Showing posts with label math. Show all posts
Showing posts with label math. Show all posts

5/16/2015

Why The Illegal NSA Data Collection Doesn't Actually Worry Me

I'm sure you've heard by now all about the illegal spying and data collection by the NSA.  A lot of people seem very concerned that their privacy has been violated and worried about being harassed, exposed, etc.

Here's why it's not a big concern of mine:
Yes, our information is being illegally mined, collected and stored somewhere for the NSA to access whenever they want.  Yes, as a matter of principal such illegal data mining should be halted and those responsible for breaking the law prosecuted.

However, with so much information to deal with how likely is it they're going to notice any specific one of us in the clutter?  Statistically, you probably have a better chance of randomly pointing to a spot in the picture and having your finger land on Waldo than the NSA actually taking enough interest in you to bother accessing any of their stored data about you specifically.  Personally, I'm not going to be losing sleep over my name being in some insurmountably massive NSA database where it's likely no human will ever lay eyes on it, even if it is an illegal invasion of my privacy.

10/18/2014

"That other place has cheaper gas..."

I'm really sick of hearing this pointless monologue.  If you are too, here's some simple figures you can toss out the next time somebody goes off on a rant about "which place has cheaper gas."

Let's be generous and assume your car gets 20 MPG driving in the city.

Let's also assume a median estimate of 10 gallons you're putting in your tank.

And gas right now is around $3 per gallon, where different stations around town likely have about 5¢ total difference in price.  For the benefit of the doubt, we'll assume the highest price is the one closest to you.



Now, if you shop around and find the absolute lowest price in town, the difference in price will be a total of 50¢.

If you drive even just 2 miles out of your way to get there, you're already losing money just at the pump alone. Round trip = 4 miles, 4 miles being 1/5 of 20 miles, 1/5 of $3 is 60¢, 60¢ subtracted from 50¢ = -10¢.  For every mile out of your way beyond that, subtract another 30¢. (3 miles = -40¢, 4 miles = -70¢, 5 miles = -$1, etc.)

In addition, let's assume you make a menial wage of $9 per hour.

If you figure in time as well (for example if you have to clock out of work while doing this) you could easily spend 10 to 15 minutes driving that 2 miles out of your way to get gas, losing another $1.50 to $2.25.

So in total, you're looking at between $1.60 to $2.35 (or the equivalent of more than half a gallon of gas) that you're losing by seeking out a lower price, even with very conservative estimates.



When you go to put gasoline in your car, quit annoying people by incessantly nit-picking about where it's a little cheaper and just fill up at the closest place.  In the end, you're actually saving money by not worrying about it.

5/06/2014

How important is redundancy in rigging?

http://www.boston.com/news/local/rhode-island/2014/05/04/report-aerial-performers-fall-during-circus-act-providence/jONRVASHacmTEy106u394M/story.html
"It has been determined that a carabiner in the rigging failed"
The carabiner used in the stunt is rated to hold 10,000 pounds, the statement said, while the total weight of the rigging and performers was less than 1,500 pounds.
The carabiner was the lone piece of equipment between the apparatus and a cable tethering the performers to the rafters.

This is a good excuse to post a rant I wrote a while ago.

How important is redundancy in rigging?

That depends on what level of risk you're willing to accept. Would you be comfortable with a hypothetical piece of equipment with a 1/1,000,000 chance of failure? If so, that's fine. However, you'd better be damn sure that 1/1,000,000 is accurate and not actually 1/500,000 or even 1/1,000. You'd also better be ready to take full responsibility if you underestimate the risk and end up dropping somebody due to equipment failure.

Is 1/1,000,000 not enough for comfort? A lot of people think doubling equipment doubles the statistical safety margin. Well, I have some good news and bad news for you. The bad news is that doubling equipment doesn't double the safety margin. The good news is that it increases it exponentially.

Let's look at it mathematically.
A 50% failure rate (1/2) with a redundancy can be plotted out to determine the statistical probability that both pieces of equipment will fail at the same time:
  • pass/pass
  • pass/fail
  • fail/pass
  • fail/fail
That works out to be 1/2² or 1/4 chance of complete failure. Similarly, a 1/3 chance of failure with a redundancy can be plotted and the statistical redundancy benefit determined:
  • pass1/pass1
  • pass1/pass2
  • pass1/fail
  • pass2/pass1
  • pass2/pass2
  • pass2/fail
  • fail/pass1
  • fail/pass2
  • fail/fail
That works out to be 1/3² or 1/9 chance of complete failure.

Having demonstrated how redundancy in equipment yields an exponential statistical safety benefit, we can calculate for more robust equipment as well:
  • 1/4² = 1/16
  • 1/6² = 1/36
  • 1/8² = 1/64
  • 1/10² = 1/100
  • 1/100² = 1/10,000
and finally,
  • 1/1,000,000² = 1/1,000,000,000,000
which, if you can hit odds like that, you can simply pay for any medical bills with your lottery winnings. Even if you're wrong about that original 1/1,000,000 chance,
  • 1/500,000² = 1/250,000,000,000
and
  • 1/1,000² = 1/1,000,000
so you're still not exactly tempting fate.

The reason for redundancy isn't necessarily that the risk of equipment failure is unreasonably high, but that it's so easy to reduce the risk of equipment failure so much.

So, how important is redundancy in rigging? You be the judge. Just be ready, whatever you decide, to take responsibility in the unlikely event something breaks and you find the person you're suspending on the floor, instead of in the air where they belong.

11/21/2013

If you stretched out your intestines, they would reach all the way around the world.

Ever hear that line as a kid? That's what we were taught in elementary school.

We were also taught, "food takes 24 hours to pass through your digestive tract."

Let's assume both of those are true.

Since the circumference of the earth is estimated at 24,901 miles, that means food travels through your intestines at a minimum of 1,037.5 miles per hour. (and that isn't even setting aside any time for it sitting in your stomach digesting)

No wonder our educational system is producing such unintelligent people. They're teaching kids that food zooms around through their body faster than the speed of sound?

10/14/2013

Math Is A Universal Language?

This is a claim that's thrown around a lot by scientists (and people who want to sound smart), but it seems the people who say this don't really understand what the term "universal" means.  Math, like any other language, is a learned system of communication.  If you don't have the specific learned cultural knowledge to decipher what somebody is trying to communicate, it's just a bunch of gobbledygook.

First, let's look at the symbols:
< = > + - x ÷ ² ³ √
These don't have any "universal" inherent meaning.  If you didn't know what these symbols meant, you wouldn't understand what was being said in the "language" of a mathematical equation.

"But wait!" you say, "It's not the symbols themselves, but the concepts they represent which are universal!"

Alright then, let's look at a mathematical language in common use:  Binary.

Computers use binary for everything, right?  Binary numbers have no inherent context beyond just being numbers.  Without knowing what patterns a computer uses to decode binary number strings, you can read the data straight from a hard drive and get nothing but a long string of 1s and 0s.  Sure, with enough time, effort and content, you could probably eventually figure out what they represented just like deciphering any other verbal or written linguistic system, but if math is such a "universal" language, shouldn't the meaning behind those numbers be intrinsically obvious?  There's actually a form of written language (Ogham) which is a bit like binary and the Trigrams from the I Ching are basically binary representations, but those are also not a "universal" language, as they require a translation key to understand what they represent.  This scene from Kyle XY simply wouldn't be possible, because not only is there insufficient context in a brief glimpse of the crash code on a computer screen to figure out the underlying patterns of information, but the intricacies of the binary information of an image file can't be properly represented by a standard ASCII text program in the first place - the format is different. (a keyboard doesn't have all the ASCII characters on it anyway)  Opening a non-text file in a text editor and then saving it, even without making any changes, will often corrupt the information within the file and make it unuseable for its original purpose.  Regardless of how smart a person is, they simply can't read and manipulate binary code from a display which isn't designed to do so and therefore is subject to fundamental interpretation errors.

Another example: Base-10 versus Hexidecimal versus Binary.
10 - 1 = ?

Base-10: 9
Hexidecimal: f
Binary: 1

If mathematics is a "universal" language, how does the same simple equation yield such staggeringly different results with such a simple modification of context?  If we assumed base-10 was the norm and sent that equation to somebody who assumed we were using a base-8 number system, there would be a big misunderstanding.

Imagine if you suddenly had to start calculating everything in the format of time.
1 x 60 = 100 and 100 x 24 = 10000 and so on.  It would make communicating with people who tended to use standard base-10 for everything not time related a bit more difficult, wouldn't it?  What if we had to communicate a concept of time with somebody from another planet, which might rotate at a different speed and orbit their sun at a different rate and where the people might have chosen to break up the increments differently?  It would be a bit like converting back and forth between Metric and Imperial measurements.  How often do you have to convert a measurement from one to the other when trying to communicate with somebody from another country?  Doesn't that require prior knowledge of the specific system they use?  That doesn't seem very "universal" now does it?

Last example: PEMDAS.
It stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction - or, the official predetermined order of functions in an equation.  That's so if you have something like 2 x 3² + 5 ÷ 3 you know which order to work the functions within the equation, because that often changes the outcome.  If there was no predetermined order, two different people could often solve the same equation in different ways and get completely different results, even though neither was technically wrong.  The official order we use is something somebody had to decide at some point.  If we ever have to communicate with an alien culture like in the movies, they might have decided to do things very differently and we simply wouldn't arrive at the same result using the same equations.


So in conclusion, mathematics requires knowledge and understanding of specific cultural symbols, specific cultural procedures and specific applicable context in order to be a useful form of communication and therefore is not a "universal" language at all.