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@ -81,22 +81,26 @@ Here is the logarithm plot, with some smoothing applied:
And furthermore, a table: And furthermore, a table:
blhah
| Year | Rate of progress before | Discontinuity in terms of time of travel = New record - current record | How much extra time would have been needed? = (point - previous predicted point)/ previous rate of progress = (discontinuity - expected progress) / previous rate of progress | | Year | Rate of progress before | Discontinuity in terms of time of travel = New record - current record | How much extra time would have been needed? = (point - previous predicted point)/ previous rate of progress = (discontinuity - expected progress) / previous rate of progress |
|------|---------------------------------------------------------|-------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| |------|---------------------------------------------------------|-------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| 1586 | (1082-1018) days /(1577-1519) years = 1.1034 days/year | 1018-781 = 237 days | (237 days - (1589-1577)*1.1 days) / 1.1 days / year= 203 years | | 1586 | 1.1034 days/year | 237 days | 203 years |
| 1870 | (781 – 605) days / (1841 – 1586) years = 0.69 days/year | 605-80 days = 525 days | (525 days - (1870-1849 years)*0.69 days / year ) / 0.69 days/year = 740 years | | 1870 | 0.69 days/year | 525 days | 740 years |
| 1931 | (80-21) days / (1929-1870) years = 1 day / year | 21-8 days = 13 days | (13 days - (1931 - 1929) years * 1 day/year) / 1 day/year = 11 years | | 1931 | 1 day / year | 13 days | 11 years |
| 1961 | (94 - 45) hours / (1957- 1949) years = 6.1 hours / year | 32 hours and 49 minutes - 108 minutes = 31 hours | ( 31 hours - 6.1 hours/year *(1961-1957) years ) / 6.1 hours / year ~ 1 year | | 1961 | 6.1 hours / year | 31 hours | 1 year |
And here is that same table if we measure progress according to the logarithm (i.e., if halving the time needed is always equally impressive). And here is that same table if we measure progress according to the logarithm (i.e., if halving the time needed is always equally impressive).
| Year | Rate of progress before (where log = log of base 2) | Discontinuity in terms of time of travel = New record - previous record | How much extra time would have been needed? = (point - previous predicted point)/ previous rate of progress = (New record - previous record - predicted advance) / previous rate of progress |
| Year | Rate of progress before (where log = log of base 2) | Discontinuity in terms of time of travel = New record - current record | How much extra time would have been needed? = (point - previous predicted point)/ previous rate of progress = (discontinuity - expected progress) / previous rate of progress | |------|-----------------------------------------------------|--------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
|------|-------------------------------------------------------------------------------------|-------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | 1586 | 0.00151660237 log2(days)/year | 0.3823431 log2(days) | 240 years |
| 1586 | (log2(1082)-log2(1018)) log2(days) /(1577-1519) years = 0.001444656 log2(days)/year | log2(1018)-log2(781) = 0.3823431 log2(days) | (0.3823431 log2(days) - (1589-1577)*0.001516602 log2(days)) / 0.08796 log2(days)/year= 240 years | | 1870 | 0.001444656 log2(days)/year | 2.9 log(days) | 1986 years |
| 1870 | (log2(781) – log2(605)) days / (1841 – 1586) years = 0.001444656 log2(days)/year | log2(605)-log2(80) days = 2.9 log(days) | (2.9 log(days) - (1870-1849 years)*0.001444656 log2(days)/year ) / 0.001444656 log2(days)/year = 1986 years | | 1931 | 0.03270527 log2(days)/year | 1.39 log2(days) | 40.5 years |
| 1931 | (log2(80)-log2(21)) days / (1929-1870) years = 0.03270527 log2(days)/year | log2(21)-log2(8) days = 1.39 log2(days) | (1.392317 log(days) - (1931 - 1929) years * 0.03270527 log(days)/year / 0.03270527 log2(days)/year = 40.5 years | | 1961 | 0.132842 log2(hours)/year | 4.18836 log2(hours) | 27.5 years |
| 1961 | (log2(94) - log2(45)log2(hours) / (1957- 1949) years = 0.132842 log2(hours) / year | log2(32 hours and 49 minutes) - log2(108 minutes) = 4.18836 log2(hours) | ( 4.18836 log2(hours) - 0.132842 log2(hours) / year *(1961-1957) years ) / 27.52888 log2(hours) / year ~ 27.5 years |
### Sources: ### Sources:
[Wikipedia: List of circumnavigations](https://en.wikipedia.org/wiki/List_of_circumnavigations) [Wikipedia: List of circumnavigations](https://en.wikipedia.org/wiki/List_of_circumnavigations)