by
Anatol W. Holt
Prof. Dr. Anastasia Pagnoni Holt Università di Milano Dipartimento di Scienze della Informazione Via Comelico 39/41 20135 - Milano - Italy _____________ Tel:+39-2-481.6251 FAX:+39-2-480.10.615 E-Mail: pagnoni@dsi.unimi.it
Printed on May 10, 1998. All rights reserved by the Author
CONTENT
1. What's this? 1
2. Mozart 1
3. Arithmetic 2
I. How come does it work? 2
II. Why do it? 3
III. How does it work? 4
4. Franco Villa 6
5. Figure and Ground 7
6. Does Science Explain it All? I 8
7. Body and Person 9
8. Concrete/Abstract 12
9. Drawing Styles 14
10. Amazing Stores 16
I. What really pleases the architetto 16
II. Only in America 17
III. The Chief Musician of Heaven 17
11. The Tao is Silent 18
A Postscript 20
12. Russel's Barber 21
13. Are People Good? How Should I Act? 23
14. Meaning in Music (and Other Arts) 26
AMBIGUITY AND META-AMBIGUITY. 29
CONCRETE/ABSTRACT? 29
ELECTRONIC MUSIC. 30
15. Thus! Now vs. Always 31
16. Language
Words and Things 33
17. Fair Division 36
Exercise 39
18. Does Science Explain It All? II 40
19. Conjectivity 41
THREE CONJECTIVITY EXCERCISES 45
20. "I " 46
SHARING AN APARTMENT. 46
LAST WILL AND TESTAMENT. 47
GHOST PADDY CAKE. 48
AT THE AIRPORT. 49
21. Organized Activity and Its Study 49
TIME AND SPACE. 51
RELATION TO SOCIAL SCIENCE 52
22. Buridan's Ass 54
23. Love, Beauty, etc. 57
24. Do Machines "do things"? 58
1. What's this?
Once a year, the salmon of the NorthWest, enter the Columbia River from the sea, swim up to its source against powerful currents, waterfalls, etc. and there, lay their eggs. Why? Who knows. Is it their spirit? Their instinct? Their quick?
Whatever it is, it's Life. We too procreate like salmon, but also in other ways. My drive to write is no different from my friend's drive to play the guitar, someone else's drive to prove theorems, to sculpt or paint, to build your children's playground, to repair the toilet. Why? our spirit?, Our instinct? Our quick.
This is a book about our quick. The form I have chosen is adapted to my character and to the historical present: a collection of bits and pieces, none of them too long or difficult, loosely connected to one another. You can read them in any order, many or few, repeatedly, or once only. I expect you will find that the fragments eventually "add up" like a hologram; but you needn't worry; they should be fun anyhow.
And if they do add up for you, what is the "big picture" that you might glimps? It is a widely encompassing view of the world, scientific and artistic, mystical and rational, very abstract and very concrete. Some fragments tell , some exhibit , and some do both
This world view matured in course of my 70 years of life. (As with everyone, my life too was composed of many fragments and these too have "added up", in spite of their great number, and seeming randomness.)
2. Mozart
It isn't very original to love Mozart, but, ... I do now, and always have done so as long as I can remember. When I was 6 or 7 years old in Riga, Latvia, where I grew up, I remember saying to my grandmother one day: "Beethoven frightens me; but Mozart delights me"; on being asked, I explained: "Beethoven frightens me like a thunderstorm, but Mozart writes beautiful melodies."
Today, I see Beethoven differently,... and about Mozart I think: he was a shimmering, ever-so-mortal butterfly, always conscious of death, always frightened, always defiant, fully aware of being better than his betters, and of his utter dependence on their good will (in that respect, a little like Shostakovich in our century); passionate, glutonous, immoderate in all things, a true clown. (This makes me think of 3 beautiful lines of ee cummings, ending "The Man on the Flying Trapeze":
I am an artist
I am a failure
I am a man )
More than three centuries have passed since Mozart died, but he speaks to me, here and now, as few others do. His unsurpassed imaginative power and paradoxical spirit never bore me. On the contrary: they constantly remind me of the terror and beauty of life, of how the most carnal and most spiritual, seemingly opposed, actually meet, of how worming money out of coarse people can be combined with genius, and how tears go with laughter (and vice versa) and finally, how singing the World's greatest songs may yet lead to an unsung pauper's grave; the very reminders that I constantly need.
3. Arithmetic
I. How come does it work?
About the time that I told my grandmother about Beethoven and Mozart, my gradeschool was teaching me arithmetic. The contrast between me and my grandfather could hardly have been greater: as much as he was an arithmetic wizzard, I was an arithmetic dunce. And although he was an adult and I a child he didn't mind impressing me with his superiority. ("Why when I was your age, I already solved problems like how much water is in the bathtub after 2 hours when it flows in at rate x and flows out at rate y.")
But I was hung up on a problem not in arithmetic, but about arithmetic that had never troubled my grandfather. I realized that the skills I was supposed to master with numbers were not the same as the skills of counting and measuring which built the bridge between the world of everyday experience, and the world of arithmetic. I also realized that if arithmetic could not be used on the numbers that came out of everyday experience, it wouldn't be a subject that all children are required to master. Now the problem that troubled me was this: why did arithmetic "work" on everyday numbers? Was this supposed to be obvious? Was it a part of physics? Could one see that this had to be so by logic alone? Was I the only one bothered?
Let's take a concrete example. Someone says to you: count the candies in that bowl. You do as he says. Of course, in doing this, you must be careful: not to lose candies; not to count the same candy twice; etc. These things require skill, and a clever use of the available surroundings. Let's say you discover: there are 13 candies in the bowl.
Now you are asked to to count the candies in another bowl. You do this too, finding the number 19.
Finally you are instructed: dump all the candies in the first bowl into the second bowl, and count the resulting number of candies. If you do as instructed, you will, in the end, find 32 candies in the second bowl. Lo and behold, this is the same result you get if you (arithmetically) add 13 to 19.
I repeat: if such correspondences were not all but universal, no one would bother with arithmetic; but of course such correspondences are all but universal, and 6-year- old me wondered "why?"
Sixty four years have passed since then. In the meanwhile, I have been heavily educated even in mathematics; I also spent many decades in the computer business; and my conclusion today about my 6-year-old question is this: there is no reason for this correspondence: the fact is, it works the very same thing that one could say about the miracle that, in general, 2 different countings of the same candies in the same bowl give the same result. And a good thing too! But startling, .... at least to me.
II. Why do it?
OK. So it works. But why bother? (a question that 6-year-old me did not consider). Perhaps it is no surprise, ... but gradeschools do not answer this question either.
Standard mathematical forms of expression only make this question harder to see and address.
42 + 37 = 79
If 42 + 37 is really equal to 79, then why bother adding them? Also: if they were really equal, people would just as frequently write:
79 = 42 + 37
but they don't!
Just last week I talked to a university professor about this. He said: well, ... 79 is more ... canonical, ... more beautiful, .... more integral; that's the reason people convert 42 + 37 into 79. I don't think this can be the right answer. People never do work for such ethereal reasons.
I have come to the following conclusion.
To get from 42 + 37 to 79 takes work; this alone shows that they are not the same not "equal" in that sense. No one does work without a reason. Here is a typical example.
Josephine's daughter is getting married, and Josephine is planning a reception. Before going shopping for suitable hotels or restaurants, she needs to know the expected number of guests. She considers: many of the guests will get to the wedding on their own; but there is a large contingent in Newark whom she could really help with a chartered coach. So she counts up: 42 self arrivers; 37 from Newark. Adding the two, she discovers she needs seating for ca. 79. Armed with this information she goes shopping.
This much is clear. Given the customs of the land, Josephine cannot say to a hotel keeper: "I am expecting 42 + 37 guests; if she did, the hotel keeper would have to add the two parts to decide what he might offer Josephine at what price. What is prototypical here is this: There are 2 or 3 actions to perform; at least one of these actions depends on the sum, and at least one of them depends on one of the two summands. Under these circumstances 3 numbers must be found: 2 numbers by counting like the candies above, but by other methods and 1 number by adding.
I made an analogous error years ago in considering the relationship between a number x, and the answer to the question "is x greater than 0?" I thought: knowing x means that you know the answer; (exactly analogous to imagining that knowing 37 and 42 means that you know 79. The fact of the matter is: if you know x you must calculate the answer to the question (as you must calculate 79 from 37 and 42.)
Neither grade school teachers, nor professors, tell you these things. And yet they really matter especially if you are an adult who pays for calculation.
III. How does it work?
The philosopher Ludwig Wittgenstein once asked the following question:
"Do, or do not, the following 2 sentences mean the same thing."
Sentence A. 42 + 37 = 79
Sentence B. People competent to add get the result 79 when adding 42 to 37
most of the time.
Most people that I know simply find his question more irritating than deep. Once having overcome their irritation they say: "Of course sentences A and B do not mean the same thing; only A, for example, states a provable fact of arithmetic.
More fully expressed: A states a fact that is provable in arithmetic; (in other words, A is a theorem); B states the result of an empirical observation; so how could these two sentences possibly mean the same thing?
But Wittegenstein might have equally asked about the difference between the following.
Sentence A'. '42 + 37 = 79' is a theorem of arithmetic
Sentence B'. Most of the time, people competent to prove theorems of arithmetic find
that '42 + 37 = 79' is such a one.
The difference between A and B becomes more haunting.
What I find fascinating about Wittegenstein's question, is the relationship he suggests between arithmetical truth (or meta-arithmetical truth) and a social practice. The social practice he identifies is, in the last analysis, all that we can ever hope to know of the truth of arithmetical propositions (or of their proofs).
But, interestingly, what Wittgenstein says about arithmetic (if only by implication) applies to much simpler things. For example: consider situations in which the assertion "This is a dollar bill" is true. Wittgenstein might just as well have asked: do sentences A and B mean the same thing?
Sentence A. This is a dollar bill
Sentence B. People competent to recognize dollar bills agree that this is a dollar bill
most of the time
In this way we see that Wittgenstein's question has less to do with arithmetic than with truth rather broadly interpreted.
I do not think all this is merely odd and philosophical. 'Truth broadly interpreted' is an indispensible basis for human society which is why lying is a serious ethical offence (and Alice in Wonderland fascinating). The right answer, the true answer, to an arithmetical problem is the one that most people competent to decide, decide on most of the time and the fact that it is demanded by a theorem only seems to affect the situation, but actually leaves it as it was. In this way we see that the right answer to an arithmetical problem has a lot in common with the right way to dress for dinner, to write a sonnet, to pronounce 'how do you do', or to drive in traffic.True, society would be much more damaged if counting, measuring, or arithmetic fail, than if my other examples fail, but society is damaged by all failures (and most especially by failures to pronounce, or failures to observe the rules of traffic). In short, it turns out that Wittgenstein's question is a peephole through which you may catch sight of a world that is even stranger than Alice in Wonderland, and practically much more important.
4. Franco Villa
On a small street in Milano, connecting via Moscova and via Montebello there was a small store impossible to classify not exactly devoted to antiques, nor to art, nor to handicrafts; not to new things, not to old things; not to things Italian, and not things from other lands; not exactly to any one of these, but to some extent, to all of these.
The proprietor was a taciturn fellow who looked to me like a cross between a carp and a frog; a little fat; bulging eyes; little hair. Over a period of a year or two, I made friends with him, mostly by spending time in his store often as the only customer and occasionally asking him a price or a provenience.
Gradually I discovered that every object in Franco Villa's store had landed there because of his special way of being in the world.
For example. On his walls there once appeared a series of drawings and paintings by a South American artist named Mendoza who as I learned from Villa had once achieved world-wide notoriety, briefly. Newspapers everywhere reported on an incident: a man wielding a knife attacked the Pope during a ceremony in South America. It turned out the knife was plastic, ... and the man was Mendoza.
Why did Franco Villa have Mendoza's on his wall? Well, he had an aristocratic lady friend in Rome who needed money (a common aristocratic disease), and decided that Franco might sell a part of her Mendoza's. I bought one of them.
But. I also bought a black lacquered Russian box from Franco Villa. Of course the box had a story. Another friend of Villa's had smuggled this box out of Russia. It had been (hand) painted by a famous artist in this genre, whose work was mostly in museums, and had been officially classified as national treasure. The smuggler had filled the box with some doubtful content; the border officials gave all of their attention to the content, ... but not the container! (so, Franco Villa).
Well, ... over time, I bought lots of other things there (including a new chinese stool!). Without a doubt, one reason I kept coming back was because there was always some unforgettable story from the otherwise unspeaking carp/frog about the thing that had just quaked my quick. Will wonders never cease? Never.
5. Figure and Ground; Science and Art
One cloudy day, walking down Beacon Street, in the vicinity of Boston University where I directed the Academic Computing Center, a thought dropped into my hands. Like one of the pebbles I collected in our garden in Latvia glittering, mysterious, prescious (to a child) I held it up to view: glitter it did; but was it real ? For a while I thought not; in due course I changed my mind; but of course, neither this thought nor any other should be made to "walk on all fours".
So here it is.
1. Everything you ever see has its repeatable and its irrepeatable aspects.
At the very least, it is yet another thing you see (repeatable). A cloudy morning? Just like hundreds of others, ... and yet unique; etc.
2. Some things are mainly valued for their repeatable properties; other things are mainly valued for their irrepeatable properties (and some things for both)
An accepted scientific experiment is valuable because it can be repeated; the same is true of an utterance, or a wood screw. As to the bed I sleep in: I value it because it is a bed like every other, but I value it also because it is uniquely mine. But in the ink and charcoal of Mendoza's I bought from Villa, I value most of all the irrepeatable trace of Mendoza's quick. This, above all, is what I paid for.
3. Form plays a key role in science as well as art.
Scientific forms of importance: a graph; an equation; a procedure of manipulation and/or observation; etc.
Artistic forms of importance: a sonata (or sonnet); Madonna and Child; a still life.
4. The function of form in science and in art are opposite (yet in another sense equal): in science, form raises the repeatable, and therefore suppresses the irrepeatable in this way distinguishing the valued from its inevitable complement; in art, form raises the irrepeatable, and therefore suppresses the repeatable in this way distinguishing the valued from its inevitable complement.
If you are of the right inclination, it will pay you to think-about/meditate-on this thought and especially: (a) the inevitability of the coexistence of the repeatable and the irrepeatable (like Yin and Yang); (b) the domains that are neither science nor art, and how they fit into this thought; (c) the ways in which this thought turns false, or is incomplete even in its stated domain of application; (d) of what practical uses this thought (or related thoughts) might have.
6. Does Science Explain it All? I
A US millionaire so I was told publicized a prize of $1,000,000 that anyone could win by coming to his office and demonstrating, under his scrutiny, any pheno-menon that ordinary science could not explain. Whoever told me this added that, up to that point of time, no one had collected the prize.
I thought quite a bit about this millionaire, and his offer. While I do not necessarily believe (or disbelieve) the para-normal, I nevertheless do not see the world as does this millionaire. No. I tend to think: most of what is real to me, whether thing or event, lies beyond science. For example: suppose it becomes clear to me that my neighbor is in the habit of violating my property rights; (I might sue him.) Can any science "explain" what I think I see, or "explain" the reason? I think not; certainly not physics; for "my property" is not a concept capable of physical definition. But I ask can "my property" be a concept in any science? If so, that science would have to be able to keep up with legal changes in what can, and what can not, be a part of "my property".
Just as "my property" cannot be scientifically understood, neither can "one US dollar" and therefore none of the events that involve dollars like buying things. I wouldn't call dollars or buying things para-normal, but I do think they lie beyond science.
I know that what I will say next is not fair to the millionaire who publicized the prize, for it lies askew to what he was probably thinking. All the same, I did consider going to his office to claim the prize. I would present myself at an agreed-upon time; I would say: "Are you ready for my demonstration?". After his "yes", I would remain before him for some minutes, doing absolutely nothing, and would finally say: "My demonstration is finished". "Really!" He would grin: "And what is the phenomenon that you have demonstrated?" "I am still here", I would answer. I insist: (a) what I would demonstrate is a phenomenon; (b) science cannot "explain" it.
The self-same Wittgenstein already mentioned above, once wrote: there are things about which one can speak clearly, and there are other things about which one can not; and about the unclear, one should not speak at all. We may not agree with his judgement, but we might accept his two-way classification (as would be my case). If I am right, then most of what you and I recognize in the world cannot be given a clear and effective verbal, definition. Interestingly, Wittgenstein himself for totally different reasons also thought that the realm of the Clear is very small, in contrast to the realm of the Unclear (and this, in spite of the fact that he consciously devoted his life's efforts to the Clear). For whatever reason, I am convinced that Science, by its very nature, can only deal with an infinitesimally small portion of what we experience with one another in the world.
(For another lump of thoughts about this, see "Does Science Explain It All? II")
7. Body and Person
You and I: we certainly are persons, and we certainly have bodies. But might I not say: we certainly have persons, and we certainly are bodies? Wrong as this may strike you, here this imaginative reversal is a good start. In what is coming I will refer to the first as the A-form, and, the (normally) rejected alternative, the B-form.
You see at once: the A-form fits with: a person can control his body (up to a point); the B-form does not. For example: a baby, in becoming toilet trained, learns control; today, a person might decide to have a face-lift; even to change his/her sex; to scream when tortured, or to remain silent; etc. (At least for now) no one thinks they can avoid getting old, or dying.
Are bodies beautiful or ugly? According to the A-form, a person may beautify his/her body. But as you know bodies can be revolting, particularly when turned into squishy, smelly, bloody, messes by disease or violence
The whole thing is not simple. Whether the next following thoughts/observations make it easier or harder to understand, ... well, ... we shall see.
Like most men, I tend to get sexually excited when I see scantily dressed girls, ... but not invariably. For example, I once spent many hours in a nudist club where I could stare at nude girls all I wanted of course some prettier than others but, ... no sexual excitement.
Recently I heard that a family, asked to dinner at the house of my 98 year-old aunt, considered the invitation in bad taste because it might, expose them to the drooling mouth of my aunt at the diner table.
All of this leads us back to the beginning: what about the "having" of bodies and the "being" of persons? I will try to convince you that there may be reasons to prefer the B-form among other things, that the B-form explains more.
None of us think that having a body is as casual as having a car, a vacation home, or a dinner. Acquiring a new property will (usually) not make you think of changing your name, but changing sex may well as you might also do when changing citizenship. (Notice: changing citizenship is likely to be seen as a change of person without a change of body.)
And I have noticed: I fall in love with and possibly marry a flesh-and-blood person; not a person who "has" a body, but a person manifested in a body, a person who necessarily dies when the body dies, a person whose "looks" are not an aspect of something that she has, but of something that she is.
On the other hand, the roles that I play definitely affect my way of behaving. (For example, as a multilingual child, I noticed that my voice changed when I switched languages). Also: Milgram (the sociologist) noticed that, when students play-acted prisoners and wardens, their normal personalities altered drammatically.
In the eyes of the law, bundles of roles in the limit, one only are sometimes treated as persons ; "juridical persons" to be sure, but persons all the same. While nothing lives for ever neither roles nor flesh-and-blood persons these lives do not coincide; a single role may be played by a number of flesh-and-blood persons (at the same time, or after one another), and a single flesh-and-blood person may play a variety of roles. The second half of the B-form suggtests this.
Is this judicial view of person incompatible with the expression "flesh-and-blood person" that I used above? Not really. For: consider me Anatol W. Holt. Of course I am "flesh-and-blood", but, ... I am also a person before the Law (of the United States). As such, I have a legal name, a permanent address, a social security number, etc.; none of these automatically become irrelevant if I suffer medical death, in spite of the fact that my legal person may also be identified by photographs and fingerprints. This suggests to me: a flesh-and-blood person is to be sure a physical fact, but, ... the mere use of the term "person" means it is also (and very significantly) a social fact, similar to yet different from the social fact of juridical persons.
Before working out the B-form the light of the details I have just discussed, I want to point out: a juridical person always has a "body", even if not a human body. In the generalized case, the "body" consists of an aggregate of material lumps which, however, need have nothing directly to do with organisms. A juridical person has an address, may possess furniture, may be a telephone subscriber, etc. A juridical person also has interests that the (juridical) person pursues.
In the light of all this, we arrive at the following approximation to the B-form.
1. Let us call a "body" a lump of material, or an aggregate of such lumps
2. Let us call a "person" a role, or aggregate of such roles, recognized in a
society.
3. Every person (juridical or otherwise) has a body
4. A flesh-and-blood person is one whose body entirely (or mainly)
consists of an organic whole (which is usually called the body of a person).
5. A flesh-and-blood person is so intimately tied to his body that, in most
societies, no major changes in his body can be tolerated without considering the person to go out of existence. (Of course this does not apply to cultures which recognize re-birth.)
6. Now begin with civil persons that is, the kind that has a flesh-and-
blood body (like Anatol Holt). For this type of person, point 5, explains the first half of the B-form that is: a (civil) person is a body.
7. The second half of the B-form is explained by assuming that a civil
person can play many roles and, in that sense, can be many persons.
Now, let us revisit the questions/observations near the beginning of this little piece to see what interpretations these 7 points suggest.
What about people's control over their bodies? What can this mean? Namely that the civil person can, among other things "decide" to undertake some degree of body change but, enlarging the range of decision is bound to raise practical and (consciously or unconsciously held) conceptual difficulties. For example. A person need not change his ID photos if he decides to change his hair style, ... but if he decides to get a face lift let alone a change of sex?
And what about the reactions of revolt at seriously diseased or damaged bodies or, in milder form, the negative reaction to my aunt's drool? I think: we are pushed towards an unwelcome boundary of what is regarded as an acceptable body for a civil person. Beyond a certain limit, we are led to feel that the civil person whose body this should be doesn't exist, or doubtfully exists. (The revulsion seems to be so profound that one thinks: there must be a genetic basis, just like the bodily attraction of sex.)
Now consider my absence of sexual arousal in a nudist club, or the same absence in a male doctor who examines a female patient. I relate these facts to the multiple persons that a civil person can "have" (according to the B-form); to feel the arousal, the male must consider his role to be that of a man, rather than a (male) nudist club member, or a (male) doctor.
8. Concrete/Abstract
There is a well-beloved game, known by many names and played in many countries. In a company, one person is chosen to be "it". The "it" person leaves the room while the rest decide on a "thing" that the "it" person should discover by asking questions. These question should be answerable by "yes" or "no". After some number of yes/no answers he should know the answer. I knew this game as a teen-ager in the USA under three names: "20 Questions", "Animal, Mineral, or Vegetable" and, ... "Concrete/Abstract". The last two names in effect recommend (or even legislate) an opening gambit for the Questioner.
I loved this game; I thought that the main challenge was greater than to discover the object; it was also to formulate a series of questions that the others could unhesitatingly answer by "yes" or "no"; and finally, I felt irked by the suggestion contained in the third name; of course I understood (then and now) that all objects might be regarded as "concrete" or "abstract" "the number 5"? "abstract"; "a horse"? "concrete"; "Love"? "abstract"; "the New York Times"? "concrete"; etc. But I thought there is something wrong here. I think this "something wrong" is interesting and important; so here goes.
I noticed:there are simple-enough cases that are not so easy to classify after all. Suppose I am thinking of "The Yellow Submarine", a famous song by the Beatles; is the song "concrete" or "abstract". Each time that it is sung there are concrete people who concretely sing it (and hear it); but the song itself, ... is it abstract? Or concrete? Actually, this classification problem isn't all that different from "a horse". It would seem that each particular flesh-and-blood horse is very concrete; but if I am simply thinking of "a horse" any horse, anytime, anywhere it seems a lot like "The Yellow Submarine".
You impatience may well be rising. Am I not bringing up an age-old philosophical problem (in a home-spun form), a problem which has plagued some of the best minds in the world over millenia? Yes, in a way; but even humble minds such as (probably) yours or mine may have something new to say about an age-old issue, "something new" that is made possible by present-day culture, something that the ancients couldn't have imagined; what is more, this "something new" might have real and important consequences to your life and mine. So bear with me.
First of all, let me disavow interest in the philosopher's question: does X exist ? Temperamentally, I take a "naive" point of view: does the song "A Yellow Submarine" exist ? The Beatles wrote it; they sang it, and sold (a lot of) copies of it; etc.; that's good enough for me: it exists . And the horse (not an example)? Well, .. for some people, the horse is an important part of their daily lives; for most people of whom I am aware "the horse" exists as also the cup-and-saucer, the christmas tree, and "The Yellow Submarine".
Recently I have tried to turn this common-sense sense of "existence" into an easy-to-understand definition.
Definition: If "a thing" matters to the life of a community the following condition and only the following condition must be satisfied: generally speaking, the members of the community must agree that something which they jointly see (or otherwise experience) is, or is not, an example. The thing exists for the community, if there are one-or-more examples.
Let us try this out. How about "The Yellow Submarine"? It will be present to the people interested in it whenever it is performed; they will (generally) agree that each performance is an example. Instead of taking "The Yellow Submarine" as an example, how about taking a particular rendition of "The Yellow Submarine" say, at Madison Square Garden, on a certain date, at a certain time as an example? Of this rendition there will only be one example; but everyone who hears it will (by and large) agree. In this way we see: "The Yellow Submarine" which is sort-of-concrete exists according to the Definition; but so does a particular one of its renditions which is certainly concrete.
Now let me climb to dizzying heights of abstraction. How about love, or beauty, or the number 5 ? Do they "exist"?
As to the number 5, the answer is a clear and resounding "yes" naively, and not-so-naively, according to the Definition just above. With "love", the answer seems to be less clear that is, there is less agreement about examples of love than about examples of 5. Still, there is enough agreement especially when counting in mutual persuasion that I am inclined to say: it exists! So too more or less with "beauty".
Now assume that all three exist. Are they "concrete" or "abstract"? Of course they are "abstract". Why? Because everyone says so! And, in an important sense, I have no more difficulty in recognizing that they are abstract than I have in recognizing examples of love, beauty, and the number 5. Now that I am no longer a child playing 20 Questions, I no longer feel (much) like saying "there is something wrong with the distinction"; (for, why should I find concrete vs. abstract more intellectually trouble-some than buns vs. roles?) Instead, I think (and feel): there is another point of view on things that exist which: (a) replaces the concrtete/abstract distinction with an indefinitely large range of possibilities, many of which are worthy of careful attention; (b) "works better". And, I cannot resist adding: even though, love and beauty "exist", I do not think philosophers should ask "what is love (or beauty)" (anymore than they should ask "what is a bun (or roll)"; Of course I know that philosophers without the benefit of my advice don't care about buns and rolls but they have always cared about love and beauty.
9. Drawing Styles
We are all taught to make drawings of certain kinds. For example: every gradeschool child learns to draw straight lines and circles with ruler and compass. In China (I noticed) every gradeschool child also learns to make free-hand perspective drawings; in Western countries this is more rare, but certainly not unheard of. And of course, art students learn much more.
Now it is usually said: ruler and compass are used to make real straight lines and circles. Sure, even these have minor imperfections, but they are much closer to the ideal than can be made free-hand. But: is this true? Let's see.
Suppose George Schultz draws a cartoon which includes a parked car, seen from the side. He draws two Schultzian circles which represent wheels. Would it have been better, more accurate, truer to life, truer to the ideal, if he had drawn these wheels with a compass? No. It would no longer have been a George Schultz cartoon.
How nearly are car wheels of circular shape? Quite a lot though of course not perfectly. Sufficient deviation from mathematical circularity would be felt by the driver. But sufficient deviation from mathematical circularity has nothing to do with the Schultz cartoon. Nor does it impair the "truth" of the cartoon; on the contrary it adds to this truth, especially Schultz's truth.
Another case. I am asked to prove a theorem in geometry. To this end, I draw a geometric construction which includes a circle. Should I draw the circle with a compass? Just as in the case of the cartoon, here, a free-hand circle may be, in a sense, better.
Drawing this circle with a compass has an advantage and a disadvantage. The advantage is not its greater veracity for most of it may well be irrelevant-at-best, and misleading-at-worst, to my proof. Indeed, insofar as the compass-produced circle suggests mathematical properties not relevant to my proof, it does damage. But the real advantage of a mechanical circle and mechanical straight lines is to tell the viewer: only the geometrical properties of this diagram "count" for, ... this is not a cartoon (and Anatol Holt is not George Schultz).
An interesting example occurs to me. I once produced instructions for a game I had invented. The instructions included many drawings. I considered it important (a) that the drawings be free-hand rather than mechanical, (b) that I should make them. Perhaps point (a) is natural for drawings that are mainly meant to communicate (game) logic (and not geometry, and certainly not art). But how about point (b)? Well, I am no George Schultz, but nevertheless I wanted to communicate person-to-person, at least a little. I thought (unconsciously): I want the instruction reader to feel: this is a game invented by a felsh-and-blood person, like himself; if it is a "message from God", it is neither more or less so than our way of dressing as a message to our fellows.
As you can see: I do not think that mechanical drawings are more perfect representations; I think everything depends on the intended context of use which may be arbitrarily subtle and complex.
10. Amazing Stores
I. What really pleases the architetto
At the intersection of Porta Nuova and Moscova in Milano is Arform, my favorite store, here in this city. It seems I am very attracted to objects and institutions which express the hardy and special character of a person as irrepeatable and admirable as a one-time evening. The object or institution might be a work of music or art, a museum, an automobile (like the Model T), a bridge, or, ... a store. And besides: Arform deals in a type of merchandise that interests me namely, clever and/or beautiful gift items some to make you handsome, some to make your house handsome, some to use, some to amuse.
I don't know much about how Arform came to be, but I will tell you what I know. Ow-ners/founders, performers in chief, are Paolo Tilche and his wife he, an architect, she, I don't know what; he, in his 80's, she, younger I think; he, radiating humor, intelligence, know-how, she, white-haired, energetic, girlish in spite of her age.
What defines the articles in Arform? They are mostly meant as presents; they are for house or person; they range in price from ca. $10 to ca. $5,000 and, regardless of price, are all worth appreciating from some point of view; all of them "please the architect". So. You might find there 4 wallets and/or 5 necklaces Arform not being a leathergoods or jewelry store. Why are they there? because they fit my description.
Not long ago Arform began to carry an unmistakeable collection of wooden objects bowls, spoons, free-form sculpture-like pieces. They are supplied by a guy in Piedmont, who finds the wood in forests where he lives, and works them in some way (as sculptor or craftsman). Every so often Arform calls him and says: "Send us $3,000-worth of merchandise" without further specification.
One block away is a small factory building that belongs to Paolo Tilche; what is it for? It is his playground. (Also, his daughter has started some kind of egg-head group that meets there.)
I go to Arform ca. 5 times a year. On the most recent occasion I went because my best beloved keyholder had worn out. At Arform I only found one keyholder which, as it happened did not serve my purpose. So I looked at other things. My gaze came to rest on an incomprehensible what's-it of black plastic and aluminium with a small red plastic pusher. "What's this for?" I asked a salesgirl. "Ahh" she replied "This is an object that really pleases the architetto". I persisted with my questioning stance. The what's-it turned out to be for cuttting your fingernails!! Since the black plastic had a hole, I bought it, and turned it into my keyholder. Now I carry something in my pocket "that really pleases the architetto"!
II. Only in America
On some state highway between Philadelphia and Trenton there is a car agency, "Reedman's".
Are you picturing colored triangular flags fluttering in the wind, surrounding rows of shiny automobiles with conspicuous prices (all ending in 9), on a lot with a new car showroom? Wrong. Reedman's is enormous in fact large enough to have its private system of vans to take customers around!
So let me tell you about Reedman's (knowing less about it than about Arform). Reedman's idea is: you drive in with your old car; you find another one that you like new or second hand; you drive out with your substitute a few hours later, cheaper and faster than you had imagined possible. Reedman's has seen to everything the new plates, your old car, the car loan if necessary, the insurance, etc.
Probably you arrive with some idea in mind such as: I'd like to get a second-hand European sportscar; or a new American stationwagon; or a really cheap 4-door anything, etc. According to your idea someone directs you to one-or-several of Reedman's "lots" each one roughly the size of a football field. So you get in a van and go. You walk around unaccompanied, looking only or mostly at innumerable cars that correspond to your description, each one with a visible price, modestly displayed. If you are pleased, you hail a salesman, whom you find more easily than an employee at a supermarket. He brings you back to "central" in his car. Once arrived, he talks to you, fills out most of the papers necessary, getting you to talk to specialists where and when needed. Two hours later you, your wife, and your 3 brats, are in the car you picked, with new plates, insurance, etc., your old car sold, driving home. Only in America.
III. The Chief Musician of Heaven
In Portland Oregon, not too far from the center, there is a large block of small houses. At one corner you see a store entrance, as you would imagine for cigarettes and newspapers. This is the entrance to Powell's book store which some people say is the biggest bookstore in the United States, if not in the world.
Over many years, Powell's bought all of the little houses of in the block. Gradually Powell's interconnected these houses by corridors; so now Powell's occupies the entire block. You enter the World of Powell's at the corner I described, and you can stay there all day, wandering from house to house, as from room to room in an unending cavern under a Mountain, drawn ever onwards by wondrous crystals.
Each Powell house is devoted to a subject. All the rooms have shelves from floor to ceiling. All the books on the subject are organized by Author and title, with new books and second-hand books freely mixed. (Only really expensive books are kept elsewhere, under lock and key.)
Once, at Powell's, I went to "Music", where I found a little second-hand volume published in Vienna 50 years ago of course in German with anecdotes about Mozart (and his favorite horse). Standing at Powell's I read:
Young Mozart, having written a violin sonata, decided to dedicate it to Haydn. He arrived at Haydn's house, violin sonata under his arm, embarassed to have dedicated anything to this great master at so young an age. However Haydn was very forthcoming, and suggested that the two of them try out the new sonata at once. Nothing loath, young Mozart sat down at the piano as Haydn tuned up his violin. When finished, Haydn turned to Mozart: "Herr Mozart" said he; "When both of us are no longer on earth, and you have become the chief musician of heaven, ... I hope you will always let me play the violin!"
11. The Tao is Silent
This is the title of a book by a friend of mine, Raymond Smullyan, who would be worth presenting to you certainly not less than Franco Villa even if the Tao was noisy, or didn't exist. Come to think of it: why not; in a postscript.
Anyway, after years and years, I ran into this book by Raymond Smullyan a few days ago a book titled "The Tao is Silent" (New York City, Harper & Row Publishers, 1977). No, I haven't finished reading it, but I feel moved to tell you about my experi-ence with it so far.
Early on in the book, Raymond asks (rhetorically): does the Tao exist just as, in the West, people have (seriously) asked (and argued about) whether God exists. Perhaps these questions seem serious and philosophical to you; No doubt they are, ... but I also think of them a little with (Smullyanesque) whimsy.
So let me ask you: do shaded blotches on lung X-rays indicating tumours to trained doctors "exist"? I don't see them, ... but then, ... I am not a doctor. How different is this from the question "does God exist"? Believers have no doubt (like doctors); what is more, they see evidence of His presence all-the-time, everywhere (like the X-ray blotches which doctors see so clearly, but I don't). To complete the analogy: Believers find that God makes a big (practical) difference in their lives; and, they recognize various degrees of religious expertise; the less expert seek the help of the more expert. That's just how it is with doctors and their patients.
Smullyan, in an early chapter, raises yet another, analogous question of existence: do melodies exist? He means, "melodies" as distinct from an aggregate of pitches, for, as he observes: there are plenty of people who perceive aggregates of pitches, while (apparently) not hearing melodies. I submit: melodies are like shaded blotches on X-rays, like God, and like the Tao; (but, according to me, so are aggregates of pitches! All of these "somethings" exist for social groups, not merely for individuals, let alone in-and-of-themselves.)
I agree with Smullyan: the Tao is a particularly interesting "something", since its adepts consider it is as much "nothing" as "something" and furthermore consider that no thing could be (or not be) without it (not even itself). Having once seen It, you can never again be alone or abandoned; (never experience the despair of Jesus on the cross who cried "Eli, Eli, lama shabachtani?")
To feel alone and abandoned is the worst fate that can befall a human being. For most people, only the context of me-and-my-kind can possibly sustain the sense of existence of anything, even of yourself; but for an adept of the Tao, no evidence of abandonment by "his kind" can cast him into despair. (Perhaps this is what "salvantion" does mean or might mean!)
This discourse naturally leads to "purpose" so fundamental to our consciousness (and so despised by Science). Story after story in Raymond's book illustrates the Tao adept's freedom from purpose. This relates to three positive aspects of his life: it opens his heart, his eye, and his mind, for purpose constrains all three: it inures him against failure and disappointments; it contributes powerfully to his creativity.
And here I close.
Once, having been asked about the "purpose of life", I replied: "Life doesn't have a purpose; Life is the source of purposes"
I might have added: "Life isn't expressive; it is the source of expression"
The Tao is silent.
A Postscript
Late one night in Chicago (1943?), I came "home" to International House where I had rented a room for the summer. In the public living area a young man played Schubert on a grand piano as much a part of nature as my heartbeat. Raymond Smullyan.
Raymond was in the midst of reconsidering a career as concert pianist, mainly because he was suffering from tendonitis in his arms. At the time, he was still supporting himself by teaching piano at Roosevelt College but casting about for alternatives.
Raymond, as it turned out, was master of the 3 M's: music, magic, and, ... mathematics. Soon he moved from Roosevelt College to a nightclub, where he did stupefying tricks, to the delight of the nightly audience.
As in a dream, I recall a period of some months, in which Raymond lived in a loft above Ohrbach's department store on 14th street in New York City. Every midnight (when piano practice had to stop) I arrived at Raymond's loft for the next lesson on Galois Theory (an astounding piece of algebra, more beautiful and mysterious than a great oriental carpet, constructed by a young frenchman who died in a duel) full of humor, special (magical) Smullyan proofs and Smullyan words, like "Trivillary".
Many years later Raymond was "discovered" by a mathematics professor at Princeton. This professor extracted Raymond from his Chicago nightclub, gave him a PhD in mathematics, and installed him as a professor of logic at Princeton University.
I will not chronicle Raymond's public career in the many years that have passed since, except to say: he has published many books and papers often whimsical and profound. Some critics have called him the Lewis Carroll of our day, but as you can tell from the few paragraphs above this is, at best, a distortion.
One more, vaguely related Raymond story of my personal experience. In ca. 1955, he came to visit me in Philadelphia. "Well, Tolly, ... what are you doing now?" he inquired. I told him about my job as computer programmer with John Mauchly and UNIVAC I (at Remington Rand). "A computer you say? What's that?" I began an explanation. Five minutes later, Raymond, a little bewildered and with a very wrinkled forehead, stopped me: "Tolly, ... Explain to me what a computer is, in words that any mathematician would understand." Well, ... I tried again; Raymond did not interrupt me this time; his consternation had transformed into "cloudy skys".
I have told you this story, not so much because it throws further light on my friend, but because of my own life. As Raymond could not have known at the time, I had tried to characterize the UNIVAC "in words that any mathematician would understand" immediately upon arriving at Remington Rand (in 1952), without ever getting beyond "cloudy skys". Today 45 years later I am convinced that no amount of effort, even by someone much more brilliant than me, would have achieved the goal. Simply put: even though computers compute, they are not mathematical machines. (It is true that mathematicians compute (as do housewives); it is not true that computation is a mathematical subject, really; (and it isn't even true that computers mainly compute!))
12. Russel's Barber
Bertrand Russel (deservedly) made a great name for himself in my Century as philosopher, mathematician, political thinker, man. Together with another English philosopher Alfred North Whitehead he wrote a world-famous book of our Century called "Principia Mathematica" dedicated to demonstrating that all of mathematics is "based on" logic.
Bertrand Russel also shook up the (world-wide) community of mathematicians and logicians by announcing the now famous "Russel Paradox". This paradox showed that an unbridled use of "classes" as was the habit of mathematicians led to logical absurdities. Therefore the Russel Paradox set the stage for a truly labor-intensive project namely, to find a class-like definition which (a) would serve the needs of working mathematicians, and (b) would exclude the "oversized" classes required to generate the paradox. (These class-like entities were later called "sets")
Russel found some additional paradoxes which although seemingly unrelated to classes (and therefore sets) nevertheless seemed to have the same intuitive origin. One of these is "Russel's Barber", which you will find easy enough to understand. Here is my paraphrase of the "Barber Paradox".
In a certain village so Russel the rule is this: the village barber shaves those-and-only-those who do not shave themselves. In other words: everyone in the village who shaves has an either-or choice: to shave himself, or be shaved by the barber. Now if the barber shaves: does he shave himself? If he does so, he is shaved by the barber (since he is the barber), and therefore does not shave himself; if, on the other hand, he does not shave himself, he must be shaved by the barber, and therefore does shave himself. Conclusion: the village rule which seems perfectly sensible leads to a paradox for the barber, who may well be male who shaves, can neither choose to shave himself, nor choose not to shave himself.
Of course Russel, and his audience regarded the "barber paradox" as an amusing appendix to the problem he raised about the definition of classes. But in the context of this book, Russel's barber is (a) of fundamental importance; (b) more natural to treat.
This paradoxical aspect of Russel's barber disappears with a "better" definition of shavers (a definition hinted at, but not clearly defined in Fragment 7 "Body and Person"). These definitions imply: Russel's barber story needs a revision not in its factual intent, but in its description. In Russel's hypothetical village there are two roles that give shaves: there is the barber, and there is the self shaver ; every adult male in the village who wants his face shaved can choose: to be shave client of the barber , or of the self shaver. It is understood that, if a flesh-and-blood person performs as self shaver, the same flesh-and-blood person must also perform as shave client (of this self shaver ) a complicated way of saying that the self shaver only shaves himself. Given this construction, we can say: every male in Russel's village who is interested in shaves, is free to decide: either he will be shave client of the barber, or of the self shaver which he himself may performs. (Of course he cannot decide on both).
Obviously this choice is open to the flesh-and-blood person who performs as barber assuming that he is a male and wants to shave. Let us call this person Arthur. Arthur can choose to be client of the barber, or of the self shaver. Regardless of what he decides, the flesh-and-blood Arthur will shave himself; but the paradox has vanished.
There are some interesting contextually related matters to consider. These contextual matters show that what Arthur decides might make a practical difference in the larger shaving transaction. Suppose Arthur decides to be the barber's client. In general, the barber expects his clients to pay for their shaves. Would the barber expect this of Arthur? The barber might, or might not. If he does, then Arthur will have to pay the barber for his shave. But he might not make Arthur pay just as he might not make the village mayor pay. At least the barber will have consider the issue of payment in the case of Arthur, as he would in the case of the mayor.
There is a second contextual issue which seems like a joke, but I think is seriously interesting. Suppose, while shaving a client, the barber damages the client. Of course the client can sue the barber. Now suppose Arthur is damaged by the barber: should he be able to sue him? It seems that the answer is 'no' for it is Arthur who plays the role of the barber, which means that the plaintif and the accused would be one-and-the-same flesh-and-blood person. But: "the barber" might be a legal corporation with many share-holders; what then?
Why have I presented this peculiar view of Russel's Barber to you? Partly because you may find interesting and pleasurable to think it through; partly, because it shows that even a great man like Bertrand Russel need not have and perhaps could not have analyzed aspects of the situation that neither he nor his society were motived to consider.
13. Are People Good? How Should I Act?
(The Tao is Silent II)
My executive summary: people are neither good nor bad that is, people are people; and as to "the right way to act": every way to act can be right and can be wrong (and, finding the question "how should I act" relevant, is a bad sign!)
So. Let me begin at the beginning.
According to me, people are much too complex for so simple-minded a dichotomy. Under some circumstances certain people act like super-saints; under other circum-stances certain people act like super-devils; occasionally, the very same people do both.
However, there is one generality that I think applies.
In any scheme of organized action, people act in their own interests
This is, I think, a universal law; however "their own interest" is admittedly not a simple thing to understand; nevertheless, .. within limits, .. it can be understood.
(Part of) the complexity of the matter rests in this. In any scheme of organized action there are roles (or functions) to perform. Associated with the role (or function) there are interests, which are supposed to drive the performer. However, the performer being a flesh-and-blood person also brings a bundle of interests with him (such as keeping warm, eating and sleeping, etc.). An effective organization will include a means for aligning personal interests and role interests usually via some system of rewards and punishments. The phrase "their own interests" in my indented pronouncement above refers to the interests that result from combining these two types of interest via "motivators".
Another part of the complexity rests in the fact that basic human interests are not as easy to identify as one might wish. Certainly, keeping warm, eating and sleeping, etc. are a part. But there are other parts usually not listed for example, being well-regarded by one's fellows. Yet, in extreme cases, this latter interest may dominate all others.
The "being liked" interest explains some simple matters of my experience (and I think of everyone's experience). People much prefer to say "yes" than "no"; the same people who treat you brutally in the end, will do everything in their power to make you feel that you are great-and-wonderful, most important to them, etc. Is this because they are "bad"? Dishonest? No. It is because of the above-mentioned principle. But: this is only one example. Many other dishonesties and brutalities may (and should) be explained in the same way.
I am not a historian, but I have (somewhat superficially) read history books. As a result I have conceived a great admiration for the framers of the American Constitution, from exactly this point of view. As far as I can see, this constitution is a masterpiece of social engineering not constructed on the basis of the prejudice"people are fundamentally bad" (or its opposite), but constructed on the basis of a tacit understanding of The Principle (above).
Years ago, I paid a professional visit to NavBuPers (Bureau of Naval Personnel) in Washington D.C. to learn of their procedures for managing the infinitely complex process of producing and allocating naval personnel in thousands of varieties, nationwide. On the way home in an airplane, with a Vodka Martini in hand I considered what I would do, where I faced with their problem. I will briefly describe my conclusions, which (a) are only half a joke, and (b) relate perfectly to The Principle announced above.
NavBuPers has a very large number of criteria for successful action to consider. Of course optimizing any one these criteria tends to be in conflict with optimizing most-or-all of the others. Examples of such criteria: (a) honoring the explicit/implicit Navy promises as regards career advancement; (b) keeping the (very many) Navy professional schools supplied with a steady flow of qualified beginners; (c) supplying the hundreds, or even thousands, of the right Navy professionals say, 4 years hence, in San Diego when (and where) a new aircraft carrier is expected to be delivered; (d) minimizing travel costs; etc.
Now my idea was this: I would organize as many offices of NavBuPers as there are important criteria to consider. Thus, there would be an office for travel costs, for professional schools, for career rules, for special needs (like the aircraft carrier) etc. Each office would be run by a chief who would be told: your job performance will be evaluated on the basis of how well you manage to satisfy the criterion for which you have responsibility. This evaluation will be a major component in our decisions about your salary and grade promotions.
Next, I would give to each of these Chiefs a budget, to use in (a) carrying out his assignment, and (b) (as part of (a)) negotiating with other Chiefs in committees that decide in detail what NavBuPers is to do. (In this way, I only partially control the rate and quantity of money that an office spends per year.)
And I, as chief of NavBuPers? What would I do? I would sit in my office and gather world-wide political/economic/strategic information. On the basis of my readings, I would make occasional changes in the budgets allocated to different office Chiefs.
You may see many objections to my proposal. But here, my presentation of it mainly serves to illustrate a spirit. This spirit is not based on views about the goodness or badness of mankind, but on the (near) universal truth of The Principle which, in its turn, captures an important part of the idea "people are people". Finally, it is easy to see that this spirit is not so different from the one that animated the framers of the American Constitution.
On to the second question in the title: "How should I act?"
In this regard, I was particularly impressed by an idea of Raymond Smullyan's that I read in "The Tao is Silent". He discusses the question: is it better to be a "quietist" that is, let the world go as it will or to be an "activist" that is, fight for what you see as right. His answer: both are fine, ... for different people. What is not fine is this: that an activist should convey to others: "Activism is in accord with God's law (as therefore Quietism is not)". Equally unfine: that a quietist convey the opposite message to others.
This does ever-so-much remind me of feelings and opinions I have had over the years. For example. Israel has been politically divided between the Hawks and the Doves. As a Jew, I care. Twenty five years ago, while there, I spent a lot of time talking to hawks as well as doves. My conclusion at the time: I am for both (even though they want opposite things). Another example (more general, and perhaps more important than the last). I have, congenitally, found people who really know what is good for others repulsive regardless of what they espouse (Communism, Hawk-ism, Watch-Tower-ism, Catholicism, etc.) On the other hand, I have admired activists (like Che) as well as quietists (like Thoreau), artists as well as scientists, doctors as well as bridge builders, Raymond Smullyian as well as Herman Wouk.
Smullyan says: the Tao is not moral. Apparently, neither am I.
14. Meaning in Music (and Other Arts)
My whole life through, music has meant a lot to me (and more recently painting as well); so I have long wondered: why ? But in spite of my wonder I could never think of anything significant to say. Now (perhaps) I finally do have something to say .
But, before proceeding, let me say: I realize communication is a two-way enterprise; why should you care? I can think of several reasons. First, you too may care a lot about music, and may therefore also have wondered; second, my explanation is relevant to many other areas of experience; third, it is a difficult, mysterious, and broadly interesting subject that you might find interesting regardless of your other investments.
My thinking about all this begins with the following observations.
Listening or performing music can give me great pleasure.
A lot of the music that I find most fascinating presents me with structural ambiguities (whereas, in science, and day-to-day life, people strive for no ambiguities).
Just like science and especially mathematics there is "pure" music, and "applied" music; (here, I mean by "applied": for dance or work; to rouse patriotism; to ease tensions; to create one or another kind of social atmosphere; etc.).
So. Why the pleasure? Here's what I think.
Pleasure is invariably the result of satisfying basic drives like making love, eating, sleeping, etc. I think that participation in music can also satisfy a basic drive namely, to experience your deep-down sameness and your deep-down difference when compared to your fellows in other words, to experience, profoundly, your identity. (As implied by fragment 5 above, both your samenesses and your differences are critical to your identity.)
It turns out that, in human life, there are no constants without maintenance. Take love; if two people love one another and mean this love to endure, they must work at it among other things, endlessly reasuring each other that their love is real. (This same fact in a less obvious form also applies to the theorems of mathematics; the truth of a theorem is necessary but in no way sufficient to its continued existence; it must cater to an ongoing interest. The interest, in turn, drives ongoing effort: to repeat it, to teach it, to re-represent it in ever-new forms, etc.) And as to the ongoing sense of identity: (a) it is necessary to survival; (b) (of course) it requires ongoing effort.
And now I ask: does this (alleged) function of music (to reinforce the sense of identity) distinguish music from many other participatory activities? Only somewhat (I think); participation in sports, committees, clubs, running the household etc. should also give this satisfaction and therefore this pleasure. But as we will soon see in detail participation in music does this more-and-better.
There are two reasons for this "more-and-better". Reason One: music (at least when it is pure) has no other purpose; therefore (if I am right) people value it for this, and for nothing else. Reason Two: music especially European, especially composed and culturally refined) is built to address people's commonality, and to address their uniqueness (Interestingly, this is also the case in certain types of folk music notably English). Both of these aspects play a vital role in defining a person's identity (for example: I am a Jew from Eastern Europe, although American, with a special bent of mind, humor, etc.). By way of contrast, other participatory activities (usually not "pure") emphasize commonality over particularity (and therefore have a more "scientific" character, according to Fragment 5). The same may be said of "non-arty" music; it too makes people feel good, but mainly by feeding their sense of commonality (There are very many examples but particularly interesting is German folk song, in contrast to English folk song, just mentioned).
Above, I have claimed: highly evolved Western music feeds our sense of commonality as well as particularity and is, in this sense, ambivalent. How does it manage this?
As to commonality, this music is highly structured; it exhibits various, often elaborate, forms. At the same time, it is replete with ambiguities: a group of notes can equally be interpreted as the end of one (musical) thought, or the beginning of another; it may be perceived as implying one harmonic progression, or another; there are also multiply interpretable rhythmic figures; (I think it is just this that makes 6|8 such an interesting meter, since it invites 3 vs 2 ambiguities.) I submit: these ambiguities so important to musical quality contribute to music's ability to address the particular in each person: I see it differently from you; perhaps I see it differently now than at another time; perhaps (mysteriously), I see both at the same time. These different "seeings" lead into the unfathomable deep of the personality. (Without a doubt, it explains the fact that I own several interpretations of the same piece on CD. Not only do these different interpretations affect me differently; they also help me to see multiple possibilities via the multiple perceptions of other people.)
In a subtle way, this aspect intertwines with choices of over-all tempo and intensity. Of course tempo and intensity are aspects of all organized activity including a assembly lines but it is never so diverse, so open to interpretation, as in the case of music. Tempo and intensity "intertwine' with the interpretation of structural ambiguities because they are (loosely) coupled.
Here ends my main thought. Recapitulated, it is this.
1. Music its composing, performing, listening, and even instrument making can be intensely pleasurable. Everything that is intensely pleasurable satisfies a human need. The need satisfied by participation in music is: maintaining one's identity. (Perhaps this is the greatest need of all!) (Nothing in human life can be constant without maintenance effort.)
(Lewis Mumford, American scholar and city planner, found evidence for the idea that the need for art (and religion) played a key role in the establishment of permanent human settlements in pre-historic times!)
2. The sense of identity depends on two complementary aspects: what I have in common with my fellows; what distinguishes me from my fellows (see Fragment 5)
3. Music especially Western, composed caters to both aspects: the first is covered by the unambiguous, the fixed; the second is covered by the ambiguous, the variable.
There are a few postscript-type thoughts to some extent illuminating, to some extent amplifying the above.
AMBIGUITY AND META-AMBIGUITY. Fragment 5 is naturally summarized as follows: Form addresses the repatable; the repatable (and therefore form) may constitute the "figure" against the ground of the irrepeatable; form may also constitute the ground which brings the irrepeatable into relief as figure. (Which of these is appropriate depends upon which aspect is valued.)
The expressions "figure" and "ground" are taken from Gestalt Psychology. Remember that early workers in this field were fascinated by visual designs with an inherent ambiguity: the presentation might be seen as resolved into figure and ground in one way, but, by turning a mental switch, the viewer could reverse what he saw: the figure became the ground, the ground became the figure. "Sophisticated" music has exactly this aspect; one sees it "double" because of the above-mentioned two (inevitable) aspects of personal identity.
CONCRETE/ABSTRACT? (See Fragment 9.) It is commonly said that "pure" music is "abstract" like "pure" mathematics like "abstract art". None of these refer to things. Abstract art is also termed "non representational". In the canvases of DeKoning, for example, you cannot literally identify what you see with romantic mountains bathed in sunlight, handsome men kissing sad but beautiful ladies, strawberries and cream. You are supposed to appreciate, ... the "rhythm", the play of colors and shapes, etc. without being moved by the mountains, the sad ladies, or the strawberries.
Of course I understand all this; but there is another reality that touches me more deeply; pure music, pure painting, pure mathematics, deal with "somethings" that, in an important sense, are no different from mountains, ladies, or strawberries. To see what I mean clearly, ask yourself: what is the difference between a couple (man and woman), and the number 2? Surely the couple is an example of "2"; but so are innumerable other "things" such as two cherries, two boys, two raindrops even two steps. Yes, but how about a couple (man and woman)? Of such a couple there are also innumerable examples: John and Mary, Alan and Clarissa, dressed in an unending variety of outfits, she on his lap, walking in the country hand-in-hand, etc., etc. So far so similar. But Alan and Clarissa might get married, and/or have children. This you cannot say of "2". But on the other hand 2 + 1 = 3, which does have a (human) couples counterpart. For example: Alan and Clarissa might have a child, and in that sense, become "3" by the "addition" of "1".
What I am trying to convey to you is this: while numbers are "more general" than mountains, ladies, and strawberries, they are not really of a different kind; of mountains, ladies, and strawberries, there are many different examples, and this is true of numbers as well (but "more so"). These examples should allow you to see that, in a certain sense, mountains, ladies and strawberries are not that different from the somethings of which mathematical, musical, or abstract viual structures are made, even if the mountains etc. are usually thought of as "concrete" and these other structures "abstract".
Indeed, my examples also allow you to see: no matter how "general" (or "abstract") the items in a structure (whether scientific or artistic), they must have verisimiltude if they are to speak to you. For example: the operation of addition in arithmetic does have verisimilitude, for otherwise the experiments such as described in 3.I above would not work. No doubt DeKoning's canvases speak to other people, but they do not speak to me. This means: "abstract" as they may be, for me at least, they lack verisimilitude.
Suppose I am right about the function of music (and by extension, painting). the "pieces" cannot serve this function without verisimilitude; for every participant must feel that these pieces show that he lives in the same world as everyone else. That is why (I think) I am so pleased when, in a painting, the moutains, ladies, and strawberries look like mountains, ladies, and strawberries to me. That is also the explanation why I have never really enjoyed twelve-tone music; I do nto perceive its verisimilitude. (The fact that it is governed by rules that I can understand changes nothing.)
ELECTRONIC MUSIC. I have heard it said: today's extraordinary technology can be used to free composers from the limitations of the past: traditional instruments of limited capacity, in the hands of performers of limited capacity (even if astounding, given what they have to work with). By using computers and associated devices, we can open the world of the composer to undreamed-of possibilities; make it possible for him to fulfil his dreams as he never could before.
Let us call this "Simpson's view". You may or may not share it, but I would like to argue against it anyhow. This will give me an opportunity to develop thoughts that may interest you regardless thoughts that certainly interest me.
First let me say: I don't think I am an old fuddy duddy; an nati-technologist; a conservative or even reactionary who thinks "the way my forefathers did it was right; the new way is wrong". But: I really think Simpson's view reflects a profound misunderstanding about Life, about human life, about music.
Life is limited. You pays your money, you takes your choice; you exist in a limited body for a limited time. With good luck your time and opportunity will be greater; but at its greatest, it will never be perfect or endless. As I see it, human beings have mistakenly tried to think of the world in other terms; mistakenly not only because counter-factual; mistakenly also because, only through this fact not around this fact can a human being fulfil his greatest desires.
I claim: whatever you admire man-made or God-made; you admire the perfection with which it succeeds in the face of its (inevitable) limitations; (what is more, the admiring itself is strictly limited). Iron rule: the less you understand its limitations, the less you understand it.
Simpson's view notwithstanding: a composer who expresses himself via technology is necessarily and inevitably still limited, only in ways that his audience will find hard to understand. (After all, his budget is finite; his time is finite; the technology, no matter how great, can only accomplish so much with only so much reliability, etc.) The less that the audience can understand the composer's limitations, the less music can fulfil its function!
(In the case of sophisticated Western music, the "music game" is particularly complex, involving as it does, the limited composer who composes for limited instruments (made by limited instrument makers), used by limited performers. At least in my case, I think that all of these limitations enter significantly into my musical experience. At the same time, I know: there are other musical games; the one in which I participate most often has not always existed, and will not always exist. This, I accept fully, ... but not Simpson's view.
15. Thus! Now vs. Always
Isn't it a shame! In dirty reality nothing seems to be forever. At once I am reminded of a cloudy sky. The cloud Giant in a (cloud) river seems to have changed imperceptibly into a group of race horses! Always, on the beach, I see children building things. I am aware that tomorrow morning there will be little or nothing left to see. And the beach itself: some hundreds of years ago it may have been elsewhere also with children building things, or perhaps without.
My upcoming gearshift should make you realize: the clouds and the beach are not an expression of Weltschmerz.
Consider (the little that there is to consider in) a game of catch. Players A and B throw a ball back and forth: A throws as B catches; then B throws as A catches and so on, into the indefinite future and the indefinite past. Obviously this description is out of historical time, but this is how one expresses the idea.
Clearly, every real game of catch is, and isn't, like that. It begins when the players decide; it stops when they don't want to play anymore; the ball may land on the ground (because it was thrown badly, or caught badly, or both); a player may say "hold it" because he remembers a phone call, or notices that his shoelaces have come undone. Briefly put: the real game is now ; the game idea contains an always. But the real game is an example of the game idea all "dirty details" not withstanding.
The game of catch as I have laid it out explains a puzzle that struck me as I stared at an announcement on a bulletin board on the USS Kiersage, as a 18 year old sailor. It said: "Company B will muster on the quarterdeck at 0600, Monday, July 23, 1946" (italics mine). What do they mean "will " I wondered. Suppose I a member of Company B decide to jump ship; suppose the whole Company decides to jump ship over the week end; suppose Sunday afternoon the USS Kiersage is unexpectedly destroyed by a natural disaster. Does the word "will" still apply? As you see from the game of catch: yes it does. It expresses a part of the human plan which lies outside of historical time (while copying some of its attributes).
Before getting to the climax of this piece, I want to register some other facts of my experience and probably the experience of many others.
There is nothing I like better than to seem necessary to keeping the universe going. "Monday at 10 I have an appointment (and so, must go)"; "Give me a lift, will you, ... I have to be downtown at 5"; etc. The words "must", and "have to" are just like the will in the announcement on the USS Kiersage. They refer to human plans; they do not refer to shoelaces, or to superior movements of the soul not to mention the Cloud Giant that imperceptibly turns into race horses before my very eyes. Like the game of catch, this makes us feel immortal and important.
Yet another fact of personal experience. Often, when contemplating the world's greatest human creations a sculpture by Michel Angelo, Galois theory (in algebra), a crying woman by Picasso, a trio sonata by Bach I am totally taken in! It seems so natural and so true that I simply can't imagine the world otherwise; I think: the world was always thus, and always will be.
In this way I fall under the spell of the creator; but I am also being unfair to him as well as me; unfair to him because, in a way, I am not appreciating his greatest achievement: to have actually created the world anew! It is unfair to me for a more subtle reason. I am better off understanding that, in the final analysis, his creation is like the cloud giant, or like the children's castles in the sand transient, even if called "timeless" by his admirers.
When all is said and done, all this even applies to the counting numbers (and therefore arithmetic). Many people rightly have felt these numbers to be so basic, so immortal, that their creator must surely have been God himself. According to me, these numbers too must die like the Cloud Giant.
The climax: it is natural to take comfort in the seeming permanence of the oceans, the mountains, our own bodily form, and, ... of our greatest works; but perhaps preversely true glory lies in mortality!
16. Language: Words and Things
What a huge and controversial subject! Discussed, debated, analyzed, theorized-to-death for millenia; obviously as critical to being human as having a body.
Most people simply have their bodies without thinking; in the same way, most people just talk, without philosophizing about it how, and why, and how come.
Personally, I have been most interested in language as a human phenomenon partly because I grew up with four of them, partly because I always thought of it as an important part of my "field" (even to the point of getting a PhD in American Linguistics), and partly just so. I want to talk with you about some of what I have seen over the years.
To begin with, let me tell you about a number of important attitudes and experiences.
A pervasive view in my society seems to be this. There is a world of non-linguistics "things" out there, pretty much the same for everyone. There is also the world of language, which somehow allows one person to communicate with another person about the "things" out there. This is why so-called reference is so importrant; words refer to things; the way that the words are composed into phrases and sentences reflects the way that the things out there are composed.
This view of language and reality underlies various ideas that have played an important role in our society. For example, there is the issue of translation from one language to another. If different languages refer to the same world of things out there, with different sounds and different rules of composition, then translation though perhaps laborious should be mechanically possible; we only need to figure out what a text in language A means, and then express the same meaning in language B. (Computers give this view great practical importance, since according to this theory they might be programmed to perform translations.)
And then, I keenly remember a course I took at Antioch College in 1943, on "General Semantics" as propounded by Korzybski in a large book of his, called "Science and Sanity". A most important principle of General Semantics was expressed in the jingo: "The word is not the thing", meaning: there are words; there are things; the words refer to the things, but should never be confused with them." (An example of the contrary, from Kozybski: at a theater performance of a popular drama involving a hero, a villain, and a beautiful lady, a cowboy suddenly rose from his seat, and shot to death the actor who played the villain. Alas, this cowboy had not internalized "The word is not the thing".)
A final recollection related. Huckleberry Fin and Jeff the black man in Mark Twain's novel, sit around a fire one evening. Huck: "You know what they call the moon in French?" Jeff: "No-sir"; Huck: "La Lune"; Jeff: "Why that's a silly thing to call it, when everyone knows it's called the moon ". Jeff implies: 'la lune' in French evidently refers to the same round yellow luminous globe we see at night, that is referred to in English as 'the moon'; the French might have saved themselves the trouble of calling it 'la lune', since it is (was) already called 'the moon' by all sensible people that is, members of Jeff's linguistic and cultural solidality.
As you have probably understood already, I am out of sympathy with the proponents of mechanical translation, with Korzybski, and with Jeff. My point of view is not "normal", so bear with me.
Number One. I only partially agree that things and words represent two separate domains the one "reality-bound", the other "convention-bound". There are two reasons. The first: people use "things" just as they use words to convey information. What is more the information conveyed by "things" and the information conveyed by words are related. Suppose, for example, I enter a store and say to the salesman "My shoe size is 12; I'd like to see some modern tennis shoes." Soon he returns from the stockroom with several boxes of modern tennis shoes, size 12; these are the onward travel (so-to-speak) of the information in the words that I spoke to the salesman.
Furthermore. I also think that words whether spoken or written are physical things. Thus, the words "size 12 modern tennis shoes" have socially understood physical properties just as do size 12 modern tennis shoes although by no means the same properties. At any rate, the conventionally understood physical properties of each (a) place these entities within a generally understood and long-standing social tradition, and (b) adapt them to their respective uses. (But notice: the words "size 12 modern tennis shoes" may be used under circumstances in which size 12 modern tennis shoes have no role to play such as, in this paragraph.) This is the reason why, in years gone by, I have occasionally spoken of the "thing" properties of words, and the "word" properties of things.
Thirdly. Things and words are not always connected as in the case of size 12 modern tennis shoes. While it is much easier to come up with examples in one direction than the other, both directions are real enough. Example in one direction: "yes" is a word in English connected to nothing; example in the other direction: as passenger in a boat on the sea, 7-year-old me called out in great excitement to my rowing uncles: "Look, .. look at that log bobbing up and down near that wave"; "What wave?" said my uncles. I couldn't answer. I had a thing in mind, but had no words with which to tell my uncles.
Number Four. Things are no less social creations than words. Suppose I ask an American to remove all books from a room; he will among other things remove the phone books. Now the Italian word for "books" is "libri". If I ask an Italian to remove all "libri" from the same room, he will not remove the phone books for, in Italian, these are not "libri", but "elenchi" (translated into English as "listings"). This example shows: not only is the word"book" a creation of American society; so is the thing book. ; neither of them exist in Italian society. (And, I have just learned: in Sweden, a phone book is a catalogue!) Clearly this very simple example is at variance with the translator's/Korzybski's/Jeff's version of language-and-reality. This is the reason I think that Jeff was wrong: not only is "moon" American; so is (the) moon. The words "la lune" are connected to la lune; they are not just another way of "calling", ... the same thing; what is more the words "la lune" are not used in the same way as the words "the moon", whether or not referring to la-lune/the-moon.
Two closing remarks.
We all have reason to believe that children learn things and words together, each reinforcing the other. At the very least I can say: I have never seen a case that contradicts this view (but I know of no scientific experiments which establish its validity).
Once, when one of my daughters was 3 or 4, she was sitting at the kitchen table while I washed up. Holding a knife in her hand, and gently running her finger over its sharp edge, she said: "Daddy, ... what's this called?" I saw: the knife had a wavy edge! "What a miracle" I thought: "My little daughter already knows what features of real objects should have a name in English!!"
These down-to-earth considerations make clear why translation especially in local rather than international subjects is bound to remain an art.
17. Fair Division
What is a "fair" way to divide a resource among a set of claimants each of whom is entitled to some fraction of what is available? Most of us, immersed in the objective-reality view of the world (supported by science) believe that the issue lies in this: a procedure is "fair" insofar as it assures an objective division of the resource into fractions which as nearly as possible correspond to the claimants' entitlements. For example: it is "fair" to let a disinterested neutral divider, armed with a scientifically perfected balance, divide and distribute the resource.
However, this method of "fair division" seems to be at variance with a well known recipe for dividing a cake between two people with equal claim. The recipe is fully described by the short phrase "You cut, I choose". You, and everyone else, recognize at once the fairness of this, but it is not in the least bit easy to turn this recognition into an explicite definition, good enough for proving mathematically that "You cut, I choose" is "fair" let alone a definition good enough to explain how this procedure relates to the impartial divider who uses a scientifically perfected balance. (Notice: "You cut, I choose" does not guarantee that you and I will get equal amounts of cake!)
Of course I too recognized the fairness in "You cut, I choose" without knowing how to define it. Still, I once set my mind to finding an equally "fair" procedure for N claimants, equally entitled to cake. After some hours of mental effort, I found such a procedure. Of course, setting N = 2, the problem which my procedure was supposed to solve is the same as the problem which "You cut, I choose" is supposed to solve. Naturally I was very curious: would my procedure for the case N = 2 reduce to "You cut, I choose" or not? Lo and behold, it did not reduce to this; not only was my procedure as "fair" as "You cut, I choose": it was more fair! This gave me two startling pieces of news: (a) that there existed something other than "You cut, I choose" that "worked"; (b) that one could improve on "You cut, I choose", in a way that everyone can easily see and understand even if not define.
There is no need for me to describe my solution for N claimants, but Iwill describe it to you for the case N = 2.
Holt's Procedure (HP) for the case N = 2
Start: Claimants A and B go in alternation; A takes Turn 1. Before the first turn begins, the whole cake is called P0, and the "empty piece" is called Q0.
the ith turn: Except on the last turn, the claimant chooses between passing and not passing ; if he passes, then Pi := Pi-1 (and therefore Qi := Qi-1);.if he does not pass, he re-divides the cake in 2 so that Pi < Pi-1 (and Qi > Qi-1). On the last turn: the claimant may not choose passing if, on all previous turns, claimants chose passing.
termination: Turn taking stops exactly one turn after the first pass.
distribution: The claimant who last reduced P gets P; the other claimant gets Q. (The rules guarantee that every sequence of turns will contain at least one reduction.)
Now the following three statements are true (as you can check for yourself if you wish).
1. To execute a turn, each of the two claimants chooses, and may also cut: he chooses whether to pass or not; if he chooses not to pass, he cuts.
2. Suppose a claimant adopts strategy S, defined as follows:
(a) If P is less than or equal to 1/2 of the cake:
he passes
(b) If P is more than 1/2 of the cake:
If he is performing the last turn:
he reduces P by the smallest amount possible
If he is not performing the last turn:
he reduces P to 1/2 of the cake
If he performs Swithout error, he is guaranteed to obtain at least 1/2 of the cake, regardless of what the other claimant does on his turn.
3. There is no strategy which, if adopted by a claimant, will give him more.
So: is HP really more "fair" than "You cut, I choose"? Yes as you can see by the following. In the case of "You cut, I choose": the "right" strategy for claimant A is to cut the cake in half; for claimant B, it is to choose a piece that is at least half the cake. Since the right strategies for the two claimants are different, a claimant will prefer to be A or B depending on which of these strategies he finds easier to follow. In point of fact, everyone finds the strategy for B easier (since it only depends on a judgement of relative size, and not on cutting skill), and would therefore prefer to be B. (This preference is unconsciously given expression in "You cut, I choose" as opposed to "I cut, You choose".) By way of contrast: in HP, the right strategy for every claimant is the same; therefore there is no reason to prefer being A or being B. This is an improvement as everyone understands.
More important yet: my description of HP makes crystal clear wherein its "fairness" lies. I will now spell out for you the definition of "fairness" which HP illustrates.
Definition of Fairness (DF)
Suppose there are N claimants to a resource, each entitled to a given fraction of the total. (In the example above, N = 2, and the entitlements are 1/2, 1/2.)
A procedure P for dividing the resource is called "fair" if it has the following property:
There exists a strategy S such that:
1. Every claimant can perform his part in P following S
2. If a claimant follows S without error he is guaranteed to receive not less than the share to which he is entitled, regardless of the manner in which any-and-all other claimants perform their part in P.
3. There is no strategy that any claimant can follow without error that will give him more than S.
From DF follows: if every claimant follows S without error, he will get neither more nor less than his entitlement at the end; furthermore, there is no better strategy that any claimant can follow.
Exercise
Claimants A and B are to divide a heap of 1,000,000 dollar bills equally between them.
Assume that A is content with an approximately correct result, while B cares about differences of as little as 1 dollar. A procedure exactly analogous to HP can be used. There follow descriptions of three possible executions.
Execution 1: A follows S
Step 1. A divides the starting heap into 2 more-or-less equal heaps at sight, calling one of them P1 at random
Step 2. B counts P1 and find 499,872 bills; he passes
Step 3. A passes
Distribution: A gets 499,872 dollar bills, if B counted correctly. Otherwise A gets a little more or a little less, but in any case, a reasonable amount from A's point of view.
Execution 2: B follows S
Step 1'. A reduces the starting heap by a few dollar bills
Step 2'. B counts out 500,000 bills from P1 and declares them to be P2
Step 3'. A observes that P2 is about 1/2 of the whole, and passes
Step 4'. B passes
Distribution: B, by his own count, gets 500,000 bills, and so does A.
If B counted wrong, he gets some other number, but in any case not much more than 1/2 of the total.
Execution 3: B follows S
Step 1''. A passes
Step 2''. B removes 1 bill from the original heap
Distribution: B gets 999,999 bills; A gets 1 bill (assuming that the original heap really contained 1,000,000 bills)
18. Does Science Explain It All? II
I have been reading a book by Gerald Holton "Einstein, History, and Other Passions" in which he presents his science-biased (but accurate) view of the modern human condition that many have called "alienation". I loosely paraphrase Holton on this point.
Before Newton, man took a man-centered view of the Universe. He had been created in God's image; the rest of the world (or even Universe) existed for his benefit. Isaac Newton one of the two giants of physics said NO. The Universe is unfathomably vast; man is unfathomably small. Less than a fly-spec, he is irrelevant to the majestic mathematical laws that govern the whole. Therefore nothing could have been farther from God's mind than Man, when he created this mathematical All for God-only-knows what reason.
As if this were not alarming enough, physics since Newton has made things much worse. The entire "solidity" of every-day experience has gone up in the smoke of mathematical expressions that no one understands perhaps not even physicists. Nevertheless this "smoke" seems to "explain" undeniable laboratory experiments and celestial observations. Physicists have papered all this over with Alice-in-Wonderland notions such as "anti-matter", "time" that runs backwards (as well as forwards), probability waves, etc. In this way, people's common sense though still relevant to every-day experience has turned worse-than-useless when confronting REALITY.
When you stop to think of it, this sketch says exactly the same thing as the last sentence of Fragment 6 ("Does Science Explain It All? I"), namely:
"For whatever reason, I am convinced that Science, by its very nature, can only deal with an infinitesimally small portion of what we experience with one another in the world."
HQ (for "Holt Quote")
But the sketch says the same thing from an opposed point of view and, as best as I can see in an unecessarily restricted historical context.
The first matter in a nutshell: Holton does not question that REALITY is what physicists say it is; HQ assumes that every-day experienceis the source of all REALITY, including the mathematically described reality of physics; for keep in mind: the Alice-in-Wonderland notions and the correlative mathematical equations are justified by experiments and observations carried out by ordinary people who describe what they do and what they see to other people without recourse to Alice-in-Wonderland notions, or mathematical equations.. If these descriptions wouldn't "work", then neither would the Alice-in-Wonderland notions and correlative equations! In that sense, the fly-spec's common sense underlies the grand designs of the Author of the All.
I plead to you, to the world, to the Author of All: it isn't that I want to rid the world of modern physics; I merely want to put it in its place. I want us all to realize: if, by common sense, I would not find my apartment or my bank account "real", I couldn't possibly find the modern-physics account of the Universe "real", ... BUT NOT VICE VERSA! And I can never forget: physicists have apartments and bank accounts, just like me; they are just as hell-bent on their careers and incomes as I am on mine. This in my opinion helps explain the widespread "alienation", partially perpetrated by physicists to promote their social power, and partially sketched by G. Holton.
19. Conjectivity
"Conjectivity" is a neologism coined by my friend and colleague, Felice Cardone, at the University of Milano. This neologism designates (a) a serious departure from a long-standing tradition in Western thought, expressed by the terms "objectivity" and "subjectivity", and (b) a point of view that underlies many of the fragments in this book. Obviously my friend also meant "conjective" and "conject", in analogy to "objective" and "object". (There are 2 now obsolete usages of "conject": (a) conjecture; (b) plan.)
So what is the new idea behind the new word? It is easiest to explain this against the background of the older distinctions: the "objective" is (understood to be) what is "really out there"; so, barring disturbances, everyone should agree about the "objective" but, whether they agree or not, the objective is as it is; the "subjective" is what one person perceives; others might agree about about this or not; (the "subjective" might even coincide with the "objective". The "conjective" is what a group bound together by practical pursuits agrees is out there. To re-emphasize and summarize what I have just said: if something is objectively there, everyone should agree (but whether they do or not is immaterial); if something is subjectively there, one person should think so; if something is conjectively there all persons to whom this "something" practically matters should agree but not others; and the agreement of these persons is material.
At first, it may seems that "conjectivity" introduces a new possibility alongside of the older distinctions, without a reason for conflict. But a conflict does arise when the "conjectivity-thinker" denies that the world really is any particular way, and that conjectivity is the prime basis of all humanly perceived reality. In this way, well identified subsets of people must agree with each other before something can be part of such a reality (even in the case of so-called "objective" reality!)
As it turns out, the objective/subjective distinction, and the idea behind "conjective" are closely related to my short piece "Language" above (Fragment 16). There, I maintained: the idea of translation (from language to language) is based on the supposition that the different languages of the world by-and-large reflect the same (objective, world-wide) reality. Therefore: given a piece in language X, one need only strip away the (historically significant, but philosophically accidental) phonology, morphology, syntax, etc. of language X, leaving the true (that is to say, objective) meaning exposed. This meaning can, in turn, be be re-encoded in the phonology, morphology, syntax of language Y.
I know this is a crude picture; I know that sophisticated people think the problem is much more complex. But I also think this "crude picture" forms the riverbed of all supervening sophistications.
However, as you may have noticed in Fragment 16: there are other ways to think about this: not only is language an expression of a society; so are the things "out there". Not only the word "libro" is part of Italian culture; so is the thing"out there" to which the word refers. (Thus, a phone book is not a "libro" (but an "elenco").) Not only the word "libro" is a conject for Italians; so is a libro (which I cannot call a "book"). So. While social agreement is at most a side issue for the distinction between objecive and subjective it is central to the idea "conjective".
It is exactly this idea which led me to imagine a conversation between myself and the English philosopher Bishop Berkeley, who achieved fame among other things for his question about the falling tree in the forest. If there is no one there to hear it he asked does it make a noise? (Obviously a question aimed at the philosophical issue: is the noise of a tree that crashes in the forest objective or subjective ?)
I imagined Berkeley coming to me with this question. I would answer him: dear Bishop Berkeley; as a responsible member of my society I cannot but answer: it makes a noise, whether or not there is anyone there to hear it. In other words, the noise of the tree that falls in the forest is a conjective fact.
This is no different from the following. Suppose I were a medical man trained to read lung X-rays. A layman shows me such an X-ray and asks: does this X-ray show a suspicious shadow that might mean a lung tumor? I say: "yes", regardless whether the asker can see it or not. The suspicious shadow is a conject for all similarly trained medics. I would be shocked if other professionals disagreed with me, but not shocked if the layman "is blind".
Why did I imagine saying to Berkeley "As a responsible member of my society .... "? Members of my society who are not philosophers like Berkeley believe without question that the tree makes a noise whether anyone is there to hear it or not. Therefore, scientific instruments accidentally placed in the forest not far from the falling tree might register the tree crash by virtue of its noise. My fellows would probably accept the instrument record as evidence in a court of law. And, as a responsible member of my society, I too would accept this; but only because I too believed that the noise is independent of its hearing.
CONJECTIVITY AND ARITHMETIC. The practices of counting, measuring, and arithmetic have spread over the globe as have a number of other things, such as rock music, Coca Cola, jeans and T-shirts, and modern science (which depends on numbers). Therefore: every-day numbers, and how to obtain them, number designations in arabic place notation, and how to operate with them arithmetically have become conjective on an international scale. Although almost anyone will agree with almost anyone else world-wide about these numbers, their representations, and operations, I think they are conjective (and not objective) nonetheless. Of course they like the other international items I mentioned are trans-language, trans-culture conjective. (And of course, arithmetic and everything else transnational exerts a "levelling force".)
CONJECTIVITY, "OBJECTIVITY", AND THE NATURE OF THE WORLD. In the light of the previous paragraph, it is no surprise that "objectivity" has become so intimately associated with Science. In the context of Science itself heavily internationalized the conjective nature of scientific reality is particularly hard to notice; (but this may also be said about tennis matches, bottles of Coca Cola, jeans, or rock songs).
Am I in the midst of denying that objectivity exists? No. I am in the midst of saying that objectivity itself is conjective perhaps internationally (or quasi-internationally) and that its association with things that are internationally recog-nized (particularly Science) is no surprise.
And now I must face the question: if conjectivity underlies everything that has public standing, how come do some things "work" and other things do not "work"? Is my position the same or different than the position which I encountered in philosophical contexts called "truth by convention"? I think, significantly different.
The most radical case is that of mathematical conjectures: they either turn into theorems (and therefore, by definition, turn out to be true), or alternatively they end up in the waste basket because a counter-example has been found. Thus, whether a conjecture is "true" or "false" is not a matter of opinion: supposedly, there are guaranteed procedures for convincing every relevant person that the conjecture "works" (is true), or alternatively "doesn't work" (is false).
Now let us consider the possibilities for a mathematical conjecture C which, in the above respect, defies classification.
1. C is proved and a counter-example is found
2. Mathematicians do not substantially agree whether C has been proved or disproved. (As to the "substantially", see Fragment 3, part III.)
3. C cannot be proved and that no counter-example can be found
But the fact of the matter is this: possibilities 1 - 3 just listed do not occur in practice . Why not? No reason. it just doesn't happen. Recall: this is just what I said in response to the rhetorical question "Why does arithmetic addition give the same result as the addition of real-world quantities to one another?" In Fragment 3, part I, I answered: no reason; it just does. By the way: Gödel's main result might be a reason for a gloss on possibility 3.
Gödel or not, I have a right to expect: even though according to me mathematical conjectures are conjective: they will be "true" if proved; they will be "false" if a counter-example is found. My expectations concerning this are no less firm than my expectation that arithmetic will "work". If this were not so, mathematics and science more generally would not have spread over the globe. (This is no different from saying: if people everywhere didn't like rock music, or Coca Cola, neither of them would have become international; is there a reason why people like these things? I doubt it.)
The long and short of it is this. There are conjectivities that work better, and there are other ones that work worse; and, while it is easy to imagine conjectivities that hardly work, they are unlikely to become established especially among many people, especially for long periods of time.
Even Science teaches us this lesson. Why do scientific approaches and theories supplant one another? Because a later one works better than an earlier one especially when taking the changing global culture into account. (That is the reason we can expect revolutions in science and even mathematics underpinned by the international spread of computer networks.) I along with many historians and philosophers of science think these supplantings are less well understood as driven by the cultural motive: being "more true to the objective facts".
In conclusion: conjectivities are in part "truth by convention"; but in part, they must work, if they are to last; they must, in some sense, be consonant with The Universe, The Great All, The Tao and what this means, ... neither I nor anyone else can say.
THREE CONJECTIVITY EXCERCISES; the first of these shows that the "society" that defines and shares conjects may be small.
[1] I am looking at some glassware, and I ask myself: is it "clean" or "dirty"? Here, I meta-ask myself: am I asking about an objective fact? In one sense, it does seem so: clearly, the glassware either is, or is not, really clean (or dirty). But, ... to decide this about glass teacups at home is not at all the same as deciding this about glass pipettes and flasks in a chemistry laboratory. To be a reliable judge of the latter, you must be a chem lab adept. To be a reliable judge of the former, ... well, ... it depends. You can do pretty well in most households that are part of your community, but it may be that your family is different; to decide "at home" you have to live at home. What I am getting at is this: "clean glassware" is conjective and it means different things to different groups co-involved in organized activities.
[2] This morning Mr. Sawyer the baker has B buns and R roles for sale. Is this an "objective" fact? If you have been trained to distinguish between buns and roles as all native English speakers have, and as most native Italian speakers have not you can check if it is true; if you have not been trained, you cannot check. Conclusion: the asserted "fact" about Mr. Sawyer's offering this morning is neither objective nor subjective, but conjective.
[3] Why did the classical Mayan Indians spend half of their yearly GNP on creating stone temples an extraordinary waste from our point of view? Because we believe in Science as a way to explain and control survival-related functions such as growing food, minimizing earth-quake damage, combatting disease; the Mayans believed in Gods and Spirits who had to be "humored" so that the Mayans might prosper. Therefore: the Mayans considered the expenditure of effort on temples as no less important than we consider the funding of scientific rese
