Editing 1017: Backward in Time
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==Explanation== | ==Explanation== | ||
− | + | [[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]]/ | ||
As far as the actual math is concerned, the formula is an {{w|exponential function}} (i.e. the variable appears in the exponent). The effect that the function grows faster and faster as p grows, is due to T(p) being exponential. More precisely, when you repeatedly add some constant to the exponent, you will repeatedly multiply some (other) constant with the value of the function. Compare how "slow" a value grows by adding even high values (1, 1001, 2001, 3001, 4001, 5001…) and how fast it grows by multiplying even low values (1, 10, 100, 1000, 10000, 100000…) | As far as the actual math is concerned, the formula is an {{w|exponential function}} (i.e. the variable appears in the exponent). The effect that the function grows faster and faster as p grows, is due to T(p) being exponential. More precisely, when you repeatedly add some constant to the exponent, you will repeatedly multiply some (other) constant with the value of the function. Compare how "slow" a value grows by adding even high values (1, 1001, 2001, 3001, 4001, 5001…) and how fast it grows by multiplying even low values (1, 10, 100, 1000, 10000, 100000…) | ||
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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. |
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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. | ||
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:90.42% 68 million years ago | :90.42% 68 million years ago | ||
:Around this time: | :Around this time: | ||
− | :First flowering plants. Chicxulub impact kills off most dinosaurs. | + | :First flowering plants. Chicxulub impact kills off most dinosaurs. |
:100% 13.76 billion years ago | :100% 13.76 billion years ago | ||
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:Download complete. | :Download complete. | ||
− | :[Cueball watches a download progress on a laptop in amazement and happiness. Megan stands nearby and looks at Cueball with a bemused posture.] | + | :[Cueball watches a download progress on a laptop in amazement and happiness. Megan stands nearby and looks at Cueball with a bemused posture.] |
:Cueball: Swoosh! Watching all that time blur past is such a rush! | :Cueball: Swoosh! Watching all that time blur past is such a rush! | ||
− | :Megan: So...you've tried to make an extreme sport out of | + | :Megan: So... you've tried to make an extreme sport out of.. ''waiting''. |
:Cueball: ''Swoosh!'' | :Cueball: ''Swoosh!'' | ||