (0.41), Jharkhand (0.41), West Bengal (0.40), Gujarat (0.40), Bihar (0.35) and Chhattisgarh (0.34) also scored below the national average on the Index.

In general, states performed better on infrastructure indicators than on budget utilisation, the study said. The inadequacy of police infrastructure can hardly be attributed to the inadequacy of budget, said the study, adding that most states by a margin underutilised their budget resources.

“Gujarat and Andhra Pradesh, despite using comparatively marginal proportion of the allocated budget, boast of a better infrastructure than many other states. Yet, both States land in the absolute bottom of ranking,” the study said. 

Uttarakhand is the exact contrary to these two States, the study pointed out. The state uses much lesser proportion of the allocated budget but boasts better infrastructure and better proportionate strength and hence a better overall ranking.

These inadequacies affect the working conditions of police personnel, with many of them being overworked, as the survey’s findings show:
 

• Police personnel work for 14 hours a day on an average, with about 80% personnel working for more than 8 hours a day
• Nearly half the personnel work overtime regularly, while 80% do not get paid for overtime work
• One half the personnel do not get any weekly off days
• About 75% believe that their workload is affecting their physical and mental health
• A quarter reported that senior police personnel ask their juniors to do their household/personal jobs even though they are not meant to do it. Personnel from the SC, ST and OBC are more likely to report this than other caste groups
• 40% personnel report the use of bad language by senior officers
• 37% personnel are willing to give up their jobs for another profession, if the perks and salaries remain the same.

Political pressure biggest hindrance in investigations

About 28% police personnel believe that “pressure from politicians” is the “biggest hindrance” in crime investigations, found the survey.

When asked about the frequency of such pressure, one in three personnel reported facing such pressure “many times” in the course of a crime investigation. A similar percentage reported that unwilling witnesses were a hindrance “many times”.

The question posed was: “Considering the past 2-3 years of your work experience, how often have you encountered political pressure during investigation of a crime?” They were asked to choose one of these responses: many times, sometimes, rarely or never.

Further, 38% personnel reported always facing pressure from politicians in cases of crime involving influential persons, the study said.

Three out of five police personnel surveyed reported transfer as the most common consequence of not complying with external pressures, the study said.

(Tripathi is an IndiaSpend reporting fellow.)

Courtesy: India Spend

The post ‘Delhi Police India’s Best On Numbers, Infrastructure & Money Use, UP Police Worst’ appeared first on SabrangIndia.

Bakhshali manuscript. Bodleian Libraries, University of Oxford

As well as giving us the concept of zero, Indian mathematicians made seminal contributions to the study of trigonometry, algebra, arithmetic and negative numbers among other areas. Perhaps most significantly, the decimal system that we still employ worldwide today was first seen in India.
 

The number system

As far back as 1200 BC, mathematical knowledge was being written down as part of a large body of knowledge known as the Vedas. In these texts, numbers were commonly expressed as combinations of powers of ten. For example, 365 might be expressed as three hundreds (3×10²), six tens (6×10¹) and five units (5×10⁰), though each power of ten was represented with a name rather than a set of symbols. It is reasonable to believe that this representation using powers of ten played a crucial role in the development of the decimal-place value system in India.

Brahmi numerals. Wikimedia

From the third century BC, we also have written evidence of the Brahmi numerals, the precursors to the modern, Indian or Hindu-Arabic numeral system that most of the world uses today. Once zero was introduced, almost all of the mathematical mechanics would be in place to enable ancient Indians to study higher mathematics.
 

The concept of zero

Zero itself has a much longer history. The recently dated first recorded zeros, in what is known as the Bakhshali manuscript, were simple placeholders – a tool to distinguish 100 from 10. Similar marks had already been seen in the Babylonian and Mayan cultures in the early centuries AD and arguably in Sumerian mathematics as early as 3000-2000 BC.

But only in India did the placeholder symbol for nothing progress to become a number in its own right. The advent of the concept of zero allowed numbers to be written efficiently and reliably. In turn, this allowed for effective record-keeping that meant important financial calculations could be checked retroactively, ensuring the honest actions of all involved. Zero was a significant step on the route to the democratisation of mathematics.

No abacus needed. Shutterstock

These accessible mechanical tools for working with mathematical concepts, in combination with a strong and open scholastic and scientific culture, meant that, by around 600AD, all the ingredients were in place for an explosion of mathematical discoveries in India. In comparison, these sorts of tools were not popularised in the West until the early 13th century, though Fibonnacci’s book liber abaci.
 

Solutions of quadratic equations

In the seventh century, the first written evidence of the rules for working with zero were formalised in the Brahmasputha Siddhanta. In his seminal text, the astronomer Brahmagupta introduced rules for solving quadratic equations (so beloved of secondary school mathematics students) and for computing square roots.
 

Rules for negative numbers

Brahmagupta also demonstrated rules for working with negative numbers. He referred to positive numbers as fortunes and negative numbers as debts. He wrote down rules that have been interpreted by translators as: “A fortune subtracted from zero is a debt,” and “a debt subtracted from zero is a fortune”.

This latter statement is the same as the rule we learn in school, that if you subtract a negative number, it is the same as adding a positive number. Brahmagupta also knew that “The product of a debt and a fortune is a debt” – a positive number multiplied by a negative is a negative.

Negative cows. Shutterstock

For the large part, European mathematicians were reluctant to accept negative numbers as meaningful. Many took the view that negative numbers were absurd. They reasoned that numbers were developed for counting and questioned what you could count with negative numbers. Indian and Chinese mathematicians recognised early on that one answer to this question was debts.

For example, in a primitive farming context, if one farmer owes another farmer 7 cows, then effectively the first farmer has -7 cows. If the first farmer goes out to buy some animals to repay his debt, he has to buy 7 cows and give them to the second farmer in order to bring his cow tally back to 0. From then on, every cow he buys goes to his positive total.
 

Basis for calculus

This reluctance to adopt negative numbers, and indeed zero, held European mathematics back for many years. Gottfried Wilhelm Leibniz was one of the first Europeans to use zero and the negatives in a systematic way in his development of calculus in the late 17th century. Calculus is used to measure rates of changes and is important in almost every branch of science, notably underpinning many key discoveries in modern physics.

Leibniz: Beaten to it by 500 years.

But Indian mathematician Bhāskara had already discovered many of Leibniz’s ideas over 500 years earlier. Bhāskara, also made major contributions to algebra, arithmetic, geometry and trigonometry. He provided many results, for example on the solutions of certain “Doiphantine” equations, that would not be rediscovered in Europe for centuries.

The Kerala school of astronomy and mathematics, founded by Madhava of Sangamagrama in the 1300s, was responsible for many firsts in mathematics, including the use of mathematical induction and some early calculus-related results. Although no systematic rules for calculus were developed by the Kerala school, its proponents first conceived of many of the results that would later be repeated in Europe including Taylor series expansions, infinitessimals and differentiation.

The leap, made in India, that transformed zero from a simple placeholder to a number in its own right indicates the mathematically enlightened culture that was flourishing on the subcontinent at a time when Europe was stuck in the dark ages. Although its reputation suffers from the Eurocentric bias, the subcontinent has a strong mathematical heritage, which it continues into the 21st century by providing key players at the forefront of every branch of mathematics.

Christian Yates, Senior Lecturer in Mathematical Biology, University of Bath
 

This article was originally published on The Conversation. Read the original article.

The post Five ways ancient India changed the world – with maths appeared first on SabrangIndia.