Billionaire Boys Club Blog [Flash: bbc_bloglinks_deepspace]
TRONDHEIM, NORWAY August 22nd, 2009 Shae better be careful with
that haircut and his antics, performing in what looks like a circus
they might try to keep him, he’s just a red nose away! Back to
basics! Fresh T out the bag, check. Cold bottle of Moet, check. Cup
of Patron with a little ice, check! COFFIN, CHECK! You need
20/20 vision to read that set list! Jump 1 in close quarters: Nice
to see FAM experimenting with the footwear: Fan love: Jump 2:
Goodnight! 22 comments 22 Comments so far 1. Veezy August 22nd,
2009 10:45 am that shit looks wild!NEEERRRRRDDD! 2. Fabien August
22nd, 2009 11:25 am Pharrell Williams in Trondheim Norway!Great !Our
best Regards! http://www.hiddengarments.cn/?tag=pharrell-williams 3.
thaflyest August 22nd, 2009 11:30 am lol it’s like rhea is the 4th
member of NERD…wonder what it’s like to have her side of things as far
as performing the songs goes…cuz from what I heard you guys aren’t
doing truth or dare on this tour are you?(that’d be really cool tho if
you were) 4. Tiara24 August 22nd, 2009 11:45 am Looked like alot of
fun!!! 5. Eurshla August 22nd, 2009 1:09 pm Cool venue, it looks
like a circus tent…. Ok so we know P gives all the girls on stage
attention, however there is always a pic of him with the “Thickest”
girl (to put it nicely), and it does seem that he gives them a little
extra attention. Makes me wonder, is he “THICK-CURIOUS”??? Do your
Thang P… =) 6. mr.southern August 22nd, 2009 1:41 pm I can’t wait
until I get the chance to tour or preform that is the shit I want to
have. Yall look like you had a ball. 7. kim August 22nd, 2009 1:50
pm Long live hip-hop… guys!hm,I’m hungry!ohno it’s his… i’ll let him
open fried chicken gizzards!Love ya! 8. Misla August 22nd, 2009 3:58
pm how many pairs of lunars did P bring? hes really feelin them
huh.lol @Fam hes is just so much fun!! 9.
startrakbbcicecreams August 22nd, 2009 6:23 pm looks awesome.Lots of
Love, i can almost feel it thru my computer lol.&N.E.R.D seems to have
made Rhea a regular! Go Rhea. Lol and she has great legs btw.Shes even
got the Star trak thing going!Go N.E.R.D! im supporting Rhea & Fam
too 10. pablo August 22nd, 2009 7:15 pm hi bbc/ic blog if you have
contact with pharrell/nerd group, submit their to do a song call “”
back to school””” that’s a good idea i tink really . please read and
submit their , with this they can do a HIT n°1.all user interesting by
this idea put a comment call “”back to school”” bye! 11.
Hatti August 22nd, 2009 7:41 pm Aw3som3!!! Ershla’s right, it does
kinda look like it was in a circus lol. 12. Urban Cutie August 22nd,
2009 7:54 pm LOVE LOVE LOVE IT! PICS R AMAZING LIKE USUAL! I HAD 2
LAUGH, WHEN I SAW THIS PAPER STICKING ON THE STAGE FLOOR.. IS THIS
MAYBE A SONG TEXT? LOL http://www.igottoomuchtime.blogspot.com 13.
MissBBCBabe August 22nd, 2009 9:00 pm looks like fun times for
sure.. 14. Mrs_PWilliams August 23rd, 2009 3:22 am Venue looks
awesome! & another great show! 15. Jan August 23rd, 2009 4:09 am
Which Shoes does Pharell wears? 16. Lolita August 23rd, 2009 5:01
am lovin the jumps in fine form guys!…fixed 17. TM August 23rd,
2009 5:56 am Wow…Norway.Show looked awesome;HEHEHE! 18.
purplerainqueen August 23rd, 2009 6:23 am ANOTHER AMAZING
PERFORMANCE. 19. ♥IblogU♥ August 23rd, 2009 2:47 pm this one was
full of high energy 20. Sarah August 24th, 2009 7:03 am These
pictures are SUPER, but don’t you have some of the show in Belgium
(Pukkelpop, 22/08/09)too? By the way I loved loved LOVED the show!
21. Flow August 24th, 2009 11:49 am some niccceee pics mike!! 22.
purplerainqueen August 25th, 2009 12:45 pm GREAT SHOW! 23.
T_H_E_N_E_R_D_H_A_S_S_P_O_K_E_N September 2nd, 2009 2:52 am Your
comment is awaiting moderation. http://m.youtube.com/watch?v=pGUlIS7euEo&hl=en&gl=CA&client=mv-google
Pharrell if you stay with this girl, “She can make you look this
good.” Her words. As an artist your creative vision and prestige has
diminished to this fan, but I am sure there is a good reason she is
there and hope you put your integrity as an artist first above
everything else. You are so talented and your music has meant so much
and brought so much vision and happiness to so many people. Keep it
at the top! For the record I am not a hater and wish Rhea all the best
success in all her endeavors. I enjoyed the Jadakiss song she did.Long
live the N*E*R*D*S! Signed, The N*E*R*D fan who only speaks once.
Archive for August, 2011
Mathematics of Computation and the Art of Three Music Critiques
A modal falacy
BBC journalists seem not to understand the difference between
Gordon Brown did not want Magrahi to die in prison.
and
Gordon Brown wanted Magrahi to die not-in-prison.
–
Which of the seven heavens / Was responsible her smile /
Wouldn’t be sure but attested / That, whoever it was, a god /
Worth kneeling-to for a while / Had tabernacled and rested.
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Kac & Ulam; Katz; Kline attempts; #44; 2nd ed; Euclid's Infinitude of Primes Proof Corrected
Looks like I have to make a-do, since Google is down.
Wish that Google have some sort of red-flag alert
whenever down as to the newsgroups saying why they
are down and an estimate of when up and running again. They allow new
posts but no followups.
— quoting old 2007 post with some snips and new
added —
Newsgroups: sci.math, sci.logic
From: a_plutonium <a_pluton…@hotmail.com>
Date: 24 Apr 2007 11:40:44 -0700
Local: Tues, Apr 24 2007 1:40 pm
Subject: #11 published examples of mistaken proofs by various authors;
monograph-book: "Correcting the Logical Flaws of Euclid’s Infinitude
of Primes Proof"
(# 14) — quoting from the book MATHEMATICS AND LOGIC , Mark Kac and
Stanislaw M. Ulam 1968 , page 3 —
The following proof, probably still the simplest, asserts the mere
existence of arbitrarily large primes. Suppose the number were finite;
there would then be a largest prime p. Consider now the number n = p!
+
1 (p! is read "p factorial" and equals 1x2x3x…xp). This number is
not
divisible by any prime up to p. If there is no prime between p and n;
as we have assumed, then n itself would be a prime, contrary to our
assumption that p is the largest one.
This remarkably simple and elegant result of Euclid’s is one of the
first known proofs by contradiction.
— end quoting MATHEMATICS AND LOGIC , Kac and Ulam —
Kac and Ulam almost have a valid Indirect Method proof. They
reason that "n itself would be prime" after having conducted a prime-
factor
search. But the real reason that "n" is prime is because of the
definition of prime
which they missed inserting as their very first step of the proof. The
Indirect Method
pivots on the first step of the proof as the Definition-of-Prime. Kac
and Ulam almost
have a valid Indirect Method but miss it by a mistaken reason.
Secondly, if
they had studied Euclid’s own proof, they may have seen that Euclid
did a Direct Method of set cardinality increase.
Again, the need for professors of mathematics to provide both a Direct
and Indirect Method whenever giving a Euclid IP proof is very much
needed.
(# 15) — quoting Victor J. Katz, A HISTORY OF MATHEMATICS, 2nd
edition,
1998, p 87 —
The final book on number theory is Book IX. Proposition 20 of
that book shows that there are infinitely many prime numbers.
Proposition IX-20 Prime numbers are more than any assigned
multitude of prime numbers.
In analogy to the proof of proposition VI-1, Euclid has no way
of writing down an arbitrary "assigned multitude" of primes.
Therefore, he again uses the method of generalizable example.
He picks just three primes, A, B, C, and shows that one can
always find an additional one. To do this, consider the number
N = ABC+1. If N is prime, a prime other than those given has
been found. If N is composite, then it is divisible by a
prime p. Euclid shows that p is distinct from the given primes
A, B, C, because none of these divides N. It follows again
that a new prime p has been found. Euclid presumably assumes
that his readers are convinced that a similar proof will work,
no matter how many primes are originally picked.
— end quoting Victor J. Katz, A HISTORY OF MATHEMATICS, 2nd edition,
1998, p 87 —
It is a relief that math professors have started to read
Archimedes Plutonium posts on Internet showing what is wrong and
flawed..
(snipped)
Katz’s above is a Direct Method with terminology of
"method of generalizable example" is that of set cardinality increase.
But Katz does not stick or stay with set cardinality increase with
his last statement.
Katz makes a blunder. His last sentence of "Euclid presumably
assumes that his readers are convinced that a similar proof will
work,"
(snipped)
>Is a point of obfuscation, because the question arises >over "presumably assumes". Does Katz mean that
>the reader is to make a reductio ad absurdum >assumption?
Here again, if Katz had been required to write out a full Direct and
also
a full Indirect method proof of Euclid IP, he may have ended up with
two crystal clear and valid proofs instead of one obfuscated and
murky attempt.
(# 16) — quoting from MATHEMATICAL THOUGHT FROM ANCIENT TO MODERN
TIMES,
1972, Morris Kline, page 80 —
Proposition 20. Prime numbers are more than any assigned multitude of
prime numbers.
In other words, the number of primes is infinite. Euclid’s proof of
this proposition is a classic. He supposes that there is just a finite
number of primes, p1,p2, . . .,pn. He then forms (p1xp2x . . .xpn) +1
and argues that if this new number is a prime, we have a
contradiction,
because this prime is larger than any of the n primes and so we would
have more than n primes. On the other hand, if this new number is
composite it must be divisible (exactly) by a prime. But this prime
divisor is not p1,p2, . . ., or pn because these leave a remainder of
1. Hence there must be some other prime; and again we have a
contradiction of the assumption that there are just the n primes
p1,p2,. . .,pn.
— end quoting from MATHEMATICAL THOUGHT FROM ANCIENT TO MODERN
TIMES,
1972, Morris Kline, page 80 —
Kline makes the usual two mistakes. First, Kline erroneously thought
Euclid’s IP was indirect proof method. Secondly, Kline
goes ahead and gives an
invalid indirect proof of IP by hunting around for a prime factor.
In the Indirect Method there can be no hunting around for a new prime
because Kline’s new number of multiply the lot add 1 is the only
prime candidate in that method and it is automatically and
necessarily prime because the first step of the proof is the
definition
of prime. When you combine the definition and the reductio ad absurdum
step, then the new number Kline forms is necessarily prime.
I do not know where mathematicians erroneously ascribed Euclid with
Indirect
Method. I believe from sketchy sources that it was Gauss
who led astray the mathematics community into believing
the Ancients used the Indirect method frequently when in fact
the Ancients seldom if ever used the method. Euclid may have used
reductio ad absurdum in some subcases of a proof but there is no
evidence that the ancient Greeks built an entire proof on the Indirect
Method:
> 9.20. Euclid wrote:
> I say that G is not the same as any of A, B, C. For, if
> possible, let it be (the same). And A, B, C (all) measure DE.
> Thus, G will also measure DE. And it also measures EF. (So) G
> will also measure the remainder, unit DF, (despite) being a number
> [Prop. 7.28]. The very thing (is) absurd.
And this is where perhaps Gauss enters the picture and leads many
astray.
Perhaps it was Gauss in his
century who most clearly used and espouses the mechanics
of the "indirect method" that would lead other mathematicians
astray.
Kline should have been clued by the fact that "reductio ad
absurdum" is a Roman term, not a Ancient Greek term, and
so should have investigated.
And although Kline failed to give an accurate
historical account of Euclid’s IP and failed to even
give a correct proof of such a simple theorem. Well, I
would still buy his book.
And if Kline was required to have given both a direct and indirect
proof of Euclid
IP, he probably would have made two valid and clear proofs thereof.
— end quoting old 2007 post —
I note that with Mr. Katz, that the math community of
book writing are beginning to read my posts on the
Internet over the correction of Euclid’s Infinitude of Primes and
although Mr. Katz had made improvements, it is still not enough and
that the standard now to follow is to do both the Direct and Indirect
proofs of Euclid’s Infinitude of Primes so that
students are not confused.
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
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