When I gently shook one of my Christmas presents, its contents clickety-clacked a little, with a heavier rolling undertone. Some kind of game-pieces perhaps? Hmmm.
The top of the box portrayed an open, four-level structure of horizontal girders supported by vertical columns. In big letters it informed me: “Here is your clock.”
A clock? You’ve got to be kidding!
The instruction booklet inside showed me how to assemble black plastic girders and columns to support troughs in which shiny metal balls could rest or run.
The arrangement is most ingenious. At the base of the structure a supply of balls waits in a sloping storage trough. An arm with an open scoop at one end is rotated vertically once a minute by a small electric motor at the back. Each time the scoop passes the storage trough’s loading place, it picks up a ball from the lineup. When it arrives at the highest level of the structure, the ball tumbles from the side of the scoop into a trough, where it runs down and around to an h-shaped, counterbalanced tiltable trough on the next lower level. The rolling ball enters the short leg of the h, runs across to the long side and comes to rest there. That long side will hold four such balls and still remain stable. Bold white numbers 1 to 4 are printed on the front of that trough. At five minutes a fifth ball enters the short leg of the h. That tips the trough, immediately sending the previously arrived four balls down a spout which returns them to the storage trough. At that same tilt the fifth ball – a five-minute ball – runs into a trough which conducts it down and back around into another h-shaped tiltable trough whose long side can contain up to eleven balls. White numbers 5 to 55 on its front side mark intervals of five minutes, as on a clock face. The sequence repeats until eleven five-minute balls have filled the long side of the long second h trough. The twelfth ball tilts the whole trough, sending the previous eleven balls back to the storage trough. The twelfth ball – an hour-ball – descends to a third and lowest h trough, which can hold up to eleven balls and is numbered 1 to 11. When this action has continued for eleven hours and fifty-nine minutes, all of the troughs have received their full quota of balls. The next minute-ball delivered at the top begins emptying in turn all three full troughs. All of the balls pour down their spouts back to the starting-trough, all of the tiltable troughs return to their “ready” position, and the whole process begins all over again.
This complicated apparatus functions fairly well as a clock. The sixty-cycle motor establishes the minute-by-minute intervals at which waiting balls enter the time-marking process: five balls in five minutes; twelve groups of five in one hour; twice twelve hour-groups in one day. Since the successive ball positions along all three troughs are numbered, the number of balls present in each trough registers the time of day or night. When I started the machine, of course, I had to note the right time and put the corresponding number of balls into the right troughs, otherwise the system couldn’t have functioned as a useful timepiece.
During Christmas week Kay and I were completely fascinated by this ingenious clock. At first, instead of waiting for the motor to do its thing, she would launch balls by hand to watch what would happen. Both of us took delight in observing the precise shape of each part of the structure and its function in the operation of the whole contrivance.
The sudden clatter of a single trough emptying is alarming enough, but the rolling cascade of all the metal balls pouring at once into brittle plastic troughs and rattling down a spout is, shall I say, sensational. Unfortunately the clock dumps its whole load of noisy balls not only at noon, but also at midnight, interrupting quiet slumber even in the next room. During the day the clock’s distracting activity every five minutes certainly kept me aware of the passage of time!
After a couple of clattery weeks the novelty had worn off and the clock was unplugged. It now sits there on a shelf under its clear plastic cover. Always an interest-catching conversation piece, it is a never-failing source of entertainment for children. As for me, my intriguing Christmas clock continues to suggest ideas which I regard as basic for an understanding of time.
Inventing and manufacturing a clock
Let’s think about how my unusual clock came into existence.
I can imagine the pleased grin on someone’s face when a fascinating notion came to mind: the novel but feasible project of constructing a clock which would keep track of time by dropping things at regular intervals and counting them. But how? It’s easy enough to drop things, but not so easy to drop them one at a time at regular intervals. To assign numbers to things as they are dropped would require some kind of counting device. Should the dropped things stack up vertically in a single column? Pile up randomly in a heap? Spread out over an area? Queue up? How could dropped things be separated temporarily into groups which would signify minutes, hours and a day? How would the whole lot of dropped things eventually be fetched back up to drop again? Hmmm.
The inventor would have to decide between a number of alternative ideas. Common ways of starting, controlling and continuing processes would come to mind. What physical motions repeat at regular intervals of time? How can gravity be turned on and off or counteracted periodically? Can its downward vertical force be diverted to power horizontal movement? How can a physical process be turned into a numbering process? What kinds of things can be dropped and retrieved conveniently?
The mental process of sorting through alternative mechanical conceptions is obviously quite different from any physical process. Anything which would drop would have to have some weight, but the idea of dropping such a thing is weightless. The idea of it dropping through a distance could not be measured by a tape. When its falling was being imagined, nothing was actually falling. Imaginary rolling metal balls have no momentum because they have no mass.
An ingenious novel idea suddenly appeared out of nowhere: the idea of h-shaped, counterbalanced, tiltable troughs with numbered positions of successive incoming rolling balls. All that remained was to develop a system incorporating the h-trough idea. Three of the troughs with lengths appropriate to minutes, hours and half a day would handle the counting. A sixty-cycle electric motor would conveniently take care of the timing. Inclined connecting troughs would link each ball’s journey through the troughs back to the beginning. A simple system – once the relations have all been related.
The unusual components of this projected clock would not be available “off the shelf” nor would they be easy to make in a home workshop. The next step therefore was drafting plans which would guide a plastics manufacturer who was willing to produce components for a prototype. While the drawings on paper had an actual physical presence, they were certainly not an actual clock. They simply set forth a set of related relations which could communicate the tentative conception of a clock which the inventor had in mind. Only when those relations had been embodied in a particular physical form would that conception become an actual time-marking system.
When a satisfactory prototype had actually been built and refined, a final set of plans could specify in detail the relations which would characterize each and every part of every clock which would be produced. A stable structure was envisioned, each part of which would have a specific shape and dimensions. The distance between the two ends of each piece of the frame had to be exactly specified. To hold the frame together, each structural member had to join and fit with each adjacent part in a specific way. The shape of each movable component – rotating arm, tipping trough, rolling ball – was prescribed according to its place and function in the whole system. The detailed, duplicable relations which made up the clock’s overall design ensured that each manufactured clock would be the same as any other.
You may have noticed that I have been using the term “relation” again and again. In my thinking, cosmic time is the process by which the relations between everything in the whole universe are always being changed. To understand time, therefore, I need to clarify what I mean by “relations.”
Two or more things may be said to be related to each other if the existence and/or activity of each of them makes a difference to the other. One of the related things may be completely passive, but where, when and how it actually exists can nevertheless determine the vectoral direction and character of influence exerted by or elicited from some other thing. Contrary to popular conceptions, emotion is not an essential ingredient of relating.
At least two things or ideas have to be involved at the same time for there to be a relation. Many important situations cannot be produced or conceived apart from a linkage of two separate factors, for example: comparison, measurement, boundary, equilibrium, collision, transaction, contract, covenant, polarity, ambiguity, fit, model, choice, complement, reference, recognition. The basic unit of systemicity – the minimal system – consists of two things which are relating, that is, mutually affecting each other, as explained above.
As for my clock, each structural piece of its frame has two ends. The span between the two ends of the piece can be referred to either as the general relation of dimensional distance, or as the particular relation of a definite length. The relation which joins two piecesin close proximity forms a joint. Three other things – the motor, its rotating arm and a ball – participated in successive relatings: scooping, raising and dumping a ball. When I was assembling the clock, putting it together piece by piece, I was relating awhole complex ofrelations, which together became a system capable of operating as a clock. Two or more relations can themselves be related. When the clock had been fully assembled, the relations which I had related had become the clock’s internal relations.
Nothing in this world ever comes into existence entirely by itself. There is always an influential accompaniment, a supportive surround, a context of relevant circumstances. Like everything else, the clock also has external relations to other things, systems and persons. The clock belongs to me. It sits on a shelf in my study in our house on our street in our community, province, country, continent, planet and solar system.
My clock is related to planet Earth by an electrical system which provides it with power and timing. When I plug its little motor into our household’s electrical outlet, the clock’s ball-lifting arm begins to rotate regularly at the rate of one revolution per minute. This motion enables it to deliver one ball per minute to the highest level of the clock. The sixty-cycle design of the motor keeps the clock’s activities in step with the Earth’s rotating – our standard for clock-time. The minute-by-minute timing of the clock’s ball-delivery system derives from the electrical current reversing its direction sixty times a second. A second, of course, is a sixtieth of a minute, a minute is one-sixtieth of an hour and an hour is one-twenty-fourth of a complete rotation of the Earth. The bold white numbers printed on the tipping troughs refer to fractional portions of Earth’s regular rotation through twenty-four hours. So through the sixty-cycle current the time registered on my clock is related to the rate at which Earth rotates. When all three of the clock’s tilting troughs have been filled with balls and dumped twice, that indicates Earth has completed a full turn on its axis: one day has passed.
My clock is related by wires to dynamos at a hydroelectric power-generating station. The speed of the rotating turbine which drives a dynamo there is regulated by controlling the volume of water which is allowed to enter its intake. The force of the rushing water is generated by the attraction which Earth’s gravitation exerts upon the depth of water impounded behind a dam. The electricity generator which is rotated by the turbine is related by a transmission line to the wire windings inside my clock’s motor. Interrelations between those windings enable the alternating electrical current to generate a magnetic field which drives the motor in the right direction for its rotating arm and scoop to lift balls to the top of the clock.
That complex set of related relations is thus able to turn the downward attracting force of Earth’s gravity upside down. What was pulling water down a flume into a generating station is being reversed to lift metal balls up to the topmost level of my clock. Once a ball has been dumped into the trough up there, Earth’s gravity resumes its normal role and pulls the ball down and around through the clock’s related series of troughs.
During twenty-four hours the planet will have moved through 1/365 of its annual orbit around the sun. It will have carried my clock and me with it, so I know that during those hours our spatial relations to all other bodies in the rest of the universe have been changing. The relations among the other celestial bodies are also always changing. No stars are really “fixed” stars.
All things in the universe are thus related to each other in a vast number of ways and directions. Those relations are always changing from moment to moment. The relation of cosmic time to Earth-time as registered by my clock is therefore unspecifiable.
Relations are mobile
The relations involved in my clock have a history. I don’t know the source of the notion that a clock could be built which would tell the time by dropping balls at a certain rate and counting them. A set of feasible relational ideas was selected. Between the inception of those ideal relations in the inventor’s mind and the marketing of the actual clocks, that set of relations went through several remarkable metamorphoses which enabled them to migrate from a merely logical status within a conscious mind into the external world of physical structures.
Those relational ideas advanced from rough sketches to formally drafted plans. Photographically reproduced, the mechanical drawings were transferred to a folio of blueprints. Those relations leaped off the paper, riding on reflected light, and entered the eyes of a production engineer. There they were transduced into serial patterns of cranial nerve impulses which were interpreted by the engineer’s brain and translated into orders for materials suppliers and detailed written instructions for machine operators. According to their settings, the machines turned materials into the various specific pieces of the clock. The right number of each kind of piece was put in a box. The boxes were sent to a distributor, then on to retail stores. One of them eventually arrived in my home and, according to the related instructions, I assembled those pieces into a clock. Sitting there on my shelf, that stolid material structure now embodies the very relations which originated years ago in the mind of a faraway, unknown inventor. Relations can be surprisingly mobile.
To bring my conception of the mobility of relations into even sharper relief, let me relate (intended word) to you the story of, say, Beethoven’s Fifth Symphony. At first Beethoven heard this music in his mind’s ear. Then he wrote out each passage in music notation, indicating which of the many possible relationships between sounds he had selected. Later, copies of the manuscript were printed and distributed as a symphonic score. Light reflected from the score brought the relations of those music symbols to the brains of many generations of musicians through their eyes and their optic nerves. There those impulses were understood and redirected to activate trained muscles which produced the prescribed sets of vibrations from various instruments in the right order and timing. In later years such patterned sound waves gave rise to vibration patterns in microphones which were transduced into variations of an electromagnetic circuit. These in turn activated a mechanical device which cut needle squiggles in a spiral groove around a rotating master disk. The complex pattern on this master disk was reproduced on many vinyl disks. The squiggles on one of those disks can be transduced into electromagnetic variations which jiggle the diaphragms of loudspeakers. The resulting sound waves, via their eardrums, can thrill music lovers.
That a pattern of musical relations which was conceived in the mind of Beethoven thousands of miles away and many, many years ago, could make such a long journey through that complex sequence of diverse media and arrive intact in my study and consciousness is truly amazing.
Relations are travelers by nature. A relation is born when one thing affects something else which is beyond itself. Every relation between things makes a difference, and every difference makes a further difference sometime somewhere. Everything that exists is always making a difference to something else, always affecting its surroundings and being affected by them. At the very least, a thing which occupies a certain place at a certain time is automatically excluding every other material body from occupying that place at that time.
“To be” means to make a difference or to be able to make a difference. What makes no difference to anyone or anything simply lacks the slightest vestige of existence. Relatedness therefore defines all existence.
Nevertheless more attention is usually paid to visible, lasting material bodies than to invisible, changeable and transient relations. That is easy to understand. Material things generally reflect light, making them easy to see. Focusing on one thing at a time is simpler than correlating the two or more things which are engaged in relating. We tend to forget that we ourselves are one of the two things involved in the relation of perceiving. All material bodies offer resistance if we attempt to change their place, speed or direction of movement. They seem to be determined to persist as they are and where they are, so to us would-be movers and shakers they always present an attention-getting challenge.
Relations can travel much faster than material bodies, since matter can never be moved as fast as the speed of light. The patterned relations which ride on electromagnetic radiation are, however, able to travel at the speed of light. Light can travel through air, glass, water, even a complete vacuum. X-ray images can pass through flesh. Radio waves go through buildings. We can converse by telephone because speech-patterned electrical impulses move so easily through wires. Well authenticated experimental evidence also shows that the polarity relation of a certain subatomic particle may be immediately influenced by a change in the polarity of a far-distant particle with which it had been formerly associated. This suggests that relations may be able to travel even faster than light. Of course the simultaneous “relational change” of the particles could possibly be due to simultaneous creative action at both places by a transcendental Agent. In that case cross-communication would not have to travel from the one location to the other.
In a game of tennis at least two players on opposite sides of a net keep trying to drive a ball over the net to land within a marked court out of reach of an opponent. Obviously the ability of a player to move quickly to an advantageous position, as well as the ability to hit the ball forcibly in a direction troublesome to the opponent, will make a decisive difference to both players. The game consists of rapid changes in the relations of distance, direction, angular inclinations of rackets, forcefulness and timing. The complexly patterned back-and-forth trajectories of the ball delineate the extreme mobility of the relations between the players, rackets, ball and court.
The space between stars, suns and planets results from changing distance and directional relations. Interconnecting gravitational relations between moving celestial bodies keep shifting in strength inversely as the squares of the changing distances between the various bodies.
Transduced by our sensory organs, relational forms have always been able to pass rather freely from the “outside” world into the “inside” world of our living body and mind. A pattern drawn on paper can travel to our eyes on reflected external light, and a correspondingly coded pattern of nerve impulses will swiftly race from our eyes to our brain, informing us that the paper pattern is out there. When audible patterns of vibrations in the air impinge upon our eardrums, the incoming impulses register in our brain not only the character of the sounds, but also the “before, simultaneously and after” temporal order of their arrival. Somehow our consciousness can retrieve such dispersed, time-related modules of information from a number of sensory inputs, put them back in their original serial order and integrate them into a meaningful whole of remembered experience.
These experiences can also be incorporated into a plan for future action. Imagined relational forms can pass freely from within our “inside” mental world to perform various functions in the “outside” world of objects. If we have grown tired of the present arrangement of our furniture, we can imagine a preferable arrangement and how to achieve it. We summon another person and together we move the furniture to new positions as planned, quickly adjusting the positions and tensions of our backs, legs, arms, hands and fingers. Relations are much more mobile than furniture.
Relations are variable
Relations may vary greatly while remaining the same relation. Just as a kitten may become a cat without becoming a totally different kind of animal, a given relation may change in value without becoming an entirely different relation. A distinction must be made between “differing somewhat” and “becoming entirely different in kind.”
If a compass needle is carried over the whole surface of Earth, the direction in which the needle points will keep changing. The relation of the needle’s magnetic poles to Earth’s magnetic poles endures, but its orientation keeps changing.
The same general relation can relate many different things at the same time. On a soccer field the general, abstract relation of space will be perceived in terms of the boundaries of the field and the particular distance relations between the players, the ball and the goal nets. When players are running with the ball, all of those particular distance relations will be changing, increasing or decreasing – and reducing to zero distance during contacts and collisions.
A linear distance relation can lengthen, shorten, change direction or spread sideways into a two-dimensional planar area. That area can expand, contract, rotate or change shape. Both quantitative and qualitative relations may increase indefinitely or diminish to zero. Light may intensify or dim, radiating heat and color. Sounds may vary in volume, pitch, timbre, duration, etc. Temperature can cool to absolute zero or heat up indefinitely high.
All of these alterations in relations require time to take place. At any given moment each general constitutive relation of the universe is at some particular phase of its complex varying. Each Now-state of the universe is a composite which includes the present state of each and every variable particular relation. Cosmic time is the succession of such momentary states of the whole universe.
The same things can be related at the same time by a number of different relations. A mother cleaning fingerprints off a mirror can be considered as being simply oriented frontally to the mirror. But she is related to those fingerprints by a mother-to-child relation. Reflected light relates her to her own image and to the images of what is behind her. In touching the mirror she has a feeling of texture and temperature. The cleanup is also related to her other activities during that day, for it took place at a certain time, before some events and after others. In short, what could be taken at first as a simple relationship may in fact be quite complex. If anyone seriously asked me to interpret the first verse of the book of Genesis, I would probably say: “In the beginning God created all possible kinds of relations, whose variations with time would develop the whole history of the heavens and the earth.”