Goodbye AT&T

The June bill for our AT&T landline increased from $34.03 to $38.49. The difference was a $2.00 "minimum usage charge", a $1.99 "carrier cost recovery fee", plus a $0.47 "federal universal service fund fee." The ostensible reason for this was because we hadn't chosen a long distance carrier.

However, we didn't use the land line for long distance calls. Aside from the target it gave the thrice-damned money seekers, we used it for our security system.

We called AT&T customer service and the agent was of no help whatsoever. He was unable to answer the question why we had to pay for a service we weren't using. After several fruitless trips around the circle, we asked to speak to a supervisor and were put back into the interminable "wait for the next agent" state.

So I drove to the nearby AT&T store. The rep was very professional and, after being on hold with AT&T customer service himself, removed the charge and supposedly waived the fee on future bills. But it was not to be so. The fee was back on the next bill. This time my wife dealt with AT&T and, again, the charge was removed from our bill. When she asked if the charge was gone for good, the agent couldn't give any assurance that it would be.

So we asked our security provider to go wireless and then dropped our land line. I would have been happy to keep the land line, but not with a junk fee, and especially not with such incompetent service. I may switch to Verizon or Sprint for mobile service, especially since the iPhone is rumored to be available for all three in October.

Two days after canceling our service, Clark Howard came out
speaking against this fee.

More years ago than I care to remember, Lily Tomlin was in this Saturday Night Live skit about AT&T. The technology has changed, but corporate stupidity abides.


Number Theory #2

This stuff is killing me. The solutions, so far, turn out to be simple. But finding them is a struggle.

2.1 #1: Show that if a, b, and c are pairwise relatively prime, then (a, b, c) = 1.

Since a, b, and c are pairwise relatively prime then (a, b) = 1, (b, c) = 1, and (a, c) = 1.

   (a, b, c) = ((a, b), c) = (1, c) = 1

I suppose I have to show that (a, b, c) = ((a, b), c). Let (a, b) = d and (d, c) = e. e | d and d | a
→ e | a, since d = ke, a = ld → a = lke → e | a. Similarly, e | b. Since e | a, e | b, and e | c, e is a common denominator of (a, b, c). So it must be shown that it is the largest. But I don't know how to do this, except by using set theory. Let A be the set of the factors of a, that is, a is the product of the elements in A. Likewise sets B and C. There is at least one element in A, B, and C, since 1 is a factor. Then (a, b) is the product of the elements A B. Likewise, (a, b, c) is the product of the elements A B C. A B C → (A B) C, so (a, b, c) = ((a, b), c).

Another proof, which is probably closer in spirit to what the book has in mind, is to let (a, b, c) = d. Then d | a and d | b. Since (a, b) = 1, by Theorem 2.3 d | 1 and therefore d = 1.

2.1 #2: Use the Euclidean algorithm to find the greatest common divisor of:
  1. 77 and 91 7
  2. 182 and 442 26
  3. 2311 and 3701 1

2.1 #3: Express (17, 37) as a linear combination of 17 and 37.

(17, 37) = 1
17r + 37s = 1

   37 = 2 * 17 + 3
   17 = 5 * 3 + 2
    3 = 2 * 1 + 1

   1 = 3 - 2
     = (37 - 2 * 17) - (17 - 5 * 3)
     = (37 - 2 * 17) - (17 - (5 * (37 - 2 * 17)))
     = (37 - 2 * 17) - (17 - 5 * 37 + 10 * 17)
     = 37 - 2*17 - 17 + 5 * 37 - 10 * 17
     = 6 * 37 - 13 * 17

2.1 #4, 5, and 6: These are all variations on problem #3 since (399, 703) = 19, (547, 623) = 1, and (398, 600) = 2. Since this is mechanical, I'd rather spend the time writing code to do the work.

(399, 703) = 19 = -7 * 399 + 4 * 703
(547, 623) = 1 = -41 * 547 + 36 * 623
(398, 600) = 2 = -101 * 398 + 67 * 600

2.1 #7: Find integers r and s such that 922r + 2163s = 7.

This is interesting, since (922, 2163) = 1. For this case, by the method in problems 3-6, one solution for 922r + 2163s = 1
is 922*556 - 2163*237 = 1. Then 7*(922*556 - 2163*237) = 7 922*3892 - 2163*1659 = 7.

2.1 #8: Are there integers r and s such that 1841r + 3647s = 1? Why?

(1841, 3647) = 7, so 1841r + 3647s
= 7(263r + 521s) → every solution to 1841r + 3647s is a multiple of 7, which 1 is not.

2.1 #9: Show that if there is no prime p such that p | a and p | b, then (a, b) = 1.

Let (a, b) = d. If d is composite, then d is divisible by a prime, q. Then q | d
q | a and q | b (Theorem 1.3). But this contradicts the premise so d is not composite. d must be prime. But this too contradicts the premise, therefore d = 1.

2.1 #11: Are the integers 101, 209, 283, and 341 pairwise relatively prime? No, (209, 341) = 11.

2.1 #12: Show that if p is prime and a is an integer then either (a, p) = 1 or (a, p) = p.

Suppose a = 0. Then (0, p) = p, since p | 0.
Suppose 0 < a < p. Then (a, p) = 1, since p is prime (a
p) and (p a) since p > a.
Suppose a = p, then (a, p) = p.
Suppose a > p. If a is prime, then (a, p) = 1, since by definition of primes, (p
a). If a is composite and (p a), then (a, p) = p. If a is composite and (p a), then (a, p) = 1.

2.1 #13: Use Theorem 2.4(c) to show that a fraction m / n can always be reduced to lowest terms.
Let (m, n) = d. Then (m / d) / (n / d) = m / n and m / d <= m, n / d <= n. So we have to show that m / d and n / d are the lowest possible terms.
Assume q, such that m / q < m / d and n / q < n / d. Then md < mq
d < q. Since q | m and q | n, by Theorem 2.3 q | d → q <= d, which is a contradiction.


Atheism and Evidence, Redux

In May I wrote "Atheism: It isn't about evidence". The gist was that the evidence for/against theism in general, and Christianity in particular, is the same for both theist and atheist. The difference is how brains process that evidence. I cited this article that said that people with Asperger's typically don't think teleologically. It also said that atheists think teleologically, but then suppress those thoughts.

Today, I came across the article "
Does Secularism Make People More Ethical?" The main thesis of the article is nonsense, but it does reference work by Catherine Caldwell-Harris of Boston University. Der Spiegel (The Mirror) said:

Boston University's Catherine Caldwell-Harris is researching the differences between the secular and religious minds. "Humans have two cognitive styles," the psychologist says. "One type finds deeper meaning in everything; even bad weather can be framed as fate. The other type is neurologically predisposed to be skeptical, and they don't put much weight in beliefs and agency detection."

Caldwell-Harris is currently testing her hypothesis through simple experiments. Test subjects watch a film in which triangles move about. One group experiences the film as a humanized drama, in which the larger triangles are attacking the smaller ones. The other group describes the scene mechanically, simply stating the manner in which the geometric shapes are moving. Those who do not anthropomorphize the triangles, she suspects, are unlikely to ascribe much importance to beliefs. "There have always been two cognitive comfort zones," she says, "but skeptics used to keep quiet in order to stay out of trouble."

This broadly agrees with the Scientific American article, although it isn't clear if the non-anthropomorphizing group is thinking teleologically, but then suppressing it (which is characteristic of atheists) or not seeing meaning at all (characteristic of those with Asperger's).

Caldwell-Harris' work buttresses the thesis of
Atheism: It isn't about evidence.

Too, her work is interesting from a perspective in artificial intelligence. One purpose of the Turing Test is to determine whether or not an artificial intelligence has achieved human-level capability. Her "triangle film" isn't dissimilar from a form of Turing Test since agency detection is a component of recognizing intelligence. If the movement of the triangles was truly random, then the non-anthropomorphizing group was correct in giving a mechanical interpretation to the scene. But if the filmmaker imbued the triangle film with meaning, then the anthropomorphizing group picked up a sign of intelligent agency which was missed by the other group.

I wrote her and asked about this. She has absolutely no reason to respond to my query, but I hope she will.

Finally, I have to mention that the Der Spiegel article cites researchers that claim that secularism will become the majority view in the west, which contradicts the sources in my blog post. On the one hand, it's a critical component of my argument. On the other hand, I just don't have time for more research into this right now.

Behold, The Power of Lisp

Nikodemus Siivola is crowd-sourcing SBCL development. One way to support him is through Lisp merchandise from CafePress. I looked at the coffee mugs with great desire but, ultimately, the Lisp logos just didn't resonate with me. So I asked my beautiful, talented daughter to design one for me. Since she starts her 2nd year of studies in graphic design in ten days, I figured it was worth a shot. I gave her a couple of images from Royalty Free Stock Photos as rough ideas of what I was thinking about, as well as the motif used by Captain Atom.

I was inordinately pleased with the result and have placed an order with
CafePress for a coffee mug with this "Atomic Lisp" logo.


Below the fold is another take on the logo.

Number Theory #1

I've started reading through An Introduction to Number Theory, by Harold Stark, and working the problems. My habit so far has been to go downstairs before bedtime, do some cardio, then open the text and work a problem or two, including the theorems proven in the text. I try to do them before seeing how they are done in the book. So far, I've been going to bed frustrated by my slowness to solve some of the problems. But sleeping on it must be doing some good, since inspiration has come in the morning. As I'm only in chapter one, this could prove to be a very long voyage. If I had to do this under deadline for a class, I'd be in trouble (although miscellaneous exercise 9 was trivial).

Misc. Ex. #7: Show that if
p n for all primes pn, then n is either a prime or a product of two primes.

If p is not prime, then it is a composite number of the form
f1 * f2 * … * fk. From the problem statement, f1 > n, therefore f1 * f1 * f1 > n. So if n is prime, it is the product of at most two primes, f1 and f2, where f1 <= f2.

Misc Ex. #8: Let
p and q be consecutive odd primes from the list 2, 3, 5, 7, …. Show that p + q has at least three, not necessarily unique, prime divisors. Example: 7 + 11 = 18 = 2 * 3 * 3.

p and q are odd primes, p = 2m + 1; q = 2n + 1. p < q m < n.
p + q = 2m + 1 + 2n + 1 = 2(m + n + 1).
So 2 is one divisor of
p + q.

m + n + 1 is even. Then m + n + 1 = 2r, and p + q = 2*2*r. Since the smallest possible p is 3, the smallest m is 1 and, likewise, the smallest n is 2; so the smallest m + n + 1 is 4. This shows r >= 2.

m + n + 1 is odd. For the theorem to be true, m + n + 1 must be composite. Assume it's the prime P'. Since m < n,
      m + m + 1 < m + n + 1 < n + n + 1
2m + 1 < m + n + 1 < 2n + 1
p < P' < q.
p and q are consecutive primes, so P' cannot be prime. Therefore, when m + n + 1 is odd it is composite.

Misc Ex. #9: Note that

     152 = 225, 352 = 1225, 852 = 7225, 1052 = 11025

(the underlined portions are for emphasis only). Find a rule for squaring an integer ending in 5 and prove that it works.

Let n = (m * 10) + 5. Then
      n2 = ((m * 10) + 5) * ((m * 10) + 5)
(10m * 10m) + 10m*5 + 10m*5 + 25
100m2 + 100m + 25
100m(m + 1) + 25

123452 = 100*1234*1235 + 25 = 152399000 + 25 = 152399025 = 123452

On to chapter 2.

C. S. Lewis: Evolutionary Hymn

C. S. Lewis wrote the following hymn to evolution on March, 4, 1954 in a letter to Dorothy Sayers. It can be sung to the tune "Angels from the Realms of Glory":

Lead us, Evolution, lead us
Up the future's endless stair;
Chop us, change us, prod us, weed us.
For stagnation is despair:
Groping, guessing, yet progressing,
Lead us nobody knows where.

Wrong or justice, joy or sorrow,
In the present what are they
while there's always jam-tomorrow,
While we tread the onward way?
Never knowing where we're going,
We can never go astray.

To whatever variation
Our posterity may turn
Hairy, squashy, or crustacean,
Bulbous-eyed or square of stern,
Tusked or toothless, mild or ruthless,
Towards that unknown god we yearn.

Ask not if it's god or devil,
Brethren, lest your words imply
Static norms of good and evil
(As in Plato) throned on high;
Such scholastic, inelastic,
Abstract yardsticks we deny.

Far too long have sages vainly
Glossed great Nature's simple text;
He who runs can read it plainly,
'Goodness = what comes next.'
By evolving, Life is solving
All the questions we perplexed.

On then! Value means survival-
Value. If our progeny
Spreads and spawns and licks each rival,
That will prove its deity
(Far from pleasant, by our present,
Standards, though it may well be).

Aside from being heretofore unaware of this poem, my reason for blogging is to note two of Lewis' observations about evolution which I will later use in another post. First, is Lewis' poetic description of evolution as an open-ended search. Second, is the linking of evolution and morality with the supposition that an open-ended search for reproductive success leads to an open-ended morality.

A Critic Raves!

Over at Vox Popoli, in the comments to the post Mailvox: A poem by Little Dick, at 8/2/11 9:21 AM, someone going by the nom de plume "Question" wrote:

My personal favorite here is wrf3, if you go to his blog that guy is crazy.

Maybe I should set up a tip jar.