1. McKay et al asked Emanuel to prepare appellations for 35 personalities and he did so and sent them the appellations. Thus McKay ordered appellations for this group of personalities, which constitute the total of several possible choices, in order to select only some of these appellations a posteriori.
   
2. McKay et al indeed chose 33 rabbis from this list a posteriori.
   
   These two stages (A and B) absolutely contradict the procedure they reported in Statistical Science:
   

   "1.          A list of rabbis was drawn from Margaliot's encyclopedia by applying WRR's criteria for their second list, while correcting the errors they made. Our list differed from WRR's in dropping two rabbis and including three others. One rabbi who fits the selection criteria could not be included because he appears incorrectly in WRR's first list.
   2.         Emanuel was shown the spelling rules and table of appellations for WRR's first list as they first appeared in WRR (1986). He then compiled a parallel table of appellations for our list of 33 rabbis, attempting to follow the rules and practices of WRR's first list." (Emphasis mine).
   

   Note how in their response they attempt to implicate Emanuel in their misdemeanor [1]:
   

   "Nevertheless, after the experiment was finished, Emanuel approved the description of it that appeared in our paper."
   

   This is baseless: 1. Emanuel explicitly said several months after the publication of their article, that he never read it. 2. He was extremely surprised when he learnt that two rabbis from his list of appellations had been "dropped".
   
   
3. The criterion for choosing the 33 rabbis was invented ad hoc and it contradicts the criterion they publicized on earlier occasions.
   
4. Concerning the dates: Contrary to their response [1], they did not instruct Emanuel to check or emendate all the dates (see later section IV). They only did so concerning one rabbi (or a few).
   
5. Concerning the appellations: Many peculiar decisions were made in "list b" (and "list c") which even Emanuel could not explain. Considering that the instructions given him concerning the dates were through "hints" ([2] chap. I sec. 1(B)), who knows how, and how often such "hints" were given concerning the appellations?
   
6. McKay et al indicated two mistakes in Emanuel's "list b" and asked Emanuel to correct them. But these were not all the mistakes they detected. In section II we will see from their own words that there were at least two more mistakes in their opinion (involving the name "Ayash"). But they chose to correct only what suited them (See [2], chap. 3).
   

1. At an earlier stage, McKay et al ordered appellations for "list a" from Emanuel. They ordered them for only the 32 rabbis of Havlin's second list.
   
2. Note that from the collection of appellations Emanuel gave them at this stage ("list a") it was possible to estimate which appellations would remain in the next stage for the 32 rabbis, after Emanuel would use the spelling rules and would work according to Havlin's first table of appellations and names. This is because McKay et al also understood Havlin's table and the spelling rules (in fact they knew them better than Emanuel, even suggesting corrections to his work).
   
3. No protocol dictated that the experiments be continued on further lists, like b or c. Spadework like this would allow one to act unrestrictedly in the next stage. For example:
   
   • If the significance expected according to #2 is about 0.00002 (many appellations would be expected to survive in the next stage) - one can choose to simply not continue to the next stage.
     
   • If the significance expected according to #2 is about 0.002 (about half of the number of the appellations in Havlin's list could be expected to survive) - one can use steps A-F above, to "sufficiently" downgrade the significance.
     

• Concerning R. Aharon of Karlin, Dr Emanuel mentioned only two appellations: "Rabbi Aharon" and "Rabbi Aharon Ha'Gadol", as I reported concerning them in [2].
  
• Concerning R. Yehudah Ayash, Emanuel originally claimed that no appellations exist. But following my retort that this was almost impossible and also most unlikely considering Emanuel's method of compiling lists b and c, Emanuel finally verified that he used the name "Rabbi Yehudah" , the surname "Ayash" and the full name "Yehudah Ayash" . I mention these names in English because Emanuel did not say whether he had written "Ayash" with one or with two yuds.
  

"2.         Emanuel was shown the spelling rules and table of appellations for WRR's first list as they first appeared in WRR (1986). He then compiled a parallel table of appellations for our list of 33 rabbis, attempting to follow the rules and practices of WRR's first list." (Pg. 163)

"The independent expert mentioned above used for the a-priori experiment the forms שאייע and שאייאע, but for our "experiment" here we follow the 'grammatical" dictum that Witztum has set in the case of Oppenheim, i.e. that must not use a "double yud" in transliterating foreign names, so we write שאיע and שאיאע." [Note that in [5] they admit that this spelling rule was already utilized in Havlin's first list.]

1. Havlin publicized his explanations to his lists after they raised questions about them. They, however, never asked Emanuel to prepare a list of explanations.
   
2. They only publicized Emanuel's lists long after they were prepared.
   
3. When I contacted Dr Emanuel and asked for his reasoning he said that so much time had passed that he no longer remembered.
   
4. McKay et al concealed the "game" they had played with Emanuel's lists (see [2], chap. 2), so they were obviously angry when my direct contact with Emanuel exposed their fraud.
   
5. In "Concerning McKay's Response to our article 'Of Science and Parody'" [6], we added more information from what Emanuel said which made it clear that the work of "Anonymous" (and McKay) relied on nonprofessional books. This is obviously embarrassing for McKay and it is understandable why he prefers that these things remain unknown.
   

"The issue of dates is not much different. In their own experiment, WRR replaced or deleted some of Margaliot's dates on the basis of historical evidence. We did not originally ask Emanuel to do the same, but of his own accord he started to make comments about the inaccuracy of some of the dates in the Margaliot encyclopedia. Emanuel is an expert on such historical questions, so we then asked him to check all the dates. This gave us a compilation of dates of the best possible historical accuracy without the need for any subjective choice of our own."

"…At a certain stage I understood that this matter interested them. Perhaps they asked it for one particular rabbi and I went and did the same for them all…"

1. On 7 November '96, Dr Bar-Natan et al wrote to Prof. Aumann outlining a proposal to have all the dates relating to our experiment examined by an independent expert. We basically accepted this proposal, and in a letter of reply to Prof. Aumann (14 November '96) we added three minor remarks. But Bar-Natan et al retracted from their proposal.
   
2. We consider this the reason they never had the audacity to ask Dr Emanuel to check the dates: It would be too obviously improper to retract from a mutually agreed examination and instead do it unilaterally.
   
3. After Dr Emanuel examined some dates they showed some interest; but they did not instruct him to check them all. This left them the freedom to use:
   
   1. All date changes,
      
   2. Or, some of them,
      
   3. Or, none of them.
      

"Emanuel is an expert on such historical questions, so we then asked him to check all the dates. This gave us a compilation of dates of the best possible historical accuracy without the need for any subjective choice of our own."

1. True, Dr Emanuel is a historian. But Mckay et al should have made clear that his expertise lies in the Middle Ages, a period encompassing only three out of the 32 personalities in the second list.
   
2. McKay and Kalai claim that they achieved:
   "a compilation of dates of the best possible historical accuracy". But this is their mere personal opinion and since they understand little of these matters –– it is worthless.
   

• R. Yehudah came to Jerusalem on Wednesday, Rosh-Hodesh Heshvan (=30 of Tishri) 5461.
  
• On Friday R. Yehudah immersed in a mikveh and became ill.
  
• A detailed description follows: R. Yehudah's behavior that Friday night, what he said, what his son in law said to him, and what his disciples did. The author mentions the name of the doctor whom they wished to bring, and why they did not call him that night. These details accord remarkably with what we know of that period and of that doctor.
  
• There is a detailed description of what happened that Sabbath (Saturday) morning. How R. Yehudah recovered and prayed, but then "fell back into bed as before".
  
• Then "he lost his speech and he could not speak at all until Monday, until he died without saying anything".
  
• "And when he died he was immediately buried on that day with absolutely no delay, and the hasid R. Zalman Byaller was also buried that same day".
  

• "And it happened that when R. Yehudah Ha'Hasid came [to the Land of Israel] with four hundred disciples, he decided that as soon as he came to Jerusalem he would go to the Western Wall and then the Messiah would come".
  
• "And behold R. Yehudah went up and came to Jerusalem, and on Friday he went to immerse in a mikveh, and after immersing he intended going to the Western Wall. But when he immersed, and his disciples were helping him immerse, he touched a reptile while he was immersing in the water, and he shouted to the disciples that they should take him out lest he die, and the disciples took him out from immersing and he died and was buried before the Sabbath (Saturday)".
  

• The testimony of an eye witness who participated in the events himself.
  
• Detailed relating of the events.
  
• Agreement of details given in it to our knowledge from other independent sources (for instance, the name of the doctor, and the fact that it was dangerous to go out because of the Arabs).
  

• Hearsay from decades (about sixty years) after the event.
  
• The story has an obvious legendary-Messianic flavor: R. Yehudah wishes to bring the Messiah straight away, but is prevented by the powers of impurity (the reptile).
  
• No details included are verifiable from another source.
  

"In our replication we tried very hard to apply WRR's rules correctly. One necessary exception was that Rabbi David Ganz had to be excluded because he was already in WRR's first list. (WRR excluded him for the same reason.) Otherwise, neither Witztum nor anyone else has found an error in our selections."

1. MBBK ordered appellations for 35 personalities from Emanuel who prepared and delivered them.
   
2. MBBK, a posteriori, chose 33 personalities from this list.
   
3. Their criterion for this choice was ad hoc, and contradicted the criterion publicized by MBBK on earlier opportunities.
   
4. Thus MBBK achieved the worst results possible.
   

1. The assumption of McKay and Kalai that Emanuel chose the most important appellations is baseless. Emanuel omitted many major appellations. He gave no reason for his decisions and claimed that he could not remember his rationales. For more about this see [2] chap. 3.
   
2. According to their theory, that there is no code phenomenon, these appellations are not "more important". So why does Emanuel's list succeed (in ratio to group size) as would be expected if there is a phenomenon?
   

1. For accuracy's sake, the complement of Emanuel's list succeeds about 90 times better than Emanuel's list. By the way, the difference in size is: "Emanuel" has 63 word pairs and the Complement has 73 pairs.
   
2. The question should be: Is the result for the Complement reasonable as compared with that for a randomly created sub-group of the same size?
   We repeated our test exactly as it is described in [2] chap. 2, and concluded that the probability of receiving such a result (or better) for a randomly created sub-group of Havlin's group, of the same size, is rather large: p=0.3.
   

1. What is the source of the result presented by McKay and Kalai and why is it different from our result in the previous paragraph?
   It turns out that they measured something completely different: They measured the probability of a randomly created sub-group of the Complement, with 63 pairs, succeeding the same as Emanuel's group (or less). This is a statistical mistake because it involves conditional probability.
   We will illustrate this with an extreme case: We have two mutually exclusive groups of word pairs. Group A has 1,000,000 pairs and group B has 1,000,001 pairs. We are given that:
   (a) The success of B is twice as that of A.
   (b) No single pair of B can raise the success of the rest of the group by a factor of two.
   Is there any sense in the following test: What is the probability that a sub-group of B, having 1,000,000 pairs, would have equal (or worse) success as A?
   It is clear in advance (according to (a) and (b)) that this cannot happen.
   But according to McKay-Kalai one would "measure" a "probability" of one in a million!
   
2. Thus all that their "measurement" proved was what is obvious with no measuring at all: That the Complement group is stronger than Emanuel's group. The correct question should be what is the probability that a sub-group of this size and strength could be randomly chosen from Havlin's group. The answer, as stated before, is p=0.3.