Editing 1017: Backward in Time

{{comic
| number    = 1017
| date      = February 15, 2012
| title     = Backward in Time
| image     = backward_in_time.png
| titletext = People tell me I have too much time on my hands, but really the problem is that there's too much time, PERIOD.
}}
Clicking the image at xkcd.com links to [https://docs.google.com/spreadsheet/pub?key=0Ak43bGxHGI1adDMtOHVWVXZrYzhKd2VtbFJJMmJPTEE&single=true&gid=1&output=html this spreadsheet], which [[Randall]] used to calculate the times and dates for the comic. It also has a lot of other percentages and dates, so take a look if you are interested.

==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.

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…)

Now, the function has to be adjusted so that, as Randall put it, "the time spent in each part of the past is loosely proportional to how well I know it." The most important adjustment is putting p to the power of three. That lowers the amount added to the exponent for low values (0.1³=0.001, 0.2³=0.008, i.e. only 7/1000 have been added for 10% workflow) and increases the amount for high values (0.8³=0.512, 0.9³=0.729, i.e. more than 1/5 has been added for 10% workflow). That means the recent past will pass even slower and the historic past even faster than it already does by choosing an exponential function.
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 years ago", or it could read "February 1992". Randall decided the latter would be better. 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 workout website mentioned initially, Fitocracy, has been mentioned previously in [[940: Oversight]].

{| class="wikitable sortable"
|-
! % !! Historic time<br/>(As of publication)
! "Around This Time" text !! Expanded description of events
|-
| 0% || Now<br/>(Feburary 15 2012)
| ''Not given in comic'' || Presumably February 15, 2012, the day the comic was published, which is consistent with the next entry taking place in late 2011.
|-
| rowspan="2" | 7.308% || rowspan="2" |December 18, 2011
| Kim Jong-il Dies. || Kim Jong-il, the president of North Korea at the time, dies of a suspected heart attack. He is succeeded by Kim Jong-un.
|-
| US Leaves Iraq.   || Early 2003, the majority of Americans supported the {{w|2003 invasion of Iraq|Iraq Invasion}}. However, a little more than a year later the majority of Americans thought that the invasion was a mistake. Representative {{w|John Murtha}} introduced a resolution in 2005 for U.S. soldiers in Iraq to be "redeployed at the earliest practicable date" and the {{w|Republican Party (United States)|Republicans}} called for "the deployment of United States forces in Iraq be terminated immediately", however this was immmeditly shot down. A year later, another bill was shot down preposing a deadline for recalling soldiers. The House Majority Leader, {{w|John Boehner}}, argued that "achieving victory is our only option". A bill finally passed congress in 2007 that called for the removal of troops within the end of the year, however it was vetoed by {{w|George W. Bush|President Bush}}. In 2008 both the American and Iraqi governments signed the {{w|U.S.–Iraq Status of Forces Agreement}}. It stated that, by June 30th of the following year, American forces would withdraw from Iraqi cities and would be completely gone by 2012. On December 18, 2011, the very last 500 solders left Iraq.
|- 
| 10% || September, 2011
| ''Not given in comic'' || This date is almost exactly 10 years after the {{w|September 11 attacks}} on the World Trade Center in New York City and the Pentagon in Washington, DC. The attack was conducted with multiple hijackers taking control of passenger aircraft and crashing them into World Trade Center buildings One and Two.
<hr/>This is also the approximate date of Randall's marriage.
|-
| rowspan="2" | 20% || rowspan="2" | 2008
| rowspan="2" | ''Not given in comic'' || The {{w|Marvel Cinematic Universe|Marvel}} movie {{w|Iron Man}} is released, kicking off the Marvel Cinematic Universe plotline, which has since followed 35 movies and many different superheroes.
|-
|                                        Democratic candiate {{w|Barack Obama}} wins the 2008 election and becomes the 44th President of the United States.
|-
| rowspan="2" | 30% || rowspan="2" | 1997
| rowspan="2" | ''Not given in comic'' || {{w|O.J. Simpson}} was found liable for the deaths of {{W|Nicole Brown}} and {{w|Ronald Goldman}}. O.J. owed the two families $35.5 million. It is worth noting that after he was found liable, he refused to pay the money and did everything in his power to avoid giving them it. However the Goldmans eventally did end up with one of his assets, the rather scandalous book "If I Did It" (O.J. writing about HYPOTHETICALLY if he HAD killed them, how and why he'd have HYPOTHETICALLY killed them) which the Goldmans rebranded from "a ghost story", as O.J. put it, to "a confession of a killer".   
|-
|                                         Princess Diana died in a car crash [http://news.bbc.co.uk/onthisday/hi/dates/stories/august/31/newsid_2510000/2510615.stm while being chased by paparazzi].
|-
| rowspan="2" | 31.12% || rowspan="2" | February 1995
| Windows 95 Debuts   || The Windows 95 was an operating system developed by Microsoft. It was the begining of the Windows 9x operating systems. It was released on July 14, 1995. 
|-
| OJ Found Not Guilty || The {{w|Murder trial of O. J. Simpson|O.J. Simpson trial}} was a famous trial where O.J. was tried for the murders of his ex-wife Nicole Brown Simpson and her friend Ronald Goldman. DNA evidence almost proved his guilt, however the defense pointed out the evidence wasn't collected correctly and could have been cross contaminated. Because of this, the jury found O.J. not guilty of the double murder. 
|-
| rowspan="3" | 40% || rowspan="3" | 1958
| rowspan="3" | ''Not given in comic'' || The European Common Market is created.
|-
|                                         Khruschev gains control of the USSR after Stalin dies.
|-
|                                         The first American satellite, Explorer 1, is launched into orbit, after the Sputnik 1 and 2 were launched.
|-
| rowspan="3" | 47.91% || rowspan="3" | 1844
| Rubber Vulcanized, || {{w|Vulcanization}} is when one heats and adds sulphur to rubber, usually {{w|Polyisoprene|polyisoprene}} (natural rubber) or {{w|Styrene-butadiene|SBR rubber}}. This helps its elasticity and improves its strength. Charles Goodyear was the inventor of vulcanization. In the early, 1800s tires quickly turned soft and sticky after they got hot (something that happens when you drive on them for miles at a time in warm weather). Charles Goodyear heated up the rubber to add various chemicals to the tires and, to his amazment, the process worked!! The strength of tire was thus improved. The only problem was that the improvement wasn't because of the chemicals but because of the heating. He would eventally learn this after dropping the rubber in a frying pan, watching the rubber not melt (as one would expect), but harden. Soon after, in 1844, he patented the process.
|-
| Bicycle Invented,  || Randell's {{w|timeline}} may be {{w|Error|wrong}} here. It could be {{w|Argument|argued}} that the {{w|1|first}} "{{w|Bicycle|bicycle}}" {{w|Name|called}} a {{w|Dandy horse|"dandy horse"}}, was {{w|Invention|invented}} in {{w|1817}} by {{w|Baron}} {{w|Karl Drais|Karl von Drais}}. However the dandy horse didn't have any {{w|Bicycle pedal|pedals}}, so another argument could be made that the {{w|Treadle bicycle|first bicycle}} was {{w|Creativity|created}} in {{w|1839}} by {{w|Kirkpatrick MacMillan}}. This bicycle didn't move by {{w|Angular momentum|spinning}} the pedals, but by {{w|Treadle|pumping them up and down}} ({{w|Similarity (geometry)|similar}} to a {{w|grindstone}} or {{w|antique}} {{w|sewing machine}}). The first time a {{w|Crank (mechanism)|mechanical crank}} was used was in the early {{w|1860}}s, when {{w|Pierre Michaux}} and {{w|Pierre Lallement}} {{w|Scaling (geometry)|enlarged}} the {{w|Direction (geometry)|front}} wheel and added the crank to that. In {{w|1869}} {{w|Thomas McCall (inventor)|Thomas McCall}} made a rear-wheel drive bicycle. On top of all that, the word bicycle wasn't used until {{w|1868}}, until then all bicycles (or not bicycles) were called {{w|velocipede}}. Around this time the {{w|French people|French}} vélocipède, made of {{w|iron}} and {{w|wood}}, turned into the "{{w|penny-farthing}}" (as it was later to be known) which was made from a {{w|steel}} form and {{w|Tire|rubber tires}}. The invention of the bicycle wasn't just one invention, but many small inventions made by people all around a {{w|continent}}. 
|- 
| Wrench Patented    || The {{w|wrench}} was patented. The first wrench was created by Charles Moncky and was called the monkey wrench.
|-
| 50% || 1776
| ''Not given in comic'' || On July 4th, the American colonies {{w|Lee Resolution|declared independence}} from Great Britain. This event started a {{w|American Revolutionary War|seven year war}}, in which the colonies won their indepence. This heralds the start of The United States of America.
|-
| 60% || 405 AD
| ''Not given in comic'' || The {{w|War of Radagaisus}} started. Radagaisus lead a group of about 100,000 men across the Alps into Rome. The three remaining {{w|Sibylline Books}} were burned. The Sibylline books were a series of nine prophesy books written by an old woman (it has never been found out who, but most likely a {{w|Cumaean Sibyl}}. It is said that they were offered to the last King of Rome, {{w|Lucius Tarquinius Superbus}}, who refused to buy them twice, which resulted in three books getting burned for each denial. She then offered them back to the emperor for the same price and, at last, the king bought them. The Roman Senate took control of the books and was extremely protective of them. The books were initially put under the care of two guardians, increasing to ten, then to fifteen. However, after eight centuries, a Roman General called {{w|Stilicho}} ordered them to be burned as they were being used to attack the government.
|-
| 70% || 22,000 Years Ago
| ''Not given in comic'' || ''Homo Sapiens'' crosses a newly-formed land bridge between present-day Russia and Alaska, entering the Americas for the first time.
|-
| rowspan="3" | 70.33% || rowspan="3" | 24,000 Years Ago
| Caves Painted,        || This is around the time some cave paintings are from.
|-
| Ceramic Art Made.     || This is around the time the oldest known ceramics are from. The earliest known are the gravettian figurines.
|-
| Neanderthals Extinct. || As a distinct species, ''Homo neanderthalensis'' goes extinct for reasons {{w|Neanderthal#Extinction|not entirely understood}}. This eventually leaves ''Homo sapiens'' as the sole remaining human genus, albeit still with a quantifiable amount of {{w|Interbreeding between archaic and modern humans|Neanderthal ancestry}}.
|- 
| 80% || 671,000 Years Ago
| ''Not given in comic'' || This date is likely a result of the equation not being calibrated for this specific percentage, as nothing significant is known to have happened around 671,000 years ago. However, 700,000 years ago, there was a major shift in the Earth's climate that changed the length and rarity of ice ages.
|- 
| 90% || 55 Million Years Ago
| ''Not given in comic'' || The Eocene Era begins around this time.
|-
| rowspan="2" | 90.42% || rowspan="2" | 68 Million Years Ago
| First flowering plants.                    || The first flowering plants evolved around this time.
|-
| Chicxulub impact kills off most dinosaurs. || A large C-type asteroid, known as the Chicxulub impactor, strikes the Earth on the Yucatan Peninsula, leading to the {{w| Cretaceous–Paleogene extinction event|extinction}} of the [[1211: Birds and Dinosaurs|non-avian dinosaurs]] and the death of approximately 75% of all life on Earth. The extinction was primarily caused not by the impactor itself, but by the large worldwide tsunamis and the large amount of dust, which obscured the atmosphere and caused a large amount of vegetation to die off, leading to the deaths of herbivores, which then lead to the deaths of the carnivores. 
|-
| rowspan="2" | 100% || rowspan="2" | 13.76 billion years ago
| Universe begins.    || The Big Bang occurred at this time (about).
|-
| First stars ignite. || The first stars were born in this era.
|}

Note that as of the time that this page was last cached, the comic was uploaded at {{#expr:100*(((ln(({{#time:U}}-1329195600)/31536000+e^3)-3)/20.3444)^.5)}}% progress.

==Transcript==
:When I have a boring task to get through — a three-hour lecture, a giant file download, or a long term point goal in fitocracy — I use this formula to convert the percentage completed (p) into a date:

:T=(Current Date) - (e^(20.3444*p^3+3) - e^3) years

:When the task is 0% done, it gives today's date, and as I make progress, I move further and further back in time

:(inverse given in lighter colors)
:Inverse: p = sqrt((ln(T+e^3)-3)/20.3444)

:[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)
:10% = September 2011
:20% = 2008
:30% = 1997
:40% = 1958
:50% = 1776
:60% = 405 AD
:70% = 22,000 years ago
:80% = 671,000 years ago
:90% = 55 million 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.

:[The following are panels detailing completion percentages, correlated time periods, and notable events from this time period.]

:7.308% December 18, 2011
:Around this time:
:Kim Jong-Il dies. US leaves Iraq.

:31.12% February 1995
:Around this time:
:Windows 95 debuts. OJ found not guilty.

:47.91% 1844
:Around this time:
:Rubber vulcanized, bicycle invented, wrench patented.

:70.33% 24,000 years ago
:Around this time:
:Caves painted, ceramic art made. Neanderthals extinct.

:90.42% 68 million years ago
:Around this time:
:First flowering plants. Chicxulub impact kills off most dinosaurs.

:100% 13.76 billion years ago
:Around this time:
:Universe begins. First stars ignite.

: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: Swoosh! Watching all that time blur past is such a rush!
:Megan: So...you've tried to make an extreme sport out of...''waiting''.
:Cueball: ''Swoosh!''

==Trivia==
There is 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, while 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.

{{comic discussion}}

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