Explanation

`Numerological & Astrological Decade Bounds' are called `Decade Bounds' in short. `Decade Bounds' is also named as `Large Bounds' in contrast of `Small Bound' which lasts only one year. `Large Bounds' is the focus of `Decade Fortune' because it shows the decade fortune in a zone of a person in ten years. So, `Large Bounds' is regarded as singular but it consists of two limits. The lower limit of `Large Bounds' is called `Lower Bound' (LB) and the upper limit of `Large Bounds' is called `Upper Bound' (UB). Their relation is UB=LB+9 because the time interval of `Large Bounds' is 10 years. The first `Large Bounds' is called the `Initial Large Bounds'. `Large Bounds' moves consecutively either clockwisely or anti-clockwisely according to the `Revolution Mode' (RM) along the zones every ten years. There are altogether twelve zones. The zones recur from 0 to 11. The `Revolution Mode' (RM) of `Large Bounds' is a mathematical expression that can show the revolving direction of `Large Bounds' in its `Fortune Track' (FT). There are altogether two different types of `Revolution Modes', namely `Clockwise Revolution Mode' (CRM) and `Anti-clockwise Revolution Mode' (ARM). The `Decade Bounds' of human being is revolving either clockwisely or anti-clockwisely in the `Fortune Track' (FT). It varies according to the `Sex Code' (SC) and the year of birth `y' in Gregorian calendar. For example, based on the calculation of Revolution Mode Formula `RM=R[(&C[SC:m=0, f=1]+y)/2]' for people born in A.D. or based on the calculation of Revolution Mode Formula `RM=R[(&C[SC:m=0, f=1]+y-1)/2]' for people born in B.C., if RM=0 it means that the `Revolution Mode' is clockwise. If RM=1 it means that the `Revolution Mode' is anti-clockwise. The age at which men and women begin menopause is related to the numerology of `Large Bounds'. When the age of men enters the sixth `Large Bounds' and the age of women enters the fifth `Large Bounds', presbyopia, weakening of sexual and physical abilities are common. This is the beginning of menopause. `Decade Bounds' following the `Decade Fortune' of people revolves consecutively along the zones either clockwisely or anti-clockwisely for every ten years. Thus, the time interval of `Decade Bounds' is 10 years. In `PT&FM', the beginning of a year is not on 1st of January in Gregorian calendar. The beginning of a year is `Joint of February'. The critical value between two consecutive years is called `Joint of Year'. `Joint of February' is the boundary of two consecutive years. It always lies on from the 3rd to 5th day of February. `y' is the year of birth in the Gregorian calendar. In general, not for precise calculations, `Joint of February' can be regarded as the 4th day of February. If the date of birth is within the 3rd to 5th day of February, precise calculations should be carried out. That is, if the time of the date of birth is after `Joint of February', the year is `y'. If the time is before `Joint of Year' in B.C., it is regarded as previous year. That is, the year is `y+1'. If the time is before `Joint of Year' in A.D., it is regarded as previous year. That is, the year is `y-1'. The time and date of `Joint of February' between two consecutive years in Gregorian calendar always change from year to year. `Joint of February' also varies according to the longitude and latitude of a place. The exact date and time of `Joint of February' of a year can be found in a Chinese lunar calendar. `m' is the month of birth after `Joint of Month'. Usually, `Joint of Month' is from 3rd to 8th of the month in Gregorian calendar. In general, if there is no need for very precise calculations, the `Joint of Month' can be regarded as 6. If the birthday falls between the 3rd and 8th day of the Gregorian calendar, the exact date and time of the `Joint of Month' must check by a Chinese calendar for accurate calculation. `d' is the date and time of birth in Gregorian calendar, expressing in units of days. `J' is a conventional symbol to denote the day and time of `Joint of Month' before or after the date of birth such that `J1' is the day and time of `Joint of Month' before the date of birth and `J2' is the day and time of `Joint of Month' after the date of birth. The units of `J1' and `J2' are days. `J2-d' is the difference between the date and time of birth and the next `Joint of Month' in Gregorian calendar. The difference should be corrected to the nearest day. `d-J1' is the difference between the date and time of birth and previous `Joint of Month' in Gregorian calendar. The difference should be corrected to the nearest day. Both `d-J1' and `J2-d' are named as `Days from Joint of Month'. `d-J1' is called `Days from Past Joint of Month' and `J2-d' is called `Days to Future Joint of Month'. 'e' is the minimum virtual age of a person to have `Large Bounds' such that e1=A[(d-J1)/3] and e2=A[(J2-d)/3]. `SC' is the `Sex Code' of a person. The `Sex Code' of male is `M' and `m=0'. The `Sex Code' of female is `F' and f=1. In general, the value of `m' is assigned to `0' and the value of `f' is `1'. The `Sex Code' of transsexual is the original sex at birth. The `Sex Code' of hermaphrodite (H), people have neutral sex (N) or genderless (N) could be either `M' or `F'. In this case, both sex codes should be used to check out which one is more accurate. 'MP' is the starting age of menopause of men and women in `Large Bounds'. It is reckoned in virtual age. The virtual age is the age of the current year regardless of birthday plus 1 year. But, remember the time of the first day of the current year is always at the `Joint of February' which is also called `Joint of Year'. The age at the end of menopause is `MP+9' years, because the range of `Large Bounds' is 10 years. The Male & Female Menopause Age Formula for people born in y A.D. is MP=&C[SC=M:&C{R[y/2]=0:50+A[(J2-d)/3], R[y/2]=1:50+A[(d-J1)/3]}, SC=F:&C{R[y/2]=0:40+A[(d-J1)/3], R[y/2]=1:40+A[(J2-d)/3]}]. The Male & Female Menopause Age Formula for people born in y A.D. can be simplified as: MP=&C[SC=M:&C{R[y/2]=0:50+e2], R[y/2]=1:50+e1}, SC=F:&C{R[y/2]=0:40+e1, R[y/2]=1:40+e2}]. The Male & Female Menopause Age Formula for people born in y B.C. is MP=&C[SC=M:&C{R[(y-1)/2]=0:50+A[(J2-d)/3], R[(y-1)/2]=1:50+A[(d-J1)/3]}, SC=F:&C{R[(y-1)/2]=0:40+A[(d-J1)/3], R[(y-1)/2]=1:40+A[(J2-d)/3]}]. The Male & Female Menopause Age Formula for people born in y B.C. can be simplified as: MP=&C[SC=M:&C{R[(y-1)/2]=0:50+e2], R[(y-1)/2]=1:50+e1}, SC=F:&C{R[(y-1)/2]=0:40+e1, R[(y-1)/2]=1:40+e2}]. It can be further simplified as follows: If the `Revolution Mode' is clockwise (RM=0), the `Male Menopause Age' Formula is: MP=50+A[(J2-d)/3] and the `Female Menopause Age' Formula is : MP=40+A[(J2-d)/3]. If the `Revolution Mode' is anti-clockwise (RM=1), the `Male Menopause Age' Formula is: MP=50+A[(d-J1)/3] and the `Female Menopause Age' Formula is: MP=40+A[(d-J1)/3]. Since the growth of the people living in cold area is slower and the age of menopause of female is remarkably later than those female who live in warm and hot area, when calculate the age of menopause of female living in cold places, the Menopause Age Formula (MP) for people born in `y' B.C. can be adjusted to MP=&C[SC=M:&C{R[(y-1)/2]=0:50+A[(J2-d)/3], R[(y-1)/2]=1:50+A[(d-J1)/3]}, SC=F:&C{R[(y-1)/2]=0:45+A[(d-J1)/3], R[(y-1)/2]=1:45+A[(J2-d)/3]}]. The Menopause Age Formula (MP) for people born in `y' A.D. can be adjusted to MP=&C[SC=M:&C{R[y/2]=0:50+A[(J2-d)/3], R[y/2]=1:50+A[(d-J1)/3]}, SC=F:&C{R[y/2]=0:45+A[(d-J1)/3], R[y/2]=1:45+A[(J2-d)/3]}]. `&C[ ]' is a conditional function of an event such that the mathematical expression after the `:' sign must be operated if the event occurs (i.e. The conditional `&C[ ]' becomes true.). `R[y/n]' is a remainder function such that it takes the remainder of `y' divided by `n'. `n' is a natural number. Natural numbers are 1,2,3,4,5,……. Zero is not a natural number. `A[n]' is an approximated integer function such that it takes the nearest whole number of `n'.

Example

Assume a male was born at 0:45 a.m. on 6th Oct., A.D.1952 in Gregorian calendar. Find the age at which he starts menopause. From the given data, the `Sex Code' (SC) is `M' and m=0. Since the date and time of birth is 0:45 a.m. on 6th October, 1952, the number of days at birth in Gregorian calendar is d=6+45/60/24 days in October. d=6.03125 days in October. According to Chinese lunar calendar, the `Joint of Month' before the date of birth is `Joint of September' which is at 1:14 a.m. on 8th Sept., A.D.1952. So, J1=8+(1+14/60)/24 days in September. J1=8.0513888 days in September. `Joint of Month' after the date of birth is `Joint of October' which is at 4:33 p.m. on 8th Oct., A.D.1952. So, J2=8+(16+33/60)/24 days in October. J2=8.6895833 days in October. Since the birthday is after `Joint of Year' which is at 4:54 a.m. on 5th Feb., A.D.1952, the year of birth is y=1952. And, because the birthday is before the `Joint of October' which is at 4:33 pm on October 8, A.D.1952, the month of birth is m=9. `J2-d' is the day and time difference between `Joint of October' and the date and time of birth. J2-d=8.6895833-6.03125 days. J2-d=2.6583333 days. `d-J1' is the day and time difference between the date and time of birth and `Joint of September'. d-J1=6.03125+(30-8.0513888) days. d-J1=6.03125+21.948612 days. d-J1=27.979862 days. According to the `Male & Female Menopause Age' Formula for people born in y A.D., MP=&C[SC=M:&C{R[y/2]=0:50+A[(J2-d)/3], R[y/2]=1:50+A[(d-J1)/3]}, SC=F:&C{R[y/2]=0:40+A[(d-J1)/3], R[y /2]=1:40+A[(J2-d)/3]}], substitute in the formula as follows: MP=&C[SC=M:&C{R[1952/2]=0:50+A[2.6583333/3], R[1952/2]=1:50+A[27.979862/3]}, SC=F:&C{R[1952/2]=0:40+A[27.979862/3], R[1952/2]=1:40+A[2.6583333/3]}]. MP=&C[SC=M:&C{0=0:50+A[0.8861111], 0=1:50+A[9.3266206]}, SC=F:&C{0=0:40+A[9.3266206], 0=1:40+A[0.8861111]}]. MP=&C[SC=M:&C{0=0:50+1, 0=1:50+9}, SC=F:&C{0=0:40+9, 0=1:40+1}]. MP=&C[SC=M:&C{0=0:51, 0=1:59}, SC=F:&C{0=0:49, 0=1:41}]. Since the `Truth value' of `&C[SC=M]' is true and the `Truth value' of `&C[SC=F]' is false, MP=&C{0=0:51, 0=1:59}. And, because the `Truth value' of `&C[0=0]' is true and the `Truth value' of `&C[0=1]' is false, MP=51. Therefore, he enters menopause at his virtual age of 51. Assume a female was born at 12:23 p.m. on 4th Feb., A.D.1925 in Gregorian calendar. Find the age at which she starts menopause. From the given data, the `Sex Code' (SC) is `F' and f=1. Since the date and time of birth is 12:23 p.m. on 4th February, A.D.1925, the number of days at birth in Gregorian calendar is d=4+(12+23/60)/24 in February. d=4.5159722 days in February. According to Chinese lunar calendar, the `Joint of Month' before the date of birth is `Joint of January' which is at 3:54 a.m. on 6th January, 1925. So, J1=6+(3+54/60)/24 days in January. J1=6.1625 days in January. `Joint of Month' after the date of birth is `Joint of February' which is at 3:37 p.m. on 4th February, 1925. So, J2=4+(15+37/60)/24 days in February. J2=4.6506944 days in February. Since the birthday is before `Joint of Year' which is at 3:37 p.m. on 4th February, A.D.1925, the year of birth is regarded as the previous year. That is, y=1924. And, because the birthday is before the `Joint of February' which is at 3:37 p.m. on 4th February, A.D.1925, the month of birth is m=1. `J2-d' is the day and time difference between `Joint of February' and the date and time of birth. J2-d=4.6506944-4.5159722 days. J2-d=0.1347222 days. `d-J1' is the day and time difference between the date and time of birth and `Joint of January'. d-J1=4.5159722+(31-6.1625) days. d-J1=4.5159722+24.8375 days. d-J1=29.353472 days. According to the `Male & Female Menopause Age' Formula for people born in y A.D., MP=&C[SC=M:&C{R[y/2]=0:50+A[(J2-d)/3], R[y/ 2]=1:50+A[(d-J1)/3]}, SC=F:&C{R[y/2]=0:40+A[(d-J1)/3], R[y /2]=1:40+A[(J2-d)/3]}], substitute in the formula as follows: MP=&C[SC=M:&C{R[1924/2]=0:50+A[0.1347222/3], R[1924/2]=1:50+A[29.353472/3]}, SC=F:&C{R[1924/2]=0:40+A[29.353472/3], R[1924 /2]=1:40+A[0.1347222/3]}]. MP=&C[SC=M:&C{0=0:50+A[0.0449074], 0=1:50+A[9.7844906]}, SC=F:&C{0=0:40+A[9.7844906], 0=1:40+A[0.0449074]}]. MP=&C[SC=M:&C{0=0:50+0, 0=1:50+10}, SC=F:&C{0=0:40+10, 0=1:40+0}]. MP=&C[SC=M:&C{0=0:50, 0=1:60}, SC=F:&C{0=0:50, 0=1:40}]. Since the `Truth value' of `&C[SC=M]' is false and the `Truth value' of `&C[SC=F]' is true, MP=&C{0=0:50, 0=1:40}. And, because the `Truth value' of `&C[0=0]' is true and the `Truth value' of `&C[0=1]' is false, MP=50. Therefore, she enters menopause at her virtual age of 50. Assume a male was born at 10:00 p.m. on 16th Jan., A.D.1962. Find the age at which he starts menopause. From the given data, the `Sex Code' (SC) is `M' and m=0. Since the time of birth is at 10:00 p.m. on 16th Jan., A.D.1962, d=16+22/24 days in January. d=16.916666 days in January. According to Chinese lunar calendar, the `Joint of Month' before the date of birth is `Joint of January' which is at 3:35 a.m. on 6th Jan., A.D.1962. So, J1=6+(3+35/60)/24 days in January. J1=6.1493055 days in January. `Joint of Month' after the date of birth is `Joint of February' which is at 3:18 p.m. on 4th Feb., A.D.1962. So, J2=4+(15+18/60)/24 days in February. J2=4.6375 days in February. `Joint of February' is also `Joint of Year'. Since the birthday is before `Joint of Year' which is at 3:18 p.m. on 4th Feb., A.D.1962, it is regarded as previous year. That is, y=1961. And, because the birthday is after the `Joint of January' which is at at 3:35 a.m. on 6th Jan., A.D.1962, the month of birth is m=1. `J2-d' is the day and time difference between `Joint of February' and the date and time of birth. J2-d=[31-(16+22/24)]+[4+(15+18/60)/24] days. J2-d=[31-16.916666]+[4+0.6375] days. J2-d=14.083334+4.6375 days. J2-d=18.720834 days. `d-J1' is the day and time difference between the date and time of birth and `Joint of January'. d-J1=[16+22/24]-[6+(3+35/60)/24] days. d-J1=16.916666-6.1493055 days. d-J1=10.767361 days. According to the `Male & Female Menopause Age' Formula for people born in y A.D., MP=&C[SC=M:&C{R[y/2]=0:50+A[(J2-d)/3], R[y/ 2]=1:50+A[(d-J1)/3]}, SC=F:&C{R[y/2]=0:40+A[(d-J1)/3], R[y/2]=1:40+A[(J2-d)/3]}], substitute in the formula as follows: MP=&C[SC=M:&C{R[1961/2]=0:50+A[18.720834/3], R[1961/2]=1:50+A[10.767361/3]}, SC=F:&C{R[1961/2]=0:40+A[10.767361/3], R[1961/2]=1:40+A[18.720834/3]}]. MP=&C[SC=M:&C{1=0:50+A[6.240278], 1=1:50+A[3.5891203]}, SC=F:&C{1=0:40+A[3.5891203], 1=1:40+A[6.240278]}]. MP=&C[SC=M:&C{1=0:50+6, 1=1:50+4}, SC=F:&C{1=0:40+4, 1=1:40+6}]. MP=&C[SC=M:&C{1=0:56, 1=1:54}, SC=F:&C{1=0:44, 1=1:46}]. Since the `Truth value' of `&C[SC=M]' is true and the `Truth value' of `&C[SC=F]' is false, MP=&C{1=0:56, 1=1:54}. And, because the `Truth value' of `&C[1=0]' is false and the `Truth value' of `&C[1=1]' is true, MP=54. Therefore, he enters menopause at his virtual age of 54. An alternative method to calculate the beginning of the virtual age of menopause is by the simplified `Male & Female Menopause Age' Formula. The first step is to find out the `Revolution Mode' (RM) of `Decade Fortune' of the client by the `Revolution Mode' Formula. Apply the `Revolution Mode' Formula for people born in A.D., RM=R[(&C[SC:m=0, f=1]+y)/2]. RM=R[(0+1961)/2]. RM=R[1961/2]. RM=1. Hence, the `Revolution Mode' of `Decade Fortune' of the client is anti-clockwise. Then, apply the simplified `Male & Female Menopause Age' Formula for `Anti-clockwise Revolution Mode' (RM=1), MP=50+A[(d-J1)/3]. MP=50+A[10.767361/3]. MP=50+A[3.5891203]. MP=50+4, MP=54. Therefore, he enters menopause at his virtual age of 54.