The history of 1975 hypothesis
It was the founder of the Bible students (as Jehovah’s Witnesses (JW) was called before) Charles Taze Russel that in 1889 wrote that 6,000 years could be connected to the 1,000-year kingdom (The Times Is at hand, chapter 2). He had this idea late in 1800. In 1904 Russel wrote in his book The New Creation that one creation day was 7,000 years, totally 42,000 years + the day God rested from His creation, 7,000 years = 49,000 years. In the book Life Everlasting—In Freedom of the Sons of God, that was released in 1966, JW reasoned that in 1975 it will be 6,000 years since Jehovah created Adam, and therefor Jehovah had rested in 6,000 of the 7,000 years of resting day. They indicated that the 1000-year would be the last 1,000 years of Gods resting day, and that it was possible that Armageddon will come in 1975. Armageddon would be followed by 1,000-years kingdom. At the same time this book warned about determining any certain events in 1975. Watchtower emphasized in 1968 that the time between the creation of Adam and Eve could be weeks and months, but not years. That created a little slack of uncertainty in the calculations, but not significant. Kingdom Ministry in 1974 (km 5/74) praised the members that sold their homes and spend the money to be pioneers and preach for the remaining time before the end. Some even postponed their medical treatment with the belief that it was a waste of time.

1975 passed and nothing happened. Members were disappointed. Therefor the Watchtower turned against their own encouragement from 1974. Now Watchtower warned about selling houses or postponing medical treatment in their expectation of the end. The organization didn’t take any responsibility for their members loss. Despite the warning, the Watchtower still argued that Jehovah had rested for about 6,000 years and that the 1,000 year-kingdom (totally 7,000 years) will be the last part of His resting day. In 1. October 1975 somebody came up with the idea that the time between Adam and Eves creation could be years and not only weeks and months, like they believed before.

As late as 1. January 1987 Watchtower still argued that every creation day is 7,000 years and that the 1,000 year-kingdom will end the resting period, the seventh day (or the Jubilee year).
The brochure Was Life Created, published by JW in 2010, Russel’s idea of 7,000-year creation days was left. Now JW stated that Bible doesn’t say how long each day is. Bible about the creation days Genisis 1:31 says that the creation finished on the “sixth day”. Genisis 2:2 states that “he began to rest on the seventh day from his work”. The Bible describes creation days and not years. If the Bible meant years, it would say years and not days. The Bible just tells us that Jehovah rested after working hard with the creation. It doesn’t give us any prophetic foresight about Armageddon or the 1,000-year kingdom. But how did Russel conclude that one creation day was 7,000 years (totally 42 000 years for six days) in the first place? I think you would be surprised how random his idea was. Russell didn’t mainly look at the Bibel. He looked at his calendar. According to his calendar, God had already been resting for approximately 6,000 years since Adam until today. Russell added the 1,000 years of Christ’s reign, which he believed would complete that rest day. Based on this, he reasoned that the resting day must have been 7,000 years. He then assumed that each of the six creation days must be equally long. The figure of 7,000 years per creation day therefore depended on his calculation of the rest day and his assumption that all seven days were the same length. He presented this argument in The New Creation (1904), pages 49–51.

But how did the original Barbour idea calculate that the resting day of 6,000 years will end in 1873 in the first place? (Russel calculated 1975). By adding biblical time periods, Barbour counted 3,592 years from Adam to the return from Babylon, which he dated to 536 BCE. Another 2,408 years completed 6,000 years, ending in 1873 CE, allowing for the absence of a year zero. See Three Worlds, pp. 76–77. He ignored the Bible saying resting “day”.
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