Moving a Petabyte of Data

This BAB's title was duplicated from the title of a blog posting by Jonathan Schwartz that started as follows:

   "I made a speech last week at which I asserted it was faster 
    to send a petabyte of data from San Francisco to Hong Kong 
    by sailboat, than by the Internet.

Schwartz is CEO of Sun Microsystems and it appears as though he knows all about "off-by-one" errors.

   "I got quite a few 'how can that possibly be true?' kinds of 
    questions, so here's the math. (Full disclosure, I am a 
    mathematician by training, which guarantees me a lifetime 
    of small 'off by one' errors in all subsequent calculations 
    - so if I get something wrong, be gentle)."

Schwartz "did the math" to explain why it takes so long to "move a petabyte of data." Schwartz began his math exercise with the following.

   "A petabyte is a thousand terabytes, which is a million 
    gigabytes, or a billion megabytes. Or 8 billion megabits. 
    With me so far?"

There are typically eight bits in one byte. [A "bit" is a binary digit (i.e. zero or one).]

With respect to SI prefixes: peta- is 10^15, tera- is 10^12, giga- is 10^9 and mega- is 10^6.

Let's check to see if one petabyte equals 8 billion megabits.

   peta- is 10^15...  1 petabyte = 10^15 bytes = 
                      1,000,000,000,000,000 bytes

   Using 8 bits per byte...  1 petabyte = 8 x 10^15 bits = 
                             8,000,000,000,000,000 bits

   Law of exponents... 10^15 = 10^9 x 10^6
                       10^9 = 1 billion; 10^6 = 1 million (mega)

   8 x 10^9 x 10^6 bits = 8 x 1 billion x 1 megabit = 8 billion megabits

Schwartz asked... "With me so far?" And the answer is "Yes!"

Schwartz continued his posting with the following.

   "So if you had a half megabit per second internet connection, 
    which is relatively high in the US (relatively low compared 
    to residential bandwidth available in, say, Korea), it'd take 
    you 16 billion seconds, or 266 million minutes, or 507 years 
    to transmit the data. Can you sail to Hong Kong faster than 
    that? At a full megabit, just divide the time in half. Even 
    at a hundred megabits (about the highest, generally available, 
    of any carrier I've seen), it's a few years."

From Tom Duff we learned (and confirmed) that there are approximately 3.155 x 10^7 seconds per year. Using Duff's input, let's check the math done by Schwartz.

   Data transmission ("move") rate:  1/2 megabit per second 

      1/2 megabit = 0.5 x 1,000,000 bits = 500,000 bits
      1/2 megabit per second = 500,000 bits per second

   Total data to transmit:  1 petabyte or 8 billion megabits

      8 billion megabits = 8 x 10^9 x 10^6 = 8,000,000,000,000,000 bits

   Time (in seconds) to transmit data...

       8,000,000,000,000,000 bits
      ----------------------------- = 16,000,000,000 seconds
             500,000 bits
               1 second

   We don't need minutes, but let's check it anyway...

       16,000,000,000 seconds
      ------------------------ = 266,666,666.6666 minutes
            60 seconds
             1 minute

   Using  3.155 x 10^7 = 31,550,000  seconds per year...

       16,000,000,000 seconds
      ------------------------ = 507.1315 years
        31,550,000 seconds
              1 year

Schwartz ended his blog posting by writing: "And I don't want to even think about moving a zettabyte."

Being the busy CEO of Sun Microsystems, Schwatz didn't have to "think about moving a zettabyte," but GDT's not so busy.

Exercise: One zettabyte equals how many bytes?

The SI prefix zetta is 10^21 (i.e. one sextillion, or 1,000 quintillion, or 1,000,000 quadrillion); therefore, since one petabtye equals one billion megabytes, one zettabyte equals one million billion megabytes.

   peta = 10^15 = 10^6 x 10^9 

   10^6 = 1 million (mega); 10^9 = 1 billion (giga)

   million billion megabytes = 10^6 x 10^9 x 10^6 bytes = 
                               10^(6 + 9 + 6) = 10^21 bytes


   1 zettabyte = 1 megabyte x 1 gigabyte x 1 megabyte =
                 (1 megabyte)2 x 1 gigabyte

   ...or, if giga- usage prohibited  
   1 gigabyte = 1000 megabytes

   1 zettabyte = (1 megabyte)2 x 1000 megabyte =
                 (1 megabyte)3 x 1000 = (1 megabyte)3 x 103 =
                 (10 x 1 megabyte)3

Generalizing... one zetta-whatever equals ten times one mega-whatever quantity cubed. Moving A Petabyte of Data [by Jonathan Schwartz]

Creator: Gerald D. Thurman []
Created: 28 March 2007

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