26 October 2010

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Baby Names: Why my boy's name is a sentence


As many of you may know, we will be having our fifth baby in just a few months (February 28th). I just recently got over the fact that next year isn't 2012, so there is no chance of the baby being born on Leap Day, so please don't bring it up.

With it being right around the corner, I've started reflecting on what kinds of names I like.

No, we're not finding out (at least until the baby is born), so we're doubling our work to come up with good boy and girl names.

Yes, our kids have very unique names. Did you know, for example, that Remi's full name is a sentence?

Joshua Remington Cummings


No, he wasn't named after the gun as hilarious as that would be now that we live in Herriman, UT.

Our first child was born in August 2004. We knew this name a couple weeks before he was born. Originally, we were going to go with "Joseph Remington Cummings," but, as you will find out, it's all about the meaning of the name for me.

Back when I was in high school, I liked to listen to John Bytheway (actually, I still do). He tells a great story about when he was in the 7th grade learning about prepositional phrases when, in a moment, it dawned on him that "Bytheway" is a prepositional phrase: "By the way". That meant that if he had a kid and gave her a middle name that was a verb, her name would be a sentence; "Sally Ran Bytheway". Thus, a life goal was set. My first child's name would be a sentence.

Of course, I didn't want my children to resent such an obviously geeky maneuver by "loving" parents, so I decided that I would encode it somehow (which, of course, makes it 10 times geekier, but, hey).

While we were looking through baby name books and websites, we found the name 'Remington'. The name's meaning is very, very important to me, and so we looked it up. It turns out that hremm is the Old English for raven. ing means 'people of' and ton means town. ington was often attached to the end of a people, group, or individual. For example, Washington means 'Wassa's place' or 'from Wassa's place' or 'from the place of Wassa'. Thus, Remington means 'Raven's place' (if Raven were a person's name) or 'from Raven's place'. It could also be 'from the raven's place' since 'raven' also refers to the bird.

If you've put two and two together, you will see that Remington, when translated back into Old English, is a prepositional phrase. Eureka! Now, all I need is a noun for the first name, and we are set!

For that, we turn to Hebrew. Lots of transliterated Hebrew names start with Jos. Josiah, Joseph, and Joshua are just a few. Also, incidentally, many end in iah for the same reason, like Jeremiah, Obadiah, Zedekiah, etc. 'Jos' is a transliteration of 'Yeh' (or 'Yesh'), which refers to 'Yehovah', or Jehovah, Savior, Lord, etc. The 'shua' comes from the Hebrew word 'yasha' meaning salvation, help, deliverance, etc.

One of the practices that was common in ancient Hebrew was to take to words and lexically intertwine them as an indication that the two concepts were inseparable. An example is the name 'Abinadi'. The name for father in Hebrew is 'Ab' and the name for son is 'Bin'. Common Hebrew practice might have lead a mother to name their child 'Abin' in order to manifest her assertion that father and son are intertwined, just like the words 'Ab' and 'Bin' have been lexically joined at the hip. Remember Mosiah 15:3 where Abinadi teaches that the Father and Son are one?

Anyway, this could be what was done with the name Yeshua. Take the word Yesh and the word Yasha and join the 'sh' to get Yeshua. Or, 'God IS salvation', 'God IS help', etc. as opposed to 'God is help' or 'God is salvation'. The implication is clear: God himself is inseparable from the concept of help and salvation.

Now, let's put them together:

Joshua = God is help
+ Remington = From the raven's home
_____________________________________
Joshua Remington = God is help from the raven's home

Success! You'll notice that I took some poetic license and used 'home' instead of 'place', but I think that's fair. He is my son, thank you very much. :)

The meaning of the name as a whole is poignant. There are a couple of instances in the Bible where raven's were important to providing help/temporal salvation to prophets. One is in Genesis when Noah sends out ravens to try and find branches, etc. After that, he sends the dove. Another is that ravens fed Elijah during a famine. The message is clear: God uses raven's to help his prophets, and God will use my son (as he can use all of us) to help them, too.

As a quick aside, you may notice that the name 'Jesus' doesn't follow any of the standard Hebrew norms norms. It starts with a J, but not 'Jos'. That's because the word Jesus is a transliteration of the Greek name Iesous (remember that the New Testament that we have was translated from the Greek). Jesus's name, as spoken by his contemporaries, was probably the Aramaic name Jeshua, which, in turn, would be Yeshua or Joshua in Hebrew.

There are a zillion other reasons why Joshua is a cool name, including the Biblical history of Joshua of Israel.

Needless to say, we did well.

Isaac Samuel Cummings



Our second son was born in June 2006. This time, Kristi and I each wrote down ten names first names that we liked for each gender. We considered several. Everett, Aidan, Zachary, etc.

We liked Zachary Aidan Cummings for several reasons. First, it is lexically cool because his short name, Zac, would also be his initials Z.A.C. That would distinguish his nerdy name from his sentence-bearing nerdy brother, too. The meaning was also neat. Zachary is a Hebrew name that means 'The Lord remembers' (zakar = remember, iah = Jehovah => Zechariah, or Zachary). Aidan is Gaelic for 'Little fire'. Since we banked on having all redheads, we thought the name 'The Lord remembers Little Fire' would be cute.

But we didn't.

Instead, we did something cooler. See, there is another name that has that 'zak' sound in it. That name is Isaac. Isaac is an interesting Hebrew name because it isn't a juxtaposition of two Hebrew names, but instead it is just one word in the present third-person:
Yitschaq or 'he laughs'. He harks back to when Abraham and Sarah were told that they would have a son at their old age and Sarah laughed at the prospect, considering herself too old to carry a child. (I also like to think that the Bible very patriarchal, according to their culture, and the fact that Sarah might have also laughed in happiness might not have been conveyed through the written word. That's the gospel by Josh, though.)

We liked Isaac because we liked the idea of calling him 'Zac' for short. Now, instead of a juxtaposition, we create a bifurcation. (I've always wanted to use that word in a sentence.) 'Zac' points both to the Hebrew name that means 'he laughs' and the Hebrew name that means 'the Lord remembers'. While there is a possibly ominous way to look at the connection of meanings, we prefer the happier one: When ever we laugh (or cry, or speak, or wonder), the Lord remembers. The two names are joined externally by the common short name instead of internally with a longer name.

Isaac was also neat because of a number of people from history that I respect. The first is Isaac from the Bible for his bravery and loyalty. The second is Isaac Cummings, the brave soul that immigrated to the United States in the 1600s. The third is Isaac Newton, the very shy but brilliant mathematician and physicist that played a key role in making our modern world possible. Unfortunately, there is a great deal of information on only the first and last individuals. I'm not aware of too many historical documents regarding Isaac Cummings, our immigrant ancestor.

Even though it would mean two Hebrew names, we really liked Samuel. There are a couple of possibilities for translation. The suffix 'el' refers to God. Bethel = house of God, Ariel = lion of God, etc. 'Sam' refers to the word shama meaning 'to hear'. When translated as the past-participle, we get
Shĕmuw'el or 'heard of God'.

If you remember those on the ark with Noah, you will remember that one of his sons was 'Shem', which looks a lot like the beginning of the Hebrew form of Samuel. One of the translations of 'shem' is like the word 'heard'; it means 'renowned' or 'known' or 'named'. You can see the semantic tie between someone who is heard and someone who is renowned. So, a possible translation of Samuel (perhaps I am taking poetic license, though) is 'renowned of God' or 'named of God'.

The point is that Isaac's name is a chorus of ancient meanings that remind us that we are God's children. We are renowed of Him, and he is aware of our laughs, our cries, our hopes, and our dreams. 'He laughs and God hears him', 'God remembers for my boy is renowned of Him'.

To be continued...


Alright, I should get to work. It looks like this will need to be a part one. I'll let you about our other two kids and about what names we might have for our new little one later!
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25 October 2010

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Teaching Your Computer to Write Your Sacrament Meeting Talks


(This post is inspired by a great post by Orson Scott Card regarding lousy sacrament meeting talks. (Which post, incidentally, was very hard to find since the search box on mormontimes.com is broken.))

So, I'm not sure about you, but it seems to me that there are a number of "musts" when it comes to giving a sacrament meeting talk, at least in Utah. When following these "musts" you can easily take up 5 minutes of your 15-minute talk without actually talking about the topic.

The three lousy talk musts



First, you must tell some story about how you received the assignment to give the talk. This will take up a minimum of 30 seconds (e.g. I was just mowing my lawn on Wednesday when I got a call from Brother So-and-so to give a talk this Sunday) and could very well take up your whole 5-minute pre-talk.

Second, you must tell a joke. It would be better to make sure that the joke has nothing to do with the topic since that might end your pre-talk earlier than you intended. Again, there is great flexibility here and, if you don't have a good how-I-received-the-assignment story, a great joke could easily take 5 minutes.

Third, you must mention what Webster's Dictionary has to say about the word. It might be hard to make the pre-talk part of this extend 5 minutes, so you will definitely want to focus on the first two.

(To read more on the above, do check out Card's article with the link at the top.)

After you include a few general authority quotes and scriptures, you're done!

So easy, my computer can do it



To demonstrate the facility of accomplishing these three items, I have harnessed the computing power of natural language generation and recursive transition networks (that's not a mouthful at all) to generate sacrament talks for me. Here is an example of a talk that it created for me in about 500 milliseconds:


I was just washing my dog last Thursday when Brother Wu invited me to give a
talk on repentance in sacrament meeting this Sunday. (turn to bishopric)
Thanks, Brother Wu! Thank you for bearing with me as I try to express you my
findings on the topic.

I want you all to raise up your left hand. Now lower it. Now you can all say
that you've been uplifted by my talk today. I heard that in a sacrament meeting
in Monticello and got a kick out of it, so thanks for letting me share that
with you.

I decided to look up repentance in the dictionary. One definition that caught
me off guard reminded me of something J. Golden Kimball clarified to us in the
April 1946 session of General Conference: "If you will remember to repent in
your every thought, you will you will increase in truth and light."

Mosiah 3:4 admonishes us that to repent, we must also have charity. I like how
J. Remington Cummings expressed to us in the October 1946 session of General
Conference: "repent and have charity. One cannot be enjoyed without the other."

May we all try today to repent. I know that the Church is true. I know that the
Book of Mormon is written for our day. In the name of Jesus Christ, Amen.


Not bad, eh?

(Warning: The techie part of the article is now beginning.)

RTN and NLG: Are those two new Church abbreviations?



A recursive transition network is a way to describe a specific language domain via a template. (There is much more to doing good natural language generation, but I won't talk about that here.) "Lousy sacrament talks" are just one of those language domains where the expressions used are typical enough that we can list the majority of them and create a human-sounding text that varies widely at each instantiation.

For example, take the first pre-talk point: Telling everyone how you got the topic and that you sooo didn't want to speak today. It typically involves mentioning the member of the bishopric that gave you the topic and what you were doing at the time when you got the call.

Here is what my very basic template looks like for the first sentence in my talk generator:


bishop: "I was just " doing-something " last " day-of-week " when " off=local-official " " issued " me to give a talk on " top=topic " " talk-when ". " sarcasm "! Thank you for " conciliatory-attitude " as I " non-yoda " to " transmit-to " you my " mental-construct " on the " subject "." ;

Whatever is in the quotes, like "I was just ", is always printed out. Whatever isn't, like doing-something, is another part of the template that the program looks up.

Here is what doing-something looks like:


doing-something: "mowing my lawn" | "at my kid's soccer game" | "washing my dog" | "watching tv" | "surfing the net" | "reading a book" ;

So, the idea is that the program can randomly choose between any of those options.

If you put the two ideas together, you can get a very complex-looking rule like the one for the first made-up quote:


future-blessing: "be blessed" | "have " the-spirit " with you" | positive-inner-change " in truth and " desirable-characteristic | find positive-difference inner-power " in your life for " reason-for-power ;

Given enough time and rules (the existing "lousy sacrament talk" RTN took me 30 minutes to write up), one could fool most listeners.

Of course, a good sacrament meeting talk would be extremely difficult for a computer since good sacrament meeting talks typically involve the personal experiences, devotions, and reflections of the individual speaking. Precisely what makes a good sacrament meeting talk is also what would be particularly difficult for a computer: Being human. That language domain is obviously much more diverse.

So, where are recursive transition networks useful?



RTNs are used in a lot of places. The most basic is when a computer will take a set of data and give the reader/listener an English version of that data. You see examples of it when you step into an elevator and it says "Going up" or "Going down" depending on which floor button you press when you get in.

A more complicated example would be a computer reading the temperature over the next 5 days and saying "It's gonna be a hot one today at 83 degrees, but things will cool off a bit by the weekend to 69 degrees." You use an RTN to vary the "language glue" bit and make the forecast sound more realistic. For example, an RTN would teach the computer that the phrase above is just as valid as "It'll be on the hot side today as the high will approach 83, but we'll cool back down by the weekend to 69." What the computer needs is 1) to know the temperature, 2) to know the average temperature for this time of year, 3) to know that the weekend is within the 5-day period, and 4) to know common vernacular surrounding weather forecasts.

Conclusion



So, may the thought of RTNs being able to replace a significant portion of our pre-talk inspire us to simply speak more like ourselves when at the podium and less like a person trying to postpone the inevitable: Giving the rest of the talk. I know that if we do this, more hearts will be knit together and more cherrios will be better spent.
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22 October 2010

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Mole Day: Get Mollified

While many of you probably already have your Mole Day activities lined up, I thought I'd take a moment to offer up some things that I consider vital to do honor to the number, the animal, and our dear chemist Avogadro this October 23rd.

First of all, I'm shocked that my Zemanta plugin hasn't suggested any links to the zillions of articles, pictures, and videos surrounding this highly-vaunted chemistry holiday... oh, wait, there it goes.

Second of all, there may be a few unenlightened souls remaining in the canvas of humanity regarding Mole Day. Every October 23rd from 6:02 AM to 6:02 PM, chemists everywhere gather to worship honor a fundamental mathematical constant, Avogadro's number, which equals 6.02 x 10^23 and is named after cute-ified versions of the miscreant rodents that tear up your front lawn, especially when you are trying to put it up for sale.

Third of all, yes, Mole Day is inferior to Pi Day, but better than Intermediate Value Day.

So, what does one do on Mole Day?

Six more weeks of Chemistry


I believe that Punxsutawney Phil is overrated. All he does it predict the weather, and we have excellent weatherpeople every where who do just that with fractionally greater accuracy.

What we really need is a Milledgeville Molly. Of course, since we don't have that, yet, you will just need to find a mole yourself (you can look for people that just put up their home for sale--they will typically pick those houses about 2-3 days after the sign goes up). Watch carefully to see if he sees his shadow. If so, he will run back into his hole which will mean six more weeks of chemistry before Christmas Break.

A Bowl-e of Guacamole



A bowl of guacamole beside a tomato and a cut ...Image via WikipediaFood is definitely important for every holiday, and Mole Day is no different. I know of know culture that would desecrate these cute little rodents, but I do know of several people that enjoy a bowl of guacamole.

Take it one step too far, and you can have a recipe in the fundamental unit of chain reactions:
  • 2.0 mol avocados
  • 0.65 mol red onion, minced
  • 1.35 mol serrano chiles, stems and seeds removed, minced
  • 0.25 mol cilantro leaves, finely chopped
  • 0.15 mol fresh lime or lemon juice
  • 0.45 mol teaspoon coarse salt
  • 0.10 mol freshly grated black pepper
  • 1.2 mol ripe tomato, seeds and pulp removed, chopped

Garnish with red radishes or jicama. Serve with tortilla chips.

Of course, I don't happen to know the atomic weight of jicama, so I offer no guarantee that this will make excellent dip.

Other possible foods... just thinking out loud here... mole (the dip), mole slaw... maybe take marshmallows and over them in shredded coconut rolled in chocolate sauce... okay guacamole is your best bet.

Visit beautiful Moldovia


Actually, Moldovia, defying common knowledge, is a principality that no longer exists.

Instead Moldova is a Eurpoean state that sits land-locked between Romania and the Ukraine. The majority of its citizens speak Romanian. It's original name is thought to have come from either the German word meaning "open-pit mine" or the Gothic word meaning "dust" or "dirt".


When you visit Moldova, you do the things that you do when you visit any European country: Visit really old buildings and try the local wine. Make sure to visit the following Mole Cathedral on the left.

Miscellaneous ideas


Just to add some zest to the day, consider renaming yourself to Molly for the day. Or renaming everyone else to Molly.

Or you could insist that Mole, Massachusetts is a city and see which of your associates get the joke (for those who aren't real chemistry geeks, mole is a chemistry term tightly related to another chemistry term mass, and the abbreviation for Massachusetts is Mass. If it still isn't funny to you, then you aren't a chemistry geek.)

Or you could tell mole jokes. Here are a couple to get you started (taken from this Mole Jokes list):

Q: What did Avogadro teach his students in math class?
A: Moletiplication

Q: Why was there only one Avogadro?
A: When they made him, they broke the Moled

Q: How much does Avogadro exaggerate?
A: He makes mountains out of mole hills

Or you could see mole songs. While I don't remember all the words, I distinctly remember Mr. Steed in 10th grade having us listen to a guy with a guitar singing: "A mole is a unit, or have you heard? It's 6 times 10 to the 23rd. something, something, something, that has no end, it's much too big a number to comprehend." Then, the song goes into all kinds of comparisons about how big 6x10^23 is.

Here are a few interesting ones, by the way (taken from this Avogadro's Number explanation, the last one is mine):

  • An Avogadro's number of soft drink cans would cover the surface of the earth to a depth of over 200 miles.
  • If you spread Avogadro's number of unpopped popcorn kernels across the USA, the entire country would be covered in popcorn to a depth of over 9 miles.
  • If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the atoms in one mole.
  • If you were to loyally celebrate Mole Day every year for Avogadro's number of years, it would take you 6.02x10^23 years to do it.

Time to celebrate!


So, if you haven't already had it on your calendar for the last six months, remember that Mole Day is tomorrow, October 23rd at 6:02 AM. Enjoy!
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21 October 2010

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Vedic Mathematics: Multiplying 2-, 3- and 10-digit numbers in your head

Addition, division, subtraction and multiplica...Image via WikipediaI remember being teased in fourth game for being able to multiply 4-digit numbers in my head.

Actually, it wouldn't have helped anyway because, had I told them that I couldn't do such a ridiculous thing, they would have simply teased me for not being able to multiply 4-digit numbers in my head.

But that's all water under the bridge, including my not being able to multiply 4-digit numbers in my head. Want to learn how?

Many cases are not that difficult once you know a couple of mental math tricks related to "Vedic mathematics".

Vedic?



While some people like to play of the mysticism of the name, Vedic Math is just a system of mathematics that was created by the Vedas people hundreds/thousands of years ago, rediscovered on old Sanskrit manuscripts by Bharati Krsna Tirthaji in 1911 and decoded from Sanskrit into modern-day mathematical notation over the following seven years. So, while not super-mystical, it is friggin' awesome.

Multiplying 2-digit numbers in your head

First Approach

Take the two digit numbers and pick the power of 10 that they are both closest to. To start simple, let's do 99x99. The closest "10", then is 100.

Write down the numbers and beside them the difference between the numbers and their "10". Since we picked 100, 100 - 99 = 1, or the difference between 99 and it's closest power of ten (100) is 1.

99 1
99 1

Next, do a subtraction across on of the diagonals. 99 - 1 - 98. This will be the first two digits of the answer.

Finally, multiply the numbers in the right column together. 1*1 = 1. This will be the end of the number.

Here we would expect a four-digit number, so the answer is 9801.

Let's try another one. How about 96x94?

So, the closest power of 10 is 100, again. Let's do the subtraction and write down our table:

96 4
94 6

Do a subtraction along the diagonal: 96 - 6 = 90. This will be the beginning of our number.

Multiply the right-hand column: 4*6 = 24. This will be the end of our number.

So 96*94 = 9024

One more before adding a wrinkle: 89*90

89 11
90 10

89 - 10 = 79

11 * 10 = 110

So, here we get into a little quandry. The answer isn't 79110. With some visualization of what the trick is trying to accomplish, we can sort it out.

What you are basically doing when you do the diagonal subtraction is finding out the most significant digits in an x-digit number. When you multiply 2-digit numbers like 89 and 90, we will expect the result to be a four-digit number (consider 90*90 = 8100). So, 79 represents 7900 in the equation.

What you are basically doing when you do the right-column multiplication is finding out the rest that you need to add to the total. So, in this case, 110 added to 7900 is 8010, which you will find to be the correct answer.

What about 45*49, though? Those are kind of far away from 100. Let's pick 50, then instead. Now 50 isn't a power of ten, but it is half of a power of 10. We just need to make one change to our algorithm to accommodate it.

45 5 (remember 50-45=5)
49 1

Do a diagonal subtract: 45 - 1 = 44

(new step) Divide that by 2 since 50 is half of 100: 44/2 = 22

Right-column multiplication: 5 * 1 = 5

(no need to adjust the right-column step)

Add them together: 2205

Let's do the same thing with 37*34

37 13
34 16

Diagonal subtraction: 37 - 16 = 21

Adjust by half: 21/5 = 10.5 (So this would mean 1050 since well get a four-digit number)

Right-column multiplication: 13 * 16 = 208

Add the two results: 1050 + 208 = 1258

So, that was kind of hard because of the 13*16. Well, there's a way to simplify that, too.

Instead of picking 50, let's pick 40. Again, not a power of 10, but we can make the appropriate adjustment.

37 3
34 6

Diagonal subtraction: 37 - 6 = 31

(adjustment) Looking downward this time, it is 4 times bigger than 10 (as opposed to being 2/5 of 100). So, we'll multiply 31 by 4. 31 * 4 = 124. (We could have multiplied by 2/5, but that sounds hard.) Since we are filling in a four-digit number, this represents 1240.

Right-column multiplication: 3 * 6 = 18

Add them together: 1240 + 18 = 1258

Second Approach

Remember that with two-digit numbers, we are filling in a four-digit number like this: _ _ _ _. As we take each step, we are filling in those blanks.

Take the two numbers and write them down like so: (in this case, we'll do 71*68)

7 1
6 8

Multiply the left-column: 7 * 6 = 42. This represents the left-most digits, or the hundreds place, so it will fill in the left-most blanks: 42 _ _

Cross-multiply and add: 7*8 + 6*1 = 56 +6 = 62. This represents the middle two digits, or the tens place, so it will fill in the middle two blanks: 482 _

Multiply the right column: 1 * 8 = 8. This represents the right-most digits, or the ones place, so it will fill in the right-most blanks: 4828

Not too bad, eh?

Let's try 84*76 now.

8 4
7 6

Left-column: 8 * 7 = 56
Cross-multiply and add: 8*6 + 7*4 = 76
Right-column: 4*6 = 24

56 _ _
_ 76 _
+ _ _ 24
--------------
6384

So, 84*76 = 6384

Muliplying three-digit numbers in your head


Don't worry, the approaches are the same, but it's good to illustrate.

First Approach

986*994. The closest power of 10 is 1000.

986 14 (1000-986=14)
994 6

Diagonal subtraction: 986 - 6 = 980 (We are going to expect a 6-digit number here, so this means 980 _ _ _)

Right-column multiplication: 14 * 6 = 84

Add the two results: 980000 + 84 = 980084

How about 452*487?

452 48
487 13

Diagonal subtraction: 452 - 13 = 439 (Six-digit number, so 439 _ _ _)

Adjust: 439 / 2 = 219.5 (so 2195 _ _)

Right-column multiplication: 48*13 = 624 (The the second approach for this multiplication)

Add: 219500 + 624 = 220124

How about 256*282? Let's pick 300 for our target.

256 44
282 18

Diagonal subtraction: 256 - 18 = 238

Adjust: 300 is three times 100, so 238*3 = 714 (here, we'll have a five-digit number, think 300x300=90000, so 714 _ _ )

Multiply: 44 * 18 = 792

Add: 71400 + 792 = 72192

Okay, one more, and then the second approach.

110*114. This one is a bugger because it is a long ways away from the nearest power of 10 above it (1000) and the nearest multiple of 100 above it (200). Would it work to look downward and just switch the diagonal subtraction to addition?

110 10 (distance from the power of 10 below)
114 14

Add instead of subtract: 124 (so, 124 _ _)

Multiply: 10*14 = 140

Add: 12400 + 140 = 12540

Second Approach

The general idea with this approach is that every number must be multiplied by every other number. It gets challenging when we have 4 or more digits, but for 2 or 3 is works really well.

So, 213*768

2 1 3
7 6 8

Now, this will be a six-digit number. _ _ _ _ _ _

2*7 = 14, so 14 _ _ _ _
2*6 = 12, so _ 12 _ _ _
2*8 = 16, so _ _ 16 _ _
1*7 = 7, so _ 0 7 _ _ _
1*6 = 6, so _ _ 0 6 _ _
1*8 = 8, so _ _ _ 0 8 _
3*7 = 21, so _ _ 21 _ _
3*6 = 18, so _ _ _ 18 _
3*8 = 24, so _ _ _ _ 24

Writing it out like this makes it seem impossible. However, if you keep a running tally in your head, it isn't so bad with some practice.

So, 140000 + 12000 + 1600 + 7000 + 600 + 80 + 2100 + 180 + 24 = 163584

Multiplying 10 digit numbers in your head. Ew...

So, there is no magical way to make this easy, but the two approaches above definitely make it easier.

Just for fun, then, let's impress our friends by multiplying 9999999999 by 9999999999. We'll get a 20-digit number.

9999999999 1
9999999999 1

Subtract: 9999999998

Multiply: 1 * 1 = 1

Add: 99999999980000000000 + 1 = 99999999980000000001

Wow!
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20 October 2010

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Starting Your Own T-Shirt Shop: So you've got a great idea for a shirt?

This is the first in a series of posts about how I started The Pi-Dye T-Shirt Shop. Hopefully, it will help you in starting your own t-shirt shop.

About six years ago, an idea sparked in my head born partly out of an obsession with pi and partly out of a desire to create something that people like so much that they would be willing to pay for it. Yes, I had a great idea for a shirt.

It would have the digits of pi on it in some cool fashion and would have the phrase "Approximation Is For Wimps" at the bottom. It would be funny for a lot of reasons: 1. Just having so many digits of pi plastered on a shirt has intrinsic humor, b. It plays off of the fact that most math nerds are seen as wimps (or they definitely don't line up with the term "jock"), and 3) It's ironic because even the 3141 digits or so on the shirt will still be an approximation.

So, we've all had this experience. Maybe yours wasn't charged with as much mathematical humor, but you have all said "That would make a funny shirt!"

Some of you have, after thinking about it for a few more seconds, have also asked "Would people pay money for it, though?"

How many people are searching your shirt for it already?

Nowadays, most people do their initial research on the Internet. I know that I almost never call someone on the phone/search for it at the library/go visit the store/etc. without trying to look it up online first. If people aren't searching for it online, then they aren't searching for it at all.

(One possible exception: You are marketing to 85-year olds from southern Mississippi who hardly know who Al Gore is let alone his invention of the Internet)

Take a moment to try out Google's keyword search tool. You can place any number of terms in the box and it will tell you how often that term is searched on, how competitively that search term is fought for by content- and service-providers, etc., etc. Here is a screen shot for 'pi shirt':



So, on average, it yields 3600 searches a month. I can then click on the "pi shirt" keyword link, and it will take me to the search results for that phrase.

Next, pay a visit to the three biggest t-shirt portals on the Internet: Cafepress, Zazzle, and Printfection. Type in the phrases that you found to be most relevant to what your idea is about and see how many products come up. Are there ones that are very similar to your own? Would your idea stand out amongst the crowd? Can you compete with the price that they are offering?

How do I give the public what they want?

Once you have ascertained how many people in the world are searching for your product each month, it's time to create your design. In another post, I'll talk about that in more detail. Today, I'll just simply give my official recommendation for Adobe Illustrator. There are a lot of graphic design products out there, including several free ones. If you really want to try this out, spend the $100 to get a used copy. You will get your return on it even if you don't ever create a shirt with it because it is simply so useful.

The second step is to advertise it online. There are three ways to do this, listing by increasing level of difficulty:

  • List it on a t-shirt portal



    This is really easy because they will handle the production and the fulfillment for you. All you do is use their online t-shirt creator tool and it will be made available to the thousands of people hitting their site each month. And it's free! In the past, I would use this route to try out a new t-shirt design, just to see if people would buy it. If I got enough sales, I would take it to the next level.

    Of course, good Internet marketing practices still apply here. You should still consider how you are going to get people to visit the portion of the t-shirt portal which contains your shirts. Things like SEO, Adwords, and blogging are a few among several strategies for doing that.

  • Create your own t-shirt website



    If you have a bit more confidence in 1) your design and 2) your ability to please customers, then you might consider creating your own website, screen printing the shirts, and fulfilling the orders on your own.

    This is a huge step from the first level, but the difference in earning potential is also enormous. It will involve registering a domain, installing a shopping cart, adding your products, images, and descriptions, marketing your site, creating a mailing list, purchasing, tracking, and maintaining inventory, purchasing shipping supplies, and shipping out product. Phew! It will also involve talking to customers on the phone, dealing with returns, and so much more.

    A lot of these things can be outsourced or hired out, but I agree with Michael Gerber: You should do each of these things on your own first until you are able to systematize your efforts. After that, feel free to hire someone if you have the margins to do so.

  • Get your design listed in someone else's online catalog



    I have tried this with very limited success; however, I believe that it is mostly due to the niche market of "pi". It may surprise you to find out that there are only a few thousand people in the world who search for pi shirts each month. That said, some of my products are, indeed, available in both online stores and one brick-and-mortar store in Seattle.

    The reason this is really hard, though, is not the relationships, but that wholesaling is a hard thing to do. It is hard to produce enough sales to keep manufacturing costs low enough to make enough profit when you are selling them to retailers at half-price (half-off retail is the typical wholesale price). I definitely make the majority of my money by being a retailer, not a wholesaler.


Well, hopefully, that provides at least a teeny bit of spark to get you going. Good luck!
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19 October 2010

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Math Games: Why My 4-Year-Old Understands Prime Numbers and the Four-Color Theorem

Some parents take pride in their kids knowing how to read by four years old. Others that their kids can ride a bike by three. Still others that their kids were potty trained by two.

Why any parent would take pride in these when topology and number theory are within their child's grasp is beyond me.

Could my kids understand Prime Numbers?



My boys over the course of about 6 months had collected a number of pennies. They were mostly garnered from doing jobs for Mom and Dad, but I'm sure they found some in our couch once or twice. I can only hope that it was always our couch.

They brought them to the table before dinner, and I was trying to think of something that we could do with them in order to teach them some principle. We decided to create mazes out of the pennies, with the pennies as the walls.

While that was pretty fun (the boys liked "trapping people" inside their maze more than actually making a functional maze), it wasn't really what I was looking for.

Then, I remembered something I read about prime numbers being "hard" numbers because they couldn't be broken down into smaller parts and how that could be shown geometrically.

So, I laid our four pennies out for the boys and asked them to make a square out of them.












No problem.

Then, I took one away, and asked them to do the same. Zac proudly showed me his:


Okay, so he didn't quite get that an "L" isn't a square and we talked about it. He already knows his shapes, so it didn't take a lot of explanation.

Anyway, "why can't we make three pennies into a square, boys?" Zac: "We could make a triangle." Remi: "Because there aren't enough pennies."

Okay, pretty good start.

Next, I gave them nine pennies, and asked them to make a square. This took a little more work, but they both figured it out.










I took a penny away to make eight. I explained that this time, they wouldn't make a square, but instead a rectangle. Again, they both know their shapes, so they knew what the end product should look like. This took a little prodding (at this point, they were starting to wonder what kind of game this was), but they made it.










Awesome. Finally, I took one more away to make seven pennies. I asked them to try and make a rectangle again.

Here is where Remi and Zac's personalities differ. Remi quickly became frustrated and tried to show me "hybrid" kind of solutions. He was upset because he thought that he should be able to do it and that he wasn't "doing it right". Zac was much calmer about the fact that it couldn't be done. In fact, I could see his mind start to wander once he couldn't find a way to make it into a rectangle.

Putting the seven pennies into a line, I explained that seven is just like three. They can't be arranged into a square or rectangle, only a line. (At this point, I had to acknowledge Zac's reminder that you could do triangles, too.)

Then came the word: Prime. If the number of pennies can't make a rectangle or a square, that number is called "prime."

The discussion kind of stopped there. Kids have about a 5-minute attention span, and, including the mazes, we had easily been talking for 15 minutes. Still, I made one last attempt and asked them about 11 pennies. Sadly, they had lost interest. Bummer. So, we'll try again another day.

Could my kids understand the Four-Color Theorem?



Another day, another mathematical principle to exercise the spatial reasoning muscles of my budding nerds.

A couple of Saturdays ago, Kristi's mom was really nice and invited Kristi to go out shopping for her birthday. So, I had the kidlets for the afternoon.

The girls were down for a nap, and I saw my opportunity.

I opened one of spiral notebooks and drew a colored map. I told Remi to come over and color it but that he could only use four colors and that no too "countries" that shared a border could be the same color. If he got "trapped," he would need to get another color from his art box. If he could keep it down to four colors, he would get an extra treat for dessert that night. (It took me several years, but I finally learned what really motivates boys: Not compelling mathematical concepts, but food.)

Remi threw himself at the problem while I started drawing a map for Zac.

Both boys concentrated a great deal while I started folding clothes. After a few minutes, I heard, "Daddy, I'm blocked!" I came over to confirm the calamity. He had indeed colored himself into a five-color corner. So, he dutifully got out another colored pencil and kept going.

The same happened with Zac a couple of minutes later.

I was pretty sure that they would be able to keep it to five, but, to our mutual dismay, Remi later exclaimed, "I'm blocked again!" The same happened with Zac.

Remi finished his with six colors, and Zac still had about a dozen countries left to color. I noticed in Zac's remaining countries a particularly insidious one that touched several other countries. So, I sat down with them and helped Zac finish his to teach the principle.

Setting aside all the colored pencils but one, I asked them how many of the remaining twelve countries we could color with just this one colored pencil. While it wasn't immediately clear to any of us, we looked at each country one by one and figured that five could be colored with that one color.

Then we pulled out a second colored pencil. How about this one? We could color four.

A third (I was starting to get a wee bit nervous, but there were only three countries left). We colored two.

A fourth, and we colored the last country.

The boys caught on right away. Again, Remi and Zac's personalities were manifest. Remi wanted me to draw another map right away. Zac decided to play with stickers or something.

Anyway, Remi succeeded on his second attempt. The map was colored with only red, pink, green, and black. Congratulations, Remi!



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18 October 2010

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LDS General Conference: The Software Guesses the Speaker

Mormon Tabernacle Choir general conference - A...Image via WikipediaLet's say that you stripped the author and photo from the online transcript of any given LDS General Conference talk. Let's also say that you didn't see or hear that talk delivered. Could you tell who gave the talk just by reading it?

My computer can. Here's how:

It turns out that modern text processing software is getting pretty good at this kind of stuff. You've always known that your inbox can tell whether or not a random email is spam with a fair amount of accuracy. Have you used cutting-edge software like Zemanta, though, that classifies and categorizes your blog post as you are typing it? Or how about companies that have software that preprocesses incoming customer feedback emails to decide whether you are happy with the product or not?

Even the most basic approaches can be very precise in some domains; this example being LDS General Conference talks.

The first thing that the computer needs is a set of training text. This text is like giving the computer the test questions and the answer key, which the computer can use to try to learn the subject matter. While "teaching to the test" might not be the best for our student population, it works great for computers that can make appropriate inferences from the smallest details.

The way I got my training text was to use a web crawler that would go to www.lds.org, download general conference talks, scrape off all the HTML, etc, and save the raw, unformatted text of each talk into a separate file. Each file's name had the name of the speaker in it, which would be where the software would look to check its answer.

The second thing that the computer needs is to know what features in the text are important to you. The most basic approach is to ask it to note individual words in the document. For example, one feature might be "the article has the word 'commandments' in it". Another might be "the article has the word 'scriptures' in it". There are a lot more ways to look at a document than just the words. How about "this article uses the passive tense" or "this article has long sentences" or "this article references '2 Corinthians'". This simply depends on your level of effort to teach the computer what to look for.

It's not quite as involved as that, though, at the most basic level. For the program that I wrote, it simply gets all the words in each document in the training set and treats each unique word as a feature. So, it builds the feature set automatically, and we get "this article has 'humble'" as well as "this article has 'seemed'" as features.

Third, the computer needs to know what it is trying to guess at. It needs a list of possible answers.

In our case, the answers are "Eyring," "Monson," "Uchtdorf," etc.

Fourth, the computer needs to search and tally those features in the training text.

The approach that I used is called Naive-Bayesian. The idea is simple. For each feature, give each document in the training text (for which it does have the answer key) a score in one of four categories:

1. This document has word X AND it is a talk by speaker Y
2. This document doesn't have word X AND it is a talk by speaker Y
3. This document has word X AND it is not a talk by speaker Y
4. This document doesn't have word X AND it is not a talk by speaker Y

Now, with all of that tallied, we can give it text that it hasn't seen before. Given enough data to work with, even this simple approach can be very accurate.

In fact, with my corpus of the last ten years of Eyring, Hinckley, and Monson talks, my computer is 88% accurate!

Here is some nifty data that it found:




















FeatureComparisonOdds
contains(prophets) = TrueEyring : Hinckl =15.1 : 1.0
contains(wants) = TrueEyring : Hinckl =12.4 : 1.0
contains(evidence) = TrueEyring : Monson =11.6 : 1.0
contains(promised) = TrueEyring : Hinckl =11.1 : 1.0
contains(seemed) = TrueEyring : Hinckl =9.8 : 1.0
contains(qualify) = TrueEyring : Hinckl =9.8 : 1.0
contains(commandments) = TrueEyring : Hinckl =9.8 : 1.0
contains(start) = TrueEyring : Monson = 9.1 : 1.0
contains(commandments) = FalseHinckl : Eyring =8.6 : 1.0
contains(answers) = TrueEyring : Hinckl =8.5 : 1.0
contains(gifts) = TrueEyring : Hinckl =8.5 : 1.0
contains(lifetime) = TrueEyring : Hinckl =8.5 : 1.0
contains(chose) = TrueEyring : Hinckl =8.5 : 1.0
contains(simple) = TrueEyring : Hinckl =8.3 : 1.0
contains(memory) = TrueEyring : Monson =7.9 : 1.0
contains(whatsoever) = TrueEyring : Monson =7.9 : 1.0
contains(resurrected) = TrueEyring : Monson =7.9 : 1.0


This table shows what the computer found to be the most helpful features, in our case 'words', in determining who gave the talk. In the first column is the feature. The second column is the two speakers, A:B, it is comparing and the third column is the odds of it being speaker A over speaker B, given that the feature is satisfied.

(Note to self: Do not show this to brother-in-law lest he decide that he can use these odds to place bets on the April general conference address.)

What do you see that's interesting to you? I think that it's really interesting to see "basic" words mixed in with religious terms. I think that it's also interesting to see most of the odds involve President Eyring. While I haven't taken it so far, yet, I would guess that this simply means that Eyring's vocabulary is more easily distinguished from the other two. That said, on my first go-round, I just used President Monson and President Hinckley's talks, and I was still at about 85% accuracy.



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15 October 2010

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How to Juggle Five Balls

Juggling ballsImage via WikipediaWay back in the summer of 1997, I attended my first World Juggling Day event in Magna, UT. There I met two fellow jugglers who would become long-time friends, Arwen and Merlyn Hall. I had already known how to juggle three and four for years at that point, so I asked Arwen about juggling five balls, and that summer's obsession was born.

It look me three months of practicing for about 30 minutes nearly every day, but by the end of the summer, I had it down and could even do a few tricks. Here is what I think were the keys:

First, the five-balls-with-a-gap, or 5-2-5 pattern



I don't think I could have done it without learning this pattern first. Since I already knew how to do four, it wasn't too difficult. The basic rhythm is to do four as a cascade, each hand throwing two balls in a row; right-right-left-left-right-right-left-left. As you get better at the rhythm, it will start to sound like one-two-three-four-(gap)-one-two-three-four-(gap). The better you get at producing the gap at an even meter, the easier it will be to add a fifth ball.

The idea is to get you used to the pattern without balls flying everywhere. :) A couple of other patterns that were helpful to me were juggling three, and then flashing three. Flashing three balls is basically throwing them faster and higher enough to have time to clap while they are all in the air. From a siteswap perspective, it is 5-5-5-0-0. The other that was helpful to me was the 5-0-5-0-5. This pattern is throwing three balls from one hand to the other; right-right-right-left-left-left. These weren't as helpful to me as the five-with-a-gap, but they were certainly nice variety.

Second, joining a juggling club


I suppose this isn't an option for everyone, but it really, really helped me to be able to show off every week. :) I would meet with Arwen and Merlyn at the Redwood Recreation Center in Taylorsville, UT every Saturday. Arwen would show me her devil sticks and I would show her five balls and we'd practice, practice, practice.

Third, perform and teach juggling


Opportunities to do this are easier to find than you think. On Saturday mornings, we would go to that rec center and, during the winter, we asked if we could juggle in a room in the rec center. The room they gave us had big windows and was right by the gymnasium where kids would play rec basketball. They would see us doing cool tricks and come in to be taught how to juggle.

It was so much fun!

Sometimes, we were teaching ten kids at a time. We learned the patterns better ourselves when we taught them to other people.

Fourth, practice, practice, practice



Oh, and did I say practice? To juggle five balls, you will need to practice every day. Focus on catches and tosses, and be patient. It will look awesome when you are done!
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13 October 2010

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Mental Math Tricks: Is this divisible by 17?

Pascal's triangle with those numbers not divis...Image via WikipediaSo, most know how to tell if something is divisible by 2 or 5, and many know how to tell if something is divisible by 9. What about other numbers?

So, here are strategies for discovering divisibility from 2 to 10, and then we'll talk about some rarer, more surprising divisibility tricks:

Divisible by two:

If the number ends in 0, 2, 4, 6, or 8, it is divisible by 2.

Divisible by five:

If the number ends in 0 or 5, it is divisible by 5.

Divisible by ten:

If the number ends in 0, it is divisible by 10.

Divisible by nine:

If you add all the digits in a number together and that new number is divisible by 9, then it is also divisible by 9.

Example #1: 189 -> 1 + 8 + 9 = 18, 18 is divisible by 9, so 189 is also divisible by 9
Example #2:
137781 -> 1 + 3 + 7 + 7 + 8 + 1 = 27, 27 is divisible by 9, so 137781 is also divisible by 9
(Note: If adding six numbers together in your head seems difficult, look for my next post on number-grouping tricks. Soon, adding six numbers together will be a cinch!)

Divisible by three:

If you add all the digits in a number together and that new number is divisible by 3, then it is also divisible by 3.

Example #1: 66 -> 6 + 6 = 12, 12 is divisible by 3, so 66 is also divisible by 3
Example #2:
15309 -> 1 + 5 + 3 + 9 = 18, 18 -> 1 + 8 = 9, 9 is divisible by 3, so 18 is divisible by 3; 18 is divisible by 3 so 15309 is divisible by 3

Divisible by six:

If the number is divisible by 2 and 3, then it is divisible by 6.

Example #1: 72, 72 is divisible by 2 because it ends in a 2, 72 is divisible by 3 because 7 + 2 = 9 and 9 is divisible by 3, so 72 is also divisible by 6
Example #2: 30618, 30618 is divisible by 2 because it ends in an 8, 30618 is divisible by 3 because 3 + 0 + 6 + 1 + 8 = 18 and 18 is divisible by 3, so 30618 is also divisible by 6

Divisible by four:

If the last two digits are divisible by 4, then it is also divisible by 4. Or, if you can cut it in half twice evenly.

Example #1: 124, 24 is divisible by 4 (cut 24 in half -> 12, then in half again -> 6), so 124 is divisible by 4
Example #2: 562312, 12 is divisible by 4, so 562312 is divisible by 4

Divisible by eight:

If the last three digits are divisible by 8, then it is also divisible by 8. Or, if you can cut it in half evenly three times.

Example #1: 200, cut 200 in half -> 100, cut 100 in half -> 50, cut 50 in half -> 25, because 200 cuts in half evenly three times, it is divisible by 8
Example #2: 429192, 192 is divisible by 8 (192 in half is 96, 96 in half is 48, 48 in half is 24), so 429192 is divisible by 8

Divisible by seven:

Take the last digit, double it, and subtract it from the rest. If that number is divisible by 7, then your original number is also divisible by 7.

Example #1: 266, take the last digit (6) and double it -> 12, subtract it from the first two digits -> 26 - 12 = 14. 14 is divisible by 7, so 266 is divisible by 7.
Example #2: 13034, take the last digit (4) and double it -> 8, subtract it from the rest of the digits -> 1303 - 8 = 1295. Is 1295 divisible by 7? Take the last digit (5), and double it -> 10, subtract it from the rest of the digits -> 129 - 10 = 119. Is 119 divisible by 7? Take the last digit (9) and double it -> 18, subtract it from the rest of the digits -> 11 - 18 = -7. -7 is divisible by 7, so 119, 1295, and 13034 are all divisible by 7. Phew!

What's with the divisible by seven rule?



So, the divisible by seven rule is a unique one. For all you budding mathematicians, here is why it works.

Let's take a number n that has more than one digit.

That means that it can be written like this:
10*x + y where y is the last digit and x is all the others.
Example: 147 can be written as 10*14 + 7

Remember that we said that if n is divisible by 7, then the difference between the rest of the numbers and twice the last digit would be a multiple of seven. So x - 2*y should be a multiple of 7. Let's write that as 7*z. So x - 2*y = 7*z, or x = 7*z + 2*y.

Thus, we get:
10*(7*z + 2*y) + y
Example: 378 can be written as 10*(7*3 + 2*8) + 8

Almost there. Now, it's just algebra.

10*(7*z + 2*y) + y = 70*z + 20*y + y = 70*z + 21*y = 7*(10*z + 3*y)

And that's it! n = 7*(10*z + 3*y), which means that n is divisible by 7

Interesting. Can that be done with other numbers? What does this have to do with 17?



Glad you asked! :)

Notice the reason that 7 could be factored out of the second term. It's because we had a multiple of 10 (20 in that case) added to 1, which created a number that was divisible by 7, in that case 21. Are there other multiples of ten that, when 1 is added to it, give us a composite number?

31 and 41 don't work, because they are prime. But, 51 does work! If we could have that multiple of 10 be 50, then we could probably come up with a new divisibility rule.

What is 51 divisible by? Well, it happens to be divisible by 17. Could we possibly get a 17 divisibility rule out of this?

Let's look at the pattern again. 7*(10*z + 3*y) is the end pattern that we are looking for. Let's replace 7 with 17. We get 17*(10*z + 3*y) => 170*z + 51*y => 170*z + 50*y + y => 10*(17*z + 5*y) + y

Does that look somewhat familiar? Check out the first equation that we got to represent the divisible by 7 rule: 10*(7*z + 2*y) + y. It looks pretty close.

So, let's try translating it back into English: If you multiply the last digit by 5 (instead of 2), and subtract it from the rest of the digits, if that number is divisible by 17, then the original number is divisible by 17.

Experiment #1: 867, multiply the last digit (7) by 5 -> 35, and subtract it from the rest of the digits -> 86 - 35 = 51. 51 is divisible by 17 (17*3), so 867 is divisible by 17.
Experiment #2: 6936, multiply the last digit (6) by 5 -> 30, and subtract it from the rest of the digits -> 693 - 30 = 663. Is 663 a multiple of 17? Multiply the last digit (3) by 5 -> 15, and subtract it from the rest of the digits -> 66 - 15 = 51. 51 is divisible by 17, so 663 and 6936 are also divisible by 17.

Wow! Will it work for other numbers?



I think you probably know the answer to that. :) The other two that I found were 13 and 27. Can you figure out divisibility rules for those? Good luck!
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