Meaning of Numbers (2): Functions, Sequences and Algorithms

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So many functions in mathematics, yet what do they really mean?

I mentioned in my previous post some key and fundamental elements of Chinese numerical superstition, namely the numbers four 4 (=’death’) and eight 8 (=’prosperity’) which permeate throughout our language and culture and have shaped our cultural understanding of numbers and portents. I also mentioned that it was possible to interpret these numbers in terms of their sequential positions and linear ordering. In this post, I propose to look at some basic elementary mathematical functions such as addition, subtraction, multiplication and division which, when applied to the numbers which are significant in Chinese culture, may tell us something interesting, not only about the meaning of numbers but also about life, at least as seen through the Chinese perspective.

The two most important numbers in Chinese, namely the numbers four 4 and numbers eight 8 mean totally opposite things (‘death’ and ‘prosperity’ respectively). These two numbers also have an intimate relationship with one other, as eight 8 is a product of four 4. In terms of multiplication, therefore, all even multiples of four 4 are also multiples of eight 8. To put it simply: every other multiple of four 4 is also a multiple of eight 8, which may be interpreted as: fail twice, win once. It is an oft-cited dictum that success is the result of failure (‘necessity is the father of invention’; ‘failure is the mother of all successes’, 失敗乃成功之母). It is only through repeated failures that we learn, make self-improvements and ultimately achieve success. Two mishaps may hence give rise to one success. That is how I think of it whenever I am having a bad day. I may be having a bad time now, but give it some time I’ll be propelled to victory. The numbers four 4 and eight 8 are hence highly significant and can be interpreted as having a motivational message.

The numerical alternations between four 4 and eight 8 show that success and failure may hang by a thread and it is the fine margins and small differences that ultimately count (annoyingly). Numerically, I have assimilated this to the numerical sequence: 7–8–9 where a propitious number eight 8 is sandwiched between two bad ones (seven 7 and nine 9, at least in Cantonese terms). I have had some nice experiences with this, so I am fully aware of how Odysseus felt when he sailed between Scylla and Charybdis. There is another sequence which seems to be the anti-type of this: 3–4–5 where a bad number four 4 occurs between two neutral numbers (there is no particular reason why three 3 and five 5 should be regarded as favourable, though one might consider the fact that their sum (3+5=8) is, which may validate their ‘membership’ into the ‘good numbers club’). While I have been trying to obtain all things eight 8 by avoiding seven 7 and nine 9, I have been doing the exact opposite with four 4 and have always tried to ‘misfire’ in the lower region and land on three 3 and five 5 instead. One must be aware of the bad technological quirks on devices where two commands take place jerkily (which may indicate that one’s device is losing its former glory and is on its way towards replacement). I hate it when I am doing eight tasks on my laptop and suddenly I get switched back to seven or nine, and I love it when dealing with four tasks I get pulled back to three or five, like a magnetic force pulling me out to safety. 3–4–5 and 7–8–9 are therefore two symmetrical numerical sequences, and it is interesting that they are separated by four 4, an ill-omened numerical unit that may, paradoxically, flip the coin and yield success, like in ancient Graeco-Roman religion where life and death have a mutually complementary and hence cyclic relationship.

There is another interesting sequence above seven 7–eight 8–nine 9, and that is eleven 11 — twelve 12 -thirteen 13 — fourteen 14. I have written before that the numbers eleven 11 and fourteen 14 are highly significant in our Chinese numerical superstition, since the former (eleven 11) is homophonous with the Cantonese phrase meaning ‘sure win’, while the latter (fourteen 14) is not, as it means ‘sure death’. In between, there is twelve 12 and thirteen 13, the former of which I have always liked for many reasons while the latter is widely interpreted as ill-fated in western culture for many reasons. All in all, this represents a very interesting sequence, since it starts with two very propitious numbers (eleven 11, twelve 12) and ends with two very bad ones (thirteen 13, fourteen 14). This is a sequence of two halves.

Numerical alternations really are fascinating. Another special sequence is 8+5. I have mentioned before that the number eight 8 and all permutations of the digit eight 8 (18, 28, 38 etc) are very significant in our Chinese culture, since eight 8 is homophonous with the Chinese word for prosperity, and ten 10 in Cantonese is homophonous with the Cantonese adverb meaning ‘definitely, certainly’, and so every eighth digit of each decade (18, 28, 38…) literally means ‘definitely prosper’. The halfway point between each digit 8, however, ends with the digit three 3 i.e. the number thirteen 13 lies halfway between eight 8 and eighteen 18, twenty-three 23 between eighteen 18 and twenty-eight 28, and so on. I have written before that in western/Christian culture the number thirteen 13 is dangerously ominous, presumably because there were thirteen disciples present at Jesus’ Last Supper. The numerical addition of eight 8 and five 5, therefore, involves a series of alternations between propitious numbers (eight 8 and all digits ending in eight 8) and negative numbers (thirteen 13, and, by extension, twenty-three 23, thirty-three 33 etc) lying in between, which beautifully demonstrates the cyclic relationship between prosperity and calamity. Between each prosperous turn lies a disaster, and one is constantly alternating between prosperity and calamity, which may be argued to symbolise the nature of human fortune as we seem to leap from success to failure and vice versa. I mentioned before a similar relationship between four 4 and eight 8 where two negatives flip into a positive one (4+4=8). Looks like there is something similar in this cyclic alternation between prosperity and calamity (8+5+5+5+5…).

Thirteen 13 is an unlucky number in Western culture. Rumour has it that it is due to the biblical tradition that it was the number of attendees at Christ’s Last Supper, which led to its supertitiously dark connotations in the West and beyond. Indeed most people I have encountered in the West try to avoid the number thirteen 13 as much as possible, as do I. If we flip it, however, we get thirty-one 31, which, at first glance, does not seem to have anything obviously good or bad about it. However, the fact that it is derived from thirteen 13 by inversion, it may be considered the inverse of this bad number thirteen 13 and hence a positive number. Also, the difference between thirteen 13 and thirty-one 31 is eighteen 18, which is a highly propitious number in Chinese. It is a well-established numerical trend that the difference between two numbers by numerical inversion is the product of the difference between the two digits and nine 9, which, in this case, consists of (3–1)*9=18. Thirty-one 31, therefore, a somewhat ordinary and random number by most accounts, may have something decidedly good and exciting about it. I have mentioned how addition and subtraction could be significant numerical functions, and here we can count inversion as significant too.

In my previous blogs about numbers, it is clear that numerical combinations have superstitious and religious significance, especially when interpreted within the Chinese numerical system e.g. addition, the sum of numbers which may yield a higher level of meaning. Another concept which is relevant here is, of course, the very opposite to addition, namely subtraction. How to interpret it, however, is open to different opinions, since we could treat it as on a par with addition, or we could see it as the anti-type of addition i.e. while addition results in a positive correlation of numerical meaning, subtraction creates the very opposite of what these numbers mean. To take an example: 100–8=92 and 100–4=96. 8 and 4 are key numbers in Chinese since the former means ‘prosperity/fortune’ and the latter means ‘death/ruin’. 100, likewise, also means ‘good fortune’. 92 and 96, being the results of subtraction from 100 by 8 and 4 respectively, can be interpreted in different ways. Either we argue that 8 is propitious and 4 is bad even in subtraction, in which case 92 (100–8) is good and 96 (100–4) is bad (and, by opposite extension, 108 (100+8) is good and 104 (100+4) is bad), or we say that the subtraction of 8 (-8) and 4 (-4) flips them into an ill-omened number and a lucky number respectively, the inherent logic being that -8 symbolises the loss of fortune and -4 the removal of death. In the latter interpretation, 92 (100–8) and 96 (100–4) become bad and good numbers respectively. I take no strong position on whether subtraction reverses the significance of numbers (though it is a very interesting idea well worth pursuing), but since I have always tried to be positive about my numerical superstition, I am willing to say that both the subtraction of 8 (-8) and the subtraction of 4 (-4) are favourable functions, which makes both 92 (100–8) and 96 (100–4) (and 108 (100+8) but not 104 (100+4)) good numbers.

For the same reasons, I have come to love the numbers 92 and 96. As explained before, these two numbers are can be interpreted in different ways, either as 100–8=92 or 100–4=96, both of which can be seen optimistically as fortune-bearing. There are many more reasons for loving these numbers. As explained before, eight 8 is twice of four 4 (4+4=8), which symbolises the famous dictum that success (8) is the result of repeated failure (4+4) (‘fall down once, get up twice’). Since eight 8 is such an important number in Chinese culture, which extends to homophones like a hundred 100, it is interesting to note that between 88 and 100 there are increments of four 4 which form a series of magical numbers: 88, 92, 96, 100. One may also note that the multiples of eight 8 here (88, 96) are extremely good in that they are the eleventh (11) and twelfth (12) multiples of eight 8 respectively, both of which are also beautiful numbers. Looks like the run from 88 to 100 through loops of 4 is pretty exciting. Although the average life-expectancy in first world countries nowadays lies somewhere between 79–82 y.o., it is not uncommon for people to reach 90+ y.o.. In my case, I shall hope that my health keeps up and that I’ll be able to reach the 88–100 territory, which should be the best time of my life. After all, age is only a number, not an attribute. Live life to the fullest!

I recently fell in love with the number ninety-one 91 too, and for good reason. The numbers eight 8 and eleven 11 are magical in our Chinese superstition, and the sequence between them (8–11) is hence particularly significant. This ascending sequence, it turns out, consists of three integers: nine 9, ten 10 and eleven 11, which, in our Chinese numerical system, constitute the number ninety-one 91. Recall that in Chinese (and in East Asian languages in general) numbers are arranged into units of tens, hundreds, thousands etc, and a number like ninety-one 91 would be pronounced as nine 9 (X) ten 10 (+) one 1 (=91), which perfectly embodies the numerical sequence between eight 8 and eleven 11. There is otherwise nothing particularly striking about ninety-one 91, though one might add that ninety-one 91 is the result of the subtraction of nine 9 from one hundred 100, the latter good and the former bad, and the fact that subtraction (and division) may be considered as an inverse function could be taken to suggest that the subtraction of nine 9 (-9) signifies fortune after all, especially when applied to a number as favourable as a hundred 100. May we all live till eighty-eight 88 and have one last crazy ride in our ninety-first 91st and one hundredth 100th year!

Based on the above principles of addition/substraction, linear sequences and numerical inversion, I have been living my life observing the numbers I see, and these are some episodes which have stuck with me in recent years:

On Mondays, I usually go to a local noodle place called Wok for my weekly dose of pot noodles. The reason for this is that they offer double loyalty stamps for every noodle pot I purchase on Mondays. On this particular Monday, I decided to buy four pots of noodle which would amount to eight stamps. As I mentioned in previous blogs, the numbers four 4 and eight 8 are hugely significant in our Chinese custom, the former meaning ‘death’ and hence misfortune and the latter ‘prosperity’ and hence good fortune. This double stamp deal, therefore, turns misfortune (4) into good fortune (8), which is not a bad way to start the week. However, when I reached Wok, I discovered that they had stopped their double stamp offer (probably due to poor sales recently) and was forced to stick with four stamps. I did not like that and got pretty desperate, but when looked at my loyalty card, I discovered that I had five stamps on it. I quickly requested to change my order to three pots, which made it eight 8 stamps on my card. The deal may have stopped, but the good fortune remains, albeit through a slight tweak. This small trick got me to start the week in high spirits.

I went to the library recently to return some books and I was anxious enough to make sure that I was carrying the ‘right’ number of items, not merely the library items which I was intending to return but also all the other bits and pieces which I wanted to add up to a ‘nice’ number. In addition to the two library books, therefore, I brought six 6 things with me, which made it eight 8, and I figured that after I had returned the two library loans I would end up with six 6 things, both very fine numbers. When I returned the two books, I realised that I probably should stay in the library for a while and take some books out, books that I had been wanting to take out for some time but had not had a chance to, and after returning those two books I discovered that I could still take five books out. I hence went on a search for five cool books and by the time I had checked them out I realised that I had eleven (6+5=11) things with me, another great number. It was pretty tiring carrying five heavy books back home from the library but when I got home I was in a pretty good mood musing over the numbers that I had just witnessed. I may have cheated slightly by making sure I had eight 8 things out when I left home, but the decision to stay behind and check five books out was entirely spontaneous and the resulting sum (eleven 11) totally incidental.

I was sifting through my notes the other night. I tend to be quite messy in the arrangement of my personal space, not that I cannot be bothered to put things in order (though there is probably an element of sloth in my daily routine), but that I prefer to leave things where they are and not shelf them away so that I would not need to dig through my archives to find them again. With my notes, there are always stacks of paper lying around which makes manouevring in my room somewhat difficult (though not impossible). Another thing about having so many stacks of paper is that although I always try my best to put them in good order and not misplace a single page of one document in the pile of another, the flipping of pages is inevitable and my notes are often placed upside down. This does not bother me at all as it does not cause any inconvenience to me or my work, though it can be quite amusing finding some inverted page numbers to which to match corresponding page numbers. Last night, I chanced upon an inverted page number sixty-nine 69 in my dishevelled pile of notes which got me looking for a corresponding page sixty-eight 68 which I found in the close vicinity. This all seems fine except that usually inverted page numbers do not match their consecutive page numbers, which in this case (68… 69) they surprisingly did. I then looked closer and realised that sixty-nine 69 rotated 180 degrees still looks like sixty-nine 69, which is rare in Egyptian numerals. I immediately got interested in finding out which other numbers/digits could be inverted and still look the same and I came up with zero 0 and eight 8, which is obvious since their symmetrical circular shape naturally retains its form on rotation, but the numbers six 6 and nine 9 are truly unusual since they actually correspond to the other on rotation (6 > 9, 9 > 6). The double digits (69, 96), therefore, retain the same shape when rotated half-turn (69 > 69, 96 > 96), which is fascinating. The numerical relationship between sixty-nine 69 and ninety-six 96 is clear, as it is a classic case of numerical inversion which creates a difference of the product of nine 9 and their difference ((9–6)*9=27). Their symmetry on rotation also shows perhaps some non-mathematical relationship, though it may not be coincidental that the numbers six 6 and nine 9 look so similar on rotation as they are products of three. The number ninety-six 96 is also a beautiful one, as it is part of an amazing sequence between eighty-eight 88 and one hundred 100, not to mention a product of eight 8 and twelve 12, both important numbers in numerology.

I recently woke up to find that I had forty-four (44) unread emails in my inbox. As explained before, the number four (4) is hugely unpropitious in our Chinese culture, and forty-four (44) is especially bad. I then started reading them and discovered that my unread emails were divided into three sections: eight (8) + eighteen (18) + eighteen (18). I do not always read and reply to my emails immediately and often there is an accumulation of emails that go back to different chronological phases, and hence this chronological division. It turned out that I had received eight (8) emails today, eighteen (18) from an earlier stage and another eighteen (18) from an even earlier stage, which adds up to forty-four (44). As mentioned before, the number eight (8) and all its permutations are highly favourable in our language, and eight (8) + eighteen (18) + eighteen (18) is a magnificent combination. I have written before about the significance not only of individual numbers but also of numerical combinations like addition. What seemed like an ominous sign turned out at closer analysis to send a somewhat different message. I guess one can interpret these things in two ways (optimist/pessimist), but in difficult times like these it is important to stay positive and avoid self-defeating talk, since positivity can never do harm but can only help.

Another occasion when I discovered that I had forty-four (44) unread messages in my inbox caused concern, though not to panick. As before, I immediately went through them and filtered out all the useless messages (solicitations for money by the US Democratic Party in their fight against Trump, various charity reports and reviews on my activities this year, numerous political flyers that looked pretty but had little substance etc). When I moved all of these messages and those in my spam folder to the recycle bin, I discovered that I had twenty-six (26) useful messages left, which is not bad at all, since it seems that I had deleted eighteen (18) messages and had a combination of eighteen (18) and eight (8) left (18 + 8 = 26), which is a fantastic numeric combination. What seemed like an ominous sign I transformed it into a propitious one. You may say that I am cheating by deliberately removing all the negatives in my life and hereby creating favourable numbers through deceitful manipulation (though I assure you that none of this was deliberate in that I really did have eighteen messages that I did not want in my inbox and wish I had not received), but there is nothing wrong in forcing the negatives out of one’s life and making one’s own luck, especially when times are tough and the situation is bleak one cannot rely purely on chance and has to take a more pro-active approach.

These terrifying days with a highly ominous number (44) looming over me were not fun, though they did motivate me to find different numerical combinations so that I could work my way out of them. Another strange portent occurred to me in the form of numbers, but it was a positive one. Whenever I leave the house, I always count the number of items I carry, since I am paranoid with losing things, and last night I went out carrying six items with me. I always try to avoid carrying four (4) or seven (7) items, since, as explained before, these two numbers carry bad luck in our Chinese superstition. Six (6), on the other hand, is a rather beautiful number that I have always liked, and I have no problem taking six belongings with me whenever I go out. As I was returning home, however, I was notified of the arrival of a new package for me, which left me somewhat anxious, since taking in an extra item in addition to the six that I was already carrying would make it seven things that I would have had to carry (6+1=7), which is a bad numerical sign. When I got to the lodge, however, they told me that I had actually received two packages, which made it eight (8) things in my possession. That was a relief for me, not only because I avoided the number seven (7), but also because eight (8) is a highly propitious number in our culture. As explained before, the numerical alternations between good fortune (e.g. 6, 8) and bad omen (e.g. 7) can be very fine, and on this occasion it seems that I managed to avoid seven (7) and stick with six (6) and eight (8). It was my lucky day.

An almost identical event happened to me right after the one above. Like last time, I went out carrying six things with me and when I came back I discovered that I had a parcel delivery, which made me feel somewhat anxious and uneasy. As explained before, the numbers seven 7 and nine 9 are vulgar and disfavourable in our Chinese (Cantonese) numerical superstition, whereas eight 8 denotes prosperity and is hence highly propitious, which yields a very fine line in terms of numerical fortune-telling. Last time I was thrilled to discover that I had two parcels waiting for me, which not only made me avoid the number seven 7 but also gave me an eight 8. Good fortune does not get better than this. This time I thought to myself that this could not happen again, as lady luck hardly smiles at you twice in a row. However, to my complete surprise and absolute dismay, I discovered that there were indeed two parcels waiting for me to collect. Furthermore, my landlord had left three pens for me to collect (as a gesture of good will), which made it eleven 11 things for me to bring home, another highly positive number. Eight 8 and eleven 11 are both fantastic numbers in our culture, and today’s experience could be summarised thus: 6 + 2 + 3 = 11, which is absolutely beautiful, since not only did I avoid all the bad numbers (seven 7, nine 9), I also managed to hit all the good ones (six 6, eight 8, eleven 11). This is a magical formula. I have no idea what is going on, but this is an amazing stroke of fortune.

Another incident happened which amazes me equally. I was doing my usual grocery shopping on Sainsbury’s (my favourite grocery store in the U.K.) and I happened to make the following order:

I used a discount voucher of 12 GBP for this particular purchase, and those of you who are regular Sainsbury’s customers as well will know that in order to qualify for grocery vouchers, one has to exceed a minimum sum. On this occasion, the minimum criterion was 100 GBP which I had to exceed, yet I did not want to go too far above the threshold than necessary. I hence decided to go just over the 100 GBP limit and ended up with a trolley worth 105.50 GBP. To my surprise, it turned out that my trolley contained numerous discounted items which brought my purchase down by 18 GBP: 105.50–18.00 = 87.50 GBP. This, along with the carrier bag charge (0.40) and delivery cost (1.00), rounded up as 88.90 GBP, to which my voucher was finally added on, which brought my purchase down further by 12 GBP: 88.90–12.00 = 76.90. As explained before, combinations of eight 8 are extremely propitious in our cultural superstition and the fact that I got 18 GBP savings which brought my original trolley down to 88.90 GBP is just breathtaking, especially since all of this was unintentional (I promise!). Furthermore, the 12 GBP deduction was just the icing on the cake, since twelve 12 is another favourite number of mine. This is truly a blessing, and I am glad that I have managed to get through my fourteenth (14) post on numbers (relatively) unscathed. I should be safe for a while, since, as mentioned before, post-14 is pretty smooth. So glad to have survived this rough period. One does not always get this lucky (in fact, one rarely has so much luck in times of crises and desperation). Looks like Lady Luck was finally smiling upon me this time. If only she had favoured me before! Let’s hope that she continues to smile upon me for a little longer.

All integers are divided into even and odd. Even and odd integers hence have different numerical properties. There is one number, though, which seems to have properties of both. This is the number twelve 12. Twelve 12 is an even number and is hence a multiple of two 2 (and of four 4). Yet Twelve 12 is also a multiple of three 3 (and of six 6). The number twelve 12 is hence a very divisible number, since not only is it divisible by two 2, it is also divisible by three 3. In order to illustrate the mixed properties and divisibility of the number twelve 12, I would like to mention the classic movie ‘Twelve Angry Men’ (1959), an all-time classic and, I dare say, an unparalleled achievement in world drama (‘Twelve Angry Men’ was originally written as a TV drama by Reginald Rose in 1954, though it is most famous in its cinematic version in 1959; nowadays it is widely adapted for TV, stage and numerous media, which shows just how influential and popular it is). I watched it in the summer of 2005 and was absolutely mesmerised by it. It was this movie that inspired me to become an academic, since it beautifully and powerfully demonstrates the power of logical reasoning and academic argumentation (I also gather that it is widely used as educational material for leadership courses). It is probably the best legal drama ever, as it portrays a team of jurors (twelve men) who engage in a fierce debate about a murder case which is seemingly one-sided in pointing towards the conviction of a murder suspect. In the American legal system, a defendant can only be declared innocent/guilty if the jury unanimously decides so i.e. all twelve men have to agree that the defendant is innocent/guilty. In this movie, we see how the twelve jurors, eleven of whom initially decide that the suspect is guilty, eventually change their decision due to the brilliant argumentation of the main character (played magnificently by Henry Fonda) and vote unanimously for innocence in the end. The initial vote is eleven 11 (guilty) to one 1 (innocent), which changes to ten 10 (guilty) to two 2 (innocent), nine 9 (guilty) to three 3 (innocent), eight 8 (guilty) to four 4 (innocent), six 6 (guilty) to six 6 (innocent), four 4 (guilty) to eight 8 (innocent), three 3 (guilty) to nine 9 (innocent), two 2 (guilty) to ten 10 (innocent), one 1 (guilty) to eleven 11 (innocent), and finally zero 0 (guilty) to twelve 12 (innocent). A brilliant and dramatic change of tide, and the progress of the movie is marked by the numerical patterns which divide the twelve jurors: at the beginning, it is one 1 versus eleven 11, as only one juror (played by Henry Fonda) is unwilling to declare the defendant guilty without discussing it first. He proposes some counterarguments and another juror is persuaded and changes his vote from guilty to innocence (two 2 versus ten 10). More counterarguments are proposed and three jurors vote for innocence (three 3 versus nine 9), which marks a quarter of the movie. Another juror is persuaded and the movie reaches a third of its way (four 4 versus eight 8). The pivot is reached when half of the jurors vote for innocence (six 6 versus six 6), and then the movie symmetrically unfolds and concludes itself: eight jurors then vote for innocence (eight 8 versus four 4), which marks two-thirds of the movie, then nine jurors vote for innocence (nine 9 versus three 3), which marks three-quarters. Then only two jurors remain unconvinced that the defendant is innocent (ten 10 versus two 2). Finally the one juror who insists on the defendant’s conviction (one 1 versus eleven 11) gives way, and the movie ends with all the jurors voting unanimously for innocence (zero 0 versus twelve 12). Only the number twelve 12, given its high divisibility, can yield such small, subtle, symmetric and dramatic gradation. Absolutely fantastic number. I have always liked the number twelve 12, since it is a fantastically divisible number, which makes it compatible with many numerical combinations. The dramatic sequences in ‘Twelve Angry Men’ are based precisely on these numerical properties as we see numbered members of the jury engage in a fantastic intellectual debate (as mentioned in the previous blog, I love ‘Twelve Angry Men’, which is an amazing demonstration of the power of reasoning and intellectual debate). The dynamics of the debate can be shown to correlate with the jury numbers, as the jury members are numerically arranged and their jury numbers are often numerically significant. Number 1 is the organizer of the jury who is regularly referred to as Mr Foreman. Number 2 is a relatively small and modest fellow who has a somewhat boyish look and high-pitched voice. Number 3 is the main antagonist in the movie who stubbornly insists (for personal reasons) that the defendant is guilty. Number 4 is another main antagonist, but his sophisticated and cold reasoning proves to be not only a contrast to Jury number 3 but also a major difficulty and threat to all those who try to argue that the defendant is innocent. Jury numbers 3 and 4, therefore, form a natural pair, as they have such contrasting styles and are the last to be persuaded. Numbers 5 and 6 are both relatively gentle fellows who are persuaded relatively early on and hence form another pair. These two pairs (5 + 6/ 3 + 4) have a very stark contrast between them. Number 7 is a disinterested fellow who is not really interested in the debate and makes cheap remarks here and there just to get himself out of the case. His lack of interest and team ethic correlates with the fact that his number (7) is right at the centre of the numerical sequence and hence does not form any pairing with any one else. Number 8 is the main protagonist, played magnificently by Henry Fonda. He is the leader of the cause as he tries to convince the others that the defendant is innocent. Number 9 is an old man and turns out to be Fonda’s greatest ally, as he is the first to be persuaded and supports Fonda throughout the movie. They also shake hands and close the movie right at the end, so numbers 8 and 9 definitely form a pair. Number 10 is another old man, though much ruder, louder and rougher than number 9 as he also stubbornly believes that the defendant is guilty based on personal prejudice. Such similarity and contrast could be used to argue that numbers 9 and 10 form a pair. Numbers 11 and 12 are both gentle fellows who are persuaded at different points of the debate which happen to be numerically significant, since Jury number 11 is the fourth to be persuaded (4 (innocent) vs 8 (guilty)) while Jury number 12 famously changes his vote towards the end (4 (guilty) vs 8 (innocent)). Such symmetry also makes them a natural pair. ‘Twelve Angry Men’ hence plays on these numerically significant patterns which add beautifully to the flow of the debate. Magnificent.

In this post, I have discussed some of the ways that numbers determine and govern our lives, especially when interpreted under common mathematical assumptions and traditional cultural and religious beliefs. It must be said, however, that not everyone holds the same assumptions, and this is shown in the following quote:

‘Unlike most people, Taylor (Swift) considers “13” her lucky number in that she was born on the 13th, turned 13 on Friday the 13th, her first album turned Gold in 13 weeks and her first #1 song d a 13-second intro.’

‘At many of her concerts she comes out with a Minnesota Vikings jersey with the #13 on the back. The Vikings had it specially made for her.’

I pointed out before that the number thirteen 13 was an unlucky number in western Christian culture and it is certainly a number that I have tried to avoid. It turns out, however, there are people like Taylor Swift who likes this number for personal reasons and maximises exposure to it (see above). She is a brave girl, much braver than me. I think I’ll stick with eight 8, eleven 11 and twelve 12 for the moment. Although I am no Christian, I wish her all the best of luck in all her endeavours. With a voice as powerful as hers, I am sure that she can handle all that comes before her. Much better than me anyway.

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