在Autistic Savants的片段中,我們看到自閉天才計算星期數。其實這些計算人人可做,現在不妨介紹一個簡單戲法,讓大家一分鐘內學會計算2007年任何一天的星期數。
第一步:2007的密碼 -> 1
第二步:由一月至十二月的密碼 -> 6,2,2,5,0,3,5,1,4,6,2,4
第三步:(年碼+月碼+日期)÷7,餘數就是答案(1=星期一...... 0=星期日)。
例子:
2007年12月31:(1+4+31)÷7=5...1,星期一
11/7/2007補記:
謝謝道士兄另文解釋,轉貼於此,方便讀者參考。
7/11/07
日曆計算術
昨日看過日曆計算2007後﹐ 便想講講其中道理。起初﹐我確實也覺得有點不可思議﹐但係稔稔下就發覺不外如是。第一次留意到日期的變化﹐已是小學的時候﹐因為年年生日都差不多在考中期試﹐不跌落五﹑六﹑日就實無得玩﹐看了幾年﹐發覺每過一年﹐星期幾便順序推後一日﹐但是後來過多兩年又發覺有不靈的時候﹐嘻﹐還是失望居多。
今天看起來﹐便覺得簡單﹐就是潤年第二十九日作怪﹐其實只要有小學數學程度﹐就足以明白當中玄妙。一年365日﹐而能夠整除7的就只得364﹐那一天便是把星期幾推後一日的原因。亦因四年一潤﹐所以28年就成一個圓滿的週期。例如00年的年碼是0﹐01﹑02﹑03年的年碼也會是1﹑2﹑3 respectively﹐但到了04年﹐由於潤年加了一日﹐因此年碼就是5﹐而不是4﹐一﹑二月卻仍是要用4去計。(也可說﹐年碼在潤年的一﹑二月要減一。) 順延而知﹐04-07的年碼是: 5﹑6﹑0﹑1. 08年不是2﹐而是3﹐08-11的年碼就是3﹑4﹑5﹑6. 如此類推。為了方便計算﹐如過把潤年的年碼記下﹐如00﹑04﹑08﹑12﹑16﹑20﹑24年﹐它的排列必定是:0531642(不用硬記﹐0-6﹐減 2減2逆向走)﹐因此2028年的年碼﹐就必定是0﹐2032就是5...如此類推。
年份沒有問題﹐便到月﹐月份日子除七的餘數﹐便是: 6, 2, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4 這系數的來源﹐如何來呢? 月份的日子是: 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31. 每個月日子除七的餘數是: 3, 0, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3. 現在想0-6﹐且先不問為何一月是6﹐但6+3日(餘數)﹐便是: 6﹐0﹐1﹐(2)﹐由於二月能整除因此三月的第一日也會和二月第一日落在同一個星期天。三月後﹐2+3日= 2﹐3﹐4﹐(5)﹐ 四月後: 5+2日= 5﹐6﹐(0)﹐五月+3: 0﹐1﹐2﹐(3)...如此類推。
至於日﹐也不用解釋了罷! 以今年為例﹐1月1是星期一﹐年碼+月碼+日碼=(1+6+1)/7=1. 月份第一個數字是6﹐就是要來adjust加完年數後能整除﹐其實如過不是6,也可set過一系列的月數﹐又重新set過年數﹐還能得到同樣效果。第一天由於剛是星期一﹐既可循公式計今天是星期幾:(1+5+11)/7=3﹐甚至既知一月一是星期一﹐月碼已知6=1﹐那麼七月的月碼既是5﹐七月一便會是早一天 = 星期日(0) + 日子餘數11/7=1...(3). 也會有相同答案。
潤年怎計呢? 4除得盡的﹐但又不是100隨得盡的﹐便是潤年。能給400除得盡又是例外﹐因此1900不是﹐但2000是﹔2100不是﹐但2400是。
嘻﹐明白歸明白﹐我卻懶得記這堆數字﹐要扮天才不如看多本書。
Posted by 道士 at 7/11/2007 09:35:00 AM
1 comments:
zostrianos said...
謝謝你的解釋。我本來還以為有一複雜公式,原來沒有。但閏年的一、二月密碼要減一,因為年碼要在三月才生效,故頭兩個月碼便要減去一日。另外,「且先不問為何一月是6」,我想6是由2000年1月1日的星期數來決定的,那天該是星期六:
6-0(year)-1(day)=5(month code)
但2000是閏年,故平年的月碼要加一,即6。
7/11/2007 11:38:00 AM
日曆計算2007
No classics, memos will do
Je ne cherche aux livres qu’à m’y donner du plaisir par un honneste amusement: ou si j’estudie, je n’y cherche que la science, qui traicte de la connoissance de moy-mesmes, et qui m’instruise à bien mourir et à bien vivre.-- Montaigne
According to a survey conducted by the Faculty of Education of HKU, Hong Kong’s proportion of students who would read for their own pleasure outside school is the lowest in the world: only 20% of students have the daily habit of reading for pleasure in Hong Kong, compared with a global average of 40%. Another survey indicates that most Hong Kong students spend less than 30 minutes on reading every day, and what they read are mostly comics, jokes, and leisure readings of low literary value. To further clarify the reading habit of Hong Kong adolescents, I shall cite the results of one more survey. Conducted by Breakthrough Organization from January to March in 2007, this latest survey shows that 75.9 % of readings among the youth of Hong Kong belong to fiction and prose, and only 4.9% of the youth have ever read books about society, culture and politics.
While the above figures tell some plain facts concerning the reading habit of our young people, what I shall say below may shed some light on the overall reading taste of Hong Kong citizens, and at the same time reveal the somewhat tragic and long-neglected career of some respectable independent bookshop owners. I was told personally, to my utmost surprise, by the owner of a ‘second floor bookshop’ in Mong Kok that, over the past few decades, the number of regular clients of New Asia(新亞書店), almost the only local bookshop that still sells quality second-hand books of literature, history and philosophy, has never exceeded 100, which more or less reflects that only an infinitesimal, and even shameful, proportion of the literate population in Hong Kong love humanities.
Why read?
Hong Kong students, nay, Hong Kong people, have long been criticized as lacking in culture (in the sense of a refined understanding and appreciation of liberal arts), and preferring shopping and entertainment to reading. But in order to maintain a competitive edge in this knowledge-based world, good skills of reading and wide horizons embracing diverse aspects of culture seem to be indispensable. Thus comes the education reform, and in this case, particularly ‘Reading to Learn’(one of the four key tasks in Hong Kong’s curriculum reform), to deal with the problem. Let us now examine, from the point of view of the education reformers, why reading ought to be promoted.
According to a letter by Mrs. Fanny Law, former Permanent Secretary for Education and Manpower Bureau, the promotion of a reading culture in school can address two of the major concerns in education, namely, ‘language proficiency and learning capacity’. A document entitled Learning to Learn - The Way Forward in Curriculum, published in 2001, also contains some ‘key messages about reading’ from the Curriculum Development Council. It is said that reading is not just for the improvement of language proficiency, but serves many other important purposes, which add value to the quality of our life, including reading for interest, appreciation, enrichment of knowledge and experience. On the website of the Education Bureau, a teaching resource package is offered to help teachers implement ‘Reading to Learn’ at school. In this package, the manifold purposes of reading are stated clearly. Apart from improving language proficiency, as repeatedly mentioned above, reading also serves other purposes like locating information, understanding instructions to perform certain tasks in our daily life, keeping in touch with friends through correspondence, reading for leisure and enjoyment, and developing our powers of imagination, creativity and appreciation.
To these purposes I am not inclined to object, for they are all beneficial in themselves. And yet, I cannot help wondering if, with ONLY these purposes in mind, we have done full justice to reading, a praxis so crucial to the construction of knowledge, the cultivation of virtue, the flourishing of life, and the quest for wisdom. All the purposes of reading set out by the official documents of the education reform not only strike a rich vein of pragmatism, but also betray philistinism: they seem to fit in better with the curriculum of a training program that prepares students for work than with that of primary and secondary schools, where students are more reasonably supposed to learn how to live as good and rational persons, for whom art and literature may hold greater appeal than money and clothes, than only to acquire such skills as necessary for being competent employees in a corporation, as if they were at school only to get themselves well-equipped for ‘the road to serfdom’ lying ahead. Consider how exceedingly strange it is to include ‘understanding instructions to perform certain tasks in our daily life’ as a purpose of reading, while leaving out, deliberately or not, the more noble ones like improving our moral virtue or looking for wisdom that helps us live better. But even these latter ones, though far more worthy to be set forth by any sane educators, are not the ultimate purpose peculiar to reading: rather, we should read for and only for ourselves in the sense that by experiencing vicariously the life and thoughts of others we augment considerably our inner self.
True, reading may well improve language proficiency, and serve many other practical purposes; yet reading, while incorporated in the school curriculum, should not be taken simply as a tool for achieving these worldly ends. Instead of just rendering some ‘useful’ information accessible, and ‘practical’ training available, to students, genuine education should rather inspire them with an ardent and noble passion for truth, virtue, and wisdom. Though it must be admitted that, to set forth these apparently high-flown ideals, I may be suspected of indulging in empty rhetoric, yet, caught in the dilemma of two evils, I would unhesitatingly put higher emphasis on such ideals as pertaining to life as a whole than on those instrumental values that would have more appropriately been attached to vocational training than to education proper, since an educational system that does not aim at lifting students, both intellectually and morally, to a higher plane of existence, and dispersing, so to speak, the mist of ignorance and folly, cannot produce any mental disposition than that of blind obedience to, even bogus, authority, and benumbed acceptance of recurrent injustices, and on this account the system can no longer deserve to be called ‘educational’.
If reading can serve some more elevated purposes, why keep the teachers from knowing them? There might be two reasons. First, I doubt if it is to instill into the students some false conception of reading, owing to which they would never take care to seek enlightenment, instead of entertainment, from books, nor could they, being unaware of the intellectual hierarchy of texts (upon which I shall enlarge in the next part), know how to reach for the really great authors. In this manner, reading is so debased by our education that no students, as long as their intellectual growth is concerned, can truly benefit from it. But this is not entirely undesirable. Quite the contrary: the ruling class, including the business tycoons, would be happy with a multitude of non-reading subjects. A few steps of reasoning suffice to explain: the less they read, the less they think; the less they think, the easier they are manipulated. QED.
Second, if the vulgarization of reading is not intended, presumably for the convenience of control, by those who draw up the educational scheme, they must be ignorant themselves of the more elevated purposes of reading. I would therefore suggest that they, the education officials, make no haste to teach others, until they are properly taught. After all, in a mercantile sort of place like Hong Kong, where the thirst for interests always supersedes the reverence for learning, we must be cautious enough to take the proclaimed objective of any government project, be it educational or cultural, with a pinch of salt.
We should also note that the documents cited supra are marked by anti-intellectualism and philistinism. For instance, do we need any educators to tell us the reason why we read, trivial as it is, is to ‘keep in touch with friends through correspondence’? This is as absurd and anti-intellectual as to ‘teach’ someone that caviar can in fact be used very effectively to feed the swine. As to philistinism, nearly all the purposes of reading given above can easily boil down to the fulfillment of the conditions that guarantee students’ competence in their future work, but alas, such qualities as are more worthy of liberal education, namely wisdom, virtue, and a keen aesthetic sense, are consigned to the limbo of oblivion. For me, a passionate reader for more than twenty years, the prime reason why we should read is not as practical as the education officials promote, nor is the effect of reading as measurable and palpable as they intend. We read, I would say, primarily because we need books, immortal embodiment of human nature, to understand ourselves, thereby learning to live better. To conclude my critique hitherto, I would like to quote Flaubert's remark on the art of reading: ‘Do not read, as children do, to amuse yourself, or like the ambitious, for the purpose of instruction. No, read in order to live.’ What a pity that the precepts of our officials fall either into the category of ‘childish reading’ or that of the ambitious one.
Major policy on the reading culture in school
As I have remarked supra, our education officials think that reading should be promoted, by and large, for the sake of language proficiency, and learning capacity related to practical and social purposes. It follows that reading is just as functional and instrumental as any other teaching kits. No doubt we cannot expect, while our teachers coldly treat books as some inanimate tools, that their students would love books as affectionately as their friends, or pay them the due respect that they would to their mentors. Reading being instrumental to some practical ends, the way it is promoted in school can only be no less target-oriented. And no less futile, I should say, so far as reading’s lifelong impact upon the students is concerned. The EMB (now the Education Bureau) documents have provided schools with ample suggestions and guidelines on the implementation of ‘Reading to Learn’, of which I shall review some.
To begin with, let us examine the reading materials. It is suggested that students’ reading habit not be confined to literary works; that they read a wide variety of text-types such as newspapers, magazines, and non-printed materials from the web and CD-ROMs to keep themselves updated on current affairs and newest information; and that they not omit to read even maps, signs, statistics, yearbooks and charts so as to ‘cope better in their daily life’, and also memos, reports, and speeches ‘for further study and work’!(Myths & Principles) Curiously, while we all concern ourselves with HOW MUCH we ought to read, as if reading many books, be they classics or bestsellers, could infallibly make us wise, nobody seems to care about WHAT to read. After all, reading rubbish in quantity cannot turn us any wiser or more knowledgeable, just like owning a kiln of bricks does not necessarily make one a mason.
For clarity’s sake, let me enumerate once again the reading materials proposed by our most scrupulous education officials: newspapers, magazines, websites, CD-ROMs, maps, signs, statistics, yearbooks, charts, memos, reports and speeches. We can easily imagine students possessing such ‘reading skills’ will be so much grist to the mill of Hong Kong’s employers, particularly those in the business sector. Strange to say, instead of motivating students to read for their benefit first-rate literary works which, as the findings of a survey show (see supra), they rarely read, our education officials choose either to encourage the students to read what they, in effect, already read in abundance on their own initiative (magazines, websites, for instance), or to urge upon them readings of little, if any, worth, among which we can name maps, signs, statistics, yearbooks, charts, memos, and reports. Among the vast treasure of human culture, are these the most valuable things that teachers ought to recommend their students to read? Is it still education, be it good or bad, to tell the youth to spend their precious time in vain on such readings, while life is short? I would let you answer at your discretion. Not exactly rocket science.
Remember, practical knowledge of daily skills and sufficient awareness of current events are good only in the sense that we are enabled by them to get on with the world, but so far as getting on with ourselves is concerned, they are of no avail at all. There cannot be any education proper if what the teachers aim at imparting is only useful skills of daily life, but not the way to make sense of life. To be honest, I dare not think of what kind of society I will be living in, surrounded by fools bred among nothing but newspapers, magazines, websites, CD-ROMs, maps, signs, statistics, yearbooks, charts, memos, reports, and speeches. Hereto I want to add but one more remark: it is indeed superfluous, or even somewhat malevolent, to warn students against reading too many ‘literary works’, while actually they are to busy themselves reading rubbish all the time.
Secondly, let us consider the teaching of reading skills. The resource package offered by the Education Bureau advises that essential reading strategies and skills (skimming and scanning, for instance) should be taught along with word identification. These skills include strategies of predicting, confirming, monitoring, reflecting and evaluating. As tools for comprehension, they are fine. But to say that these skills are fine is one thing, it is, nevertheless, quite another to advise them to be taught. The education officials, I would say, are just no less mistaken and misleading as regards WHAT to read than HOW to read. After leafing through nearly all the documents concerning ‘Reading to Learn’ available on the Web, I have not yet come across a single line that tells how to distinguish classics from rubbish, nor have I learnt even some vague idea about how to read well. The officials seem to care so little about the quality of reading materials that it suffices for their clear conscience to merely direct students to various sources of text types, in spite of the fact that, among what they put at the disposal of students, hardly anything is worthy to be read. As regards reading skills, so much the worse. In the light of what the officials have proposed to teach, I believe that they have confounded the elementary instruction of reading, which it is groundless to single out for special treatment on the teachers’ part, with the more valuable teaching of reading well, which is as yet neglected by our educators. In other words, the officials are as much unaware of the profound difference between reading and reading well as between good and bad books.
It is indeed questionable whether the skills as mentioned in the documents should be taught in school. If so, to what good? Drawing upon my own experience, I find the teaching of these reading skills quite unnecessary for students overall. The fact is that many children of normal intelligence can, in due course, develop these elementary skills independently and spontaneously, just as I did while a child, provided that they are intrinsically motivated to read (with which I shall deal shortly afterwards). And for those more advanced in school level, the recommendable reading skills should not be such as only to help students read fluently business letters or efficiently cull information from lengthy texts, which has been the sole concern of teachers and students for decades in Hong Kong. Ideally speaking, it is the art, not techniques, of reading that teachers should impart to the senior students. By ‘the art of reading’, I mean the habitual exercise of our mind to make critical responses to a text, to appreciate its intellectual and aesthetic values, and, most important of all, to relate the text, however long ago it was written, and however distant is the place where it was composed, to our present life so as to establish continuity with the past and the otherness. In so doing, we succeed in elevating ourselves to a higher and broader level of experience, and laying open, as it were, the way back to Paradise, having drawn ourselves out from the status quo of transient and limited being. Such is the art of reading that can give full play to educatio, the Latin word from which ‘education’ derives, and which, in its most literal sense, signifies the action of ‘drawing out’.
Thirdly, let us deal with the method of motivation our education officials suggest. Teachers are told that all students, whether they be interested in reading or not, need to be motivated in two ways: at the outset, ‘by material rewards like prizes, certificates, etc’, and afterwards by creating ‘opportunities for students to enjoy reading and demonstrate their achievements in reading’ in order to secure intrinsic motivation. These strategies can be exemplified by the so-called reading scheme (like ‘Best Reader of the Year’) which usually awards to students, who have read a certain number of books within a certain period of time, something like certificates and prizes (corresponding to the first type of bait, namely material rewards), and which also requires students to produce book reports or create reading profiles containing such tasks as oral presentations, story re-telling, role-play, model-making, picture drawing, etc. (corresponding to the second type of bait, i.e., demonstration of their achievements) Now we should first ask: are the guidelines given above really helpful in motivating students to read? The answer is affirmative according to a survey conducted in 2001 by the Education Department on the reading habits of students. The findings reveal that in primary schools, students appear to spend more time on reading in those schools that offer awards to encourage reading.
Nevertheless, I invite you to look deeper into the long-term consequences behind the apparent success about which our educators are often too ready to be complacent. This is mere common sense that whatever habit, especially the mental one, we acquire in childhood will be deep-seated in our nature for a lifetime. Seeing that Hong Kong students have been enticed into reading since childhood by certificates, prizes, and ‘demonstration of achievements’, which must depend on others’ approbation and recognition, alas, they will be led astray for ever without running across the real nature of reading: solitude, independence and silence. Let us hear what the gurus of reading say: for Harold Bloom, reading is rather ‘a solitary praxis’ than ‘an educational enterprise’, and ‘it matters, if individuals are to retain any capacity to form their own judgments and opinions, that they continue to read for themselves’ ; in The Uncommon Reader, George Steiner, one of the greatest literary critics of our time, tells us that ‘genuine reading demands silence’. What is the point of quoting them? Here are the illuminating opinions on reading penned by two of the greatest readers in our time, and it is only by contrasting their opinions with our education officials’ that we can debunk the prevalent creed of reading in Hong Kong.
I have to side with the gurus to argue that reading is essentially a solitary act in which we have to learn how to think (for this, silence is a prerequisite) and judge independently; it is therefore quite ironic to promote reading, which consists in solitude and independence, by means of extrinsic motivation and external approbation. In spite of the temporary success concerning the reading habit of primary school students, as reported above, the general lack of interest in serious reading among the Hong Kong populace, I believe, must partly be attributed to the inadequate use of enticements in school, and partly to the prevailing apathy towards books among the teachers themselves. In regard to the former, students ‘trained’ to read for material rewards would not care for books anymore when they get nothing in return, or simply outlive the childish desire for ‘useless’ certificates. With respect to the latter, the Education Reform is once more to blame, for the teachers who, apart from their routine work, have to put in extra time to develop cross-curricular activities or a school-based curriculum, as the reform requires, are already so overworked as to be deprived of all leisure and strength that could have otherwise been devoted to reading. Is it reasonable to expect that teachers, in the circumstances, can still keep on reading and sharing that mythical ‘joy of learning’ with students?
Analogous to virtue, reading is neither to be taught by words, nor by enticement, but by deeds. Socrates, when asked to declare his notions of justice, replies, ‘Haven’t you noticed that I never cease to declare my notions of what is just? I declare them by my deeds, anyhow, if not by my words. Don’t you think that deeds are better evidence than words?’ In my opinion, the only justifiable motivation for students to read is the unaffected and insatiable passion, on the part of teachers, for books, and good books alone, not whatever rubbish one happens to find in the newspaper columns or magazines. Arguably, the present practice of reading, marked by extrinsic motivation and pragmatic ends, will bear far less fruit in long term than when students are moved to read for themselves by teachers’ genuine love of books, though material rewards and show of achievements may produce some immediate and observable success. But if lifelong education is to be sustained, if the objectives of our education can be taken at their face value, and if educators ought not to strive for measurable results of which they can readily boast, I must call to your attention that the success our schools have hitherto achieved is somewhat overstated.
Examples of school-based practices
From all these false conceptions of reading, it naturally results that the grand educational project our officials have formulated cannot yield much healthy fruit. In this part we will briefly review three examples of school-based practices found in the resource package of the Education Bureau website, presumably held to be the best models on which schools can plan the implementation of ‘Reading to Learn’. Instead of commenting on the three projects separately, I shall make some overall remarks after describing them all in broad outline.
The first project, entitled ‘Inter-disciplinary Studies’ (Levels: S1-S3), seems to be designed by the education officials themselves, for the source is left unmentioned. It is essentially divided in four parts: first, in two English lessons allocated for this reading program, students are asked to read some materials and perform the tasks designed by various subject teachers; second, reading files are kept to review the progress; third, the reading skills learnt in these two lessons are to be assessed formally in the examination; fourth, students are required to read books chosen from a list of non-fiction graded readers. The second project , entitled ‘Census 2001’ (Levels: S1-S7), comes from Buddhist Ho Nam Kam College. The objective of this project is to promote civic education through reading, and the reading materials are selected from various websites related to population census. The task is no more than discussion and doing a worksheet with nine simple questions. The last example is called ‘Reading Award Scheme’ (Levels: S1-S4, S6), from HKTA The Yuen Yuen Institute No.2 Secondary School: students are here required to read 10-11 books at minimum; book reports are to be submitted afterwards and their reading ‘achievements’ are recorded in the Student Handbooks.
Having thus outlined the three projects, I am now to subject them to a critical review. So obvious is their unanimous stress on the demonstration of tangible products (such as records and worksheets), as well as their shared indifference to the choice of reading materials, that we should not fail to note that the three examples given above are perfectly in line with the mind-set, as discussed previously, of the education officials themselves. Doing tasks for different subjects, filling in worksheets after browsing through this website or that, and handing in book reports to the school, are nothing new under the sun. What is the point of highlighting ‘Reading to Learn’ then? Even back to a thousand years ago, at the time of the Northern Song dynasty, did a student not read likewise, without the prompting of the ‘key task’, in order to learn? So are we being told that this is what ‘Reading to Learn’ can achieve at its best? Well, I simply do not think the result is impressive enough to be proud of: reports, worksheets, records, etc, continue to dominate, nay, disrupt in the field of reading, while reading itself is forgotten. Can any of the officials in charge of the Education Reform, with all sincerity, say that students, having these flat and insipid projects thrust upon them, will take to reading afterwards? And even if they do, what are they likely to read? Websites? Newspapers? Magazines? Bestsellers?
But upon our inspection, the Education Reform, in so far as reading is concerned, seems to attend less to the interests of students than those of employers: instead of curbing cultural vandalism, it takes further steps with the crowd to reinforce it so much so that classics are leveled down to go hand in hand with newspapers, yearbooks, reports, statistics, charts, and memos, most of which being commercial stuff of no intrinsic value. Students are exhorted and trained to read for purposes more compatible with the need of the Hong Kong business sector than that of their own souls. Hardly convinced of the merit of reading in this way, schools only go through the motion of following the trend set by the officials, and keep on designing perfunctory school-based projects to little avail. Whether our students are thus manipulated to satisfy the needs of a certain influential social stratum, I cannot say for certain, but the making of a competent employee for a corporation, I firmly believe, more often than not proves to be the undoing of an authentic reader for himself.
Autistic Savants
1. Can you tell a savant from an idiot?
2. An extraordinary person who practically memorizes everything
3. You don’t have to be handicapped to be different. Everybody is different.
淺談中世紀的記憶秘術
記憶術在今天漸趨復甦,坊間課程更如雨後春筍,其招徠學生(即顧客)的方法則往往訴諸功利目的,如“應付考試”、“有助事業”等。但記憶術實源遠流長,最早可上溯至公元前五百多年的古希臘,到中世紀更一變而為倫理學,再與猶太教神秘哲學結合,二變為包羅天下知識的字母符號系統,不但上承希臘羅馬的雄辯術傳統,更下開笛卡兒、萊布尼茲的現代科學方法,絕非今天那種以市場主導的所謂“超級記憶術”可相提並論。我寫這篇文章,旨在扼要地說明記憶術在中世紀的變化,並解釋它和中世紀人思維模式的關係,最後再通過與中世紀的對照,反省一下現代人對記憶和記憶術的態度。
記憶術的創始人相傳是古希臘的西蒙尼德(Simonides of Ceos)。 據西塞羅在《論演說家》(De oratore, II, lxxxvi, 351-4)所記,西蒙尼德出席一宴會,那宴會廳突然倒塌,被壓死的人面目模糊,無法辨認;但西蒙尼德記得他們的位置,於是便把座位次序和面孔聯想起來,藉以分辨屍體是誰,由此他領悟出一套以形象和位置為基本元素的記憶術。最早期載有此術的著作是以下四種﹕(1) 阿里士多德的《論記憶及回憶》(De memoria et reminiscentia);(2) 西塞羅(Cicero)《論演說家》(De oratore);(3) 昆體良(Quintilian)《修辭教育》(Institutio oratoria);(4) 無名氏的《獻給赫倫尼》(Ad Herennium)。
四書詳略不同,而最清晰詳盡的則是《獻給赫倫尼》。此書大約成於公元前86-82,作者是一修辭教授,全書以一類似教科書的形式,涵蓋了修辭演說的五個範疇,其中第四項就是記憶。這兒我們要了解,在古希臘羅馬時期,學習記憶術的目的不是為了應付考試或當作娛樂表演,而是為了在演說時(主要用於法庭上的辯論)能流利無礙且一字不漏地講出所有要點,所以記憶術就順理成章屬於修辭學的範疇了。
根據《獻給赫倫尼》Ad Herennium, III, xvi, 29.,記憶術由位置和形象組成(Constat igitur artificiosa memoria locis et imaginibus) 。所謂“位置”(loci),就是一個我們容易記憶的地方,如房間、走廊等;“形象”(imagines)則象徵我們要記的事物。記憶的方法就是把“形象”擺放在“位置”之上,我們要回憶時,就在腦海中默觀那坐落在既定位置的形象;如是者我們就可通過一連串的形象,把大量事物按其擺放次序回憶起來。據說古羅馬作家塞尼加(Seneca the Elder)就是用這種記憶術,一口氣記牢二千個名字的。以下我嘗試把記憶術中“形象”和“位置”這兩大元素的特點用一圖表列出﹕
為說明如何運用記憶,《獻給赫倫尼》的作者還舉了兩個例子。第一個例子說明如何記憶事物(memoria rerum),即記憶內容重點﹕假設有人因遺產問題被毒殺,事件涉及很多證人,而你是辯護律師,那麼當你要記憶上述內容時,就要想像一個睡在床上的病人(即死者),身邊站着被告,那被告右手拿着杯(象徵毒藥),左手持記事板(代表遺囑)和公羊睪丸(“睪丸”的拉丁文為testiculus,跟“證人”testis發音相近)。如此,你就可用一個圖像輕鬆記下一堆資料了。至於第二個例子,主要用來說明“逐字記憶”(memoria verborum),由於這種記法較難亦較少用,對後世影響不大,故這兒從略了。 詳情可閱Ad Herennium, III, xxi.
到中世紀,《獻給赫倫尼》一書被視為西塞羅所作,其權威和影響便更大了,初期尤以在北非的修辭學者圈子中流傳最廣。但到羅馬帝國滅亡後(476),記憶術便似乎逐漸失去價值:一方面因為社會動盪不安,大家已不再有耐性安心地聆聽長篇大論的演說;而另一方面,學問已退守深山修院之中,修辭和雄辯的作用也顯得可有可無了。
到十二世紀,西塞羅的《論發明》(De inventione)和託名為西塞羅所作的《獻給赫倫尼》經常被相提並論,例如前者叫“第一修辭”,而後者則被稱為“第二修辭”,由是載於《獻給赫倫尼》的記憶術便發生了一個很有趣的變化﹕由修辭學一變而成倫理學。這種變化的起因,主要是源於在《論發明》一書中,西塞羅把“記憶”視為“智、義、勇、節”四宗德中的“智德”(Prudentia)一部分,於是記憶術便可從一個倫理學的角度去研究了。這個趨勢在士林哲學中得到確認,因為大雅博(Albertus Magnus)和多瑪斯(Thomas Aquinas)在討論記憶術(ars memorativa))的作品中,都不把它視為修辭學(像古典時期),而視之為智德的一部分。這種帶有道德價值的記憶術是中世紀一大特色,也是古代及現代人所想像不到的。
我認為記憶術之所以能如此“怪異”(從現代人或古典修辭學者的角度來說)地跟倫理結合,其實表現了中世紀文化的兩大特點﹕
(一)中世紀文化要在整體結構中理解,我們不能把某一文化活動領域孤立出來,所以中世紀的哲學、神學、科學、法學,不像今天那樣各有各的專業語言,相反,那時各門學科其實都是基督教文化語言中的一個“方言”,不同學問根本是相通的。 中世紀人關心的,是永恒的真理、天主的旨意和靈魂的拯救,所有個別文化領域,都應該從這種中世紀獨特的思維習慣中尋找意義。既然學問間的界限本來就是模糊的,那麼記憶術由修辭變成倫理便一點也不值得詫異了。既然哲學可以是“神學的婢女”,那麼記憶術同樣也可以是“救贖的工具”。
(二)中世紀文化有很強烈的象徵主義:當時的人相信,可見的自然界是整個看不見的世界的象徵,而對可見事物的思考,實在是為了在一個更高水平去揭示永恒世界的奧秘。 簡而言之,“以有形指涉無形”就是中世紀人的思維習慣,所以大敎堂(有形之物)象徵了宇宙的結構和秩序(無形之理);但丁在《飲宴》Convivio, II, i.中亦提示讀者在詮釋文字時,可找出四重意義──即字面(litterale)、比喻(allegorico)、道德(morale)和超越(anagogico)意義──而“字面意義(按﹕即有形)永遠是其他意義(按﹕即無形)的主體和質料,我們不可能在掌握字面意義之前,便理解到其他意義。”(Onde con ciò sia cosa che la litterale sentenza sempre sia subietto e materia de l'altre, massimamente de l'allegorica, impossibile è prima venire a la conoscenza de l'altre che a la sua.) 記憶術的特點,正是利用可見的形象承載不可見的觀念,這和中世紀人的思維是一脈相承的。所以當記憶術被視為倫理學去理解時,人的各種抽象的、無形的善惡特性便搖身一變成為形象鮮明的“角色”了,例如“崇拜偶像”(Idolatry)此一抽象的人類罪性,便由一個被割掉耳朵,面容哀傷兼雙目失明的妓女形象來代表。Yates F. The Art of Memory, London: Pimlico, 1992, pp.105-6.
這時,記憶術的作用已不是演說,而是“拯救自己靈魂”。彭岡巴諾(Boncompagno da Signa)的《最新修辭學》(Rhetorica Novissima)寫於1235年,在此書有關記憶的章節中,作者提及了一種特殊的記憶──對天堂和地獄景象的記憶。緊接於此的,自然是對各種德行和罪性的記憶了。天堂和地獄的“景象”,成為了記憶術中的“位置”(loci),而德行和罪性就是各式各樣的“形象”(imagines),人通過這種記憶,就可指導自己的行為,時時刻刻行善避惡,找到通往永生的方向。至此,古典記憶術已完全被中世紀的基督教文化吸納且轉化了。
上文對《最新修辭學》一書的介紹,其實已為記憶術的轉變提供了背景,現在再讓我們看看在士林哲學中,學習記憶術到底有何意義。
聖大雅博在《論善》(De bono)一書中討論過記憶術,他大致上承襲了《獻給赫倫尼》的記憶方法,即利用形象以隱喻(metaphorica)的方式來代表本物(propria),藉以輔助記憶。這兒我想帶出一個也許只有在中世紀才成“問題”的問題﹕士林哲學既然崇尚理性、抽象而貶斥形象與詩歌,那麼着重比喻的記憶術豈非該受道德譴責?
大雅博的回應是﹕(一)由於形象能強烈鼓動我們,並印入我們的靈魂,故一切跟生命和判斷相關(ad vitam et iudicium)之事物──即道德真理──都要依賴形象才能寄存於我們心中;(二) 按照西塞羅所論,記憶是一種“智德”,它指引了我們的現在和將來,所以記憶術也是富道德價值的,絕對不該受譴責。
聖多瑪斯在《神學大全》和對阿里士多德《論記憶與回憶》所寫的注疏中,都講及記憶術。他跟大雅博一樣,都繼承了古希臘羅馬的記憶術原則,這兒我只想強調以下兩點(都是傳統記憶術所沒有的)﹕
(一)多瑪斯在論證記憶術的合理性時,也承認了人性的弱點。“沒有形象,人便無法理解任何事物”(Nihil potest homo intelligere sine phantasmate)是他的座右銘,他認為人容易記憶粗淺、可感之物,但總會忘記微妙和具靈性的內容。所以他贊成“Tullius”的方法,利用形象來記憶抽象、知性的事物。
(二)多瑪斯(有意無意地)為記憶術注入了宗教熱情。他說明記憶規則時,誤引了《獻給赫倫尼》的一句話,原文是叮囑讀者要在安靜無人之處選擇“記憶位置”(loci),因為“孤獨可確保表象的形狀完好無缺”(solitudo conservat integras simulacrorum figuras) ,免卻外物的干擾。但多瑪斯卻引作﹕“sollicitudo conservat integras simulacrorum figuras”,即是“細心關注可確保表象的形狀完好無缺”。原文的“孤獨”(solitudo)一詞,於此變成了帶有感情色彩的“關心”(sollicitudo),而記憶術的意義亦隨之大變。正如《記憶術》(The Art of Memory)的作者法蘭西絲.葉茲(Frances Yates)所言,多瑪斯向記憶的對象賦予感情,引入了一種虔敬氣氛(devotional atmosphere),這是古典記憶術完全欠奉的。 由此可見,記憶術已由最初的修辭術,經過基督教倫理學吸納後,漸漸與宗教信仰融為一體了。
古典記憶術在中世紀基督教文化下漸變而為倫理學,到十三世紀再由士林哲學的聖師一錘定音,正式成為一種輔助德行的學問。但和多瑪斯同時的方濟會哲人雷蒙.陸爾(Raymond Lull, 1235-1315),卻別出心裁地把卡巴拉(Kabbalah)神秘哲學化為記憶術,另闢蹊徑之餘,更開了後世萊布尼茲代數符號系統的先聲,亦啟發了不少哲學家如培根、笛卡兒等。
陸爾自創記憶術,主要是為了傳敎﹕他自信只要能說服猶太人和穆斯林跟他學習他的“技藝”(Ars),他們就會皈依基督教。所以他的記憶術基礎,必須是三教所共同承認的宗教概念,那就是“神的名字”(Names of God),亦即神之屬性。他把神性用九個字母──B,C,D,E,F,G,H,I,K──代表,如B代表善(Bonitas),C代表偉大(Magnitudo),D是永恒(Eternitas)等,再把字母放進一個分三層的輪盤上(見圖一),字母在旋轉中產生不同的組合,新的想法便可由此衍生出來。陸爾依照中世紀慣用的世界等級架構,由神以降,把受造物分成九級,而九個字母又可在不同等級中運作,象徵不同事物,由是而建構出一個既包羅萬有且富創造力的超級記憶系統。
圖二綜上所述,中世紀的記憶術是不能獨立於宗教信仰之外去談論的。一方面,它助我們記憶種種德行的內容,使靈魂得到救贖;另一方面,它讓我們默想神的名字和大能,藉此理解被造物的秩序和天主的旨意。在中世紀,理性、德行、信仰是並行不悖的,而在記憶術中,我們看到三者是如何和諧地統一起來。記憶術不但影響了中世紀的學者和教士,更透過詩歌、繪畫和聖像等藝術滲入了平民百姓的生活中(惜乎篇幅所限,本文只好略而不談)。可以說,中世紀的記憶術如鹽入水中一樣,早已融化在整個社會的不同文化領域中,亦深深被當時濃厚的宗教精神所穿透。
反觀今天,記憶術與真理、德行和神都徹底脫鈎了,只淪為一種為世俗目的而服務的工具。弔詭的是,現代所謂的“記憶術”與社會竭力鼓吹的“失憶”(如教育制度普遍不主張背誦、消費文化要人貪新忘舊等),其實都是以資本主義為代表之現代文明的一體兩面──記憶的好處(如有的話)不外乎達到功利目的,提升我們的競爭力,幫助賺取更多的錢,而失憶就是要我們忘卻過去,盲目“發展”、迷信“進步”,和不自覺地花更多的錢於“最新”的商品上。
眼看記憶術由中世紀的神聖學問,墮落為現代的賺錢或應試工具,究竟現代和中世紀,哪一個更像“黑暗時代”呢?實在值得我們仔細思量。
相關閱讀:
Yates F. The Art of Memory, London: Pimlico, 1992.(是目前為止關於記憶術歷史的最佳參考書,台灣有中譯本。但陸爾的記憶術佔比重不多,而且亦說得不夠清晰,相信是作者本人的局限,因為她從未親身運用過記憶術。)
一個愛煮麵條的女人

當婚姻變成冷漠的習慣,你的伴侶就是地獄。灼熱如火的情慾,本來是生命之源,但只要黑風襲人,熊熊烈火就會鏗然一聲,凝作冰刀從你的內心破體而出。
如果你不是廚子,你會煮飯給陌生人吃嗎?我不會。煮飯是一種富有象徵意味的儀式,由菜單、買餸、選料、調味、烹煮、上碟,每一刻都存想着對方吃時的表情,而每一步的目的,其實都是為了令對方有種即使短暫即使平凡,卻又是最實質最鮮甜的幸福感。
在土耳其東北部的特拉布宗,有一對夫婦,丈夫叫K.C.,五十三歲。這一個月來,給丈夫做飯忽然變成了她的苦差,因為她覺得世上最無聊的事,就是選擇菜式。昨天你吃過什麼,你記得嗎?前天呢?大前天呢?選擇菜式永遠是一件很頭痛的事,而最令她沮喪的,是一整天辛勞的成果,翌日總會被徹底忘記,就像花瓣上的露水,在清晨旭日初升時便會溘然消散。一切都被忘記。一切。
反正要被遺忘,倒不如每天都煮麵條吧,她忽然靈機一動。但人生就是充滿諷刺:你努力,別人偏偏忘記;你一馬虎,全世界就會牢記。這一個月來,K.C.每天都吃麵條,但他沒說什麼,只是暗自猜疑。下一餐不會又是麵條吧......我不信每餐都是麵條......他每次用膳時都這樣想。但三天,五天,十天,十五天,二十天,二十五天,依然是麵條麵條麵條麵條麵條麵條......直到永遠。
的確是永遠的麵條,以後也不會有其他款式的菜了,因為在第三十天,即上星期五,K.C.用鐵錘把她活生生的打死了。鮮血染滿廚房,灑滿餐桌。她受不了被遺忘的痛苦,他也不。他要繼續活着,就非得把「麵條陷阱」的主謀幹掉不可,因為重覆就意味着虛無。被警察拘捕時,他喃喃自語:「她對我已不再有興趣了,實在無法忍受,這個月來她只是煮麵條。」看吧,一離開了柴米油鹽,愛情根本就沒有落腳處。
每一個愛煮麵條的女人背後,都必定有一個吃厭了麵條的男人,而女人幸福的秘訣就是如此簡單:要避免丈夫出外偷食(或用鐵錘殺你),請不要老煮麵條。
希望
瑤草一何碧。春入武陵溪。溪上桃花無數。枝上有黃鸝。
我欲穿花尋路。直入白雲深處。浩氣展虹霓。

只恐花深裏。紅露濕人衣。
走過桃花林,我們扶持着,到了闃寂無人的沙漠。烈日當空,天淨無雲。
苦熱而冷酷的陽光,無情地穿透我們肉身的每一個毛孔,也殘暴地照明了我們靈魂的每一寸角落。
「怎麼會到了這裡?」他問。
「過了桃花林,就是沙漠。」我木然而對。
「沙漠太大了,再走下去,你我都會死。與其如此,不如就這樣依偎着死吧。只要我們相親相愛,神便會憐憫而拯救我們,這就是信心和希望!」他忽然滿懷自信,雙眼閃出愉悅的光采。之後便安心地躺在沙上,等待着我。
我默然轉身,沒再回頭,獨自向前走去,因為我也相信,也盼望。


