October 2005


What is a trillion between friends?

I just can't wait until this information is hopelessly outdated and antiquated.  Weather it will be in one year or five or even ten and even then exactly how I must just wait and see.

Just for fun many of the questions are formatted as one of my favorite professors called it, "in multiple guess."  Please email with any errata, comments or clarification.

Large internet companies are currently collecting as much as one tera byte of user data per day.  Computer science numbers are noted in their own binary prefix for convenience so a computer kilo is 1024 is bigger than an  SI 1,000 , a computer mega 1048576 is larger than an even million, etc.  The following questions address this computer notation peculiarity and the magnitude of the grand 1T (terabyte).
  1. In todays money ($US) just the difference of a tera-dollars and a trillion dollars would
  2. How much is 1 tera of  H20 molecules? It is
  3. If you, as the writer Issac Asimov once suggested in one of his fictional works, were to store information by notching individual atoms off of molecules, how long would a 1 Tera byte chain be?  ( For the sake of this exercise assume that the simplest way to store information is the bi polymeric chain of A and B components where A and B are monomer representing 0's and 1's.  )
  4. As the numbers grow larger due to the root difference or the relative error between the International System of Units (SI) and the binary prefixes go out of wack. With 1 killo and 1000, the deviation represents a 2.4% the value, 1 mega  to 1,000,000 deviates 5% and 1T to 1 trillion of 10%.  When does an  intolerably large error of say 50+% occur?
  5. Theory and Probability

  6. Theoretically speaking, what would a potential application or purpose of a virtual constructor be?
  7. Given that a valued prize is hidden behind one of three doors.  You must select correct door to win the prize, however once you make your initial guess a knowing game host reveals one of the empty doors.  At this point you are given the opportunity to change your initial guess in favor of the only remaining door.  What should you do, and what is the probability of obtaining the prize given this choice?

  1. The difference is a mere $500M shy of the $100B mark.  If you picked (a) my cousins are selling.  If you picked (b) they could convince their neighbors to sell too.  If you selected (c) Bill Gates you are correct assuming the MSFT stock is still relatively flat ( October 2005, MSFT last double of value brings you back to 1997 )You now top the Forbes top ten list in net worth.  Regarding  (d) , assuming a multiple of 10-20 times the GDP would do, $100B should definitely score 20 island or small African nations and even some mid size countries like Madagascar, Georgia, etc.(ref. wiki ) .
  2. 1 tera H2O molecules is (c)
    1099511627776 *  18 grams/6.0E23 AvNum *  .001 L/gram = 3E-14 L = 30 fL
  3. Given simplest monomers you can use are polyethylene(–(CH2-CH2)n–) and polypropylene (–[CH2-CH(CH3)]n), where the methyl group (CH3) is the "atom" functional group storing the "1" .  A chain of 01010011 would look like ABABAABB, or The chain unit has the unit length of approximately 3 angstroms (3E-10 meters) so the total length of a tera byte chain would be
    1099511627776 bytes * 8 bits/byte * 3e-10 meter/bit= 2.6 km.  Answer (a).
    Mind you that it would be a very thin string taking, when bunched up, not much more space than the water in question 2 -  just a few femto-liters.
  4. Note: Chemical structures grow combinatorially, so the simplest bi polymer, the polyethylene polypropylene bi polymer is not likely the densest possible format.  If one had the technology to rapidly build and read a specified chain of two different monomers, one should presume that they would be able to select a myriad of just slightly larger molecules .  With a slight increase in atoms the larger molecules could permute in to a large base X number system.  
  5. I believe (a).  You do not need to worry, by the time you get as far out as the 21st suffix all the good alphabet symbols are pretty much taken up anyways.  Perhaps another notation similar to scientific notation (e.g. speed of light 2.99e8) will replace letter suffixes.  As for the answer (b) in the year 2013 assuming if Moor's Law holds we will be still working our way through P (peta) or Quadrillion which has an error of a perhaps tolerable 13%.   The rest of the options 2015 and 2042 are there to just throw you off.  Perhaps you just choose 2015 because it was closely grouped to 2013 and in the middle?
  6. The correct answer is (b), although my first inclination was that it was strictly Dirk Gentley stuff, I saw a good argument on the web (at parashift) for its potential practical use.  A dynamic abstract class definition first must be added to  C++ so you can somehow still specify the class& of interest.
    Dirk Gentley is a fictional detective, a creation of  Douglas Adams and the kind of gumshoe who would follow random automobiles under the premise that while following random people, "he would rarely go to where he was heading for, but the destination was almost always very interesting."
  7. Unambiguously (d) "None of the above." is the correct answer.  If your choice was (a) then why would you not want to sweeten your odds a bit given that you now have some inside information.  Your probability of 1/3 here is absolutely true however and thus the revealing the perhaps unintuitive truth of this problem.  The probability of all the states any system sums to 1.  This if 1/3 of the probability goes to your initial guess the other 2/3 are evenly distributed to the remaining two doors ... that is until someone reveals one of the cards as not  the prize card.  Following this, the probability distribution must readjust to the remaining unselected face down card.  In summary you should select the not yet selected, not yet revealed card as it holds a 2/3 chance of being the prize card.  If you don't believe me and particularly if you guessed (b) then you are in good company with the famous mathematician Paul Erdos whose initial trouble with this problem is described in The Man Who Loved Only Numbers.  You may look up the problem as The Cadillac Problem, or else download my CadillacProgram and run a simulation of it for yourself.  

    $ time ./CadillacProblem.exe 1073741824
    of 1073741824 trials

    Strategy "keep first choice" wins :  357915152   (33.333446)
    Strategy "Switch door"       wins :  715826672   (66.666554)
                                      -----------   ----------
                                total : 1073741824   (100.000000)

    real    11m46.656s
    user    0m0.015s
    sys     0m0.000s