Definitions and Concepts Used in Cycle Study, by Edward R. Dewey

Definitions and Concepts Used in Cycle Study, by Edward R. Dewey

I have often been asked to provide authoritative. definitions for words used in cycle study. Only if all of us who are engaged in this work use words to mean the same thing can we understand each other clearly. This article is a first attempt to satisfy this demand.

First, let us turn to the dictionary to get some preliminary meanings for some of the more common words. ORDER. L. ordo, order. Conformity to law. PATTERN. OF. patron, from L. pater, father. An arrangement or composition that suggests or reveals a design; a configuration; formal or regular arrangement. CYCLE. Gr. kyklos, ring, circle, cycle. A complete course of operation returning to the original state. FLUCTUATION. L. fluctuate, to wave, Fr. fluctum, to flow. Wavelike motion. Fluctuate suggests irregular or alternating movements, especially up and down. OSCILLATION. L. oscillare, to swing. The act of fluctuating within or between relatively fixed limits. (In physics, a single swing from one extreme to the other of an oscillating body.) WAVE. A. S. wafian, to wave. One of a series of undulations. Something that swells and has a crest, or rises and falls, like a wave. RECURRENCE. L. from re currere, to run. The act of occurring again, especially after an interval. RHYTHM. Gr, rhythmos, measured motion. Movement marked by reasonably regular recurrence, or reasonable regularity of alternation. PERIODICITY. Gr. periodos, a going around. A perfectly regular idealized motion.

Dictionary meanings are good for a starter but they are not precise enough for scientific purposes. Moreover, there are many concepts for which there are no single words -male Manx cats, (or white) for example! If you are to get an adequate idea of the various sorts of cycles it is preferable to start with the concepts and try to find words-where they exist-that will more or less correspond. This is better than starting with the words and trying to pick meaning for them; or, like Humpty Dumpty (and some others) making up meanings of your own! (“When I use a word,” Humpty Dumpty said, as you will remember, “’it means just what I choose it to mean – neither more nor less.’”)

“Cycle” – to use a catch-all or omnibus word – is a subdivision of the basic concept of “order”, but to see how we get from the one to the other it will be helpful to refer to the diagram on the next page. The various boxes contain words describing concepts. The boxes are under each other in ever-increasing order of limitation of meaning. To the right of the boxes I have placed the contrasting concept. To the left of the boxes I have placed the popular word – where there is one – that more or less expresses the concept described within the box. In the topmost box I have placed the word order. Order, of course, is fundamental. Order is the antithesis of chaos. Order is law. For me, order comes closer than any other single word to the meaning of the universe. (If you will permit me to use all of four words, I would express the meaning of the universe as “fulfillment of the law.”)

Pattern is the broadest of the words we use in cycle study. It is any arrangement that suggests or reveals design or order. It is the antithesis of unpattern – for example, the surface of a mirror, or sheets of polished steel, as they appear to the naked eye. Pattern is one of the eight or ten prime constituents of the universe. It is as fundamental as time, space, energy, matter, life, change, motion, emotion, thought, consciousness.
(If you were God, sitting down to create the universe, as we know it, what other basic building blocks would you first need to create? What else is there in the universe?)

Examples of pattern are infinite. They run from a straight line to an oriental rug, from a circle to an oceanliner. Pattern can be one, two or three dimensional. It can represent, either in one, two, or three dimension, the passage of time. Time is not a necessary condition of pattern. You can have pattern in space – for example, a colonade; or a maple leaf; or the capital of a Corinthian column. However, the only kind of pattern with which we are concerned in cycle study is pattern in time (or its two-dimensional representation on a chart). Unfortunately I can think of no single word to express the concept of pattern in time in contrast to the concept of pattern in space (design).

Pattern in time can be cyclic or non-cyclic. Cyclic, as you know, means a complete course of operation returning to the original state. It is a series of changes regarded as leading back to its starting point. It involves sequence in contrast to separate (discrete) events. Many examples of cyclic pattern in time could be given. A business cycle, for instance, or a four-cycle engine, or a seasonal weather cycle (summer, fall, winter, spring, and summer again), or the life cycle of an insect (egg, larva, pupa, adult, and egg again). In all instances, what we have is a succession of events from a starting point through a variety of changes back, more or less, to the starting point.

Non-cyclic patterns in time are time patterns that do not return to the place of beginning – populations growth is a good example, or the daily weight of a growing baby. Both of these sequences are definitely patterns in time, but because they do not return to the original state they are not cyclic. The popular word that most nearly describes cyclic patterns in time, as the phrase is being used here, is fluctuation. (This is not to say that the words “cycle” or “cyclic” do not have other perfectly valid meanings. Most words have other meanings. For example, my dictionary gives 23 different meanings for the word “order”!)

Cyclic pattern in time can be repetitive or nonrepetitive – many cycles, or just one cycle. Business exhibits repetitive cyclic patterns in time. Starting, let us say, with a depression, business rises and falls and comes around to another depression, time after time. Also, one can speak of a single business cycle: the sequence from one depression to the next. The best popular word for repetitive cyclic pattern might be fluctuations (plural). A nonrepetitive cycle could perhaps best be called a wave, but the words cycle, fluctuation, oscillation, undulation are also used.

Note that we have not yet introduced the idea of regularity of time. Two consecutive business depressions could be 3 years or 20 years apart. We are talking merely of repetition. At this point a new concept must be introduced-the concept of recurring events. Recurring events are similar to recurring cycles in that they are both recurring in time, both (at this point in our outline) may be any interval apart. The point of difference is that the recurring cycle is a sequence, a coming around again, whereas the recurrent events are discrete. Art forms that repeat again and again over the ages are good examples of recurrent events. So are certain religious symbols. So are volcanic eruptions or earthquakes. So are the deaths of presidents in office. (In any given year, or month, week, or day, the president dies or he doesn’t.) All these examples are “yes” or “no” matters.
Do not overlook the importance of recurrent events. First, they require different statistical treatment than do repetitive cycles. Second, sequences that we observe as repetitive cycles may sometimes be triggered by recurrent events. From now on these two concepts occupy parallel positions on our diagram.

Repetitive cyclic patterns and recurrent events (which, by definition, must also be repetitive) can be ordered or random. In cycle and pattern study we are of course interested in the ordered patterns and in separating the ordered from the nonordered. The fact that the behavior is ordered has two aspects to it. These need to be clearly distinguished. Almost any cyclic behavior is ordered in that the consecutive states are related, one
to the other. It has what the statisticians call “serial correlation”. Stock prices tomorrow are related to stock prices today. They may be a little higher or a little lower, but never drastically up or down. They do not go from 900 to 200 in one day and back to 600 the day after as they would do if they were completely random. When we talk about ordered cycles we are not talking about this kind of randomness, but rather about the randomness or lack of it of the period or length of the cycle (or, in the case of recurrent events, of the intervals between the events). We ask, are these spacings ordered or random?

The word oscillation, which implies a little more regularity than the word fluctuation, could perhaps be used for ordered, repetitive, cyclic pattern in time, but it is not entirely satisfactory. M. G. Kendall uses the word oscillation to denote fluctuations that are “subject to law, and therefore predictable”. The trouble here is that you can have ordered repetitive cyclic patterns in time that are not predictable, at least in any practical sense of the word. And of course the word oscillation does not apply to recurrent events at all.
Ordered repetitive cyclic patterns in time can be rhythmic or nonrhythmic (and ordered recurrent events can be, too). A complication here is that rhythm, or reasonably regular repetition, can be found in random repetitive cyclic patterns and in random recurrent events, too. This fact is indicated by the run-around lines  on the diagram.

Rhythm means that the length of the successive waves -or the intervals between successive recurring events – are “reasonably” regular, so that the behavior repeats with a beat. Your heart beats are rhythmic. Old Faithful geyser is rhythmic (or at least it was until the earthquake).
Rhythm, of course, is a relative, not an absolute, concept. One time series is more rhythmic than another.
Therefore, although you can say that “nonrhythmic” is the contrasting concept, it is not really a question of black or white but of progressive shades of grey. “Reasonable” regularity is, of course, a subjective measure, but it can be made mathematically exact such as “80% on the regularity index scale”.
The importance of rhythm is that rhythm involves regularity (of timing), and where you have regularity (regularity not the result of chance) you have predictability. Predictability is what w e are all after. When rhythmic cyclic patterns or rhythmic recurrent events evidence complete regularity they are called periodic and the pattern is called a periodicity. It is, of course, much harder, by mere chance, to get true periodicity than to get mere rhythm, but, even so, it can be done. Toss a coin, for example. Nothing could be more random. Yet you might easily get a head, a tail, a head, a tail, a true periodicity if there ever was one. You might even get three repetitions: a head, a tail, a head, a tail, a head, a tail. And yet it would mean nothing!

On the other hand, if your cycle were longer, a true periodicity would be much harder to get. Suppose you had five heads followed by five tails, you would hardly expect the pattern to repeat even once.

And now for a recapitulation:
1. Order includes pattern and everything else in the universe except chaos.
2. Pattern includes pattern in time and all other sorts of pattern, but does not include other basic concepts.
3. Pattern in time includes cyclic pattern in time and non-cyclic pattern in time, but excludes pattern in space.
4. Cyclic pattern in time includes repetitive cyclic patterns in time and non-repetitive or single cyclic patterns in time, but excludes non-cyclic pattern in time.
(There is no corresponding “recurrent” event, because, unless repetitive, there is no recurrence. You could, of course, put “event” as a concept, but from our point of view here the pattern consists of the intervals between the events, and there are no intervals until you have at least two occurrences.)
5. Repetitive cyclic patterns in time (or in recurrent events) can be ordered or random, rhythmic or nonrhythmic, but do not include one single cyclic sequence (wave) or one single event.
6. Ordered repetitive cyclic patterns in time (or ordered recurrent events) can be rhythmic or not.
7. Rhythmic cyclic patterns in time or rhythmic repetitive events, both of which, by definition, must be repetitive, (but which may be either ordered or random), may or may not be truly periodic.
8. Truly periodic cyclic patterns in time and truly periodic recurrent events-are both patterns developed to the nth degree and are therefore necessarily special cases of recurrent cyclic patterns in time or recurrent events.

I trust that these distinctions will prove helpful.

This article originally appeared in the
Foundation for the Study of Cycles
Magazine Cycles in May 1965

What are Cycles? by Edward R Dewey, 1951

 Cycles are the simplest thing in the world, at least in principle.

 Let me give you an example. Suppose you are visiting my house and, looking out of the window, notice a bus pass by at 10:00 a.m. Half an hour later at 10:30 you notice another bus pass. At 11:00 you see another one, “Ah ha!” you say. “Buses here run every thirty minutes.” You have discovered a cycle all by your little lonesome, without benefit of slide rule or gobbledygook. Cycles are just as simple as that.

Now what?

 Well, first of all, you have a basis for predicting the probabilities of the future. If we go in to lunch and come out of the dining room at 1:05 you will know that you probably missed the 1:00 o’clock bus and that, if the cycle is continuing, your next bus will pass in 25 minutes. So you-chat for about 20 minutes and leave at 1:25 so as to have to stand in the wind and the rain the least amount of time.

Of course the schedule may have changed, or the bus have been delayed by an accident. You can’t count for sure on a bus at 1:30. You are merely playing probabilities.

Regularity Gives Predictability

Where you have regularity you have predictability – at least to the extent that the regularity governs, and is not present by chance.

Now let’s do some more supposing.

You are overlooking a street near the center of a small town. Every ten minutes or so 10 or 15 people come along, more or less in a bunch. Another cycle! Again you can predict (with qualifications). More than this, with this regular result appearing before you, you have a right to assume a cause – if the time intervals have been regular enough and have repeated enough times so that the behavior cannot reasonably be the result of chance.

You don’t know the cause but there is no law against guessing. So you guess that, there is a bus station around the corner and that every ten minutes a bus comes in and discharges its passengers. If you then find out that there is a bus station, and that a bus does come in every ten minutes, your guess is bolstered. It is bolstered still more if you find that the buses arrive just about the time your bunches of people have been coming. But you still don’t know that your people are coming from the buses. You would have to go out on the street and go around the corner to find out for sure.

Other Cycles

You continue to watch and count the people. You see other patterns. Every other ten-minute group of people is bigger. Perhaps there is a second bus with a twenty-minute schedule that reinforces the crowd from the first bus.

This is really the whole story about cycles.

You can predict that part of the traffic that comes in regularly recurring bunches. You cannot predict by your 10- or 20-minute cycles the crowd of people that will come along when the feature of the local movie house is over. Your predictions are only partial. But they are good as far as they go if the cycles keep on coming true, and if you have timed them right. Moreover, by finding something else (in the example given, a bus schedule) with regularly recurring cycles of the same length you get a clue as to possible cause and effect and relationship – But to make sure, you need to run your clue down. Where you have partial regularity you have partial predictability. For example, suppose you have a chart recording your heart beats over the period of a minute. Now look at the first half of it only. If you count 30 beats in the 30 seconds You have under examination you will not be far wrong if you forecast another beat at 31 seconds, another at 32 seconds, etc.

Perhaps, if your heart speeded up a little, you would be quite wrong if you made your projection ten beats ahead, but by making your forecast only a beat at a time and revising your forecast each beat, you could probably make your prediction come out fairly well.

Another example of partial predictability: Suppose you knew that February 1st is, in New York City, on the average, the coldest day of the year. Suppose, on the basis of this information, you forecast February 1, 1952 as the coldest day of next winter. It is almost certainly true that February 1st will be colder than August 1st, but in any given year it may not be the very coldest day by as much as one or two months. The cycle of the year influences the weather but it does not completely dominate it. From a knowledge of the cycle of the year alone you could forecast the coldest day only with wide tolerances, yet the cycle of the year is very real.

Almost everything fluctuates with rhythm – that is, in more or less regular cycles. Putting it another way, almost everything acts as if it were influenced by regularly alternating up and down forces which first speed it up and then slow it down.

Random Ups and Downs Too

Everybody would know this fact were it not for two things: First, in addition to the cycles there are accidental (random) fluctuations in things, too. These randoms hide the regularities so that at first glance you do not see them. Second, things act as if they were influenced simultaneously by several different rhythmic forces, the composite effect of which is not regular at all.

 If we had several moons, the ups and. downs of the tides would be very irregular. All the other moons would mix things up. It might have taken us much longer to find out about the tides.

Separating Cycles Easy

If you have a long enough series of figures with which to work it is not too hard to separate the different regular cycles from each other. When this has been done, you can project each regular cycle into the future – Then you can easily find out the combined or composite future effect of all the various cycles. When you have done this you have a preview of what is going to happen (a) if the cycles continue, and (b) except as the cycles may be upset or distorted by accidental random non-cyclic events.

Why wouldn’t the cycles continue?” you may ask.

I’ll give you one reason: The cycles may have been present in the figures you have been studying merely by chance. The ups and downs you have noticed which come at more or less regular time intervals may have just happened to come that way. The regularity – the cycle – is there all right, but in such circumstances it has no significance. If you are zealous enough you can find regularity in almost anything, including random numbers where you know that the regularity has no significance and know it will not continue.

Many Repetitions Needed

How can you tell in any given instance whether or not the regularity you see is the result of a real underlying cyclic force which will continue to fluctuate regularly in the future?

The answer is, if the cycle has repeated enough times with enough regularity and with enough dominance, the chances are that it is the result of real cyclic forces.

Let me give you an example: Pick up a pack of playing cards and start to deal. The first card is red, the second is black, the third is red, the fourth is black. You have two waves of a regular cycle, red, black, red, black. But this sequence could easily come about by chance. You continue to deal: red, black, red, black. Four times in a row now, this regular alternation. It could still be chance, but it couldn’t be chance very often. Continue to deal. Red , black, red, black, red, black. Seven times now! It could still be chance, but it is less and less likely. It begins to look as if somebody had stacked the cards. You go through the entire deck.

Twenty-six times! “Somebody certainly stacked the deck,” you say. “It couldn’t happen this way by chance once in a million.”

Less and Less Likelihood of Chance

Exactly the same sort of reasoning applies to the cycles you see in the ups and downs of the stock market, or the sales of your own company, or the weather, or anything else in which you may be interested. The more the cycle has dominated, the more regular it is, and the more times it has repeated, the more likely it is to be the result of a real cyclic force that will continue. If it has not dominated enough, or has not been regular enough, you must have more repetitions to get equal assurance.

Well then, supposing that there are these rhythmic cycles in something. Suppose further that you have some knowledge of cycles. So what?

 By using nothing more complicated than simple arithmetic you can find the cycles. By seeing how many times each cycle has repeated in the past you can have a pretty fair idea of its significance (i.e. whether or not it will continue). And by projecting all the significant cycles into the future you can get some light on what is ahead insofar as the cycles govern.

Cycle Forecast Like a Weather Forecast

In weather we are used to forecasts in terms of probabilities. “The probability for the Pittsburgh area is for snow.” When you hear such a forecast on the radio you don’t rush out to put on your chains. The weather man may be wrong. You wait for the snow to fall. Then you put on your chains. But the forecast warns you that snow is likely, and on the strength of this fact you do make sure that you have your chains with you. If you are to make use of cycles in your business or your stock market forecasting you are going to have to use the same approach. Moreover, just as you refrain from shooting the weather man when he is wrong, I hope you will refrain from shooting the cycle analyst too.

Cycles Indispensable

Cycles are not the whole answer, but on the other hand they are indispensable in attempting to arrive at the whole answer.

 Cycles remind me of women. Women are not perfect (with individual exceptions, I hasten to add). But they are the best thing so far invented for the purpose. Until something better comes along we will have to make shift with them as they are – or else miss the values they have to offer.

 Let’s find out all we can about them!

Cycles Show Us Our Ignorance

The second reason that the study of cycles is important arises from the fact that wherever you have rhythmic variation – or for that matter pattern of any sort – you probably have a cause. For example, if you scatter iron filings on my desk you would expect them to be distributed at random over its surface. If, to the contrary, you find them arranging themselves into a pattern, you have a right to assume that some unknown force is present – perhaps a powerful magnet in my top drawer.

Similarly, if you find pattern, or more specifically rhythm (reasonably regular cycles), in the alternate thickness and thinness of tree rings or rock strata, or in the abundance of insects, or in the prices of common stocks, you may be sure that there is a cause for such behavior. Also you may be sure that if you do not know that cause you do not fully understand the behavior with which you have to deal. Thus the study of cycles reveals to us our ignorance, and is therefore very disturbing to people whose ideas are crystallized. “If there are regularly recurring ups and downs in business or in prices, all I have ever learned is wrong” an eminent economist once told me; and he added, in a moment of unusual candor, “I simply cannot afford to accept such an idea. All my life’s work would be ruined.” Many doctors in the days of Pasteur must have felt much the same way about germs.

Identical Cycles Suggest Interrelationship

The study of cycles has a third value. Such study can indicate possible cause-and-effect relationships, thus helping to solve the very problems it reveals.

For example, when I was a boy I noticed that the moon came up at about an hour later each night. When I visited the seashore I noticed also that the tide came in half an hour or so later each twelve hours. I did not have the wit to go on from there to note that two consecutive tides were delayed by exactly the same amount of time as was the moon, and therefore that there was perhaps some connection between the two. I did not have the wit to make this observation, I say, but one of the older astronomers did. In doing so he demonstrated the third value of a knowledge of cycles: Where the rhythms in two different phenomena have the same average time span, you are justified in suspecting a possible direct or indirect interrelationship between the phenomena.

Scientists Interested

For these three reasons many scientists are interested in the study of cycles.

First, it is the business of science to predict; second, it is the business of science to solve mysteries and to learn the “how” of things; and third, the true scientist welcomes any tool that gives him hints as to possible cause and effect relationships. Perhaps 3,000 scientists, the world over, have concerned themselves with the subject, and have written scientific papers embodying the results of their observations.

Scientists however, like all the rest of us, are pretty self centered. Thus the mammalogist interested in cycles in animal abundance is usually not much interested in geological cycles, or in astronomical cycles, or in business cycles. He is primarily, and usually exclusively, a mammalogist. Likewise the men in each of perhaps thirty different aspects of natural and social science are likewise specialists, each involved in his own little field.

However, the techniques of cycle analysis are the same whether one is studying biological data or financial data. And – much more important – it is only by studying cycles in all sorts of phenomena, and finding which phenomena have cycles of identical average time span, that we are likely to get hints of cause and effect relationships.

A New Science

These two facts cry aloud for the creation of a new science – the science of cycles – which is concerned with rhythmic fluctuation per se, which will develop techniques of cycle analysis, which will isolate cycles in all the 30 or 40 different branches of science where cycles are important, and which, having assembled enough facts, will perhaps someday venture to advance some theories in regard to cause and effect.

The Foundation for the Study of Cycles was created, in 1940, to found such a new science, and to develop it to the point where it could serve mankind. In the eleven years which have elapsed since its creation, the Foundation has made slow but steady progress.

It should be clear from the above remarks that the Foundation is purely an educational and scientific body and in no sense a commercial organization. It exists, not to make money but to serve mankind.

An eminent group of scientists and administrators have lent their names to the Committee of the Foundation. Various scientific societies have appointed advisors to help with its awards, and many individual scientists have joined the Foundation as scientific members. On its part, the Foundation has tried to maintain the high scientific standards of the many universities and institutions here and abroad which are, through their professors, connected with it, and I think we have pretty well succeeded.

Cycles Can Help You, Too

The research of the Foundation is of immediate practical value to the average citizen, too. By uncovering cycles in production and trade it throws light on the probabilities of booms and depressions. By uncovering cycles in international conflict it throws light on the probabilities of war. By uncovering cycles in the prices of commodities and of securities it throws light on the probabilities of panics and of other financial disturbances.

 The results of the Foundation’s research are made available to the general public by means of reports, bound together and issued 12 times a year in – the form of a magazine called Cycles – A Monthly Report.

Cycles Graphs

The following graphs come from Dewey’s articles in Cycles magazine and later published in the above mentioned collection. Because they are historical data they do not include the recent past. Please excuse the quality of the reproduction. Note also that for most of the graphs Dewey removed the trend of the series by subtracting a moving average from the data with a length approximately equal to the cycle period. The dotted lines show an “ideal” regular cycle of the stated length.

Canadian Lynx abundance has varied by a very wide factor on a 9.6 year cycle. This is very clear cycle with over 230 years data and is considered to be one of the clearest cycles known.

The 9.6 year cycle has been found in the populations of insects, fish and mammals. It is also present in the propensity for humans to have heart attacks. This seems entirely weird until the last member of the group is added, the variation in ozone. Is this a hint at the connection? The following two graphs are presented as percentage variations from a trend.

Real estate activity is another clear cycle, this time of about 18 years.

Wholesale prices in different continents show not only the same 9 year period, but also are in phase. This tendency for equal periods, even for unrelated series, to have synchronized phases is called “Cycles Synchrony” by Dewey.

The 11 year Sunspot Cycle is one of the better known cycles

Industrial production is shown to be closely correlated with the rate of change of sunspot activity. This is an area which has often been criticized, but the graph is interesting. It would be interesting to have an update on this old graph to see what has happened since.

About Edward R. Dewey (From Wikipedia, the free encyclopedia)

Edward Russel Dewey - 1895-1978 – was an economist who studied cycles in economics and other fields. His views are generally regarded as inconsistent with mainstream economics. He was the founder of the Foundation For The Study Of Cycles