Time Travel and Mental Math

     So here's the deal. I get to travel through time lots these next couple days. Not just the standard forward at a constant rate like we are all used to, but no backwards and forwards at varying speeds. Am I part of a sci-fi novel that is come to life? Maybe a sci-fi novel from the middle ages where airplanes where just as far fetched of an idea as the earth being round. But no, I simply get to sit in a tiny personal space for an extended duration of time as I fly around the earth in a large metal vehicle at really fast speeds. The sun gets to do the disorienting. For those of you who care, and for my own personal stability, here's what time travel looks like for me.


Flight # 1: Greenville to Charlotte.
   Duration: 57 minutes.
   Time Traveled: 57 minutes (into the future)
   Relative to Greenville: Correct
   Level of Disorientation: None


Flight # 2: Charlotte to LAX
   Duration: 5 hours and 28 minutes
   Time Traveled: 2 hours and 28 minutes (into the future)
    Time Relative to Greenville: 3 hours in the past
   Level of Disorientation: Slight


Flight # 3: LAX to Brisbane
   Duration: 14 Hours
   Time Traveled: 33 hours (into the future)
   Time Relative to Greenville: 16 hours ahead
   Time Relative to LAX: 19 hours ahead
   Level of Disorientation: Fully


Flight # 4: Brisbane to Cairns
   Duration: Don't care
   Time Traveled: Too confused to care
   Time Relative to Greenville: 16 hours ahead of me caring
   Level of Disorientation: Shouldn't I be eating dinner instead of breakfast....?


So there you go. I travel 3 hours backwards, then 19 hours forwards all while time is really moving forward. I spend a  total of 22 hours 45 minutes (real time) on an actual airplane. And finally, I end up 46 hours in the future (from 2ish Greenville time on the 15th to 12ish Cairns time on the 17th.)


My mind is preparing to be boggled.


Oh, and eventually I get to come home and leave Sydney at 1 in the afternoon and arrive in LAX at 9:45 the same morning. That is when I will really be screwed.

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Now, for some math.

Let x and y be integers. 

Let a and b be integers as well. 

It follows by the properties of binomial multiplication that:

     (x + a) ∗ (y + b) = xy + ya + xb + ab 

By the properties of equality, it holds that:

     (x + a) ∗ (y + b) - ya - xb - ab = xy

What does this mean? Basically, it is binomial multiplication using variables, basic math that you did in algebra 1. (Think (x +3) * (x + 4) [which is x^2 +7x +12 by the way.]) How could this possibly be used and why on earth did I think about it?

Well, I was trying to multiply 49 times 49 in my head earlier. 49 times 49 is hard to do mentally, however 50 times 50 is easy: 2500. I knew there was a way to quickly get  back to 49 times 49, and it is shown in the proof.

49 * 49 = 50 * 50 - 49 - 49 -1

49 * 49 = 2500 - 99

49* 49 = 2401

Easy. No calculator necessary. 

Why was I trying to do 49 * 49 in my head? Well, if you really want to know, I was wondering if Australia needed area codes for their phone numbers. The number of possible combinations of phone numbers is just 10 ^ 7, which is 10000000 or ten million. Which alone is enough to tell me that they need at least three area codes (population ~ 22 million.) But then I started thinking about all the numbers they couldn't use. You can't start a phone number with 0 (at least I have never seen one), the triple 5s are  reserved for the entertainment industry, and whatever three digit emergency number can't start a phone number, ect. Which leaves 7 choices for the first three digits apiece. I figured for the forth I would use another 7 to take out anything else i forgot, then multiply by 1000 for the last three digits. Leaving 2401000 (2.4 million) numbers in one area code. Anyways, Thats why I started trying to calculate 49 * 49. 

If you followed all of that (the thought process more than the math), we should hang out more. (If you followed the math, you get props for understanding algebra, mental math, and jargon.)

I hope you enjoyed a glimpse into the mind of this time traveling math major.