A Place for My Stuff

Got Mites?

As if there weren't enough cluttery things in the home to worry about!  Check out these pics:

"Creepy crawlies: Amazing Scanning Electron Microscope pictures of insects and spiders".

You may just have a bunch of these lurking in your bed.  The moral of the story: change your sheets.  That means more than just once a year.

Speaking of dust mites, see my earlier blog post about dust.

More Crop Circle Idiots

Recently I found this article on crop circles:

http://www.dailymail.co.uk/sciencetech/article-1280930/Complex-crop-circle-appears-rape-seed-field--does-mean.html

It seems that every once in a while, some crop circle appears in a field, then some UFO conspiracy theorist with a wild imagination studies it, and jumps to wild conclusions.

One of the recurring themes seems to be complicated mathematical properties showing up. The underlying argument of course is that this "proves" the circles were made by some masterfully intelligent being, which of course implies that we're being visited by some technologically advanced alien species. 

There are several problems with this:

• Humans have been able to make crop circles themselves, without the help of aerial devices.  All you really need is a some rope and plywood to flatten out the crops.  And if you want to make circle shapes, tie a rope to steak and sweep the radius.  The two guys who created the whole hoax came out and admitted it in 1991.  If pranksters can make them, then there's really no need to bring in notions of spaceships and Martians to explain them.
• Even the more complicated-looking crop circles can be done by repeating the same geometric patterns or shapes over and over, in a circle.  This is how toys such as Skedoodle work to draw designs. (If you don't remember this toy from the 80s, click on the link and see the video clip.)  So you don't need to be master artist or mathematical genius to make such shapes.
• Similarly, just because you can derive mathematical numbers from a shape doesn't mean that the shape was designed with that in mind.  A child can trace the base of a coffee mug on a piece of paper to draw a circle; that doesn't mean she knows anything about pi.
• This all begs the question of why such advanced beings would be leaving us messages this way.  Why the ambiguity?  Why only in the middle of the night?  Why in the middle of fields of crops, where the population is so sparse?  The old claim used to be that the crop circles were marks where spaceships landed.  Obviously, the conspiracy theorists have changed that idea.

Lucy Pringle, the "renowned crop circle researcher" quoted in the article, painfully reveals her ignorance when she claims "Historically over the years, crop circles have been associated with diatonic scales (white notes on the piano)".

• Again, "connections" to things like musical intervals are really just speculative, and not all that hard to "find".  Crop circles are overlapping geometric shapes, which means they have some whole-number ratios that you can pick out and compare (e.g. "the lengths of this line and this other line are in a 3:2 ratio"). Years ago, we used to construct all musical notes out of whole-number ratios too.  For example, if hear a note when you pluck a string it makes a note, and plucking a string that's half the length gives you a note that's one octave up.  But there are lots of other things that use whole-number ratios: baking recipes, mixed alcohol drinks, the approximates we use for statistics we report, etc.  Just because you can measure and compare lengths or areas in different parts of a crop circle, doesn't mean there are aliens encoding musical sequences.
• Another problem with the musical ratio argument is that the numbers aren't so special.  If you pick ANY two single-digit numbers and take the ratio of one to the other, there's an over 75% chance that you'll get a "diatonic ratio" (1/1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, 2/1) when you reduce it and adjust for octaves. Yes, I did the math to get the "75%".
• The biggest problem with the musical crop circle claim is that our modern music system simply DOES NOT USE these ratios. For the past several centuries, all the music of the western world (classical, hip-hop, metal, jazz, you name it) has used what's called equal temperament.  This is where the ratio between consecutive notes is always the 12th root of 2 (approximately 1.0594).

Now let's actually get into the math (or "maths" as it's called on the other side of the Atlantic), and the claims about the "Complex Maths Circle":

Their use of "complex" here is a bit misleading.  In mathematics, "complex" is a specific term used to refer to a particular type of number.  It doesn't necessarily mean complicated or intricate, which is what "complex" means in general English usage.

It took me a while to understand how they were deriving the formula from the crop circle picture.  Part of the reason for this, is because the photo is incorrectly labeled.  The outside characters (e, ^, (, h" etc.) should appear at the end of each radial line, not in between.  This is because each of the 12 lines represent a character.  The picture on the other hand makes it look like the crop circle is broken up into 12 pie wedges, and that each wedge is a letter. 

There are additional mistakes in the photo.  The "Ao" and "Th.c" marks on the axes are gibberish, or more likely (ironically enough) bad ASCII character renditions.  And the formula is supposed to be "e^(i pi)+1=0".  Actually, it's supposed to be written with the "pi" as the Greek letter pi (π) and both the i and the pi superscripted.  But this is the way you'd write out Euler's formula if you evaluate it with theta=pi, and could only type it out instead of normally being able to write it with a pencil. It's not e^(i)pi+1=0, as the article incorrectly put it.  That gives you an incorrect formula.

Regardless, I get it now.  Here's how you supposedly derive the formula from the photo:

1. Start from the center of the circle, and pick a line.
2. As you move across this line from the inside to the outside, you'll see perpendicular bars on either side.  Each bar falls on either the left side or the right side.  If it falls on the left, write down "0".  If it falls on the right, write "1".
3. When you're done with the line, you'll have a total of eight numbers.  This gives you a binary number.
4. Translate the binary number into a decimal number.  This corresponds to an ASCII code for some keystroke.
5. Starting with the top number in the photo and moving clockwise, you get the following twelve characters: e ^ ( h i ) p i ) 1 = 0

This certainly resembles "e^(i pi)+1=0", but why would somebody who came up with such an elaborate system, get 25% of the characters wrong?

Hey, I love both music and mathematics.  They're my two big passions in life.  So I'd love for stories like this to have some validity.  But the math has to add up.  And it doesn't.

Happy 9/9/09

I was in Portland, Oregon last summer on August 8th.  And I was truthfully able to tell some acquaintances, "Hey, today is 8/8/08, and the last time I saw you was on 6/6/06!" No, I don't recall anything special happening on 7/7/07.  And who knows what I'll be doing on October 10th next year.

I'd like to take this opportunity though to talk about numbers and people's obsession with them.  Mathematics is a passion of mine, so yes, you could say I'm obsessed with numbers in some ways.  But there's a difference between formally studying and being in awe of the mathematical properties of special numbers such as Pi (3.14159...), and freaking out over arithmetic that somehow equates "GEORGE W BUSH" with the number 666.  Even in the 21st century, many people are still convinced by apocalyptic "calculations" like the latter.  Numbers and calculations do have a way of astounding some people. 

I'm sure many of you have seen "mind reading" websites that are able to guess a symbol or a card you're thinking of just after answering a few simple math questions.  This is actually a branch of stage magic called mentalism. I learned my first mentalism trick around the age of 8, from a Disney activity coloring book.  I still remember the illustrated Goofy showing how to do it.  It went like this. "Pick a number.  Now multiply your number by 3.  Add 6 to the total, and divide the final result by 3.  What do you get?"  Upon hearing the person's reply, you (the magician) then immediately tell them what their original number was.

Isn't this AMAZING?!?  Not really if you actually sit down to do the algebra.  If x is your original number, then the calculation is (3x+6)/3 which simplifies to x+2.  So the final answer is always going to be 2 more than the original number.  When you hear the participant's result, you simply subtract in your head 2 from that number, and (provided they made no arithmetic mistakes) know the original number.  And that was how the secret was presented in the activity book: "Secretly subtract 2 from the number they give you, and that will always be their original number!"

There are countless other ways to make "amazing" calculations like this.  Just about any book on magic tricks will include a few of them.  The reason they work as magic tricks, is because the magician gives the impression that the choice and result are either completely random or way too much for a normal person to calculate inside of their heads.  It looks either beyond coincidental, or too complicated for a human mind to calculate at lightning speeds.  The secret, of course, is that it's neither.  Like most other magic tricks, it's just "smoke and mirrors".  In this case, the distracting smoke is the illusion that the math is complicated.

Here's another mathematical magician's secret: random numbers are not really all that random when a human picks them.  Another magic trick I had as a kid was a business card that said "PICK A NUMBER"along the top, and "1 2 3 4" listed underneath.  Do that now.  Pick one of those numbers.

After asking the person which number they chose, I would then flip over the card, which read "Why do all ___ people pick 3?"  The blank was for inserting whatever word you liked: "stupid", "sexy", etc.

Did you pick 3?  You would think that the chances of me guessing that correctly are 25%, but the reality is that when posed the question, most people (over 80% of them, I believe) will in fact pick "3".  Yet if we asked a computer to randomly pick the number, it would pick 3 just as likely as it would pick 1, 2, or 4.  It's because of our human bias.  Picking 1 or 4 doesn't "feel" like we're picking a random number, because these are numbers that fall on the end.  Or they're numbers we hear if being asked "Pick a number between 1 and 4".  So we find ourselves picking something "in the middle" because it just seems like it would be a more "random" place to "hide" one's guess.  3 seems a little stranger than 2, because it's further away from the beginning and it doesn't seem as simple of a number as 1 or 2.  Thus, most people end up choosing 3.

Now let's get back to what Dogbert says in the comic strip above. 

In a somewhat similarly ways, there are sadly still a lot of adults in the 21st century who dupe themselves into believing the magic of numbers, in instances where it simply doesn't exist.  For example:

1. "The world is going to end in 2012!  Really!"
2. "Every time I look at my alarm clock, it says 11:11.  This must MEAN something."
3. "If you translate the words of the Bible in to numbers, you always get '777' for passages that reference Jesus.  You also get '666' for the name of the Pope [or President, or some other politician].  It's a miracle!  The Bible must be divine!"

The first one of these is easily explained by popularity and hysteria.  People seem to forget that a decade ago, people were "convinced" that the world would come to an end in 2000.  A further study of history shows that people were equally "convinced" that the world would end in 1000, and many dates before and after.  The Jehovah's Witnesses (an apocalyptic cult, best known for ringing your doorbell on Saturday mornings to come and proselytize you) made MANY exact predictions throughout their history, only to be proven wrong again and again.  Check out this partial list of failed end-of-the-world predictions.

#2 and #3 are largely due to a psychological phenomenon called the confirmation bias.  I think this was beautifully summed up in one of my all-time favorite quotes, which is from the movie Pi:

"When your mind becomes obsessed with anything,
you will filter everything else out
and find the thing everywhere."

To elaborate, you tend to remember the things you're obsessed about, and forget the things that aren't so interesting.  This gives the illusion that something is happening more often than it really is.  Why does that clock "always" seem to say '11:11' or '3:33' when you turn to look?  Why does your lucky number, say 8, "always" show up?  It's because you're not placing any emotional investment in all of the times that it doesn't show up.  You do actually look at that clock more than twice a day.  But a time like "3:04" isn't all that exciting looking.  It looks "random" because it doesn't look interesting.

As for #3, let me start by saying this.  As a man who holds both a Bachelor's and Master's degree in mathematics, trust me when I say: it's not all that hard to play around with numbers until they give you the result that you want to see. If you want to relate a certain person or name with the number 666, you'll find some way of doing it.  All it proves is how creative you are at dreaming up number game associations and doing arithmetic.  This is not science.  It's mysticism.  Science examines data and comes up with a conclusion, whereas this sort of mysticism starts off with a conclusion and plays with the data until it fits.

I could write an entire book of how this goes wrong and how I can debunk all of the "gematria" alphabet systems out there, but instead I'll just leave you with one example.  The Bible Code was a book that showed how you can take the letters of the Bible and after lining up the columns in a certain way and circling every so many letters, you could get all of these historical predictions (e.g., one column down reads "LINCOLN" and diagonally you find the letters "BOOTH" and "ASSASSINATION").  Christian zealots point to exercises like this as "proof" that the Bible (the KJV English translation, of course) is eternal and "predicted" such events.  Again, it looks impressive, but it's not.  It looks like the odds are astronomical, but they're not.  Given the vast size of the Bible, it's very easy to "find" things like this if play around with the letters long enough.

The author said "When my critics find a message about the assassination of a prime minister encrypted in Moby Dick, I'll believe them."  Well, guess what?  Somebody did.  So much for the Bible being a special divination device.

But I'd like to end this blog entry on a positive note.  Not all number biases are harmful.  We like counting down the last 10 seconds of our calendar year and throwing confetti on December 31st.  We like celebrating the anniversary of our birth date or wedding, especially if the number is "Biiigg and roooound!", ending in a 0.  Like I said, I'm a mathematician; I love numbers.  Besides giving a way to quantify the unknown, they also add a nice spice to life.  So happy 9/9/09, everybody!  And happy birthday, Mom.