KB, MB, GB, What Giga Mean?

Kilo = 10^3
Mega = 10^6
Giga = 10^9

I was fatuously believing this conversion rate is true.
But...I just found out that the story is a bit different in case of "byte".

When I was checking my data usage on verizon,
I noticed that the first few digits of GB, MB, and KB are different!
That can't be true if Kilo means 1000 and Mega means 1000,000.
Soon I found out the following fact.
1000 Bytes  is not Equal to 1 Kilobyte.
1 Kilobyte is very close to 1000 bytes, but it is 1024 bytes in exact.
That makes sense as the computer data is in binary.
However when I checked about this with wikipedia, I found out that the story is not that simple.
It seems that both are in use...well who cares about it?
The difference between 1000 and 1024 is probably negligible.
But 1000^K and 1024^K's difference will become significant as K increases.
Going to Tera, Peta, and larger, the huge difference will be a problem, I believe.
....I think someone has to resolve this issue in near future.

Harmonic Mean

In mathematics there are several ways to take the mean (average) value.
The most well known is the arithmetic mean, which is the just average we usually think about.
But today I would like to mention about "Harmonic Mean".
Harmonic Mean of two numbers X and Y is

2/(1/X   +  1/Y)

I come up with an instance to use harmonic mean.
Suppose I live at the foot of a hill, my office is at the top of the hill, and
I drive a roundtrip between my home and my office.
Furthermore, suppose my MPG( millage per gallon) is 10 for upward and 40 for downward for sake of simplicity.
Then my MPG for the round trip must be computed as follow:
MPG = # miles driven/ # gallon consumed.
Let D be the # miles in one way.
So #miles driven for the round trip is 2D

then #gallon for up should be D/10, and
       #gallon for down should be D/40.
So  # gallon consumed for the round trip is the sum D/10 + D/40.

Hence, MPG = (2D) / (D/10 +D/40)

                     = 2/(1/10 + 1/40) = 80/5 = 16 mpg.

Notice that the distance D is irrelevant to find the average fuel consumption for the round trip.
The blue part (obtained from above line by dividing top and bottom of the expression by D.)
is exactly the harmonic mean of 10 and 40. So in this sense 16 is the average mpg of 10 and 40.

Now I want to improve my overall mpg by driving mildly.
Which strategy  works better?
1. Improve only my uphill consumption rate from 10mpg to 20mpg.
2. Improve only my down consumption rate from 40mpg to 80mpg.

The first strategy will result to 26.666 mpg, pretty good.
But....
the second strategy will result to 17.777 mpg......Not much change!

Here is the lesson.
To improve the harmonic mean, one should consider improving the lower value.
Improving the lowest performer will result a better overall performance.
Help the most struggling worker will do better than help the talented one to go further.
Isn't it Harmonic??
Anyway, in reality, my commuting route has lots of short sloped roads, disgusting traffic lights,
and entrance to a freeway. If I can pass these mpg-killing points with mild loss of fuel, my over all mpg will improve a lot. In fact after I realized this, my MPG is improving from 39 to 46!
Thinking mathematically saves lots of fuels and money!
(I lied here, it doesn't save much money for me because I live close to my office.)

Give Up to Leave Fame!

After my little dinner, I noticed sound of fireworks.
The loudness indicates that the fireworks were held nearby. 
I expected to see it from here, so I went outside. T
here was a drizzling, but I found out a good view spot under a tree in front of my apartment. 
A bit too far to feel the sonic vibration.
But I did enjoy the incessant sequence of fireworks for 10 minutes or so.  

While watching the show, I felt how short the life of each one of fireworks’ bombs.
I don’t know how challenging to create an exquisite and enchanting bomb.
Anyway its life is so short, much shorter than cherry blossoms which are famous representation for a short lived life in Japanese culture.
Each bomb was glorious for a second and was already in oblivion in another second.

So sad isn’t it? What a pitiful life! Or Am I wrong!?
After all, human’s life is very short. It is as short as the fire bombs.
Yeah, I remember now that everything is in relative scale.
Each one of us is just like a single bomb in the sequence of the firework show.

Hey, don’t try to live for leaving fame!
If one bomb’s smoke remained in the air for long, people can’t enjoy the rest of the show.
Just exit the stage without hesitation!

Ok, I try to reset my mind and I’m not going to fear of a life like the bomb or the cherry blossoms.
Yes, spectators forget each one of the explosions but they feel something by seeing the fireworks and their hearts reshape by the end of the show. They forget all the details, but they gain something!
If a bomb can do it, I can live like that!

On Reading News Articles on Economy

              These days I push myself reading articles on economy. Today’s my choice was an article on Chinese economy (please see the link below) based on PMI.  I had no idea about PMI and I was actively enough to do a little search for it. I learned that PMI stands for “Purchasing Manager Index” and it is just a weighted average of +1 (as Improvement), 0.5 (as No Change), and 0 (as Deterioration) from answers of monthly surveys of private sector companies. I don’t know how the surveys are conducted, but need I know it? I learned that PMI (Purchasing Manager Index) is announced at the beginning of each month and it has a strong positive correlation with GDP. No wonder I found out this news article today! Since I haven’t seen China by myself and haven’t thought about it much either, I can’t judge how reliable and trustful this article is. Yet I found some yield from this reading experience.

First is the very fact that I clicked the link to this article and read it. Unthinkable! What’s wrong with me! My interest toward the world is getting wider and wider. In the last month I read two books about future Chinese economy. One of the books was advertised in the economic magazine I was reading.  Then why I gradually was drawn to reading economics?  It was simply because significant portion of my students were majoring economics and business/commerce. So I wanted to find out how important mathematics in these field.  

Second was my activeness googling PMI and understood the main logic behind this article. I was impressed to myself for being able to read the economic article this clearly. I couldn’t do this at all before!

The I want to gain more core knowledge in various fields so I will be able to read many more quickly and deeply.