Mathematics
Gann was a rare mathematician. He was a student of numbers, number theory, and the progression of numbers. He often said his analysis theory was based on natural law and mathematics.
Since time progresses as the earth turns on its axis, and time is measured by numbers and progressions of numbers, and since prices in their movement upward and downward are measured in numbers, we can understand why Gann had an intense interest in numbers, number theory, and mathematics. And remember….he did not have a personal computer, or even a handheld or desktop calculator-just a pencil.
Gann said his trading method was based on natural and mathematical law. For years he
refused to reveal any part of this method. The method was based on natural law, but the theory behind it was based on mathematics. Since price and time are denoted in mathematical terms (numbers), his system involved numbers and number progressions. He simply said he had researched far back into history and even went to India for old pre-Hindu records and philosophies as well as the ancient archives of the pre-Hindu period.
As we study Gann’s works, we begin to see the some numbers took a dominant place in his trading method. The square of numbers was an important issue with him, namely: 16, 25, 36, 49, 64, 121, and 144. He thought that markets moved in patterns sensitive to the price movement of these squares in terms of both price and time. For example, a rally in a specific market may have a tendency to find resistance 64 cents or 64 days from a bottom. Similarly, a decline in a market may find support 144 dollars or weeks from a top. This technique was combined with others that he developed, and it became a major part of his analysis tools.
Key Numbers
At this point, some of you may be discounting Gann’s methods because of their relative obscurity, but I would ask you to suspend disbelief. Gann found several numbers for a variety of reasons, some religious or spiritual, some historical, and some psychological. Whether or not his belief was reasonable or based on probable fact is largely irrelevant here-he used them as the basis for his trading, and they can work if incorporated properly into a technical trading system.
Gann researched numbers and cycles in many unique ways. Much of his research focused on the specific meaning of a number and how it relates to market movement. His research included the study of early Egyptian writings as well as cycle information. He also did extensive research of the cycles highlighted in the Bible. Records indicate that the early Egyptians considered the number seven to be the symbol of both earthly and eternal life. It is thought of as a number symbolizing a complete cycle, for seven is denoted as the number of time and rhythm. This information was used by Gann to develop a seven-day-cycle theory for short-term market moves.
Gann deemed three and one-half important, as it is half of seven, and in the Bible it occurs several times- for example, in the Book of Revelation, where the woman was sent into the wilderness for three and one-half years; during Daniel’s vision of 42 months (3 ½ years); when the Christ child was hiding in Egypt for three and one-half years; and during Christ’s public ministry, which lasted exactly three and on-half years. Gann used this information to study and research the 3 ½-day, -week, - month, and –year cycle, and applied the knowledge he gained to trade the market
Gann also considered the number nine important, as it occurs in the nine beatitudes recorded in Matthew’s Gospel, and he believed that nine corresponds with the number of stages of a disciple’s advance to a higher life. The number 12 was important to Gann, as it denoted space for him. He found it recurring in the twelve tribes of Israel, the 12 disciples, and the 12 houses of the Zodiac.
Other important Gann numbers are derived as follows: One year is 365 days, as this is the time it takes the sun to enter a hemisphere, move to the opposite hemisphere, and then return to the starting point. The movement of the sun produces definite seasons, affects crops and weather, and therefore has a dominant effect on our lives. For this reason the 30-day or sun cycle has dominance. Besides what has already been said about the number seven, it is important because of its link to the lunar cycle.
The number 144 was also important to Gann, whether because of there being 1440 minutes in a day (the decimal point is disregarded), it is 40% of a circle (360° x 0.40) = 144°), or because it is the square of 12. Numbers that occur repeatedly in the different sciences-such as mathematics, geometry, physics-cycles, and other natural studies were very important to Gann.
After studying mathematics and researching number patterns, Gann had to find a practical use for his newly acquired knowledge. Armed with this information Gann turned to the stock and commodity markets. After applying his strong background in mathematics to these markets, he concluded that markets adhere to mathematical law. From this conclusion he was able to develop his trading theory. This theory basically stated that market movement is governed by the forces of pattern, price and time.
PATTERN
In Gann Theory, pattern is defined as the study of market swings. Swing charts determine trend changes. For example, a trend changes to up when the market crosses swing tops and it changes to down when the market crosses swing bottoms. The trader can also gain information from swing charts about the size and duration of market movements. This how price, which is size, and time, which is duration, are linked to a pattern. In addition, the trader can learn about specific characteristics of a market by analyzing the patterns formed by the swing charts. For example, the charts delineate a market’s tendency to form double tops and bottoms, signal tops and bottoms, and the tendency to balance previous moves.
PRICE
In Gann Theory, price analysis consists of swing-chart price targets, angles, and percentage retracement points.
Swing-chart Price Targets
After constructing a swing chart, the trader creates important price information that can be used to forecast future tops and bottoms. These prices can be referred to as price balance points. For example, if the swing chart shows the market has had a recent tendency to rally 7 – 10 cents before forming a top, then from the next bottom, the forecast will be for a subsequent 7 – 10 cent rally. Conversely, if the market has shown a tendency to break 10 – 12 points from a top, then following the next top, the trader can forecast a break of 10 – 12 points. If the swings equal previous swings, then the market is balanced.
Angles
Geometric angles are another important part of the Gann trading method. The markets are geometric in design and function, so it follows that they will follow geometric laws when charted. Gann insisted on the use of the proper scale for each market when charting to maintain a harmonic relationship. He therefore chose a price scale that was in agreement with a geometric design or formula. He mainly relied on a 45-degree angle to divide a chart into important price and time zones. This angle is usually referred to as the “1X1” angle, because it represents one unit of price with one unit of time. He also used other proportional geometric angles to divide price and time. These angles are known as 1X2 and 2X1 angles because they represent one unit of price with two units of time and two units of price with one unit of time, respectively. All of the angles are important because they indicate support and resistance. They also have predictive value for future direction and price activity. All of which is necessary to know in order to forecast where the market can be in the future and when it is likely to be there.
Percentage Retracement Points
Just as Gann angles offer the trader price levels that move with time, percentage retracement points provide support and resistance that remain fixed as long as a market remains in a price range. Gann is commonly acknowledged to have formulated the percentage retracement rule, which states that most price moves will correct to 50%. Other percentage divisions are 25% and 75%, with the 50% level occurring the most frequently.
Gann believed traders would become successful if they used price indicators such as swing-chart balance points, angles, and percentage retracement points to find support and resistance. In essence, however, the combination of the two price indicators provides the trader with the best support and resistance with which to work. For example, while the uptrending 1X1 angle from a major bottom and a 50% price level provide strong support individually, the point where these two cross provides the trader with the strongest support on the chart.
TIME
According to Gann, time had the strongest influence on the market because when time is up, the trend changes. Gann used swing charts, anniversary dates, cycles, and the square of price to measure time.
Swing-Chart Timing
A properly constructed swing chart is expected to yield valuable information about the duration of price swings. This information is used to project both the duration of future upmoves from a current bottom and the duration of future downmoves from current tops. The basic premise behind swing-chart timing is that market patterns repeat: this is why it is necessary to keep records of past rallies and breaks. As a swing bottom or top is being formed, the trader must utilize the information from previous swings to project the minimum and maximum duration of the currently developing swing. The basic premise is that price swings balance time with previous price swings. However, in strong upmoves the duration of a rally is greater than the duration of a break, and subsequent upswings are equal to or greater than previous upmoves. Conversely, in strong downmoves the duration of a break is greater than the duration of a rally, and subsequent downswings are equal to or greater than previous downmoves.
Anniversary Dates
Among the timing tools Gann used is a concept he referred to as “anniversary dates.” This term refers to the historical dates the market made major tops and bottoms. The information collected in effect reflects the seasonality of the market because often an anniversary date repeats in the future. A cluster of anniversary dates indicates the strong tendency of a market to post a major top and bottom each year at the same time. For example, in order to predict future tops and bottoms in wheat, Gann claimed to have studied prices back to the twelfth century, noting not only the prices, but the anniversary dates – top to top, top to bottom, bottom to bottom, and bottom to top – were fundamental factors in this thinking. This information he learned from the research was very important to his analysis, and these dates gave obvious clues to another of his approaches to the market: time cycles.
Cycles
As mentioned earlier, Gann tried to build analysis tools that were geometric in design. When looking at anniversary dates he saw a series of one-year cycles. In geometric terms, the one-year cycle represented a circle or 360 degrees. Building on the geometric relationship of the market, Gann also considered the quarterly divisions of the year to be important timing periods. These quarterly divisions are the 90-day cycle, the 180-day cycle, and the 270-day cycle. In using the one-year cycle and the divisions of this cycle, you will find a date where a number of these cycles line up (preferably three or more) on a single point in time in the future. A date where a number of cycles line up is called a time cluster. This time cluster is used to predict major tops and bottoms. Time cycles are a major part of Gann analysis, and should be combined with price indicators to develop a valid market forecast.
[1] All quotations in this chapter about the Master Egg Course are from the W.D. Gann Commodities Course, and are reprinted with permission per Nikki Jones of Lambert-Gann Publishing Co., Box O, Pomeroy, Washington 99347
[2] As reprinted in the W. D. Gann Technical Review, vol. 1, no. 11, p.1, November 12, 1982
[3] From a missive on Gann letterhead with the title, “Soy Beans: Price Resistance Levels,” which originally came with the W. D. Gann Commodities Course, but which was left out of later reprints of the course.
Gann was a rare mathematician. He was a student of numbers, number theory, and the progression of numbers. He often said his analysis theory was based on natural law and mathematics.
Since time progresses as the earth turns on its axis, and time is measured by numbers and progressions of numbers, and since prices in their movement upward and downward are measured in numbers, we can understand why Gann had an intense interest in numbers, number theory, and mathematics. And remember….he did not have a personal computer, or even a handheld or desktop calculator-just a pencil.
Gann said his trading method was based on natural and mathematical law. For years he
refused to reveal any part of this method. The method was based on natural law, but the theory behind it was based on mathematics. Since price and time are denoted in mathematical terms (numbers), his system involved numbers and number progressions. He simply said he had researched far back into history and even went to India for old pre-Hindu records and philosophies as well as the ancient archives of the pre-Hindu period.
As we study Gann’s works, we begin to see the some numbers took a dominant place in his trading method. The square of numbers was an important issue with him, namely: 16, 25, 36, 49, 64, 121, and 144. He thought that markets moved in patterns sensitive to the price movement of these squares in terms of both price and time. For example, a rally in a specific market may have a tendency to find resistance 64 cents or 64 days from a bottom. Similarly, a decline in a market may find support 144 dollars or weeks from a top. This technique was combined with others that he developed, and it became a major part of his analysis tools.
Key Numbers
At this point, some of you may be discounting Gann’s methods because of their relative obscurity, but I would ask you to suspend disbelief. Gann found several numbers for a variety of reasons, some religious or spiritual, some historical, and some psychological. Whether or not his belief was reasonable or based on probable fact is largely irrelevant here-he used them as the basis for his trading, and they can work if incorporated properly into a technical trading system.
Gann researched numbers and cycles in many unique ways. Much of his research focused on the specific meaning of a number and how it relates to market movement. His research included the study of early Egyptian writings as well as cycle information. He also did extensive research of the cycles highlighted in the Bible. Records indicate that the early Egyptians considered the number seven to be the symbol of both earthly and eternal life. It is thought of as a number symbolizing a complete cycle, for seven is denoted as the number of time and rhythm. This information was used by Gann to develop a seven-day-cycle theory for short-term market moves.
Gann deemed three and one-half important, as it is half of seven, and in the Bible it occurs several times- for example, in the Book of Revelation, where the woman was sent into the wilderness for three and one-half years; during Daniel’s vision of 42 months (3 ½ years); when the Christ child was hiding in Egypt for three and one-half years; and during Christ’s public ministry, which lasted exactly three and on-half years. Gann used this information to study and research the 3 ½-day, -week, - month, and –year cycle, and applied the knowledge he gained to trade the market
Gann also considered the number nine important, as it occurs in the nine beatitudes recorded in Matthew’s Gospel, and he believed that nine corresponds with the number of stages of a disciple’s advance to a higher life. The number 12 was important to Gann, as it denoted space for him. He found it recurring in the twelve tribes of Israel, the 12 disciples, and the 12 houses of the Zodiac.
Other important Gann numbers are derived as follows: One year is 365 days, as this is the time it takes the sun to enter a hemisphere, move to the opposite hemisphere, and then return to the starting point. The movement of the sun produces definite seasons, affects crops and weather, and therefore has a dominant effect on our lives. For this reason the 30-day or sun cycle has dominance. Besides what has already been said about the number seven, it is important because of its link to the lunar cycle.
The number 144 was also important to Gann, whether because of there being 1440 minutes in a day (the decimal point is disregarded), it is 40% of a circle (360° x 0.40) = 144°), or because it is the square of 12. Numbers that occur repeatedly in the different sciences-such as mathematics, geometry, physics-cycles, and other natural studies were very important to Gann.
After studying mathematics and researching number patterns, Gann had to find a practical use for his newly acquired knowledge. Armed with this information Gann turned to the stock and commodity markets. After applying his strong background in mathematics to these markets, he concluded that markets adhere to mathematical law. From this conclusion he was able to develop his trading theory. This theory basically stated that market movement is governed by the forces of pattern, price and time.
PATTERN
In Gann Theory, pattern is defined as the study of market swings. Swing charts determine trend changes. For example, a trend changes to up when the market crosses swing tops and it changes to down when the market crosses swing bottoms. The trader can also gain information from swing charts about the size and duration of market movements. This how price, which is size, and time, which is duration, are linked to a pattern. In addition, the trader can learn about specific characteristics of a market by analyzing the patterns formed by the swing charts. For example, the charts delineate a market’s tendency to form double tops and bottoms, signal tops and bottoms, and the tendency to balance previous moves.
PRICE
In Gann Theory, price analysis consists of swing-chart price targets, angles, and percentage retracement points.
Swing-chart Price Targets
After constructing a swing chart, the trader creates important price information that can be used to forecast future tops and bottoms. These prices can be referred to as price balance points. For example, if the swing chart shows the market has had a recent tendency to rally 7 – 10 cents before forming a top, then from the next bottom, the forecast will be for a subsequent 7 – 10 cent rally. Conversely, if the market has shown a tendency to break 10 – 12 points from a top, then following the next top, the trader can forecast a break of 10 – 12 points. If the swings equal previous swings, then the market is balanced.
Angles
Geometric angles are another important part of the Gann trading method. The markets are geometric in design and function, so it follows that they will follow geometric laws when charted. Gann insisted on the use of the proper scale for each market when charting to maintain a harmonic relationship. He therefore chose a price scale that was in agreement with a geometric design or formula. He mainly relied on a 45-degree angle to divide a chart into important price and time zones. This angle is usually referred to as the “1X1” angle, because it represents one unit of price with one unit of time. He also used other proportional geometric angles to divide price and time. These angles are known as 1X2 and 2X1 angles because they represent one unit of price with two units of time and two units of price with one unit of time, respectively. All of the angles are important because they indicate support and resistance. They also have predictive value for future direction and price activity. All of which is necessary to know in order to forecast where the market can be in the future and when it is likely to be there.
Percentage Retracement Points
Just as Gann angles offer the trader price levels that move with time, percentage retracement points provide support and resistance that remain fixed as long as a market remains in a price range. Gann is commonly acknowledged to have formulated the percentage retracement rule, which states that most price moves will correct to 50%. Other percentage divisions are 25% and 75%, with the 50% level occurring the most frequently.
Gann believed traders would become successful if they used price indicators such as swing-chart balance points, angles, and percentage retracement points to find support and resistance. In essence, however, the combination of the two price indicators provides the trader with the best support and resistance with which to work. For example, while the uptrending 1X1 angle from a major bottom and a 50% price level provide strong support individually, the point where these two cross provides the trader with the strongest support on the chart.
TIME
According to Gann, time had the strongest influence on the market because when time is up, the trend changes. Gann used swing charts, anniversary dates, cycles, and the square of price to measure time.
Swing-Chart Timing
A properly constructed swing chart is expected to yield valuable information about the duration of price swings. This information is used to project both the duration of future upmoves from a current bottom and the duration of future downmoves from current tops. The basic premise behind swing-chart timing is that market patterns repeat: this is why it is necessary to keep records of past rallies and breaks. As a swing bottom or top is being formed, the trader must utilize the information from previous swings to project the minimum and maximum duration of the currently developing swing. The basic premise is that price swings balance time with previous price swings. However, in strong upmoves the duration of a rally is greater than the duration of a break, and subsequent upswings are equal to or greater than previous upmoves. Conversely, in strong downmoves the duration of a break is greater than the duration of a rally, and subsequent downswings are equal to or greater than previous downmoves.
Anniversary Dates
Among the timing tools Gann used is a concept he referred to as “anniversary dates.” This term refers to the historical dates the market made major tops and bottoms. The information collected in effect reflects the seasonality of the market because often an anniversary date repeats in the future. A cluster of anniversary dates indicates the strong tendency of a market to post a major top and bottom each year at the same time. For example, in order to predict future tops and bottoms in wheat, Gann claimed to have studied prices back to the twelfth century, noting not only the prices, but the anniversary dates – top to top, top to bottom, bottom to bottom, and bottom to top – were fundamental factors in this thinking. This information he learned from the research was very important to his analysis, and these dates gave obvious clues to another of his approaches to the market: time cycles.
Cycles
As mentioned earlier, Gann tried to build analysis tools that were geometric in design. When looking at anniversary dates he saw a series of one-year cycles. In geometric terms, the one-year cycle represented a circle or 360 degrees. Building on the geometric relationship of the market, Gann also considered the quarterly divisions of the year to be important timing periods. These quarterly divisions are the 90-day cycle, the 180-day cycle, and the 270-day cycle. In using the one-year cycle and the divisions of this cycle, you will find a date where a number of these cycles line up (preferably three or more) on a single point in time in the future. A date where a number of cycles line up is called a time cluster. This time cluster is used to predict major tops and bottoms. Time cycles are a major part of Gann analysis, and should be combined with price indicators to develop a valid market forecast.
[1] All quotations in this chapter about the Master Egg Course are from the W.D. Gann Commodities Course, and are reprinted with permission per Nikki Jones of Lambert-Gann Publishing Co., Box O, Pomeroy, Washington 99347
[2] As reprinted in the W. D. Gann Technical Review, vol. 1, no. 11, p.1, November 12, 1982
[3] From a missive on Gann letterhead with the title, “Soy Beans: Price Resistance Levels,” which originally came with the W. D. Gann Commodities Course, but which was left out of later reprints of the course.
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