Facts About the Google Gmail Algorithm: A Grasp for Infinity
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Facts About the Google Gmail Algorithm: A Grasp for Infinity

Google's Gmail service revolutionized space limitations. But just how fast does space accumulate on the popular free email service?

Although the internet mogul Google loves a good April Fool's Day prank, a 2005 announcement on the same date was not a prank. Gmail, the Google service that broke open the Pandora's Box of space limitations for e-mail a year prior, announced that it would be increasing its space limitations one again to allow users even more space, this time doubling the space limitations to 2GB. In 2004, Google had shocked the world by offering users 1GB of space for free when most competitors only offered 2 to 4MB (about 1/500th or 1/250th of Gmail's initial offering).

As competitors began catching up in 2007, Google once again jumped up and reached 6.2GB of storage by January 2008. It also increased its rate of storage increase by ten times the previous amount.

As of this Wednesday, the 30th of June 2010, at 9:39:00 A.M. (Eastern Standard Time, U.S.), Google Gmail had 7,471.176735MB of storage. If you look carefully, you will notice that the amount of storage reads "X megabytes (and counting) of free storage," and that the number increases each second. Upon closer inspection, you can see that Gmail storage increases by .000004 or 4 X 10 ^ -6 every second; if you look even closer, you will notice that it increases by .000005 or 5 X 10 ^ -6 every fifteenth second.

To give the service a cleaner look and remove ugly negative exponents and nonterminating and repeating (rational) numbers from the screen, Gmail simplified the service so that it looks like it increases as above, .000004MB for fourteen seconds and then .000005MB on the fifteenth second. Some basic math reveals what is actually happening; here are the steps I took to arrive at the exact value that Gmail storage increases every second.

1. We know that the variable value is .000001 every 15 seconds. Other than that single value (that fifteenth second), Gmail indicates that the storage increases by 4 X 10 ^ -6 every fifteen seconds.

2. We can divide that value by 15 and spread it evenly among each second. So, .000001 divided by 15 equals 6.66 (repeating) X 10 ^ -8. An easy way to think of it is also the decimal equivalent of 2/3 without the first 7 6's after the decimal point: .00000006666667. The six repeats until infinity, and adding this value to each second nets 4.066 (repeating) X 10 ^ -6.

3. Basically, we have just taken that extra .000001 on the fifteenth second and spread it evenly among all fifteen seconds.

Whether you express it purely mathematically or by Gmail's much more aesthetically-pleasing approximation, however, it works out to the same value: Gmail storage increases by .000244 megabytes (MB) per minute or 2.44 X 10 ^ -4. The rest is simple multiplication.

  • .01464MB per hour
  • .35136MB per day
  • 2.45952MB per week
  • 10.6872MB per month (calculating 30.416 repeating days per month)
  • 128.2464MB per year (assuming 365 days per year)

What this means, then, is that if Gmail's algorithm for space limitation does not change within the next year, then at 9:39:00 A.M. (Eastern Standard Time) on June the 30th 2011 (because 2011 is not a leap year), Gmail will have exactly 7,599.423135 megabytes of storage space. Thus, if the math remains the same, the range of storage should be somewhere between 7,599.422MB and 7,599.424 MB at that minute and second (I allowed for about four minutes of error above and below that value considering time calibration). Do you have your calendar marked?

****UPDATE 23JAN 2011****

Google changed the algorithm slightly (changes were noticed in November and have continued since then). It appears that they have introduced a randomizer into their algorithm. As previously noted, space increase by .000004 megabytes on every second but those seconds that it increases by .000005 megabytes. The difference is that the .000005 second is no longer predictably the 15th second, but has instead been measured at 11, 13, 14, and 15 seconds alternately in no particular pattern. More detailed measurements to follow.

SOURCES

http://www.internetnews.com/xSP/article.php/3494491

http://googlesystem.blogspot.com/2007/10/gmails-storage-increases-dramatically.html

https://www.google.com/accounts/ServiceLogin?service=mail&passive=true&rm=false&continue=http%3A%2F%2Fmail.google.com%2Fmail%2F%3Fui%3Dhtml%26zy%3Dl&bsv=1eic6yu9oa4y3&scc=1&ltmpl=default&ltmplcache=2

http://commons.wikimedia.org/wiki/File:Exquisite-gmail_red.png

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Comments (5)

Wow, very interesting. I have a few gmail accounts, Just don't like them as much as my hotmail. Weird I know.

Very interesting Math! All I can say is I love my gmail account!

Good to know. Thanks.

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