13 January 2023

ଓଡିଶା ଗୋଇଁଗ ଗ୍ଲୋବାଲ ବେଳା

 ଓଡିଶା ଗୋଇଁଗ ଗ୍ଲୋବାଲ ବେଳା

ଶ୍ରୀଜିତ୍ ମିଶ୍ର (୧୩/୦୧/୨୦୨୩)

ଓଲି ନାନୀର ଦେଖ ବ୍ରହ୍ମାଣ୍ଡ ପଇଁତରା,
ଓଡ଼ିଶାରେ ହେଉଛି ବିଶ୍ୱ ହକି କପ ମେଳା।

ବାରବାଟୀରେ ସ୍ୱାଗତ ସମାରୋହ ପରା,
ଭୁବନେଶ୍ୱର ଓ ରାଉରକେଲାରେ ଖେଳା।

କଳିଙ୍ଗ ଓ ବିର୍ଷାମୁଁଣ୍ଡା ପଡ଼ିଆରେ ଡେରା,
ମିଲି ମାଉସି ର ପୌଷ୍ଟିକ ବ୍ୟଞ୍ଜନ ଠେଳା।

ଖାଇ ସୁଆଁ କାଙ୍ଗୁ ମଣ୍ଡିଆ ପିଜ଼ା କାକେରା,
ଦେଖ ଷୋହଳ ଦେଶର ଭେଣ୍ଡିଆଙ୍କ ଲିଳା।

ବିଶ୍ୱ ପୁଷ୍ଟିଶସ୍ଯ ବର୍ଷ ଓଡିଶା ଚେହେରା,
ମାଣ୍ଡି ମା ଦେସିଆରୁ ଗୋଇଁଗ ଗ୍ଲୋବାଲ ବେଳା।







-୦-×-୦-

(Odia transliteration using English alphabet)

Odisha Going Global Bela
Srijit Mishra (13/01/2023)

Olly Nanira Dekha Bramhanda Paintara,
Odishare Heuchi Biswa Hockey Cup Mela.

Barabatire Swagata Samaroha Para,
Bhubaneswar O Rourkelare Khela.

Kalinga O BirsaMunda Padiare Dera,
Milli Mausira Poushtika Byanjana Thela.

Khai Suan Kangu Mandia Pizza Kakera,
Dekha Sohala Deshara Bhendianka Lila.

Biswa Pushtishasya Barsha Odisha Chehera,
Mandy Maa Desiaru Going Global Bela.





-୦-×-୦-
English translation (literal, work in progress)

Odisha's Going Global Time
Srijit Mishra (13/01/2023)

Olly's Sojourn across Universe,
Odisha Hosts Hockey World Cup.

Barabati enthralls with inaugural,
Bhubaneswar and Rourkela will have play-offs.

Kalinga and Birsa Munda Stadium is the place to be,
Visit Aunt Milli's Nutritious Meals Stall.

Eat millet-based recipe's like pizza and sweets,
Enjoy stickwork of players from sixteen countries.

In International Year of Millets Odisha Shows,
Mother Mandy's Time from Local to Going Global has come.



-୦-×-୦-
Olly is 2023 Hockey World Cup's Mascot (she was also the mascot in 2018)
Milli is Odisha's Mascot for International Year of Millets 2023
Mandy is mascot of Odisha's Annual Agricultural Fest (Krushi Mela) in 2020 catapulting Odisha Millets Mission 
-୦-×-୦-


01 January 2023

FIFA 2022 Final and Vipratisidhe Parama Kāryam

Abstract: This post on FIFA 2022 World Cup Final between Argentina and France (or, Lionel Messi and Kylian Mbappé, respectively) is a continuation of my curiosity on  Pānini’s conflict resolution ruleVipratisidhe Parama Kāryam, beyond Sanskrit grammar, contextualized through the adage, "Let the best one win." We now look forward to Hockey World Cup 2023, and welcome 2023, the International Year of Millets. 

“Let the best one win,” is a powerful adage, a wishful one, as it may not always turn out to be true. However, this adage seems to have been echoed by many football lovers after the final match between Argentina and France in the FIFA World Cup 2022 suggesting that in their view the best team did indeed win.





In this post, in sync with the adage, I will touch upon the ups and downs of that match through the lay reading of Pānini’s celebrated conflict resolution rule “In conflict the stronger (or, better) one prevails,” Vipratisidhe Parama Kāryam. This draws from a recent post of mine wherein I had indicated that the lay reading renders the rule for wider application beyond Sanskrit grammar. I had also  indicated there how the lay reading of the rule resonates with Mahatma Gandhi’s talisman, John Rawls’ veil in an original position, and Adam Smith’s impartial spectator. In the spirit of that wider application, we now get back to that final match.  

Supporters of Argentina and France would have wanted their teams to win. The fan following of Lionel Messi and Kylian Mbappé would have wanted their idols to be in the winning side. There, however, was an undercurrent of support for Messi, as this would perhaps be his last World Cup and that his caliber as a player has been borne out by the fact that till that final match, he had been in the winning squad of all major football tournaments. In the last four years, Mbappé has also created a fan following of his own since his performance in the 2018 edition of the World Cup that France won, and he has been going from strength-to-strength thereafter.

When the 2022 FIFA final match between Argentina and France began many, so-called neutral supporters (perhaps talismanic, in a veil, and impartial spectators), wanted Argentina to win so that Messi can be part of the winning squad and will have in his repertoire the one Cup that is missing, and they also wanted Mbappé to score at least a goal. It was very much possible that Argentina would have won without Mbappé or his team scoring a goal, or for Argentina to have lost. Given the two competing wishes, it is only after the match that one could know which of these got fulfilled and who of the two teams was better and whether the better team won.

As the match progressed, Argentina and Messi were doing well. They were 2-0 up with Messi having scored one and assisted the other. But, Mbappé had not scored. He fulfills  the neutral supporters wish and around the 80th minute scores a goal. Hold on, within another minute or so, he goes beyond that and scores another goal. With Mbappé’s two back-to-back goals, France was level with Argentina and by the end of regular time the score line read 2-2.

Now, with the match going into extra time, the neutral supporters wanted Messi to show his magic and were all delighted when he does that by scoring another goal with Argentina now leading again at 3-2. With this, our neutral supporters were somewhere feeling a little let down for Mbappé but this does not last long as he scores again, a hat-trick in a Wrold Cup final, and France levels the score again with Argentina at 3-3 at the end of extra time. With no clear winners, the match goes to penalty kicks.

Mbappé and Messi score their respective penalty goals. France misses out the second and third one with a good save by Damián Martínez the Argentine goalkeeper, but scores their fourth, while Argentina players, after Messi, score their subsequent three and go on to win the World Cup 2022 with the penalty kicks score reading 4-2.

Some non-connoisseur's of the game would suggest what was this ado all about, they could have started with the penalty kicks and decided the match. No, that cannot be. The beauty of the game lies in the the laws of the game along with the ups and downs and the upheavals therein. If there is no decision after the regular time of 90 minutes then the match goes to extra time, and if there is still no decision after the extra time of 30 minutes then the match goes to penalty kicks.

The application of the laws of the game for determining the outcome of a match follows  a sequence, which, in a convoluted sense, seems to support Vipratisidhe Param Kāryam. No decision at the end of a stage of the match (that is, end of regular or extra time) indicates that at the end of that stage the two teams continue to be of equal strength (vipratisidhe) and this requires that the progress of the match to the next or subsequent stage (param) be brought into action or invoked (kāryam). Further, as the match progresses to kicks from the penalty mark the penalty kicks can go on ad infinitum till a decision on the winner is reached.  

To get back to our adage, the best team won, Argentina won the Cup in the penalty shoot out. But, our neutral supporters got more, Messi gets the golden ball as the best player of the championship including his goals and assists (see all goals by Argentina in the World Cup), Mbappé gets the golden boot as the maximum goal scorer in the tournament, and Martínez gets the golden glove as the best goalkeeper of the competition.

There was no decision to be made by our neutral supporters, but in their personal emotional space they felt vindicated and it is this that supports our lay reading of Vipratisidhe Parama Kāryam beyond Sanskrit grammar. The feeling by our neutral supporters also seems to resonate Gandhi’s talisman, Rawls’ veil in an original position and Smith’s impartial spectator. What more would they want. The laws of the game to decide a winner in a World Cup final match also seems to, in a convoluted sense, fall in line with Pānini’s conflict resolution rule. It has been a win-win for all. 

Now, we look forward to the Hockey World Cup 2023 that is to take place in Bhubaneswar and Rourkela of Odisha, India in January 2023. Wishing you well-being and happiness for 2023, the International Year of Millets.

[I reiterate of having no knowledge of Sanskrit, as indicated in my pervious post. This is just a continuation of my curiosity of Pānini’s conflict resolution rule, in my lay understanding, beyond Sanskrit grammar. My apologies to Sanskrit grammarians and football aficionados.]

© Srijit Mishra

CC BY-SA


-x-o-x-

28 December 2022

Rishi on Pānini’s Vipratisedhe Param Kāryam and Beyond

Rishi on Pānini’s Vipratisedhe Param Kāryam and Beyond 

Srijit Mishra


28 December 2022


Abstract

The post provides a generic interpretation and a lay reading of Rishi Rajpopat’s interpretation of Pānini’s metarule vipratisedhe param kāryam for conflict resolution. This opens up possibilities for the application of this metarule beyond Sanskrit grammar. For instance, Mahatma Gandhi’s talisman in his social philosophy, John Rawls’ veil in the original position as an aid in his political philosophy, and Adam Smith’s impartial spectator in his moral philosophy.


Keywords:   Adam Smith, Aṣṭādhyāyī, John Rawls, Kāryam, Mahatma Gandhi, moral philosophy, Pānini, param, political philosophy,  Sanskrit, social philosophy,  vipratisedhe.



 


The Context 

Rishi Rajpopat’s doctoral thesis In Pāṇini We Trust: Discovering the Algorithm for Rule Conflict Resolution in the Aṣṭādhyāyī  addresses an important problem for conflict resolution. Pānini’s celebrated Aṣṭādhyāyī on Sanskrit grammar has only one metarule for that, 1.4.2, vipratisedhe param kāryam, “if there are two conflicting rules, the subsequent one prevails.” 


Conventional Interpretation

Conventionally, grammarians had suggested different approaches to conflict resolution. First, the stronger rule prevails. 

  • Nitya (obligatory) is stronger than its counterpart anitya (not obligatory). An example of the latter is when the sense in a compound word can be equally expressed by the constituent parts). 

  • Antaraṅga (internally conditioned), as the rule has the cause of its application embedded in another rule, the bahiraga (externally conditioned), making the application of the former a prerequisite for the latter and in that sense the former is the stronger one.

  • Apavāda (exception) is a special rule that sets aside utsarga (the general rule) and thereby makes exception rules stronger. 

Second, if rules are of equal strength, the subsequent one in Pānini’s Aṣṭādhyāyī will prevail. However, all these also led to a host of additional metarules for umpteen exceptions. 


Rishi’s Contribution

Rishi Rajpopat’s contribution is in three parts. First, it classifies whether the conflict (that is, application of two rules) is for the same operand or for different operands. 


Second, in the case of a single operand, it develops a method to identify the specific rules. This would further aid in the application of the exception rules, as being specific gives greater clarity. 


And, third, in the case of two different operands, it provides a novel interpretation wherein param in the metarule means the rule that should apply to the subsequent one or the next one from the two operands (say, the rule that is applicable to the latter of the two independent words that aid the formation of a new compound word). Here, I use the subsequent one and not the one that will come to the right-hand side, as indicated by Rishi Rajpopat, because the subsequent one is generic and should hold for people who learn Sanskrit in a script where the writing is not from left to right (while recognizing the limits of the usage because of the script) or even for those who learn (or, have learnt)  Sanskrit largely through an oral tradition.  Independent of this generic usage, this novel interpretation has solved a long-standing puzzle and opens up the logical structure of Sanskrit grammar for wider application.  


A Lay Reading

A lay reading of the metarule could imply that “if there are two conflicting rules, the stronger one prevails.” This presumes that param (or, parama) means the stronger one or the better one or the best. Such a reading is different from the perspective provided by the Sanskrit grammarians and leaves room for interpretation on what one means by ‘the stronger one’. This reading would be counterproductive as it does away with the clarity involved in interpreting param as the subsequent one or the next one (either in the sequence of rules in the conventional interpretation or in the sequence of operands in the novel interpretation). Nevertheless, we go ahead with this usage as, in our view, it subsumes different aspects of the conventional interpretation as also Rishi Rajpopat’s contribution and also opens up the metarule to a wider application.


In the conventional interpretation, by default, the stronger rules such as nitya, antaraṅga, and apavāda prevail over their corresponding weaker rules anitya, bahiraga, and utsarga, respectively. Only when the two rules in conflict are of equal strength then the one that comes later in the Aṣṭādhyāyī is considered to prevail. This interpretation draws from an implicit understanding that in the Aṣṭādhyāyī the sequencing of the rules is from the simpler to the complex ones. And, thereby, making the rules that come later in the sequence in the Aṣṭādhyāyī the stronger ones, albeit the exceptions.      


Rishi Rajpopat’s contribution suggests two things. One is the identification and application of specific rules as exceptions in case of the conflict in a single operand. And, the other is the one that applies to the subsequent operand in case of conflict between two operands. Thus, in case of conflict in a single operand the exception rule prevails and is the stronger one while in case of conflict between two operands the one that applies to the subsequent operand prevails and is the stronger one. 

   

Beyond grammar: Gandhi, Rawls and Smith

The lay reading is subjective to what one considers as param or, more specifically in our lay reading to what one considers to be stronger or better.  However, this lay reading opens up the application of the metarule beyond grammar, including for decision-making in other situations of conflict.


For instance, Mahatma Gandhi’s invoking of the talisman, John Rawls’ recourse to be under a veil in an original position, or Adam Smith’s reliance on the impartial spectator are the basis to guide decision-making to resolve some conflict. Gandhi’s is a powerful social philosophy for the individual to rely on thyself to resolve a conflict in one’s own mind when in doubt, Rawls’ is a transcendental political philosophy that requires a democratic ethos with identities under wrap to move forward in a reasonably plural world, and Smith’s is a moral philosophy where an individual falls back on thy conscience by being in the shoes of an impartial spectator.


Getting back to Pānini’s metarule on conflict resolution, one sees that the param kāryam (that is, the stronger one or better one prevails) in Gandhi’s talisman is a reliance on  thyself (one’s own conscience), in Rawls’ veil in an original position is the focus on the democratic ethos with individual identities being under wrap (the free and equal citizens deciding for themselves while being blind to their own identities or self-interest), and in Smith’s impartiality is in identifying thy conscience by putting on the hat of independent and disinterested persons (being open to other perspectives to help visualize propriety in the larger social space).


Conclusion

A novel interpretation of  Pānini’s metarule vipratisedhe param kāryamIn by Rishi Rajpopat  has opened it up for wider application. It is in this spirit that we have suggested a generic interpretation followed by a lay reading of the metarule, “if there are two conflicting rules, the stronger one prevails.” This lay reading is not for usage in Sanskrit grammar. Nevertheless, this lay reading, in our opinion, subsumes the conventional and new contributions on the interpretation of the metarule. It also opens up the lay reading to applications beyond Sanskrit grammar. For instance, in understanding some specific rules that aid decision-making to deal with conflict resolution by thinkers like Mahatma Gandhi’s talisman in his social philosophy for an individual in doubt, John Rawls’ veil in an original position with a set of other fundamental ideas leading to his principles of justice as a political philosophy, and Adam Smith’s impartial spectator that aids his moral philosophy.


Acknowledgements

At the outset, I must state that I have no knowledge of Sanskrit, less so of its grammar. My limited understanding is in having heard some recitation and their interpretation as a proximate illiterate.  This note is out of my curiosity, as I was intrigued by the recent discovery that has aided a long-standing puzzle in Sanskrit grammar. I am thankful to PK Viswanathan and through him Br Achutamrita Chaitanya for helping me in my understanding of the word param (परम्), and how it is different from parama (परम), and the metarule.


© Srijit Mishra

CC BY-SA



-x-o-x-

04 November 2021

Essence of Deepawali by Sant Jnaneswar: Odia and English Interpretation

The Bhandarkar Oriental Research Institute have put out a nice Deepawali greetings based on Sant Jnaneswar's c.1290 commentary on Bhagavad Gita. My Odia and English translations as also original Marathi and Bhandarkar Institute's English message are given below.


ଅବିବେକତା କୁ ଜଳାଞ୍ଜଳି ଦିଅ। 

ଫେଡ଼ଣମୋଚନ ସହ ବିବେକରଦିପ କୁ ଉଜ୍ବଳ କର। 

ଯାବତ ଯୋଗସାଧକଙ୍କ ପାଇଁ ଦୀପାବଳି। ନିରନ୍ତର ॥୫୪॥ 


ସନ୍ତ ଜ୍ଞାନେଶ୍ୱର, ଜ୍ଞାନେଶ୍ୱରୀ (ଭାଗବତ ଗୀତାର  ବ୍ୟାଖ୍ୟାତ୍ମକ ମରାଠୀ ନିବନ୍ଧ), ୧୨୯୦।

ଅନୁବାଦରେ ତୃଟିଥିଲେ କ୍ଷମା କରିବେ।

ଶ୍ରୀଜିତ୍ ମିଶ୍ର

https://twitter.com/srijitmishra/status/1455748206663372801?s=20


Burn away thy moral turpitude. 

Let go and get liberated by lighting thy conscience. 

This for a seeker will be enlightenment (or, Deepawali).

https://twitter.com/srijitmishra/status/1455826864845377540?s=20


Original Marathi Verse

मी अविवेकाची काजळी । 

फेडूनी विवेकदीप उजळीं ।

तैं योगियां पाहे दिवाळी । निरंतर ॥ ५४ ॥

Sant Jnaneshwar (संत ज्ञानेश्वर) in his epochal commentary on Bhagavad Gita, "Jnaneshwari" (completed in 1290 AD), articulates the most profound essence of Diwali. #Diwali2021 

https://twitter.com/BhandarkarI/status/1455568734521729032?s=20


Bhandarkar Institute's English message of the verse. The verse means:

(Written from the perspective of lord Shri Krishna)

"As I erase the gloom of ignorance and apathy, 

the light of knowledge burns bright within the conscience. 

Such an enlightened mind experiences immanent diwali"

https://twitter.com/BhandarkarI/status/1455568736430145541?s=20

 

I must admit that my knowledge of Marathi is limited and that of Odia is no where near to attempting to any translation. But, perhaps the spiritual essence behing Sant Jnaneswar's message pulled me into it. 

In attempting the Odia translateion I benefitted by going over Bhandarkar Institute's Marathi and English versions and Odia-English and English-Odia dictionaries at my disposal. One thing that I had to struggle was whether to write or not to write the verse in the first person from the perspective of Sri Krishna, which the Marathi versio does, as it begins with मी (or, I, referring to Sri Krishna). I did try that. See the highlights in bold below. 

ମୁଁ  ଅବିବେକତା କୁ ଜଳାଞ୍ଜଳି ଦିଏ। 

ଫେଡ଼ଣମୋଚନ ସହ ବିବେକରଦିପ କୁ ଉଜ୍ବଳ କରେ। 

But,  decided against that because I thought Sri Krishna's Bhagavad Gita can also be a call to self. The latter I thought would be represented if one considers that Sri Krishan represents each and every individual rathe than rather than Sri Krishna speaking to one. It is true that Sri Krishna speaks to Arjuna. But, it is also true that Sri Krishan wants Arjuna to see for thyself. It is a matter of interpretation and I leave it to you the reader.

In the third sentence I was thinking of beginning with ତାହା ହିଁ as I thought that was perhaps closer to Marathi तैं. I decided in favour of ଯାବତ.

My English translation was done after I did the Odia one and also exluded the first person version, which has been used in the interpretation shared by Bhandarkar Institute.

At some point, I was contemplating the second sentence to be: 

Let go and liberate thyself by the light of consciousness.

But then I thought through and decided that "get liberated by lighting thy conscience" would better convey than "liberate thyself by the light of consciousness."   

In the third sentence, an earlier version read:

This, for a true seeker, will be enlightenment (or, Deepawali).

I decided to do away with the word true because each seeker is a true seeker in their own way.

Your comments and perspectives are welcome.

20 June 2021

Meaning of Protective Efficacy from Vaccines

The other day I came across a debate in a vernacular channel where there was a reference to at least 60% protective efficacy from vaccines against COVID-19 even for some new variants of the virus even if one cannot say much about future variants. From the discussion, there seems to be a popular misconception in the understanding of protective efficacy. The purpose of this write-up is to address that misconception.

In popular understanding, 60% of protective efficacy from vaccines could mean that if 100 people take vaccines then 60 of them would be protected from the disease.

In actual practice, protective efficacy refers to relative risk reduction (RRR). Or,

RRR=1-RR.

RR is relative risk, that is, the ratio of the risk in the treatment group (proportion infected from among those who have been administered with the vaccine, Rt) with the risk in the control group (proportion infected from among those who have not been administered with the vaccine, Rc). In other words,

RR=Rt/Rc.

If the proportion of infected is equal in the two groups then a benchmark relative risk, Rtb/Rcb=1. RRR is a reduction from this benchmark. Hence, 60% of protective efficacy in the debate should have been identified with RRR%=RRR*100.

Now, what could this 60% of protective efficacy imply. If the treatment and control groups had 100 people each and if the number of people infected in the two groups are 2 and 5, respectively, or, Rt=2% and Rc=5%, then RRR=60%. This means that if there are 100 people each in the two groups then 2 could be infected from those vaccinated and 5 from those not vaccinated.

But, one would get the same value of RRR=60% with umpteen other possibilities where both the above-mentioned values of Rt and Rc are multiplied by a common factor, k. An extreme situation can be when Rt=40% and Rc=100%, which was the position taken by a panelist in the debate who conveyed that among those vaccinated 40% would be infected and among those unvaccinated everyone would be infected. This is an extreme scenario and in some sense a misrepresentation of facts.

It calls for the relevance of absolute risk reduction, ARR=Rc-Rt. A Lancet Microbe paper (see discussion in earlier blogs here and here), drawing from phase 3 trials of five COVID-19 vaccines indicated that RRR was in the range of 67%-95% while ARR was in the range of 0.84%-1.28%. And, in a population setting for which data was available in one case, ARR comes down to 0.46%.

Based on this, it is quite likely that RRR=60% is to be commensurate with ARR in the range of 0.2%-1.5%, that is, Rt=0.2% and Rc=0.5% where ARR=0.3%, or, if one wants to give some benefit of doubt then Rt=1.0% and Rc=2.5% where ARR=1.5%. By not doing this, the panelist amplified the risk by 40-200 times. This can create panic and fear among the public and should be avoided.

The role of the State in providing vaccination to people by considering it as a public good is a relevant matter. Equally important, in a democratic polity, as conveyed by another panelist in the debate, is the fact that that vaccines being administered are with Emergency Use Authorization and that it is a voluntary act by an individual  who has to weigh the information provided. An informed consent and right to refuse, after being provided with information that leaves questions unanswered, is not the same as hesitancy. For a complex, evolving and uncertain scenario, questions would be the first step for better science.

04 June 2021

Comparing Deaths from COVID-19 among Uttarakhand Police in Two Periods

The Indian Express put up a write-up on incidences of COVID-19 and fatality among police personnel of Uttarakhand. It indicates that the police personnel of the state had started vaccination in January 2021 and more than 93% among them have been vaccinated. This is an impressive figure because for a disease with reproduction number or R0 "R naught" around three (R0=3), the proportions needed for herd immunity (including natural infection) should be around 67%.

Given this backdrop, it might be a matter of concern that in April and May of 2021 the number of police personnel inflicted by the disease in Uttarakhand were 2,382. However, it is comforting that from among these 2,204 have already recovered while five (5) of them, bless their souls, are no more with us. The proportion of death from those inflicted by the disease is 0.21% (which could increase if there are additional deaths from the remaining 173 who have not recovered). The write-up further points out that the severity of the disease and and the number of deaths were lower than previously observed.

For instance, the proportion of deaths from the start of the pandemic till March 2021 was 0.40% (that is, 08 deaths from among 1,982 inflicted by the disease). Even if one ignores the fact that we are comparing more than 13 months of data with two months and that there are 173 cases for which we still do not know the final outcome but consider them to have recovered, a proper comparison would be to estimate absolute risk reduction (ARR) and relative risk reduction (RRR) and their statistical significance for deaths among those inflicted by the disease in the two periods. 

The ARR and RRR estimates and their 95% confidence intervals are:

ARR%=0.19% (95% CI: -0.14%, 0.53%) and

RRR%=48.1% (95% CI: -58.7%, 83.0%). 

This indicates that when one compares the second period with the first, ARR in per cent is 0.19% and RRR in per cent is 48.1%, but more importantly both the estimates are not statistically significantly different from zero. This suggests that one should be cautious with the comparative statements between the two periods by using absolute numbers.

ARR is d1-d2 

95% Confidence Interval (CI) for ARR is ARR±1.96*Standard Error (SE) of ARR

SE of ARR is {[(d1*r1)/N1]+ [(d2*r2)/N2]}^(1/2)

RRR=1-RR; RR is d2/d1

95% CI for RRR is 1-95% CI of RR

95% CI of RR is {exp^[Ln(RR)±1.96 SE of RR]}SE of RR is {[(r1/d1)/N1]+ [(r2/d2)/N2]}^(1/2)

In the above calculations, d  and r denote share of death and share of recovery from among those inflicted by the disease with subscripts 1 and 2 denoting periods 1 and 2, respectively, such that in each period their sums add up to unity, d1+r1=d2+r2=1. N1 and N2 denote number of people inflicted by the disease in periods 1 and 2 respectively.

The write-up also had mentioned that from among the family members of the police personnel 751 were inflicted by the disease and from among them there were 64 deaths. This is indeed an important sacrifice by their family members. The adverse effects, in terms of deaths, is much higher then that on the actual force and this should be an important concern.

One is also curious to know what would be the incidences and deaths by family members across the two time periods. Has that number increased in the second period then a question that comes to mind is the possibility of adverse impact having increased after a public health intervention among police personnel. A period wise break of the data will help us examine that.