Editing 1017: Backward in Time
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==Explanation== | ==Explanation== | ||
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[[Cueball]]/[[Randall]] creates this formula which helps him wait for long stretches of time which goes increasingly faster into the past as more time goes by, which gives him the effect of looking like the time goes by quickly. Which assists in the waiting process. | [[Cueball]]/[[Randall]] creates this formula which helps him wait for long stretches of time which goes increasingly faster into the past as more time goes by, which gives him the effect of looking like the time goes by quickly. Which assists in the waiting process. | ||
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The remaining adjustments are technical. The coefficient in front of p³ adjusts the constant by which the result will be multiplied while adding some constant to p, while it also roughly ensures that p=1 yields the lifetime of the universe. The 3 added to the product in the exponent further adjusts the actual values of the power without touching the slope (the multiplicative constant). In the parentheses, e³ is subtracted to put the time to 0 when p=0. Otherwise the function would start approx. 20 yrs and 1 month ago. For bigger p, this offset does not matter much. Imagine subtracting 20 yrs from the lifetime of the universe! | The remaining adjustments are technical. The coefficient in front of p³ adjusts the constant by which the result will be multiplied while adding some constant to p, while it also roughly ensures that p=1 yields the lifetime of the universe. The 3 added to the product in the exponent further adjusts the actual values of the power without touching the slope (the multiplicative constant). In the parentheses, e³ is subtracted to put the time to 0 when p=0. Otherwise the function would start approx. 20 yrs and 1 month ago. For bigger p, this offset does not matter much. Imagine subtracting 20 yrs from the lifetime of the universe! | ||
− | Finally, the result is subtracted from the current date for aesthetical reasons. The formula could tell you "20 | + | Finally, the result is subtracted from the current date for aesthetical reasons. The formula could tell you "20 yrs ago", or it could read "February 1992". Randall decided the latter would be better. |
There is actually a mathematical error in this comic; the inverse function in grey writing off at the bottom right of the main formula involves a square root, when the actual inverse of Randall's main function would involve a cube root. In addition, this function does not contain the current date, meaning that T, in the inverse, refers to how long ago a point in time was, rather than the point in time itself. When the T in the inverse is 20, it means that the date referenced by T is 20 years ago. | There is actually a mathematical error in this comic; the inverse function in grey writing off at the bottom right of the main formula involves a square root, when the actual inverse of Randall's main function would involve a cube root. In addition, this function does not contain the current date, meaning that T, in the inverse, refers to how long ago a point in time was, rather than the point in time itself. When the T in the inverse is 20, it means that the date referenced by T is 20 years ago. | ||
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The punchline "Swoosh!" is about how fast the last few percents of Cueball's download happen in "such a rush". For most humans waiting for a download to complete tends to become really boring and progress would instead seem to get slower and slower. | The punchline "Swoosh!" is about how fast the last few percents of Cueball's download happen in "such a rush". For most humans waiting for a download to complete tends to become really boring and progress would instead seem to get slower and slower. | ||
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[[940|(Also, the workout website, Fitocracy has been mentioned previously in xkcd.)]] | [[940|(Also, the workout website, Fitocracy has been mentioned previously in xkcd.)]] | ||
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:Inverse: p = sqrt((ln(T+e^3)-3)/20.3444) | :Inverse: p = sqrt((ln(T+e^3)-3)/20.3444) | ||
− | :[Line Graph explaining the correlation between completion percentages and temporal deltas. | + | :[Line Graph explaining the correlation between completion percentages and temporal deltas. |
:0% = now (Date of comic is 2012-02-14T00:00-0500, approx. 1329195600 UNIX) | :0% = now (Date of comic is 2012-02-14T00:00-0500, approx. 1329195600 UNIX) | ||
:10% = September 2011 | :10% = September 2011 | ||
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:90% = 55 million years ago | :90% = 55 million years ago | ||
:100% = 13.8 billion years ago | :100% = 13.8 billion years ago | ||
+ | :] | ||
:It moves slowly through the first few years, then steadily accelerates. I tuned the formula so the time spent in each part of the past is loosely proportional to how well I know it. This means I hit familiar landmarks with each bit of progress, giving me a satisfying sense of movement. | :It moves slowly through the first few years, then steadily accelerates. I tuned the formula so the time spent in each part of the past is loosely proportional to how well I know it. This means I hit familiar landmarks with each bit of progress, giving me a satisfying sense of movement. |