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Tuesday, 3 February 2009
math with 6 and 9, Prime and Feynman Pi
Nine is a composite number, its proper divisors being 1 and 3. It is 3 times 3 and hence the third square number. 9 is a Motzkin number. It is the first composite lucky number.

Nine is the highest single-digit number in the decimal system. It is the second non-unitary square prime of the form (p2) and the first that is odd. All subsequent squares of this form are odd. It has a unique aliquot sum 4 which is itself a square prime. 9 is; and can be, the only square prime with an aliquot sum of the same form. The aliquot sequence of 9 has 5 members (9,4,3,1,0) this number being the second composite member of the 3-aliquot tree.

There are nine Heegner numbers.[1]

Since 9 = 3^{2^1}, 9 is an exponential factorial.

8 and 9 form a Ruth-Aaron pair under the second definition that counts repeated prime factors as often as they occur.

A polygon with nine sides is called an enneagon[2] A group of nine of anything is called an ennead. (technically) or nonagon (in common usage).

In base 10 a number is evenly divisible by nine if and only if its digital root is 9.[3] That is, if you multiply nine by any whole number (except zero), and repeatedly add the digits of the answer until it is just one digit, you will end up with nine:

    * 2 × 9 = 18 (1 + 8 = 9)
    * 3 × 9 = 27 (2 + 7 = 9)
    * 9 × 9 = 81 (8 + 1 = 9)
    * 121 × 9 = 1089 (1 + 0 + 8 + 9 = 18; 1 + 8 = 9)
    * 234 × 9 = 2106 (2 + 1 + 0 + 6 = 9)
    * 578329 × 9 = 5204961 (5 + 2 + 0 + 4 + 9 + 6 + 1 = 27 (2 + 7 = 9))
    * 482729235601 × 9 = 4344563120409 (4 + 3 + 4 + 4 + 5 + 6 + 3 + 1 + 2 + 0 + 4 + 0 + 9 = 45 (4 + 5 = 9))
    * (Exception) 0 x 9 = 0 (0 is not equal to 9)(though it can be considered -1 in the tens place and 10 in the ones place(10-1=9))



The only other number with this property is three. In base N, the divisors of N − 1 have this property. Another consequence of 9 being 10 − 1, is that it is also a Kaprekar number.

The difference between a base-10 positive integer and the sum of its digits is a whole multiple of nine. Examples:

    * The sum of the digits of 41 is 5, and 41-5 = 36. The digital root
      of 36 is 3+6 = 9, which, as explained above, demonstrates that it is
      evenly divisible by nine.
    * The sum of the digits of 35967930 is 3+5+9+6+7+9+3+0 = 42, and
      35967930-42 = 35967888. The digital root of 35967888 is 3+5+9+6+7+8+8+8
      = 54, 5+4 = 9.



Subtracting two base-10 positive integers that are transpositions of
each other yields a number that is a whole multiple of nine. Some
examples:

    * 41-14 = 27. The digital root of 27 is 2+7 = 9.
    * 36957930-35967930 = 990000, which is obviously a multiple of nine.



This works regardless of the number of digits that are transposed.
For example, the largest transposition of 35967930 is 99765330 (all
digits in descending order) and its smallest transposition is 03356799
(all digits in ascending order); subtracting pairs of these numbers
produces:

    * 99765330-35967930 = 63797400; 6+3+7+9+7+4+0+0 = 36, 3+6 = 9.
    * 99765330-03356799 = 96408531; 9+6+4+0+8+5+3+1 = 36.
    * 35967930-03356799 = 32611131; 3+2+6+1+1+1+3+1 = 18, 1+8 = 9.



Casting out nines
is a quick way of testing the calculations of sums, differences,
products, and quotients of integers, known as long ago as the 12th
Century.[4]

The Nine Chapters on the Mathematical Art
is a Chinese mathematics book, composed by scholars between the 10th
century BC, and the 1st century AD; it is the one of the earliest
surviving mathematical text from China.

Every prime in a Cunningham chain of the first kind with a length of 4 or greater is congruent to 9 mod 10 (the only exception being the chain 2, 5, 11, 23, 47).

Six recurring nines appear in the decimal places 762 through 767 of pi. This is known as the Feynman point.

If an odd perfect number is of the form 36k + 9, it has at least nine distinct prime factors.[5]

Nine is the binary complement of number six:



The decimal expansion of p begins
3.14159265358 … and the number is defined as the ratio of a circle’s
circumference to its diameter. If you fast forward to about the 760th
digit in the decimal expansion of p, you will see the string “…34
999999 83…”  That group of six repeating 9s in the center is known as
the ‘Feynman Point.’
p is a real number that is irrational and transcendental, meaning it
is not the ratio of two integers and it is not the solution of a
polynomial with rational coefficients. Although it hasn’t  been
proved, it’s generally believed that any finite set of digits will
eventually occur in the decimal expansion of any irrational number due
to their non-repeating behavior. For example, it’s thought that at some
point in the decimal expansion of, say, v666 that the string
‘6660066600666′ will occur, and the string ‘12345432123454321′ will
occur, and any other finite string you come up with. Thus, the
appearance of six 9s in the decimal expansion of p isn’t that unusual.
But the fact that it occurs after only 762 digits is what makes it a
genuine curiosity. (For comparison, the earliest location of any four
repeating digits is at position 1589, in which four 7s appear.)
The group of six 9s in p referred to as the Feynman Point is named
after Nobel Prize winning physicist Richard Feynman (1918 - 1988), who
was awarded the prize in 1965 for his work on quantum electrodynamics.
Feynman once stated in a lecture that he wished he could memorize all
the digits of p up to the group of six 9s so he could continue: “nine,
nine, nine, nine, nine, nine, and so on.” Of course that would be
misleading because if the digits went on as repeating 9s, p would cease
being an irrational number.
Quite a bit of research has been done on patterns that occur in the
decimal expansions of irrational numbers. But if one becomes too
intrigued with the digits for their own sake, it is not looked upon
favorably by most mathematicians. In Petr Beckmann’s book, A History of
p, he has a chapter titled “Digit Hunters,” and uses the phrase
disparagingly since there is no practical use for computing more and
more digits of p, or for locating patterns in their decimal expansions.
(Only 10 digits are needed for any real-world problem).
Nevertheless, when you have a computer it’s fun to search for
patterns in anything. So taking inspiration from the Feynman Point I
thought of this sequence: The first position in the digits of p (not
counting the initial 3) at which a string of n copies of the digit n
occurs. For example, the first occurance of four 4s is at position
54525, “…11793 4444 82014…” and that is the fourth term of our
sequence. Here are all the known terms: 1, 135, 1698, 54525, 24466,
252499, 3346228, 46663520, 564665206. Because all finite patterns of
digits are believed to eventually appear in irrational numbers, surely
this sequence is infinite. But where will the string of one hundred
100s occur?
I’ll close this article with two strange mathematical curiosities only loosely related to the Feynman Point.
Consider v666 = 25.8069758011278803151884206 …  The first ‘666′
string occurs in its decimal expansion at position 503, and the
locations for the next 666s are 928, 975, 2705, 4229, 7021, 9195, 9338,
and 9349. Those are all positions of 666s among the first 10,000
digits, and I have dubbed it ‘Lucifer’s sequence’ because it is
believed that if a person recites the terms backwards while spinning
counterclockwise six times, upon their final revolution they will
either become totally omniscient, or their head will burst into flames.
Only kidding.Â
The second curiosity is based on primes, my favorite type of number,
and we’ll use some information from the Feynman Point. The six
repeating 9s start at the 762nd place and end at the 767th place. If we
concatenate those three numbers we get this prime: 762999999767. And if
we continuously add zeros between those three numbers we’ll continue to
find more. The next one is  76200009999990000767. Let f(n) = (762 *
10n+6 + 999999) * 10n+3  + 767. It is prime for n = 0, 4, 11, 15, 32,
215, 408, 461, 1489, 9349, 9470 and no more up to 10000. The last two
have 18710 and 18952 digits, respectively (but they’re actually only
probable primes since their form is not easily provable). Surely there
must be infinitely many Feynman Point primes.






Posted by Tracy at 5:41 AM EST
Updated: Tuesday, 3 February 2009 5:46 AM EST
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Number 9, Number 9 and the Battle Hymn

Number 9..Number 9..and the Battle Hymn Dream
Category: Dreams and the Supernatural



I hate these type of dreams, they are the ones that stick with you all day and won't leave. They wake you up with a sick feeling in your stomach and you know if you fall asleep again you will be put right back in the same dream again. Over and over and over and over and over.. I wake up, look at the clock and it's 3 am. Just in case you've never heard ...3AM is the demonic witching hour. It's a way for demons to mock the holy trinity. It's inversion is 3PM.. the miracle hour.. Which is traditionally accepted as the hour of christ's death. Or so they say...anyway.. So what was the dream? Just fucking weird is all. It goes like this:




I was in the big gigantic warehouse with alot of different levels.  I
was with some people there although I did not know who they were in
real life, I knew them in the dream.  I don't even remember why we were
there but it was full of alot of strange escalators and just alot of
strange stuff.  Mostly religious stuff, or at least it looked like
religious stuff?  A cult maybe?  That is what it gave me the feeling
of, a cult. 



I was going up this escalator and this man just kind of floated by me
and I had the sense that he was demonic.  He was smiling but it was
like just a head, all I remember was his face and he kind of looked
like Jesus, but it wasn't and I knew it, I felt it, but all these
people in the place were worshipping this guy.  Like I said, it was
like his head was floating and he was smiling at me like he was trying
to get into my head somehow and I told him to get away from me..  He
laughed and came closer to me.  I told him again to get the fuck away
from me because he gave me a creepy ass feeling and I knew he was a
fake.  He laughed again and I really started getting this really bad
evil demonic feeling from him like he was the devil or something.  I
said "In the name of Jesus get the FUCK AWAY FROM ME".  This usually
works in dreams against these scary dream people, but nope not this
time.  He acted stunned for a minute and then came back.  Laughing.  I
said it again and he winced and came back again.  I was still in the
elevator and and it was still going up and on the wall I saw that
picture of Jesus with the heart in barbed wire- I think they call it
the sacred heart of jesus picture or something so I was trying to think
of something to get this fucked up guy/creature/demon away from me
before he devoured my soul or something, and I imagined that picture
and remembered one time someone told me if you dream of demons to tell
them the blood of jesus was going to get them.  So I yelled really loud
at this thing "The blood of Jesus is ON YOU, GET THE FUCK AWAY FROM ME"
like I was throwing it on him.  His eyed rolled in the back of his head
and he disappeared after I said it a few times. 



Throughout this place there were pictures of Jesus and religious
pictures everywhere, like this was a religious place, but they all felt
like fakes to me.  Like it was set up to look like a religious place
but it was actually a cult.  I rode this elevator to the basement and I
could see that demon guy I struggled with earlier in the basement with
a bunch of bloody body parts.  Maybe they were his body parts since he
only had a head earlier...but I got the feeling that they were just a
bunch of random body parts that he collected and I was looking at
everything and started getting caught up in the body parts, like
tangled, and blood everywhere (maybe it was his body parts and that was
the jesus blood I threw on him, haha)  and I broke free and ran back to
the elevator and went back upstairs.



The demon left me alone after that but he had minions.  I think he
decided if I was throwing Jesus blood around he would rather it got on
one of his flunkies instead of him.  I mean, hell that shit might burn
or something?   Who knows what Jesus blood does.   So this crazy ass
woman is stalking me now and I am doing everything to stay away from
her.  Dodging her like crazy.  But she kept trying to come up to me and
she kept acting like she was spiritual, like I needed to be saved. And
I felt like she was brainwashed and was worshipping that demon- or
whatever that guy was.  She kept trying to talk to me, touch me.  I
kept avoiding her.  I rode up this elevator to the top, these were some
cool ass elevators and I had a drink that I laid at the side at the top
and I went to grab it before the elevator started going back down and I
couldnt grab it.  So I lost my drink! Damn it.  Going back down.  I saw
a friend of mine on one of the levels and jumped off.



He was a tattoo artist, but I didn't know the guy in real life.  We
were looking at tattoos and I was sitting in the tattoo chair and that
crazy stalker lady came up and put this dark green stone with a hole in
the middle of it on my toe and said it would help me.  I threw it off
and jumped out of the chair!  I couldn't get this bitch to quit
stalking me!  She kept trying to convert me into what I don't know! 



I walked down this long corridor and there was this old man, maybe a
priest or something?   And I was telling him about that demon guy and
he asked me "When he laughed, did he just laugh or was it a cackle?" 
and I said "It was more like a cackle, why?" and he shook his head,
"that's how you can tell..."  but I'm still walking down the corridor
and didn't hear the last part and I'm still walking and then there is
that lady again. 



She stops me and I don't know how she sucked me in this time but she
got me engaged in something she was doing.  It was like a painting but
at the same time some kind of puzzle.  Maybe some kind of math puzzle
or something but we had to figure out how many of something there
were.  I started adding them up and I was putting x's in boxes.  1 x, 2
x's, 3 x's , etc, all the way across this big sheet of green
construction paper but after I got done the paper turned white and all
my x's turned blood red and started disappearing/fading away.  the lady
laughed and she flipped my paper upside down and it read 66666666666
but I started saying "Number 9, Number 9 Number 9" and she said "Same
thing dipshit!"  and walked away triumphantly like she just proved what
she had to prove the whole time she was stalking me and was now done. 
Then I heard music playing and it was the 'Battle Hymn of the Republic"
playing....



weird ass dream.

 


Posted by Tracy at 4:49 AM EST
Updated: Tuesday, 3 February 2009 4:54 AM EST
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Sunday, 28 December 2008
Snakes and scary Monsters
Topic: Regular Dreams
Maybe it's the ritalin.  They just get weirder and weirder.  I dreamt I  was in a public place, it looked like a toilet but it was as big as a bathtub and I looked in the toilet/bathtub and there was a snake , a big green snake, so I tried to hurry and flush it and this big giant toilet/bathtub thing, I mean it looked like a bathtub but it flushed like a toilet, maybe a hot tub?  the snake would not go down and I thought it was  going to bite me.  Then there were other creatures and I couldnt figure out what or where they came from but they were SCARY.  Ok, so I thought I got most of them to flush down and I found JR, so it obviously had something to do with all the nasty shit at Irvine, haha.  I told him that there were creatures in the toilet/bathtub thing.  Later there was a shelf by the bathtub thing and it had a bunch of stuff on it, cool stuff- jewelry- cosmetics- all kinds of cool stuff- and so I thought wow there was all this stuff in the bathtub thing- JR must have pulled it out- so I figured it was free and started grabbing some of it.  Jr walked by and I said 'did you get this stuff out of that thing?" and he was like "huh?  I don't know where that stuff came from"  Then Chris Adams walked by and I asked her where it came from but she didn't know either, so I was like fuck it, it's mine!  lol...  then I saw someone who just got their hair cut, and decided to go get mine cut. I went to where they told me and got my hair cut.  It was a restaurant /hair salon (that just sounds gross, lol)  hair on one side/ restaurant on the other.  Then I noticed Stacey, from Irvine, she said that she went and learned to cut hair and now worked there, it took her 50 weeks.  Then the dream switched to Universal Tae Kwon Do.  Ok, now Universal is closed for real but Eddie used to go there.  Sean is gone but Nancy was teaching class, she was the black belt in charge.  There were quite a few people there I didn't know and a few I did, but she was the only one who seemed to have a higher belt, weird.

Posted by Tracy at 7:40 AM EST
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Saturday, 27 December 2008
RED
Mood:  down
Topic: Red Balloons
They're back

Posted by Tracy at 2:45 PM EST
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PRISON AND JEFF
Mood:  down
Topic: Regular Dreams
Lots of weird dreams lately, I don't know if it's this ritalin or what but my dreams are getting so strange.  that and the red balloons are back..

Last week I dreamt that I asked Jeff if he loved me and he told me no, and then I said I already knew that and then he turned into someone I don't know- kind of resembled big Eddie but it wasn't big Eddie, it was weird, then Lisa said 'he's lying because I asked him and he said he did' lol....I'm like whatever.   Then the visiting jail dreams, I have dreamt 3 times that I've visited someone in prison, twice I think it was big Eddie but one of the places was this same place that I've dreamt about alot but I've never visited there and I haven't dreamt about it since Scott was in prison.  I don't know why all the prison dreams, maybe because Jeremy is in trouble again.  Then I dreamt again that I told Jeff to move out, but we were at my moms house up on the lake and Jeffs best friend was there with his girlfriend (and he doesn't have a girlfriend, lol), there's more I can't remember

Posted by Tracy at 2:45 PM EST
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Monday, 17 November 2008
Testing
Topic: Other

I'm just testing this moblogging out to see how well it works


remote Posted by Tracy at 7:51 PM EST
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Testing
Topic: Other

just testing out this remote blogging to see how well it works!


remote Posted by Tracy at 7:51 PM EST
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Sunday, 27 July 2008
Scotty
Mood:  down
Topic: Telepathy
Ok, I'm posting this as a telepathic dream but I'm really not sure what category it falls under.  I dreamt about my first 'love' the other night.  I haven't thought about him for maybe a year or so, and we had been keeping in contact off and on since we were teenagers but we lost contact in the last few years and I haven't heard from him, and really haven't thought of him, especially not enough to have a dream like this about him.  So the dream was that I went to his house, and he was in this room.  He told me to go take his car for a ride, so I did.  It was a really nice, fast car.  I came back to the place he was staying, and his wife and kids were there.  I went around looking at the place and it looked alot like a warehouse or something.  I went up to where he was sleeping (and he was sleeping in his bed for alot of the  dream which was strange) and I sat on the bed and talked to him.  I can't remember a whole lot of what he was saying but he was having trouble with his wife.  I woke up.  Thinking how odd this was, the whole dream and basically dreaming about him since I hadn't thought of him in quite a while I decided to do some investigating.  He has been in trouble with the law many times, although not so much in the last 5 or so years, so I decided to start looking at the county records in the town he lives in, and what I found was quite a suprise.  His wife filed a charge against him 3 days before my dream.  Was I picking up on that?  I think so.   I know that in the past when he was having trouble he would sometimes come back here (he lives 1200 miles away), was I picking up on his thoughts to leave that place and come back here?  Interesting.  I have no way of checking, I did however find a mailing address for him and I pinged it to see if it would reach him, if I find out more, I'll edit this post and comment further. 

Posted by Tracy at 4:53 PM EDT
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Chantix dreams part 3
Mood:  don't ask
Topic: Regular Dreams
I'm going to post one dream seperately because it falls in a different category.  I've been taking the Chantix for almost 2 weeks but have discontinued it due to the feelings of depression and the strange antisocial feeling I get with it.  The dreams have been very vivid however.  Last night I dreamt about my friend Scott who was in prison before, he was in some sort of half way house and I went to go see him, I was talking about him yesterday to someone so I imagine that is what triggered the dream.  I can't remember all the dreams, one was  of my son's father who is also in prison.  I dreamt I went to go visit him, and I was also talking about him the same day so that is probably why I dreamt about him.  The rest of the dreams are just fragments.  The next dream I post was a little odd...

Posted by Tracy at 4:48 PM EDT
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Monday, 21 July 2008
Telepathic dreams and Emotions
Topic: Telepathy
I wanted to get this down before I forgot to do it.   I have often wondered about telepathic dreams, the link between two people that will cause one person to dream about the other.  It seems at times the connection is opened by merely thinking about the other person, looking at their picture, but what I am thinking also is that there has to be some kind of strong emotion to really cause an effect.  Like say for instance, I have a strong emotion- whether it is related to the person or not- and while I am having the strong emotion I think of the person at the same time- the emotion will open the channel and because of the thought of the person at the same time that channel connects to them, which causes them to dream that something is wrong?  Thinking out loud, I'll finish this later hopefully with a better explanation of what I'm thinking here...

Posted by Tracy at 11:58 PM EDT
Updated: Tuesday, 22 July 2008 12:04 AM EDT
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