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Injectable Chips Use Ultrasound to Monitor Body

Tiny, Wireless, Injectable Chips Use Ultrasound to Monitor Body Processes

Columbia Engineers develop the smallest single-chip system that is a complete functioning electronic circuit; implantable chips visible only in a microscope point the way to developing chips that can be injected into the body with a hypodermic needle to monitor medical conditions

MAY 12 2021 | BY HOLLY EVARTS | IMAGE CREDIT: CHEN SHI/COLUMBIA ENGINEERING
 

MEDIA CONTACT

Holly Evarts, Director of Strategic Communications and Media Relations

212-854-3206 (o), 347-453-7408 (c), holly.evarts@columbia.edu

ABOUT THE STUDY

The study is titled “Application of a sub-0.1-mm3 implantable mote for in vivo real-time wireless temperature sensing.”

Journal: Science Advances

Authors are: Chen Shi 1, Victoria Andino-Pavlovsky 1, Stephen A. Lee 2, Tiago Costa 1,3, Jeffrey Elloian 1, Elisa E. Konofagou 2,4, Kenneth L. Shepard 1,2

  1. Department of Electrical Engineering, Columbia University
  2. Department of Biomedical Engineering, Columbia University
  3. Department of Microelectronics, Delft University of Technology, The Netherlands
  4. Department of Radiology, Columbia University

The study was supported in part by a grant from the W. M. Keck Foundation and by the Defense Advanced Research Projects Agency (DARPA) under Contract HR0011-15-2-0054 and Cooperative Agreement D20AC00004.

Chen Shi and Kenneth L. Shepard are listed as inventors on a provisional patent filed by Columbia University (Patent Application No. 15/911,973). The other authors declare no competing interests.

Schematic representation of the device.

Schematic representation of the device.

New York, NY—May 12, 2021—Widely used to monitor and map biological signals, to support and enhance physiological functions, and to treat diseases, implantable medical devices are transforming healthcare and improving the quality of life for millions of people. Researchers are increasingly interested in designing wireless, miniaturized implantable medical devices for in vivo and in situ physiological monitoring. These devices could be used to monitor physiological conditions, such as temperature, blood pressure, glucose, and respiration for both diagnostic and therapeutic procedures.

To date, conventional implanted electronics have been highly volume-inefficient—they generally require multiple chips, packaging, wires, and external transducers, and batteries are often needed for energy storage. A constant trend in electronics has been tighter integration of electronic components, often moving more and more functions onto the integrated circuit itself.

Researchers at Columbia Engineering report that they have built what they say is the world’s smallest single-chip system, consuming a total volume of less than 0.1 mm3. The system is as small as a dust mite and visible only under a microscope. In order to achieve this, the team used ultrasound to both power and communicate with the device wirelessly. The study was published online May 7 in Science Advances.

“We wanted to see how far we could push the limits on how small a functioning chip we could make,” said the study’s leader Ken Shepard, Lau Family professor of electrical engineering and professor of biomedical engineering. “This is a new idea of ‘chip as system’—this is a chip that alone, with nothing else, is a complete functioning electronic system. This should be revolutionary for developing wireless, miniaturized implantable medical devices that can sense different things, be used in clinical applications, and eventually approved for human use.”

The team also included Elisa Konofagou, Robert and Margaret Hariri Professor of Biomedical engineering and professor of radiology, as well as Stephen A. Lee, PhD student in the Konofagou lab who assisted in the animal studies.

The design was done by doctoral student Chen Shi, who is the first author of the study. Shi’s design is unique in its volumetric efficiency, the amount of function that is contained in a given amount of volume. Traditional RF communications links are not possible for a device this small because the wavelength of the electromagnetic wave is too large relative to the size of the device. Because the wavelengths for ultrasound are much smaller at a given frequency because the speed of sound is so much less than the speed of light, the team used ultrasound to both power and communicate with the device wirelessly. They fabricated the “antenna” for communicating and powering with ultrasound directly on top of the chip.

The chip, which is the entire implantable/injectable mote with no additional packaging, was fabricated at the Taiwan Semiconductor Manufacturing Company with additional process modifications performed in the Columbia Nano Initiative cleanroom and the City University of New York Advanced Science Research Center (ASRC) Nanofabrication Facility.

Shepard commented, “This is a nice example of ‘more than Moore’ technology—we introduced new materials onto standard complementary metal-oxide-semiconductor to provide new function. In this case, we added piezoelectric materials directly onto the integrated circuit to transducer acoustic energy to electrical energy.”

Konofagou added, “Ultrasound is continuing to grow in clinical importance as new tools and techniques become available. This work continues this trend.”

The team’s goal is to develop chips that can be injected into the body with a hypodermic needle and then communicate back out of the body using ultrasound, providing information about something they measure locally. The current devices measure body temperature, but there are many more possibilities the team is working on.

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Aluminum-Ion Battery Charges 60 Times Faster Than Lithium-Ion

Developer Of Aluminum-Ion Battery Claims It Charges 60 Times Faster Than Lithium-Ion, Offering EV Range Breakthrough

Michael Taylor

 
2022 will see a new aluminum-ion battery charging 60 times faster than lithium-ion tech.

A breakthrough graphene aluminum-ion battery technology could blow lithium-ion away for power, … [+]

 GRAPHENE MANUFACTURING GROUP

Range anxiety, recycling and fast-charging fears could all be consigned to electric-vehicle history with a nanotech-driven Australian battery invention.

The graphene aluminum-ion battery cells from the Brisbane-based Graphene Manufacturing Group (GMG) are claimed to charge up to 60 times faster than the best lithium-ion cells and hold three time the energy of the best aluminum-based cells.

 

They are also safer, with no upper Ampere limit to cause spontaneous overheating, more sustainable and easier to recycle, thanks to their stable base materials. Testing also shows the coin-cell validation batteries also last three times longer than lithium-ion versions.

GMG plans to bring graphene aluminum-ion coin cells to market late this year or early next year, with automotive pouch cells planned to roll out in early 2024.

Based on breakthrough technology from the University of Queensland’s (UQ) Australian Institute for Bioengineering and Nanotechnology, the battery cells use nanotechnology to insert aluminum atoms inside tiny perforations in graphene planes.

PROMOTED

The GMG technology drops aluminum atoms into perforations in graphene.

The Graphene Manufacturing Group’s aluminum-ion technology can charge an iPhone in less than 10 … [+]

 GRAPHENE MANUFACTURING GROUP

Testing by peer-reviewed specialist publication Advanced Functional Materials publication concluded the cells had “outstanding high-rate performance (149 mAh g−1 at 5 A g−1), surpassing all previously reported AIB cathode materials”.

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GMG Managing Director Craig Nicol insisted that while his company’s cells were not the only graphene aluminum-ion cells under development, they were easily the strongest, most reliable and fastest charging.

“It charges so fast it’s basically a super capacitor,” Nicol claimed. “It charges a coin cell in less than 10 seconds.”

The new battery cells are claimed to deliver far more power density than current lithium-ion batteries, without the cooling, heating or rare-earth problems they face.

“So far there are no temperature problems. Twenty percent of a lithium-ion battery pack (in a vehicle) is to do with cooling them. There is a very high chance that we won’t need that cooling or heating at all,” Nicol claimed.

“It does not overheat and it nicely operates below zero so far in testing.

“They don’t need circuits for cooling or heating, which currently accounts for about 80kg in a 100kWh pack.”

The battery can swap three aluminum electrons per ion, compared to lithium's one.

When aluminum-ion batteries recharge, they return to the negative electrode and swap three aluminum … [+]

 GRAPHENE MANUFACTURING GROUP

The new cell technology, Nicol insisted, could also be industrialized to fit inside current lithium-ion housings, like the Volkswagen Group’s MEB archicture, heading off problems with car-industry architectures that tend to be used for up to 20 years.

“Ours will be the same shape and voltage as the current lithium-ion cells, or we can move to whatever shape is necessary,” Nicol confirmed.

“It’s a direct replacement that charges so fast it’s basically a super capacitor.

“Some lithium-ion cells can’t do more than 1.5-2 amps or you can blow up the battery, but our technology has no theoretical limit.”

Aluminum-ion battery cells are a hot bed of development, particularly for automotive use.

Recent projects alone have included a collaboration between China’s Dalian University of Technology and the University of Nebraska, plus others from Cornell University, Clemson University, the University of Maryland, Stanford University, the Zhejiang University’s Department of Polymer Science and the European Alion industrial consortium.

The differences are highly technical, but the GMG cells use graphene from made from its proprietary plasma process, rather than traditional graphite sourcing, and the result is three times the energy density of the next-best cell, from Stanford University.

The GMG aluminium-ion coin cell will be in production in early 2022.

The Graphene Manufacturing Group aluminium-ion coin cell will be in production in early 2022. Photo: … [+]

 GRAPHENE MANUFACTURING GROUP

Stanford’s natural graphite aluminum-ion technology delivers 68.7 Watt-hours per kilogram and 41.2 Watts per kilogram, while its graphite-foam bumps up to 3000W/kg.

The GMG-UQ battery heaves that forward to between 150 and 160Wh/kg and 7000W/kg.

“They (UQ) found a way to make holes in graphene and a way to store aluminum atoms closer together in the holes.

“If we drill holes the atoms stick inside the graphene and it becomes a whole lot more dense, like a bowling ball on a mattress.”

The peer-reviewed publication Advanced Functional Materials found surface-perforated, three-layer graphene (SPG3-400) had “a significant amount of in-plane mesopores (≈2.3 nm), and an extremely low O/C ratio of 2.54%, has demonstrated excellent electrochemical performance.

“This SPG3-400 material exhibits an extraordinary reversible capacity (197 mAh g−1 at 2 A g−1) and outstanding high-rate performance,” it concluded.

Aluminum-ion technology has intrinsic advantages and disadvantages over the preeminent lithium-ion battery technology being used in almost every EV today.

When a cell recharges, aluminum ions return to the negative electrode and can exchange three electrons per ion instead of lithium’s speed limit of just one.

There is also a massive geopolitical, cost, environmental and recycling advantage from using aluminum-ion cells, because they use hardly any exotic materials.

“It’s basically aluminum foil, aluminum chloride (the precursor to aluminum and it can be recycled), ionic liquid and urea,” Nicol said.

“Ninety percent of world lithium production and purchasing is still through China and 10 percent is through Chile.

“We have all the aluminum we need right here in Australia, and they can be safely made in the first world.”

Battery researchers Dr Ashok Kumar Nanjundan (left), and Dr Xiaodan Huang at UQ.

The Graphene Manufacturing Group’s Chief Scientific Officer, Dr Ashok Kumar Nanjundan (left), and Dr … [+]

 GRAPHENE MANUFACTURING GROUP

Listed on the TSX Venture exchange in Canada, GMG hooked itself in to UQ’s graphene aluminum-ion battery technology by supplying the university with graphene.

“Our lead product scientist Dr Ashok Nanjundan was involved in the University of Queensland project in its nanotechnology research centre in its early days,” Nicol said, admitting GMG almost “lucked into” the technology by supplying research projects with its graphene at no cost.

GMG has not locked down a supply deal with a major manufacturer or manufacturing facility.

“We are not tied in to big brands yet, but this could go into an Apple iPhone and charge it in seconds,” Nicol confirmed.

“We will bring the coin cell to market first. It recharges in less than a minute, and it has three times the energy than with lithium,” the Barcaldine product said.

“It’s a lot less adverse effect on health, too. A kid can be killed by lithium if it’s ingested, but not with aluminum.”

The first GMG production battery will be its coin cell, starting early next year.

The coin battery will be the first Graphene Manufucturing Group aluminium-ion battery in production, … [+]

 GRAPHENE MANUFACTURING GROUP

Another benefit would be cost. Lithium has risen from US$1460 a metric tonne in 2005 to US$13,000 a tonne this week, while aluminum’s price has edged up from US$1730 to US$2078 over the same period.

Another advantage is that the GMG graphene aluminum-ion cells do not use copper, which costs around US$8470 a tonne.

While it is open to manufacturing agreements, GMG’s preferred plan is to “run” with the technology as far as it can, with 10 gigaWatt to 50gW plants, first, even if Australia may not be the logical first choice for the manufacturing facility.

It’s not the only Brisbane-based company pushing battery solutions onto the world, either.

PPK Group has a joint venture with Deakin University to develop lithium-sulphur batteries and the Vecco Group has confirmed a deal with Shanghai Electric for a Brisbane manufacturing plant for vanadium batteries for commercial energy storage.

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UN says India must halt mass evictions of 100,000

Khori Gaon Demolition

GENEVA (16 July 2021) – UN human rights experts* today called on India to halt evictions of some 100,000 people – including 20,000 children – that began this week in the midst of monsoon rains.

Demolition of homes began on Wednesday, 14 July, in a village in Haryana State built on protected forest land, even though the forest was actually destroyed decades ago by heavy mining.

“We appeal to the Indian government to respect its own laws and its own goal of eliminating homelessness by 2022 and to spare homes of 100,000 people who mostly come from minority and marginalised communities,” the experts said. “It is particularly important that residents be kept safe during the pandemic.”

The experts said residents “have already been hard hit by the COVID-19 pandemic, and the eviction order would put them at greater risk and bring even more hardship to some 20,000 children – many of whom may remain out of school – and 5,000 pregnant or breastfeeding women.”

They live in Khori Gaon (village) in Faridabad, in India’s north-central Haryana State, on land that was designated as a protected forest in 1992, despite there being no forests on it. Some 2,000 homes were demolished earlier in two waves in September 2020 and April this year. Residents challenging the evictions received a severe setback when the Supreme Court last month ordered the complete removal of the settlement by 19 July.

“We find extremely worrying that India’s highest court, which has in the past led the protection of housing rights, is now leading evictions placing people at risk of internal displacement and even homelessness, as is the case in Khori Gaon,” the experts said. “The role of the Supreme Court is to uphold the laws and to interpret them in light of internationally-recognized human rights standards, not to undermine them. In this case, the spirit and purpose of the Land Acquisition Act 2013, among other domestic legal requirements, have not been met.”

The experts added that “lockdowns imposed during the pandemic have made it difficult for settlement residents to earn a living, and they are suffering psychologically because of the eviction threat.”

Water and electricity were cut off several weeks ago. Human rights defenders and residents who organised protests say they have been beaten by police and arbitrarily detained. There have also been arbitrary orders against the exercise of the right to peaceful assembly, the experts said.

“We call on India to urgently review its plans for razing Khori Gaon and to consider regularizing the settlement so as not to leave anyone homeless,” the experts said. “No one should be forcibly evicted without adequate and timely compensation and redress.”

They urged India, currently a member of the Human Rights Council, to ensure that its policies and practices fully comply with international human rights standards governing relocations, evictions, and internal displacement especially on government’s own land.

“It is especially important that this act of mass displacement does not happen during the pandemic,” they said.

ENDS

* *The expertsMr. Balakrishnan Rajagopal , Special Rapporteur on adequate housing as a component of the right to an adequate standard of living, and on the right to non-discrimination in this contextMs. Mary Lawlor, Special Rapporteur on the situation of human rights defenders . Ms. Cecilia Jimenez-DamarySpecial Rapporteur on the Human Rights of Internally Displaced Persons. Fernand de Varennes, Special Rapporteur on minority issues. Mr Pedro Arrojo-Agudo, Special Rapporteur on the human rights to safe drinking water and sanitationMr. Olivier De Schutter, Special Rapporteur on extreme poverty and human rights. Ms. Koumbou Boly Barry, Special Rapporteur on the right to education. 

Special Rapporteurs are part of what is known as the Special Procedures of the Human Rights Council. Special Procedures, the largest body of independent experts in the UN Human Rights system, is the general name of the Council’s independent fact-finding and monitoring mechanisms that address either specific country situations or thematic issues in all parts of the world. Special Procedures’ experts work on a voluntary basis; they are not UN staff and do not receive a salary for their work. They are independent from any government or organization and serve in their individual capacity.

UN Human Rights, Country Page:

For more information and media requests, please contact Ms. Mariya Stoyanova-Bahchevanova at mstoyanova@ohchr.org.

For media enquiries regarding other UN independent experts, please contact Renato de Souza  rrosariodesouza@ohchr.org).

 


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DARUL ULOOM DEOBAND’S FATWA ABOUT SAAD KANDHLAWI

AN ANALYSIS OF DARUL ULOOM DEOBAND’S FATWA ABOUT MAULANA SAAD KANDHLAWI

Due to the letters and questions regarding some of the incorrect ideologies and thoughts and the questionable Bayaans of Janaab Moulana Saad Saheb Kandhelwi received from within the country as well as from beyond, with the signatures of senior Asaatizah Kiraam and the panel of Muftis, an official stance has been taken.

However, before releasing this document, it was brought to our notice that a delegation wishes to come to Darul-Uloom and discuss matters on behalf of Moulana Muhammed Saad Saheb. Hence, the delegation came and delivered the message on behalf of Moulana Muhammed Saad Saheb that he is ready to make Rujoo’ (retract). Therefore, the unanimous stance was sent with the delegation to Moulana Muhammed Saad Saheb. A reply was then received from him, however, Darul-Uloom Deoband was not satisfied with his reply completely, upon which some explanation was sent to Moulana Muhammed Saad Saheb in the form of a letter.

In order to protect the blessed effort of Tableegh started by the Akaabir Ulema of Darul-uloom Deoband from becoming mixed up with incorrect ideologies, to keep it on the pattern of the Akaabir and also in order for its benefit and to keep the reliance of the Ulema-e-Haq upon this effort, it is regarded as a Deeni responsibility to present our unanimous standpoint to the Ahl-e-Madaaris, Ahl-e-Ilm and the unbiased people. May Allah Ta’ala protect this blessed effort in every way and grant all of us the ability to remain ideologically and practically on the path of truth.

بسم الله الرحمن الرحيم
الحمد لله رب العالمين، والصلاة والسلام على سيد الأنبياء والمرسلين، محمد وآله وأصحابه أجمعين. أما بعد:

Recently a request has been received from many Ulema and Mashaaikh that Dar-uloom Deoband present its stance regarding the ideologies of Moulana Muhammed Saad Saheb khandhelwi. Very recently, letters have been received from the reliable Ulema of Bangladesh and some Ulema from our neighbouring country (Pakistan), together with which various Istiftaas [requests for Fatwas] have come to the Darul-Ifta at Dar-uloom Deoband from within the country. 

Without getting involved in the disagreements within the Jamaat and the administrative matters, we wish to say that since the last few years, the ideologies of Moulana Muhammed Saad Saheb khandhelwi were received in the form of letters and Istiftaas. Now, after investigation, it has been proven that, in his Bayaans, incorrect or unfavourable explanation of the Qur’aan and Hadeeth, incorrect analogies and Tafsir bir Ray’ [interpretations based on self-opinion in conflict with Qur’an and Hadith] are found. Some statements amount to disrespect of the Ambiyaa’ (alayhis salaam) whilst many statements are such, wherein he moves beyond the bounds of the majority and Ijmaa’ of the Salaf. 

In some Fiqhi matters also, without any basis, he contradicts the unanimous Fatwa of reliable Darul-Iftas and emphasises his new view upon the general people. He also stresses upon the importance of the effort of Tableegh in such a manner that other branches of Deen are criticised and belittled. 

The method of doing Tableegh by the Salaf is also opposed, due to which the respect of the Akaabir and Aslaaf is lessened, rather, they are belittled. His conduct is in stark contrast to the previous Zimm-e-Daars of Tableegh, viz; Hazrat Moulana Ilyas Saheb (rahmatullahi alayh), Hazrat Moulana Yusuf Saheb (rahmatullahi alayh) and Hazrat Moulana In’aamul Hasan Saheb (rahmatullahi alayh).

Hereunder are some of the quotations we have received from the Bayaans of Moulana Muhammed Saad Saheb which have been proven to have been said by him:

“ Hazrat Moosa (alayhis salaam) left his nation and went in seclusion to engage in Munaajaat with Allah Ta’aala, due to which 188 000 individuals went astray. The Asl was Moosa (alayhis salaam), he was the Zimme-Daar. The Asl was supposed to remain. Haroon (alayhis salaam) was a helper and partner.”

“Naql-o-Harkat is for the completion and perfection of Taubah. People know of the three conditions of Taubah, they don’t know the fourth. They have forgotten it. What is it? Khurooj! [i.e. coming out specifically for Tabligh]. People have forgotten this condition. A person killed 99 people. He first met a monk. The monk made him despair. He then met an Aalim. The Aalim told him to go to a certain locality. This killer did Khurooj, therefore Allah Ta’aala accepted his Taubah. From this it is understood that Khurooj is a condition of Taubah. Without it, Taubah is not accepted. People have forgotten this condition. Three conditions of Taubah are mentioned. The fourth condition, i.e. Khurooj is forgotten.”

“There is no place for getting Hidaayat except the Masjid. Those branches of Deen where Deen is taught, if their connection is not with the Masjid, then, by the oath of Allah Ta’aala there will be no Deen in it. Yes the Ta’leem of Deen will take place, not Deen.”

(In this quotation, by connection with the Masjid, his intention is not going to perform Salaah in the Masjid. This is because he said this while talking about the importance of the Masjid and talking about Deen only after bringing a person to the Masjid. He said it while speaking about his specific ideology, the details of which is in the audio. His ideology is thus: to speak about Deen outside of the Masjid is contrary to the Sunnah, and contrary to the manner of the Ambiyaa’ (alayhis salaam) and the Sahaabah (radhiyallahu anhum))

“To teach Deen for a wage is to sell Deen. People who commit Zina will enter Jannah before those who teach Qur’aan for a wage.”

“According to me Salaah with a camera phone in ones’ pocket is invalid. Get as many Fatwas as you want from the Ulema. Listening to and reciting Qur’aan on a camera phone is a disgrace to the Qur’aan, there will be no reward for it. A person will be sinful by doing so. No reward will be attained. Because of doing so Allah Ta’aala will deprive one from the ability of practising on the Qur’aan. Those Ulema who give the Fatwa of permissibility in this regard, according to me they are Ulema-e-Soo, Ulema-e-Soo’. Their hearts and minds have become affected by the Christians and Jews. They are completely ignorant Ulema. According to me, whichever Aalim gives the Fatwa of permissibility, by Allah Ta’aala his heart is devoid of the greatness of the Kalaam of Allah Ta’aala. I am saying this because one big Aalim said to me: “What is wrong with it?” I said that the heart of this Aalim is devoid of the greatness of Allah Ta’aala even if he knows Bukhari. Even non-Muslims may know Bukhari.”

“It is Waajib upon every Muslim to read the Qur’aan with understanding it. It is Waajib. It is Waajib. Whoever leaves out this Waajib act will get the sin of leaving out a Waajib act.”

“I am astonished that it is asked: “With whom do you have Islaahi Ta’alluq?” Why is it not said, that my Islaahi Ta’alluq is with this effort? My Islaahi Ta’alluq is with Da’wat. Have Yaqeen that the A’maal of Da’wat is not just enough for reformation, rather, it guarantees reformation. I have contemplated deeply, this is the reason why those involved in the effort do not stay steadfast. I am saddened over those people who sit here and say that six points is not complete Deen. The person who himself says his milk is sour cannot do business. I was completely shocked when one of our own Saathis asked for leave for a month saying that he wanted to spend I’tikaaf in the company of so and so Sheikh. I said that until now you people have not joined Da’wat and Ibaadat. You have spent at least 40 years in Tableegh. After spending 40 years in Tableegh a person says that he wants leave because he wants to go for one month I’tikaaf. I said that the person who requests leave from Da’wat in order to do Ibaadat, how can he improve his Ibaadat without Da’wat? I am saying it very clearly that the difference between the A’maal of Nubuwwat and the A’maal of Wilaayat, the difference is only that of not engaging in Naql-o-Harkat. I am saying it extremely clearly that we do not make Tashkeel to merely go out to learn Deen, because there are other avenues of learning Deen. Why is it necessary to go out in Tableegh only? The object is to learn Deen. Learn in a Madrasah. Learn in a Khaanqah.”

Some quotations from his Bayaans have also been received from which it becomes apparent that Moulana Muhammed Saad Saheb khandhelwi regards the vast meaning of Da’wat to be confined to the current form present in the Tableegh Jamaat. Only this form is expressed as the manner of the Ambiyaa’ (alayhis salaam) and the Sahaabah (radhiyallaahu anhum). Only this specific form is regarded to be Sunnah and the effort of the Ambiyaa’ (alayhis salaam), whereas it is the unanimous viewpoint of the majority of the Ummah that Da’wah and Tableegh is a universal command, regarding which the Shariah has not stipulated any specific form, which, if left out, will equate to leaving out the Sunnah. 

In different eras Da’wat and Tableegh took on different forms. In no era was the divine command of Da’wat completely ignored. After the Sahaabah (radhiyallahu anhum), the Taabi’een, Tab-e-Taabi’een, A’immah Mujtahideen, Fuqahaa’, Muhadditheen, Mashaaikh, Awliyaa’ of Allah and in recent times our Akaabir made an effort in different ways to bring Deen alive on a global scale.

In order to maintain brevity we have only mentioned a few things. Besides these, many other points have been received that go beyond the scope of the Jumhoor Ulema and have taken the shape of a new ideology. These things being incorrect is very apparent, therefore, a detailed treatise is not required here.

Before this, on numerous occasions, attention was drawn to this in the form of letters sent from Darul-Uloom Deoband. It was also brought to the attention of the delegations from “Bangla Wali Masjid” on the occasion of the Tableeghi Ijtimaa’. To date no reply to the letters was received.

Jamaat-e-Tableegh is a purely Deeni Jamaat, which cannot be left to operate in a manner that is ideologically and practically apart from the majority of the Ummah and the Akaabir (rahmatullahi alayhim). The Ulema-e-Haq can never be unanimous nor can they adopt silence over disrespect to the Ambiyaa’ (alayhis salaam), deviant ideologies, Tafsir Bir Raay and whimsical explanation of the Ahaadeeth and Aathaar, because, these types of ideologies will later on cause the entire group to deviate from the path of truth as has happened to some Deeni and Islaahi Jamaats.

This is why we consider it our Deeni responsibility to inform the Ummah in general and the Tableeghi brothers specifically in light of these points that:-
 
Moulana Muhammed Saad Saheb khandhelwi Saheb, due to a lack of knowledge has strayed from the path of the majority of the Ulema of the Ahlus Sunnah Wal Jamaa’ah in his ideologies and his explanation of Qur’aan and Hadeeth, which is undoubtedly the path of deviation. Therefore, silence cannot be adopted regarding these matters, because, even though these ideologies are those of a single person, they are spreading with great speed among the general masses.

The influential and accomplished Zimme-Daars of Jamaat who are moderate and composed also wish to turn our attention that an effort needs to be made that this Jamaat which was established by the Akaabir be kept upon the pattern of the majority of the Ummah and that of the previous Zimme-Daars. An effort also needs to made so that the incorrect ideologies of Molvi Saad that have spread amongst the general masses may be rectified. If immediate action is not taken, there is fear that a great portion of the Ummah, which is affiliated to the Tableegh Jamaat will succumb to deviance and take on the form of a Firqah Baatilah.

We all make Du’aa that Allah Ta’aala protect this Jamaat and keep the Jamaat-e-Tableegh alive and flourishing with Ikhlaas upon the manner of the Akaabir. Aameen. Thumma Aameen.

Note: These types of inappropriate statements were made previously by some individuals connected to the Tableegh Jamaat, upon which the Ulema of that time, for example, Hazrat Sheikhul Islam (rahmatullahi alayh) etc. cautioned them after which those individuals desisted from such statements. Now, however, the Zimme-Daars [i.e. the leaders of Tabligh Jama’at] themselves are saying such things, rather, even worse things are being said, as is apparent from the above quotations. They were cautioned, however, they did not heed the caution, due to which this decision and Fatwa is being approved, in order to save the people from deviance.

[END OF STATEMENT FROM DARUL ULOOM DEOBAND]

The original Urdu version is available at this link:
http://www.darulifta-deoband.com/home/ur/Dawah–Tableeg/147286

THE KUFR IDEOLOGY OF MOLVI SA’D  (Detailed Analysis by Majlisul Ulama)

QUESTION: Maulana Sa’d of the Tablighi Jamaat, had in a bayaan made some serious claims which have caused some consternation and confusion. Kindly listen to his bayaan and guide us. Are the views expressed by him in conformity with the belief of the Ahlus Sunnah Wal Jama’ah? He claimed: 

1. Khurooj (emerging and travelling in Tabligh) is the Asal (actual objective). He basis his view on the Hadith of Hadhrat Ubay Bin Ka’b (Radhiyallahu anhu).
2. Allah and His Rasool are displeased with those who do not make khurooj in Tabligh.

3. The greatest calamity of this age is that Muslims do not consider it a crime to abstain from khurooj.

4. Hidaayat is not in the Hands of Allah Ta’ala. He had therefore sent the Ambiya to impart Hidaayat.

5. Hidaayat is the effect of mehnet (effort). People had received hidaayat because of the mehnet of the Ambiya.

6. The Ambiya did not spread hidaayat with their tawajjuh and roohaaniyat.  

ANSWER 

Ghulu’ (nafsaani extremism) is a satanic affliction bringing bid’ah and even kufr in its wake. A person suffering from the affliction of ghulu’ disgorges any rubbish without applying his mind and without reflecting on the consequences of his stupidities.  

Molvi Sa’d is guilty of ghulu’ (haraam extremism). Unfortunately, the Tabligh Jamaat in general has slipped into ghulu’.  He believes that the specific methodology of the Tabligh Jamaat is Waajib whereas it is not so. The Tabligh Jamaat’s method is mubah (permissible), and will remain mubah as long as ghulu’ and bid’ah do not overtake and destroy the Jamaat by deflecting it from its original path. 

He is confusing or intentionally misusing the Jihaad campaigns of the Sahaabah with the Tabligh Jamaat’s specific methodology, especially of its ‘khurooj’ method. He is equating Tabligh Jamaat khurooj to the Khurooj of the Sahaabah whose Khurooj was for Jihaad – Qitaal –  to subjugate the lands of the kuffaar and to open and prepare the way for the conversion of the kuffaar nations of the world.  In contrast, the methodology of the Tabligh Jamaat excludes non-Muslims. Its field of activity is limited to Muslims. While there is nothing wrong with this, it is wrong and not permissible to find a basis for the specific method of the Tabligh Jamaat in the Jihaad campaigns of the Sahaabah. There is no resemblance. The analogy is fallacious. There is no resemblance between the Tabligh Jamaat’s khurooj and the Jihaad campaigns of the Sahaabah. The Tabligh Jamaat’s khurooj groups do not encounter a thousandth of the hardships, dangers and trials which the Sahaabah had to face and bear in their Jihaad campaigns. The Tabligh Jamaat’s khurooj groups move and live in comfort and even luxury.

The claim that Allah and His  Rasool are displeased with those who do not make khurooj in  Tabligh, is a monstrous lie  fabricated on Allah Ta’ala and  Rasulullah (Sallallahu  alayhi  wasallam). Did Molvi Sa’d receive  wahi with which he could back  up his preposterous falsehood?   This contumacious claim comes within the purview of the Hadith:

“He who intentionally speaks a lie on me, should prepare his abode in the Fire.”  

His ghulu’ has constrained him  to disgorge this haraam flotsam. The baseless premises on which  he has raised this palpable falsehood is that the only method of tabligh is the Tabligh Jamaat’s methodology. Allah Ta’ala and  Rasulullah (Sallallahu alayhi  wasallam) are not displeased  with anyone who does not adopt the methods of the Tabligh Jamaat.Sa’d has absolutely no Shar’i evidence for substantiating his preposterous claim of ghulu’.

His claim: The greatest calamity  of this age is that Muslims do not consider it a crime to abstain  from khurooj, is nafsaani drivel disgorged without applying  the  mind. The greatest calamity of the Ummah is gross disobedience fisq, fujoor, bid’ah and even kufr.  This is the actual cause for the  fall and disgrace of the Ummah,  not non-participation in Tabligh  Jamaat activities. The Shariah has not ordained Tabligh Jamaat  participation as an obligation.    The Jamaat’s specific methodology is mubah as long as it is not disfigured with ghulu’  and  bid’ah. Presenting it as ‘waajib’  and even ‘fardh ain’, is ultimately  destroy the dangerous. This ghulu’ will original Tabligh  Jamaat. It will then become a deviant sect. With the Sa’d character, the process of deviation has gained much momentum. The Tabligh Jamaat elders have the incumbent obligation of arresting the slide of the Jamaat into deviation. 

His claim: Hidaayat is not in the Hands of Allah Ta’ala. He had therefore sent the Ambiya to impart Hidaayat is tantamount to kufr. This is the most dangerous of Sa’d’s claims. He is clearly espousing an entirely new concept of kufr. The Qur’aan Majeed is replete with aayaat which categorically state that Hidaayat comes from only Allah Ta’ala. Some random Qur’aanic aayaat follow to show the gross and dangerous deviation which Sa’d has introduced under cover of the Tabligh Jamaat.  

(a) “Verily you (O Muhammad!) cannot give hidaayat to those whom you love. But Allah gives hidaayat to whomever He wills, and He knows best who are to be guided.”  

This Aayat explicitly negates the ability of granting hidaayat from Rasulullah (Sallallahu alayhi wasallam). 

(b) “And, We have  guided them (given them hidaayat) to Siraatul Mustaqeem. This is Allah’s Huda (guidance/hidaayat) with which He guides whomever He wills from His servants.  [Al-An’aam, Aayat 89]      

It is Allah, Alone who provides hidaayat.

(c) “If Allah had willed, then they would not have committed shirk. And, We did not make you (O Muhammad!) a protector over them nor are you over them a guard.”      

The obligation of the Nabi (Sallallahu alayhi wasallam) was to only deliver the Message – the Deen. Providing hidaayat was beyond the capability of the Ambiya, hence the Qur’aan repeatedly instructs them to say: “Upon us is only to deliver the Clear Message.”  

(d) “Thus, Allah leads astray whomever He wills, and He guides (gives hidaayat) to whomever He wills.”  [Ibraaheem, Aayat 4] 

(e) “Therefore, on the Messengers it is only the Clear Delivery (of the Deen) Verily, We have sent for every Ummat a Rasool so that they (their people) worship Allah and abstain from (worshipping) the devil. Thus, from them are those whom Allah guided, and among them are those upon whom dhalaal (the deviation of kufr) has been confirmed.”  [An-Nahl, Aayats 35 and 36] 

(f)  “(Even) if you (O Muhammad!)  ardently desire that they be guided, then too, verily Allah does not guide those whom He has caused to go astray, and for them there is no helper.”  [An-Nahl] 

(g) “If  Allah had so wished, He would have made you all one Ummah, but He misleads whoever He wills and He guides whomever He wills.”  [An-Nahl, Aayat 93]

(h) “And, if your Rabb had willed, He would have made all mankind one Ummah, then they would not have differed.”  [Hood, Aayat 118] 

(i) “If Allah had willed, He would have gathered them on guidance. Therefore never be among the jaahileen (believing that you can guide them all).”  [An-Aaam, Aayat 35] 

(j) “Whomever Allah wishes, He leads him astray, and whomever He wishes, he establishes him on Siraat-e-Mustaqeem.”  [An-Aaam, Aayat 39] 

(k) “If Allah had so desired, they would not have committed shirk. And, We did not make you (O Muhammad!) a guard over them, nor are you for them a protector.” [An-Aam, Aayat 107] 

(l) “If He had willed, then most certainly He would have guided you all.”   (An-Aam,  Aayat 150) 

(m) “If your Rabb had desired, then all people on earth would have accepted Imaan. What! Do you want to compel people until they become Mu’mineen?” [Yoonus, Aayat 99] 

(n) “And, whomever Allah misleads, there will be no guide forhim.”  [Ra’d, Aayat 33]

The aforementioned are merely  some Qur’aanic Aayaat chosen at  random for the edification of  Molvi Sa’d. The Qur’aan, replete with Aayaat of this kind,  categorically confirms that Hidaayat is a prerogative  exclusively of Allah Azza Wa Jal. Hidaayat is in entirety reliant on Allah Ta’ala, NOT on mehnet (effort) as Molvi Sa’d contends. Apportioning Hidaayat  to human beings is ordained by Allah Ta’ala. It is not the effect of the effort of the Ambiya, and to a greater extent not the effect of mehnet of the Tabligh Jamaat. 

While all people are required to  strive and struggle in whatever occupation/profession they are  involved, the end result, its success or failure, is the decree  of Allah Azza Wa Jal. Thus, a man  makes mehnet in the quest of his  Rizq; in the quest of Knowledge,  and in many other pursuits. But  the final result is Allah’s decree.  The Rizq we received is not on  account of our effort. It is not  permissible, and it is nugatory of  Imaan to believe that the  consequences of Taqdeer are  reliant on personal and not on  Divine Directive.

The Qur’aan repeatedly declares  that Hidaayat effort, is Allah’s prerogative, not the effect of the was mehnet of the Ambiya. If mehnet is the criterion and imperative requisite for Hidaayat, Rasulullah’s uncle Abu Talib,  Hadhrat Nooh’s wife and son, Hadhrat Loot’s wife, Hadhrat  Ibraaheem’s father and innumerable others closely  associated with the Ambiya would not have perished as kuffaar
They would all have acquired the treasure of Imaan as a direct  effect of the supreme Ambiya.  Thus, Sa’d’s contention that mehnet of the Hidaayat is not in  the control of Allah Azza Wa Jal  is blatant kufr. He must renew his Imaan. It is haraam for the Tabligh Jamaat elders to tolerate such a deviate within the ranks of the Jamaat.  

Molvi Sa’d with his jahaalat, pivots hidaayat on mehnet (struggle/striving). This is a capital blunder which is the effect of ignorance. If the basis of hidaayat was mehnet, then his argument will imply that Rasulullah (Sallallahu alayhi wasallam) had, nauthubillah, failed in his duty of mehnet because there were many who did not accept Imaan despite all the efforts of Rasulullah (Sallallahu alayhi wasallam). And the same ‘failure’ stemming from the kufr view of Sa’d, will apply to all the Ambiya.  

On the death occasion of his beloved uncle, Abu Taalib, Rasulullah (sallallahu alayhi wasallam) pleaded with all his heart in the effort to guide his uncle. But Abu Talib rebuffed Rasulullah’s mehnet, and died without Imaan. Rasulullah (Sallallahu alayhi wasallam) spared no effort – he left no stone unturned in his mehnet to guide people. But, many remained mushrikeen and rebuffed all his efforts. It is palpably clear that hidaayat is not the consequence of the muballigh’s mehnet. It is the effect of Allah’s Will. He guides whomever He wills. The Qur’aan is categorical in this averment. 

This Sa’d character is incapable of understanding even simple Qur’aanic aayaat and the facts of reality. The Nabi was Allah’s Messenger. His duty was to only discharge the obligation of delivering the message of Allah Ta’ala. Hence the Qur’aan repeatedly instructs the Ambiya to say: “Upon us is to only deliver the Message.”  

The Maqsood is not mehnet. The Maqsood (Objective) is to discharge the obligation with which the Bandah has been entrusted. Whether a person will be guided or not, is beyond the control and ability of the muballigh. Hidaayat is the prerogative of Allah Ta’ala. 

Molvi Sa’d claims that the deception of Muslims is their belief that change in the Ummah will occur by way of the spiritual state (Roohaaniyat) of the Auliya. This is obviously wishful thinking and the charge is false. No one entertains this idea. It is merely Sa’d’s hallucination. The Ummah’s condition will change only if Muslims obey Allah’s Shariat whether they make Tablighi Jamaat type of khurooj or not. The Ummah’s rotten state is not because Muslims do not participate in Tabligh Jamaat activities. It is because of the flagrant transgression of fisq, fujoor, bid’ah and kufr in which the Ummah is sinking.  

Abstention from Tabligh Jamaat activities is not sinful. Participation is not Waajib. Non-participation in Tabligh Jamaat activities never was the cause of the fall and humiliation of the Ummah. In fact, the Ummah had scraped the dregs of the barrel of disgrace and degeneration many centuries before the birth of the Tabligh Jamaat.   

The Khurooj during the era of the Salf-e-Saaliheen and even thereafter was always only for the purpose of Jihaad – Qitaal Fi Sabeelillaah. There never ever was mass khurooj for tabligh. While khurooj for tabligh is permissible and meritorious, it is not Waajib and the idea of it being waajib is haraam ghulu’ which culminates in Sa’d type dhalaal and kufr.  Applying to the Tabligh Jamaat activities the narrations which relate explicitly to Jihaad, is dangerous deviation. The thawaab of tabligh –i.e. tabligh of any method, not of only the Tabligh Jamaat, is immense. But to mislead the masses by presenting the Jihaad narrations as if they apply to the specific methodology of the Tabligh Jamaat is not permissible. It is a fabrication for which there is no basis in the Shariah

Molvi Sa’d’s istidlaal from Hadhrat Ka’b’s Hadith is utterly baseless. His interpretation of the Hadith is baseless and erroneous. He is gumraah (astray) and leading others into gumraahi. Firstly, his claim that Khurooj whether it is khurooj in actual Jihad, or khurooj for Tabligh Jamaat activity, is the asal (i.e. actual objective), is manifestly baatil, baseless and corrupt. The objective of Jihaad is I’laa Kalimatullah for the sole purpose of gaining Allah’s Pleasure. This is the Asal, not khurooj.  Khurooj is merely a method for the acquisition of the Asal. But, Sa’d has placed the cart in front of the horse. 

The displeasure incurred by Hadhrat Ka’b (Radhiyallahu anhu) for failure to participate in the specific Jihad campaign of Tabook, was ‘disobedience’. He had failed to observe the command to emerge. He had unilaterally without valid reason decided to remain behind. This was his error for which Rasulullah (Sallallahu alayhi wasallam) had ordered the boycott. 

Furthermore, Hadhrat Ka’b’s error pertained to Khurooj related to actual Jihaad – Qitaal fi Sabeelillaah. It was not a khurooj for the specific method of tabligh which the Tabligh Jamaat had innovated some decades ago.  If Sa’d’s logic is to be accorded  any credibility and validity, it will  follow that the Hadhrat Ka’b’s  failure to make Khurooj consequences of should be  extended to all those who refuse  to make khurooj for Tabligh  Jamaat activity. The logical result  would be to boycott the almost  3 billion Muslims of this era who  not only do not participate in  Tabligh Jamaat khurooj,  but they  also deny  the essentiality  of participation in the specific methodology of the Tabligh Jamaat.

A grave error of the Tabligh Jamaat is the predication  of all the Jihaad narrations to their specific method of tabligh, whilst there is absolutely no  affinity between the Tabligh  Jamaat and Jihaad, i.e. the type  of Jihaad of the Sahaabah.  Whilst the absence of this affinity is not sinful, the appropriation of  the Hadith narrations pertaining  to Jihaad is inappropriate and  not permissible. The Tabligh  Jamaat has as its goal the  reformation of Imaan and the impartation of the basic teachings of the DeenQitaal in our era for  the  acquisition of  these  fundamental requisites is not a condition as it was during the era  of the Sahaabah. Qitaal was imperative to subjugate the lands of the kuffaar for removing the obstacles in the path of  establishing the Deen. But this  method of Qitaal does not form  part of the Tabligh While  the  Tabligh Jamaat’s methodology. Jamaat may not be criticized for  this, the criticism for misusing the Jihaad narrations is valid.

Molvi Sa’d’s claim:“In this age  people do not regard as a crime and a sin reduction in  emerging  in the Tabligh Jamaat’s way  (of khurooj).”, is another stupid  fallacy. There is no Shar’i basis  for believing that it is a crime and sinful to refrain from the specific khurooj methodology of the  Tabligh Jamaat. Sa’d has no  affinity with the Ilm of the Deen,  hence he acquits himself as do  the juhala, disgorging just any  drivel of his nafs.

He presents the fallacious analogy of gheebat,  speaking lies, theft, zina and riba  in his ludicrous attempt to liken  the so-called ‘sin and crime’ of  non-participation in Tabligh Jamaat khurooj the  aforementioned kabeerah sins. 
This is a monstrous lie fabricated  against the Shariah. The major  sins of zinariba, liquor, etc.  are substantiated by Nusoos of  the Qat’i category, while the  contention of abstaining from Tabligh Jamaat khurooj being a crime and a sin is the horrid  product of corrupt personal opinion stemming from ghulu’.   

He finds fault with those who say  that it is sinful to indulge in zina,  liquor and gheebat, but not  sinful to abstain from the Tabligh Jamaat khurooj. This haraam  opinion is scandalously baatil. Sa’d’s ideology is scandalous. He constitutes a grave danger for proper functioning of the Tabligh  Jamaat. The deviation from the  Jamaat’s original principals  bodes evil for the Tabligh Jamaat. It is Waajib for the elders of the  Tabligh Jamaat to eradicate the evil and eliminate the rot which  is gnawing at the foundations of the Jamaat.

Related Posts: THE TABLIGHI JAMAAT – DEOBAND’S FATWA AND AN ERRONEOUS PERCEPTION

Darul Ifta Deoband’s Fatwa on the Tabligh Jama’at

Resolutions of the Tablighi Jama’at [Nizamuddin Markaz Dispute]

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At last! Environment friendly plastic polymer breaks down in sunlight and air

Degradable plastic polymer breaks down in sunlight and air

While most plastic is slow to decompose, a recently developed polymer degrades in a week and doesn't leave microplastics behind. Image credit: Larina Marina/ Shutterstock

Most plastic persists in the environment. A recently developed polymer degrades in a week and doesn’t leave microplastics behind. Image credit: Shutterstock/Larina Marina

Plastic trash chokes shorelines and oceans, in part because plastic polymers do not easily decompose. But a new kind of environmentally degradable plastic could help change that: It breaks down in about a week in sunlight and air, according to a recent study in the Journal of the American Chemical Society (JACS). Chemical characterization using nuclear magnetic resonance (NMR) and mass spectroscopy, among other techniques, revealed that the plastic decomposed rapidly in sunlight from a petroleum-based polymer into succinic acid, a naturally occurring nontoxic small molecule that doesn’t leave microplastic fragments in the environment.

Although a sun-sensitive plastic might not be a good choice for bottles or bags that need to last more than a week on shelves, integrating the environmentally degradable polymer as a minor ingredient, or with other biodegradable polymers, could help speed breakdown of these materials in landfills, says coauthor Liang Luo, an organic materials scientist at Huazhong University of Science and Technology in Wuhan, China. The flexible and degradable material would be potentially useful inside electronics, he says. Sealed inside a cell phone or other flexible electronic device, the polymer could last for years isolated from light and oxygen, Luo notes, while making smartphones easier to dispose of at the end of their service life. And the byproduct succinic acid could be upcycled for commercial uses in the pharmaceutical and food industries, Luo adds.

When Luo first developed the plastic in 2020, he intended it to change color with pH, for use as a chemical sensor. But then he noticed that the plastic’s natural deep red color faded quickly and the plastic film broke apart over several days in sunlight. In conjugated polymers such as this, which have a long backbone chain of alternating double and single bonds, the material’s color comes from its molecular structure—long chains of monomers—rather than a dye. Loss of that color means the chains have broken down into their monomer units. Cleaving polymer chains is often a challenging step in breaking down plastics Luo says. “But for our polymer, we can simply use sunlight.”

The red plastic film breaks apart in sunlight and air over 7 days. Here, each vial represents a day from 0 to 7, left to right. Image credit: Qiang Yue

The red plastic film breaks apart in sunlight and air over 7 days. Here, each vial represents a day from 0 to 7, left to right. Image credit: Qiang Yue

Luo and coauthors sought to understand the chemistry of how the plastic breaks down. They used NMR to characterize the polymer’s structure based on its magnetic field. The intact polymer has two broad NMR peaks corresponding to chains of polymers. But after exposure to sunlight, the material just gives a single sharp peak, “like a needle,” Luo says, indicating its molecular composition has changed. The sharp NMR peak corresponds to the structure of succinic acid, which forms during the degradation reaction. The process seems to use photo-oxidative degradation, in which sunlight irradiation breaks the polymer’s double- and triple-bonded carbon backbone.

The postulated degradation mechanism is totally different from the breakdown of other degradable plastics, for instance by hydrolysis of ester or amide bonds, says materials chemist Zhibin Guan at the University of California, Irvine, who was not involved in the new study. The mechanism clearly doesn’t occur in the consumer plastics that litter sunny beaches. It’s possible the degradation could occur in other conjugated polymer plastics, but “it will take more work to demonstrate the generality of this mechanism,” Guan says. Ultimately, the work is “an exciting example of degradable conjugated polymers,” he adds, which could be valuable for a variety of applications, such as electronics, in the future. Polymer chemist Eugene Chen at Colorado State University in Fort Collins calls the recent work a “tour de force” that addresses several key challenges in plastic design and achieves “nearly ideal plastic degradation.” In particular, using sunlight and oxygen rather than focusing on microbial activity to break down the plastic is an advance for the field, he says.

“We will continue to explore the degradation of plastics,” Luo says, looking ahead. Though he doesn’t have a timeline for commercialization, he says the ballpark “could be 5 or 10 years.”

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Mathematics in medieval Islam

Mathematics in medieval Islam

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Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics (EuclidArchimedesApollonius) and Indian mathematics (AryabhataBrahmagupta). Important progress was made, such as full development of the decimal place-value system to include decimal fractions, the first systematised study of algebra, and advances in geometry and trigonometry.[1]

Arabic works played an important role in the transmission of mathematics to Europe during the 10th to 12th centuries.[2]

Concepts[edit]

 

Omar Khayyám‘s “Cubic equations and intersections of conic sections” the first page of the two-chaptered manuscript kept in Tehran University

Algebra[edit]

The study of algebra, the name of which is derived from the Arabic word meaning completion or “reunion of broken parts”,[3] flourished during the Islamic golden ageMuhammad ibn Musa al-Khwarizmi, a scholar in the House of Wisdom in Baghdad, is along with the Greek mathematician Diophantus, known as the father of algebra. In his book The Compendious Book on Calculation by Completion and Balancing, Al-Khwarizmi deals with ways to solve for the positive roots of first and second degree (linear and quadratic) polynomial equations. He also introduces the method of reduction, and unlike Diophantus, gives general solutions for the equations he deals with.[4][5][6]

Al-Khwarizmi’s algebra was rhetorical, which means that the equations were written out in full sentences. This was unlike the algebraic work of Diophantus, which was syncopated, meaning that some symbolism is used. The transition to symbolic algebra, where only symbols are used, can be seen in the work of Ibn al-Banna’ al-Marrakushi and Abū al-Ḥasan ibn ʿAlī al-Qalaṣādī.[7][6]

On the work done by Al-Khwarizmi, J. J. O’Connor and Edmund F. Robertson said:[8]

“Perhaps one of the most significant advances made by Arabic mathematics began at this time with the work of al-Khwarizmi, namely the beginnings of algebra. It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which allowed rational numbersirrational numbers, geometrical magnitudes, etc., to all be treated as “algebraic objects”. It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for the future development of the subject. Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before.”

Several other mathematicians during this time period expanded on the algebra of Al-Khwarizmi. Abu Kamil Shuja’ wrote a book of algebra accompanied with geometrical illustrations and proofs. He also enumerated all the possible solutions to some of his problems. Abu al-JudOmar Khayyam, along with Sharaf al-Dīn al-Tūsī, found several solutions of the cubic equation. Omar Khayyam found the general geometric solution of a cubic equation.

Cubic equations[edit]

 

To solve the third-degree equation x3 + a2x = b Khayyám constructed the parabola x2 = ay, a circle with diameter b/a2, and a vertical line through the intersection point. The solution is given by the length of the horizontal line segment from the origin to the intersection of the vertical line and the x-axis.

Omar Khayyam (c. 1038/48 in Iran – 1123/24)[9] wrote the Treatise on Demonstration of Problems of Algebra containing the systematic solution of cubic or third-order equations, going beyond the Algebra of al-Khwārizmī.[10] Khayyám obtained the solutions of these equations by finding the intersection points of two conic sections. This method had been used by the Greeks,[11] but they did not generalize the method to cover all equations with positive roots.[10]

Sharaf al-Dīn al-Ṭūsī (? in Tus, Iran – 1213/4) developed a novel approach to the investigation of cubic equations—an approach which entailed finding the point at which a cubic polynomial obtains its maximum value. For example, to solve the equation \ x^{3}+a=bx, with a and b positive, he would note that the maximum point of the curve \ y=bx-x^{3} occurs at x=\textstyle {\sqrt  {{\frac  {b}{3}}}}, and that the equation would have no solutions, one solution or two solutions, depending on whether the height of the curve at that point was less than, equal to, or greater than a. His surviving works give no indication of how he discovered his formulae for the maxima of these curves. Various conjectures have been proposed to account for his discovery of them.[12]

Induction[edit]

The earliest implicit traces of mathematical induction can be found in Euclid‘s proof that the number of primes is infinite (c. 300 BCE). The first explicit formulation of the principle of induction was given by Pascal in his Traité du triangle arithmétique (1665).

In between, implicit proof by induction for arithmetic sequences was introduced by al-Karaji (c. 1000) and continued by al-Samaw’al, who used it for special cases of the binomial theorem and properties of Pascal’s triangle.

Irrational numbers[edit]

The Greeks had discovered irrational numbers, but were not happy with them and only able to cope by drawing a distinction between magnitude and number. In the Greek view, magnitudes varied continuously and could be used for entities such as line segments, whereas numbers were discrete. Hence, irrationals could only be handled geometrically; and indeed Greek mathematics was mainly geometrical. Islamic mathematicians including Abū Kāmil Shujāʿ ibn Aslam and Ibn Tahir al-Baghdadi slowly removed the distinction between magnitude and number, allowing irrational quantities to appear as coefficients in equations and to be solutions of algebraic equations.[13][14] They worked freely with irrationals as mathematical objects, but they did not examine closely their nature.[15]

In the twelfth century, Latin translations of Al-Khwarizmi‘s Arithmetic on the Indian numerals introduced the decimal positional number system to the Western world.[16] His Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear and quadratic equations. In Renaissance Europe, he was considered the original inventor of algebra, although it is now known that his work is based on older Indian or Greek sources.[17] He revised Ptolemy‘s Geography and wrote on astronomy and astrology. However, C.A. Nallino suggests that al-Khwarizmi’s original work was not based on Ptolemy but on a derivative world map,[18] presumably in Syriac or Arabic.

Spherical trigonometry[edit]

The spherical law of sines was discovered in the 10th century: it has been attributed variously to Abu-Mahmud KhojandiNasir al-Din al-Tusi and Abu Nasr Mansur, with Abu al-Wafa’ Buzjani as a contributor.[13] Ibn Muʿādh al-Jayyānī‘s The book of unknown arcs of a sphere in the 11th century introduced the general law of sines.[19] The plane law of sines was described in the 13th century by Nasīr al-Dīn al-Tūsī. In his On the Sector Figure, he stated the law of sines for plane and spherical triangles and provided proofs for this law.[20]

Negative numbers[edit]

In the 9th century, Islamic mathematicians were familiar with negative numbers from the works of Indian mathematicians, but the recognition and use of negative numbers during this period remained timid.[21] Al-Khwarizmi did not use negative numbers or negative coefficients.[21] But within fifty years, Abu Kamil illustrated the rules of signs for expanding the multiplication (a\pm b)(c\pm d).[22] Al-Karaji wrote in his book al-Fakhrī that “negative quantities must be counted as terms”.[21] In the 10th century, Abū al-Wafā’ al-Būzjānī considered debts as negative numbers in A Book on What Is Necessary from the Science of Arithmetic for Scribes and Businessmen.[22]

By the 12th century, al-Karaji’s successors were to state the general rules of signs and use them to solve polynomial divisions.[21] As al-Samaw’al writes:

the product of a negative number — al-nāqiṣ — by a positive number — al-zāʾid — is negative, and by a negative number is positive. If we subtract a negative number from a higher negative number, the remainder is their negative difference. The difference remains positive if we subtract a negative number from a lower negative number. If we subtract a negative number from a positive number, the remainder is their positive sum. If we subtract a positive number from an empty power (martaba khāliyya), the remainder is the same negative, and if we subtract a negative number from an empty power, the remainder is the same positive number.[21]

Double false position[edit]

Between the 9th and 10th centuries, the Egyptian mathematician Abu Kamil wrote a now-lost treatise on the use of double false position, known as the Book of the Two Errors (Kitāb al-khaṭāʾayn). The oldest surviving writing on double false position from the Middle East is that of Qusta ibn Luqa (10th century), an Arab mathematician from BaalbekLebanon. He justified the technique by a formal, Euclidean-style geometric proof. Within the tradition of medieval Muslim mathematics, double false position was known as hisāb al-khaṭāʾayn (“reckoning by two errors”). It was used for centuries to solve practical problems such as commercial and juridical questions (estate partitions according to rules of Quranic inheritance), as well as purely recreational problems. The algorithm was often memorized with the aid of mnemonics, such as a verse attributed to Ibn al-Yasamin and balance-scale diagrams explained by al-Hassar and Ibn al-Banna, who were each mathematicians of Moroccan origin.[23]

 

Other major figures[edit]

Sally P. Ragep, a historian of science in Islam, estimated in 2019 that “tens of thousands” of Arabic manuscripts in mathematical sciences and philosophy remain unread, which give studies which “reflect individual biases and a limited focus on a relatively few texts and scholars”.[24][full citation needed]

Gallery[edit]

See also[edit]

References[edit]

  1. ^ Katz (1993): “A complete history of mathematics of medieval Islam cannot yet be written, since so many of these Arabic manuscripts lie unstudied… Still, the general outline… is known. In particular, Islamic mathematicians fully developed the decimal place-value number system to include decimal fractions, systematised the study of algebra and began to consider the relationship between algebra and geometry, studied and made advances on the major Greek geometrical treatises of Euclid, Archimedes, and Apollonius, and made significant improvements in plane and spherical geometry.” Smith (1958) Vol. 1, Chapter VII.4: “In a general way it may be said that the Golden Age of Arabian mathematics was confined largely to the 9th and 10th centuries; that the world owes a great debt to Arab scholars for preserving and transmitting to posterity the classics of Greek mathematics; and that their work was chiefly that of transmission, although they developed considerable originality in algebra and showed some genius in their work in trigonometry.”
  2. ^ Adolph P. Yushkevich Sertima, Ivan Van (1992), Golden age of the Moor, Volume 11, Transaction Publishers, p. 394ISBN 1-56000-581-5 “The Islamic mathematicians exercised a prolific influence on the development of science in Europe, enriched as much by their own discoveries as those they had inherited by the Greeks, the Indians, the Syrians, the Babylonians, etc.”
  3. ^ “algebra”Online Etymology Dictionary.
  4. ^ Boyer, Carl B. (1991). “The Arabic Hegemony”. A History of Mathematics (Second ed.). John Wiley & Sons. p. 228ISBN 0-471-54397-7.
  5. ^ Swetz, Frank J. (1993). Learning Activities from the History of Mathematics. Walch Publishing. p. 26. ISBN 978-0-8251-2264-4.
  6. Jump up to:a b Gullberg, Jan (1997). Mathematics: From the Birth of Numbers. W. W. Norton. p. 298ISBN 0-393-04002-X.
  7. ^ O’Connor, John J.Robertson, Edmund F.“al-Marrakushi ibn Al-Banna”MacTutor History of Mathematics archiveUniversity of St Andrews
  8. ^ O’Connor, John J.Robertson, Edmund F. (1999), “Arabic mathematics: forgotten brilliance?”MacTutor History of Mathematics archiveUniversity of St Andrews
  9. ^ Struik 1987, p. 96.
  10. Jump up to:a b Boyer 1991, pp. 241–242. sfn error: multiple targets (2×): CITEREFBoyer1991 (help)
  11. ^ Struik 1987, p. 97.
  12. ^ Berggren, J. Lennart; Al-Tūsī, Sharaf Al-Dīn; Rashed, Roshdi (1990). “Innovation and Tradition in Sharaf al-Dīn al-Ṭūsī’s al-Muʿādalāt”. Journal of the American Oriental Society110 (2): 304–309. doi:10.2307/604533JSTOR 604533.
  13. Jump up to:a b Sesiano, Jacques (2000). Helaine, Selin; Ubiratan, D’Ambrosio (eds.). Islamic mathematicsMathematics Across Cultures: The History of Non-western Mathematics. Springer. pp. 137–157. ISBN 1-4020-0260-2.
  14. ^ O’Connor, John J.Robertson, Edmund F.“Abu Mansur ibn Tahir Al-Baghdadi”MacTutor History of Mathematics archiveUniversity of St Andrews
  15. ^ Allen, G. Donald (n.d.). “The History of Infinity” (PDF). Texas A&M University. Retrieved 7 September 2016.
  16. ^ Struik 1987, p. 93
  17. ^ Rosen 1831, p. v–vi; Toomer 1990
  18. ^ Nallino (1939).
  19. ^ O’Connor, John J.Robertson, Edmund F.“Abu Abd Allah Muhammad ibn Muadh Al-Jayyani”MacTutor History of Mathematics archiveUniversity of St Andrews
  20. ^ Berggren, J. Lennart (2007). “Mathematics in Medieval Islam”. The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton University Press. p. 518. ISBN 978-0-691-11485-9.
  21. Jump up to:a b c d e Rashed, R. (1994-06-30). The Development of Arabic Mathematics: Between Arithmetic and Algebra. Springer. pp. 36–37. ISBN 9780792325659.
  22. Jump up to:a b Mat Rofa Bin Ismail (2008), Helaine Selin (ed.), “Algebra in Islamic Mathematics”, Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures (2nd ed.), Springer, 1, p. 115, ISBN 9781402045592
  23. ^ Schwartz, R. K. (2004). Issues in the Origin and Development of Hisab al-Khata’ayn (Calculation by Double False Position). Eighth North African Meeting on the History of Arab Mathematics. Radès, Tunisia. Available online at: http://facstaff.uindy.edu/~oaks/Biblio/COMHISMA8paper.docArchived 2011-09-15 at the Wayback Machine and “Archived copy”(PDF). Archived from the original (PDF) on 2014-05-16. Retrieved 2012-06-08.
  24. ^ “Science Teaching in Pre-Modern Societies”, in Film Screening and Panel Discussion, McGill University, 15 January 2019.

Sources[edit]

Further reading[edit]

Books on Islamic mathematics
Book chapters on Islamic mathematics
Books on Islamic science
  • Daffa, Ali Abdullah al-; Stroyls, J.J. (1984). Studies in the exact sciences in medieval Islam. New York: Wiley. ISBN 0-471-90320-5.
  • Kennedy, E. S. (1984). Studies in the Islamic Exact Sciences. Syracuse Univ Press. ISBN 0-8156-6067-7.
Books on the history of mathematics
Journal articles on Islamic mathematics
Bibliographies and biographies
  • Brockelmann, CarlGeschichte der Arabischen Litteratur. 1.–2. Band, 1.–3. Supplementband. Berlin: Emil Fischer, 1898, 1902; Leiden: Brill, 1937, 1938, 1942.
  • Sánchez Pérez, José A. (1921). Biografías de Matemáticos Árabes que florecieron en España. Madrid: Estanislao Maestre.
  • Sezgin, Fuat (1997). Geschichte Des Arabischen Schrifttums (in German). Brill Academic Publishers. ISBN 90-04-02007-1.
  • Suter, Heinrich (1900). Die Mathematiker und Astronomen der Araber und ihre Werke. Abhandlungen zur Geschichte der Mathematischen Wissenschaften Mit Einschluss Ihrer Anwendungen, X Heft. Leipzig.
Television documentaries

External links[edit]

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Arabic mathematics : forgotten brilliance?

Arabic mathematics : forgotten brilliance?


Recent research paints a new picture of the debt that we owe to Arabic/Islamic mathematics. Certainly many of the ideas which were previously thought to have been brilliant new conceptions due to European mathematicians of the sixteenth, seventeenth and eighteenth centuries are now known to have been developed by Arabic/Islamic mathematicians around four centuries earlier. In many respects the mathematics studied today is far closer in style to that of the Arabic/Islamic contribution than to that of the Greeks.

There is a widely held view that, after a brilliant period for mathematics when the Greeks laid the foundations for modern mathematics, there was a period of stagnation before the Europeans took over where the Greeks left off at the beginning of the sixteenth century. The common perception of the period of 1000 years or so between the ancient Greeks and the European Renaissance is that little happened in the world of mathematics except that some Arabic translations of Greek texts were made which preserved the Greek learning so that it was available to the Europeans at the beginning of the sixteenth century.

That such views should be generally held is of no surprise. Many leading historians of mathematics have contributed to the perception by either omitting any mention of Arabic/Islamic mathematics in the historical development of the subject or with statements such as that made by Duhem in [3]:-

… Arabic science only reproduced the teachings received from Greek science.

Before we proceed it is worth trying to define the period that this article covers and give an overall description to cover the mathematicians who contributed. The period we cover is easy to describe: it stretches from the end of the eighth century to about the middle of the fifteenth century. Giving a description to cover the mathematicians who contributed, however, is much harder. The works [6] and [17] are on “Islamic mathematics”, similar to [1] which uses the title the “Muslim contribution to mathematics”. Other authors try the description “Arabic mathematics”, see for example [10] and [11]. However, certainly not all the mathematicians we wish to include were Muslims; some were Jews, some Christians, some of other faiths. Nor were all these mathematicians Arabs, but for convenience we will call our topic “Arab mathematics”.

The regions from which the “Arab mathematicians” came was centred on Iran/Iraq but varied with military conquest during the period. At its greatest extent it stretched to the west through Turkey and North Africa to include most of Spain, and to the east as far as the borders of China.

The background to the mathematical developments which began in Baghdad around 800 is not well understood. Certainly there was an important influence which came from the Hindu mathematicians whose earlier development of the decimal system and numerals was important. There began a remarkable period of mathematical progress with al-Khwarizmi‘s work and the translations of Greek texts.

This period begins under the Caliph Harun al-Rashid, the fifth Caliph of the Abbasid dynasty, whose reign began in 786. He encouraged scholarship and the first translations of Greek texts into Arabic, such as Euclid‘s Elements by al-Hajjaj, were made during al-Rashid’s reign. The next Caliph, al-Ma’mun, encouraged learning even more strongly than his father al-Rashid, and he set up the House of Wisdom in Baghdad which became the centre for both the work of translating and of of research. Al-Kindi (born 801) and the three Banu Musa brothers worked there, as did the famous translator Hunayn ibn Ishaq.

We should emphasise that the translations into Arabic at this time were made by scientists and mathematicians such as those named above, not by language experts ignorant of mathematics, and the need for the translations was stimulated by the most advanced research of the time. It is important to realise that the translating was not done for its own sake, but was done as part of the current research effort. The most important Greek mathematical texts which were translated are listed in [17]:-

Of Euclid‘s works, the Elements, the Data, the Optics, the Phaenomena, and On Divisions were translated. Of Archimedes‘ works only two – Sphere and Cylinder and Measurement of the Circle – are known to have been translated, but these were sufficient to stimulate independent researches from the 9th to the 15th century. On the other hand, virtually all of Apollonius‘s works were translated, and of Diophantus and Menelaus one book each, the Arithmetica and the Sphaerica, respectively, were translated into Arabic. Finally, the translation of Ptolemy‘s Almagest furnished important astronomical material.

The more minor Greek mathematical texts which were translated are also given in [17]:-

… Diocles‘ treatise on mirrors, Theodosius‘s Spherics, Pappus‘s work on mechanics, Ptolemy‘s Planisphaerium, and Hypsicles‘ treatises on regular polyhedra (the so-called Books XIV and XV of Euclid‘s Elements) …

Perhaps one of the most significant advances made by Arabic mathematics began at this time with the work of al-Khwarizmi, namely the beginnings of algebra. It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry.

Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc., to all be treated as “algebraic objects”. It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of the subject. Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before. As Rashed writes in [11] (see also [10]):-

Al-Khwarizmi‘s successors undertook a systematic application of arithmetic to algebra, algebra to arithmetic, both to trigonometry, algebra to the Euclidean theory of numbers, algebra to geometry, and geometry to algebra. This was how the creation of polynomial algebra, combinatorial analysis, numerical analysis, the numerical solution of equations, the new elementary theory of numbers, and the geometric construction of equations arose.

Let us follow the development of algebra for a moment and look at al-Khwarizmi‘s successors. About forty years after al-Khwarizmi is the work of al-Mahani (born 820), who conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra. Abu Kamil (born 850) forms an important link in the development of algebra between al-Khwarizmi and al-Karaji. Despite not using symbols, but writing powers of xx in words, he had begun to understand what we would write in symbols as x^{n}.x^{m} = x^{m+n}xn.xm=xm+n. Let us remark that symbols did not appear in Arabic mathematics until much later. Ibn al-Banna and al-Qalasadi used symbols in the 15th century and, although we do not know exactly when their use began, we know that symbols were used at least a century before this.

Al-Karaji (born 953) is seen by many as the first person to completely free algebra from geometrical operations and to replace them with the arithmetical type of operations which are at the core of algebra today. He was first to define the monomials x, x^{2}, x^{3}, …x,x2,x3,... and 1/x, 1/x^{2}, 1/x^{3}, …1/x,1/x2,1/x3,... and to give rules for products of any two of these. He started a school of algebra which flourished for several hundreds of years. Al-Samawal, nearly 200 years later, was an important member of al-Karaji‘s school. Al-Samawal (born 1130) was the first to give the new topic of algebra a precise description when he wrote that it was concerned:-

… with operating on unknowns using all the arithmetical tools, in the same way as the arithmetician operates on the known.

Omar Khayyam (born 1048) gave a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections. Khayyam also wrote that he hoped to give a full description of the algebraic solution of cubic equations in a later work [18]:-

If the opportunity arises and I can succeed, I shall give all these fourteen forms with all their branches and cases, and how to distinguish whatever is possible or impossible so that a paper, containing elements which are greatly useful in this art will be prepared.

Sharaf al-Din al-Tusi (born 1135), although almost exactly the same age as al-Samawal, does not follow the general development that came through al-Karaji‘s school of algebra but rather follows Khayyam‘s application of algebra to geometry. He wrote a treatise on cubic equations, which [11]:-

… represents an essential contribution to another algebra which aimed to study curves by means of equations, thus inaugurating the beginning of algebraic geometry.

Let us give other examples of the development of Arabic mathematics. Returning to the House of Wisdom in Baghdad in the 9th century, one mathematician who was educated there by the Banu Musa brothers was Thabit ibn Qurra (born 836). He made many contributions to mathematics, but let us consider for the moment consider his contributions to number theory. He discovered a beautiful theorem which allowed pairs of amicable numbers to be found, that is two numbers such that each is the sum of the proper divisors of the other. Al-Baghdadi (born 980) looked at a slight variant of Thabit ibn Qurra‘s theorem, while al-Haytham (born 965) seems to have been the first to attempt to classify all even perfect numbers (numbers equal to the sum of their proper divisors) as those of the form 2^{k-1}(2^{k} – 1)2k1(2k1) where 2^{k} – 12k1 is prime.

Al-Haytham, is also the first person that we know to state Wilson’s theorem, namely that if pp is prime then 1+(p-1)!1+(p1)! is divisible by pp. It is unclear whether he knew how to prove this result. It is called Wilson’s theorem because of a comment made by Waring in 1770 that John Wilson had noticed the result. There is no evidence that John Wilson knew how to prove it and most certainly Waring did not. Lagrange gave the first proof in 1771 and it should be noticed that it is more than 750 years after al-Haytham before number theory surpasses this achievement of Arabic mathematics.

Continuing the story of amicable numbers, from which we have taken a diversion, it is worth noting that they play a large role in Arabic mathematics. Al-Farisi (born 1260) gave a new proof of Thabit ibn Qurra‘s theorem, introducing important new ideas concerning factorisation and combinatorial methods. He also gave the pair of amicable numbers 1729618416 which have been attributed to Euler, but we know that these were known earlier than al-Farisi, perhaps even by Thabit ibn Qurra himself. Although outside our time range for Arabic mathematics in this article, it is worth noting that in the 17th century the Arabic mathematician Mohammed Baqir Yazdi gave the pair of amicable number 9,363,584 and 9,437,056 still many years before Euler‘s contribution.

Let us turn to the different systems of counting which were in use around the 10th century in Arabic countries. There were three different types of arithmetic used around this period and, by the end of the 10th century, authors such as al-Baghdadi were writing texts comparing the three systems.

1. Finger-reckoning arithmetic.
This system derived from counting on the fingers with the numerals written entirely in words; this finger-reckoning arithmetic was the system used by the business community. Mathematicians such as Abu’l-Wafa (born 940) wrote several treatises using this system. Abu’l-Wafa himself was an expert in the use of Indian numerals but these:-

… did not find application in business circles and among the population of the Eastern Caliphate for a long time.

Hence he wrote his text using finger-reckoning arithmetic since this was the system used by the business community.

2. Sexagesimal system.
The second of the three systems was the sexagesimal system, with numerals denoted by letters of the Arabic alphabet. It came originally from the Babylonians and was most frequently used by the Arabic mathematicians in astronomical work.

3. Indian numeral system.
The third system was the arithmetic of the Indian numerals and fractions with the decimal place-value system. The numerals used were taken over from India, but there was not a standard set of symbols. Different parts of the Arabic world used slightly different forms of the numerals. At first the Indian methods were used by the Arabs with a dust board. A dust board was needed because the methods required the moving of numbers around in the calculation and rubbing some out as the calculation proceeded. The dust board allowed this to be done in the same sort of way that one can use a blackboard, chalk and a blackboard eraser. However, al-Uqlidisi (born 920) showed how to modify the methods for pen and paper use. Al-Baghdadi also contributed to improvements in the decimal system.

It was this third system of calculating which allowed most of the advances in numerical methods by the Arabs. It allowed the extraction of roots by mathematicians such as Abu’l-Wafa and Omar Khayyam (born 1048). The discovery of the binomial theorem for integer exponents by al-Karaji (born 953) was a major factor in the development of numerical analysis based on the decimal system. Al-Kashi (born 1380) contributed to the development of decimal fractions not only for approximating algebraic numbers, but also for real numbers such as π. His contribution to decimal fractions is so major that for many years he was considered as their inventor. Although not the first to do so, al-Kashi gave an algorithm for calculating nnth roots which is a special case of the methods given many centuries later by Ruffini and Horner.

Although the Arabic mathematicians are most famed for their work on algebra, number theory and number systems, they also made considerable contributions to geometry, trigonometry and mathematical astronomy. Ibrahim ibn Sinan (born 908), who introduced a method of integration more general than that of Archimedes, and al-Quhi (born 940) were leading figures in a revival and continuation of Greek higher geometry in the Islamic world. These mathematicians, and in particular al-Haytham, studied optics and investigated the optical properties of mirrors made from conic sections. Omar Khayyam combined the use of trigonometry and approximation theory to provide methods of solving algebraic equations by geometrical means.

Astronomy, time-keeping and geography provided other motivations for geometrical and trigonometrical research. For example Ibrahim ibn Sinan and his grandfather Thabit ibn Qurra both studied curves required in the construction of sundials. Abu’l-Wafa and Abu Nasr Mansur both applied spherical geometry to astronomy and also used formulas involving sin and tan. Al-Biruni (born 973) used the sin formula in both astronomy and in the calculation of longitudes and latitudes of many cities. Again both astronomy and geography motivated al-Biruni‘s extensive studies of projecting a hemisphere onto the plane.

Thabit ibn Qurra undertook both theoretical and observational work in astronomy. Al-Battani (born 850) made accurate observations which allowed him to improve on Ptolemy‘s data for the sun and the moon. Nasir al-Din al-Tusi (born 1201), like many other Arabic mathematicians, based his theoretical astronomy on Ptolemy‘s work but al-Tusi made the most significant development of Ptolemy‘s model of the planetary system up to the development of the heliocentric model in the time of Copernicus.

Many of the Arabic mathematicians produced tables of trigonometric functions as part of their studies of astronomy. These include Ulugh Beg (born 1393) and al-Kashi. The construction of astronomical instruments such as the astrolabe was also a speciality of the Arabs. Al-Mahani used an astrolabe while Ahmed (born 835), al-Khazin (born 900)Ibrahim ibn Sinanal-QuhiAbu Nasr Mansur (born 965)al-Biruni, and others, all wrote important treatises on the astrolabe. Sharaf al-Din al-Tusi (born 1201) invented the linear astrolabe. The importance of the Arabic mathematicians in the development of the astrolabe is described in [17]:-

The astrolabe, whose mathematical theory is based on the stereographic projection of the sphere, was invented in late antiquity, but its extensive development in Islam made it the pocket watch of the medievals. In its original form, it required a different plate of horizon coordinates for each latitude, but in the 11th century the Spanish Muslim astronomer az-Zarqallu invented a single plate that worked for all latitudes. Slightly earlier, astronomers in the East had experimented with plane projections of the sphere, and al-Biruni invented such a projection that could be used to produce a map of a hemisphere. The culminating masterpiece was the astrolabe of the Syrian Ibn ash-Shatir (130575), a mathematical tool that could be used to solve all the standard problems of spherical astronomy in five different ways.


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Written by J J O’Connor and E F Robertson
Last Update November 1999
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Thabit ibn Qurra: A pioneering Muslim polymath of the 9th century

Thabit ibn Qurra: A pioneering Muslim polymath of the 9th century

 
 
 

Thabit ibn Qurra: A pioneering Muslim polymath of the 9th century

Mathematician, astronomer, physicist, physician, geographer, philosopher, historian and more, here is the inspirational story of a man who dedicated his life to several branches of science.

Born in Harran, in Turkey’s Sanliurfa province in 836, Abu al-Hasan Thabit ibn Qurra al-Harrani al-Sabi, also known as Thabit Ibn Qurra, was a prolific scientist of the ninth century whose contributions have shaped modern mathematics, astronomy, mechanics, physics and more. 

He belonged to a family that raised many scholars. They were part of the Sabian community, mentioned in the Quran; the Sabians descended from the Babylonian star worshippers and their beliefs are what led them to produce so many astronomers and mathematicians.

Between 892 and 902, he was a distinguished scientist and physician in Baghdad, mainly under the reign of the Abbasid Caliph al-Mu‘tadid. 

There he studied philosophy and he translated the works of Greek mathematicians into Arabic. Thabit Ibn Qurra also wrote volumes on mathematics and astronomy, and was engaged in medicine. Besides this, Thabit also corrected some works that had been translated before him. Most of his scientific works were written in Arabic, but some in Syriac, too. 

He mainly contributed to science with translations in the fields of philosophy, mathematics, astronomy, medicine and natural sciences. According to some sources, Sabit has about 150 works in these fields.

Along with Hunayn ibn Ishaq al-Ibad, he is considered one of the two greatest translators in Islamic history.

Qurra’s contributions to mathematics can be summarised in three stages. The first is the translation of important works of Greek mathematicians into Arabic, or the correction of previous translations. In particular, Sabit translated all of Archimedes’ mathematics into Arabic. Today, since the Greek originals belonging to Archimedes’ have been lost, they have hugely benefited from Thabit’s translations.

Qurra translated or edited, in full or in part, many of the Greek works by Euclid, Archimedes, Apollonius, Theodosius, and Menelaus. He also wrote commentaries on Euclid’s Elements and Ptolemy’s Almagest.

The second stage is Sabit’s contribution to the formation of an Arabic mathematical language through translation and corrections. With the efforts of Thabit, Arabic, Greek or Syriac works of fixed mathematics found appropriate Arabic equivalents.

Some of the concepts he identified were replaced by Muslim mathematicians who lived after him, but many remained in use. Thabit Ibn Qurra’s contributions to in the third stage are original works that he authored in the fields of mathematics such as arithmetic (number theory), algebra, geometry, cone sections and trigonometry.

His work on integral calculus, some theorems of spherical trigonometry, analytic geometry, and non-Euclidean geometry, left lasting traces, especially in the expansion of the concept of numbers to include positive real numbers.

One of Thabit’s most important contributions to the theory of numbers was his translation of the Greek mathematician Nicomachus’s introduction to arithmetic. Later, Euler generalised the formula developed by Thabit for friendly numbers with new possibilities given by modern Western European mathematics.

Furthermore, there is some evidence that shows Thabit was the first to solve the Menelaus problem. As it’s known, Menelaus’ theorem relates ratios obtained by a line cutting the sides of a triangle. The converse of the theorem is also true and is extremely powerful in proving that three points are collinear.

Ptolemy was the one who also used Menelaus’ complete spherical quadrilateral theorem to solve problems of spherical astronomy. Thabit Ibn Qurra revisited the subject in his own work and gave perfect proof of Menelaus’ theorem.

He used a method similar to the integral calculation technique used in modern “calculus” during this calculation. Therefore, Thabit was introduced by David E. Smith (History of Mathematics) as one of the first founders of calculus.

As one of the first reformists to attempt to correct Ptolemy’s system in the history of astronomy, he put forward the assumption of kinematics and tried to explain the phenomenon of motion with the eighth stroke.

Considered the founder of statics in the science of mechanics, he dealt with the issue of weights and reformulated Aristotle’s dynamic principle, studying the problem of equilibrium. 

In astronomy, Thabit was the author of many treatises on the movement of the sun and moon, sundials, visibility of the new moon, and celestial spheres. In a well-known treatise extant only in a Latin version (De motu octave sphere), he added an eighth sphere, that of the fixed stars to Ptolemy’s spheres (those of the sun, moon, and five planets). He proposed the theory of “trepidation” to explain the precession of the equinoxes. This theory first appeared in Islamic astronomy in connection with his name.

In addition to all these, in other pieces he covered general medicine, diseases, embryology, blood circulation, anatomy of birds and veterinary medicine. 

After a decades filled with science and contributions to several disciplines, Thabit Ibn Qurra passed away on 19 February 901, in Baghdad.

Source: TRT World
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Thabit ibn Qurra: A pioneering Muslim polymath

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Thabit ibn Qurra: A pioneering Muslim polymath of the 9th century

 
 
 

Mathematician, astronomer, physicist, physician, geographer, philosopher, historian and more, here is the inspirational story of a man who dedicated his life to several branches of science.

Born in Harran, in Turkey’s Sanliurfa province in 836, Abu al-Hasan Thabit ibn Qurra al-Harrani al-Sabi, also known as Thabit Ibn Qurra, was a prolific scientist of the ninth century whose contributions have shaped modern mathematics, astronomy, mechanics, physics and more. 

He belonged to a family that raised many scholars. They were part of the Sabian community, mentioned in the Quran; the Sabians descended from the Babylonian star worshippers and their beliefs are what led them to produce so many astronomers and mathematicians.

Between 892 and 902, he was a distinguished scientist and physician in Baghdad, mainly under the reign of the Abbasid Caliph al-Mu‘tadid. 

There he studied philosophy and he translated the works of Greek mathematicians into Arabic. Thabit Ibn Qurra also wrote volumes on mathematics and astronomy, and was engaged in medicine. Besides this, Thabit also corrected some works that had been translated before him. Most of his scientific works were written in Arabic, but some in Syriac, too. 

He mainly contributed to science with translations in the fields of philosophy, mathematics, astronomy, medicine and natural sciences. According to some sources, Sabit has about 150 works in these fields.

Along with Hunayn ibn Ishaq al-Ibad, he is considered one of the two greatest translators in Islamic history.

Qurra’s contributions to mathematics can be summarised in three stages. The first is the translation of important works of Greek mathematicians into Arabic, or the correction of previous translations. In particular, Sabit translated all of Archimedes’ mathematics into Arabic. Today, since the Greek originals belonging to Archimedes’ have been lost, they have hugely benefited from Thabit’s translations.

Qurra translated or edited, in full or in part, many of the Greek works by Euclid, Archimedes, Apollonius, Theodosius, and Menelaus. He also wrote commentaries on Euclid’s Elements and Ptolemy’s Almagest.

The second stage is Sabit’s contribution to the formation of an Arabic mathematical language through translation and corrections. With the efforts of Thabit, Arabic, Greek or Syriac works of fixed mathematics found appropriate Arabic equivalents.

Some of the concepts he identified were replaced by Muslim mathematicians who lived after him, but many remained in use. Thabit Ibn Qurra’s contributions to in the third stage are original works that he authored in the fields of mathematics such as arithmetic (number theory), algebra, geometry, cone sections and trigonometry.

His work on integral calculus, some theorems of spherical trigonometry, analytic geometry, and non-Euclidean geometry, left lasting traces, especially in the expansion of the concept of numbers to include positive real numbers.

One of Thabit’s most important contributions to the theory of numbers was his translation of the Greek mathematician Nicomachus’s introduction to arithmetic. Later, Euler generalised the formula developed by Thabit for friendly numbers with new possibilities given by modern Western European mathematics.

Furthermore, there is some evidence that shows Thabit was the first to solve the Menelaus problem. As it’s known, Menelaus’ theorem relates ratios obtained by a line cutting the sides of a triangle. The converse of the theorem is also true and is extremely powerful in proving that three points are collinear.

Ptolemy was the one who also used Menelaus’ complete spherical quadrilateral theorem to solve problems of spherical astronomy. Thabit Ibn Qurra revisited the subject in his own work and gave perfect proof of Menelaus’ theorem.

He used a method similar to the integral calculation technique used in modern “calculus” during this calculation. Therefore, Thabit was introduced by David E. Smith (History of Mathematics) as one of the first founders of calculus.

As one of the first reformists to attempt to correct Ptolemy’s system in the history of astronomy, he put forward the assumption of kinematics and tried to explain the phenomenon of motion with the eighth stroke.

Considered the founder of statics in the science of mechanics, he dealt with the issue of weights and reformulated Aristotle’s dynamic principle, studying the problem of equilibrium. 

In astronomy, Thabit was the author of many treatises on the movement of the sun and moon, sundials, visibility of the new moon, and celestial spheres. In a well-known treatise extant only in a Latin version (De motu octave sphere), he added an eighth sphere, that of the fixed stars to Ptolemy’s spheres (those of the sun, moon, and five planets). He proposed the theory of “trepidation” to explain the precession of the equinoxes. This theory first appeared in Islamic astronomy in connection with his name.

In addition to all these, in other pieces he covered general medicine, diseases, embryology, blood circulation, anatomy of birds and veterinary medicine. 

After a decades filled with science and contributions to several disciplines, Thabit Ibn Qurra passed away on 19 February 901, in Baghdad.

Source: TRT World
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Muslim Contribution to the Geometry

Muslim Contribution to the Geometry

 

By Islamic-study.org

geometryThe greatest scientific contribution Muslims made to the world is the creation of mathematical science. Algebra, geometry, algorithm and arithmetic are at the heart of every scientific and social aspect of life.

There is hardly a single device, business entity, industry, architecture built without the Arabic numerals, the decimal point, the sign and cosine, the ruler and the compass, all of which are Islamic inventions.

Many of the intellectual sciences Muslims developed were a direct result of the Qur’anic inspirations and of their need to fulfill the rituals and duties of worship.

The Islamic duty of Zakah or alms giving, and the distribution of properties in the will are examples of the duties laid the foundation of geometry and arithmetic.

A Muslim is to give annually in charity and in taxation detailed amounts of currency and/or crops. Figuring out the exact distribution of Zakah and property distribution of the will do not come without complicated math. Each commodity requires precise scaling and percentage.

For example, for an acre of an irregular piece of land is to be split among a family of two boys and two girls with the male share twice as that of the girl, a complicated formula and exact geometry of the land must take place before this duty is accomplished.

Thus, mathematics and geometry came to existence.

The prominent historian, De Vaux , in his book, “The Philosophers of Islam” said: “they (the Muslims) were indisputably the founders of plane and spherical geometry.”

He further stated: “By using ciphers, (Arabic for zero) the Arabs became the founders of the arithmetic of everyday life; they made algebra an exact science. The Arabs kept alive higher intellectual life and the study of science in a period when the Christian West was fighting desperately with barbarism.”

According to Gerard De Vaucouleurs, in his book, Discovery of the Universe, Page 35. Al Battani, (939-998) was a great astronomer and mathematician. He published an original Almagest and developed the science of trigonometry and discovered the inequality in the moon’s motion known as the variation.

Gerard De Vaucouleurs, further said: “Albattani made new observations for the Sun’s position improved the value of the tropical year, rectified Ptolemy’s precession constant and measured the obliquity of the elliptic with care. He introduced the sine into trigonometry.”

Albattani composed a work on astronomy, with tables, containing his own observations of the sun and moon and a more accurate description of their motions than that given in Ptolemy’s “Almagest”.

In it moreover, he gives the motions of the five planets, with the improved observations he succeeded in making, as well as other necessary astronomical calculations. Some of his observations mentioned in his book of tables were made in the year 880 and later on in the year 900.

Nobody is known in Islam who reached similar perfection in observing the stars and scrutinizing their motions.

 

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Courtesy www.islamic-study.org with slight modifications.