A rare Sumatran tiger was shot and killed by the
head of a Florida zoo

post from The Surging Waves on 24 August 2006 11:37:00 PM. © The Surging Waves

Rare Sumatran tiger killed at Florida zoo A rare Sumatran tiger was shot and killed by the head of a Florida zoo after it escaped from its cage and charged at a veterinarian, zoo officials said.

Enshala, a 180-pound (81 kg) female tiger, was being put into her night house when she slipped past an unlocked latch and headed toward a public area on Tuesday. A veterinarian shot Enshala with a tranquilizer dart but she then charged at him, and zoo president Lex Salisbury killed her with a shotgun.

"I feel sick to my stomach," Salisbury, head of the Lowry Park Zoo in Tampa, told the St. Petersburg Times. He said he felt he had to shoot to protect the veterinarian.

Sumatran tigers are found in the wild only on the Indonesian island of Sumatra, where fewer than 500 remain, according to the World Wildlife Federation.

image : ©wildanimalpark.co.uk

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Open Access Education Materials

post from Curious Cat Science and Engineering Blog on 24 August 2006 11:23:00 PM. © Curious Cat Science and Engineering Blog

Watch a video of Richard Baraniuk (Rice University professor speaking at TED) discussing Connexions: an open-access education publishing system. The content available through Connexions includes short content modules such as:What is Engineering??:Engineering is the endeavor that creates, maintains, develops, and applies technology for societies’ needs and desires.…One of the first distinctions that must be [...]

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Scientific Innovation and Economic Growth

post from Curious Cat Science and Engineering Blog on 24 August 2006 10:19:00 PM. © Curious Cat Science and Engineering Blog

Reform, Innovation, and Economic Growth by President Levin, Yale University president, speaking at the University of Tokyo:Performance scores in mathematics, problem solving, science, and reading for Japanese students are significantly ahead of their peers elsewhere; and the Japanese public and private financial commitment to education is also among the strongest. Taken together, the result has [...]

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ic-growth/

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Now Behe puts D. James Kennedy at arms length

post from Pharyngula on 24 August 2006 10:17:31 PM. © Pharyngula

Darwin's Deadly Legacy, the program that Coral Ridge Ministries is airing this weekend that supposedly links Hitler to Darwin, is beginning to look like a public relations catastrophe for the organization. First Francis Collins repudiated the show, then the ADL put the hammer down, and now another of the "featured guests" is distancing himself from the content. Andrew Arensburger wrote to Michael Behe to find out about his contribution, and got this reply:

I'm "associated" with it only in the sense that a clip of my appearance on a TV show of Dr. Kennedy's from years ago apparently is used in the film. I didn't know this program was in the works, have had no conversations with anyone from Coral Ridge about it, and had no input into it.

This looks more and more like a pastiche of generic creationist interviews slapped together to prop up a weak thesis.

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Topological Spaces

post from Good Math, Bad Math on 24 August 2006 09:20:32 PM. © Good Math, Bad Math

Yesterday, I introduced the idea of a metric space, and then used it to define open and closed sets in the space. (And of course, being a bozo, I managed to include a typo that made the definition of open sets equivalent to the definition of closed sets. It's been corrected, but if you're not familiar with this stuff, you might want to go back and take a look at the corrected version. It's just replacing a ≤ with a <, but that makes a big difference in meaning!)

Today I'm going to explain what a topological space is, and what continuity means in topology. (For another take on continuity, head on over to Antopology where Ofer has posted his explanation.)

A topological space is a set X and a collection T of subsets of X, where the following conditions hold:

∅ ∈ T and X ∈ *T.
∀ C ∈ ℘(T); : ∪(c ∈ C) ∈ T. (That is, the union of any collection of subsets of T is an element of T. )
∀ s, t ∈ T : s ∩ t ∈ T. *(The intersection of any two subsets of T is also in T.)

The collection T is called a topology on T. The members of T are the open sets of the topology. The closed sets are the set complements of the members of T. Finally, the elements of the topological space X are called points.

The connection to metric spaces should be pretty obvious. The way we built up open and closed sets over a metric space can be used to produce topologies. The properties we worked out for the open and closed sets are exactly the properties that are required of the open and closed sets of the topology. There are many ways to build a topology other than starting with a metric space, but that's definitely the easiest way.

One of the most important ideas in topology is the notion of continuity. In some sense, it's the fundamental abstraction of topology. We can now define it.

A function from topological space X to topological space U is continuous if/f for every open sets C ∈ T the inverse image of f on C is an open set. The inverse image is the set of points x in X where f(x) ∈ C.

That's a bit difficult to grasp. What it's really capturing is that there are no gaps in the function. If there were a gap, then the open spaces would no longer be open. Think of the metric spaces idea of open sets. Imagine an open set with a cube cut out of the middle. It's definitely not continuous. If you took a function on that open set, and its inverse image was the set with the cube cut out, then the function is not smoothly mapping from the open set to the other topological space. It's mapping part of the open set, leaving a big ugly gap.

Now, here's were it gets kind of nifty. The set of of topological spaces and continuous functions form a category. with the spaces as objects and the functions as morphisms. We call this category Top. It's often easiest to talk about topological spaces using the constructs of category theory.

So, for example, one of the most important ideas in topology is homeomorphism. A homeomorphism is a bicontinuous bijection (a bicontinuous function is a continuous function with a continuous inverse; a bijection is a bidirectional total function between sets.) A homeomorphism between topological spaces is a homomorphism in Top.

From the perspective of topology, any two topological spaces with a homeomorphism between them are identical. (Which ends up corresponding exactly to how we defined the idea of equality in category theory.)

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Sparrow convention

post from Ponderfodder - Because Great Minds Discuss Ideas | Community Blog on 24 August 2006 08:52:34 PM. © Ponderfodder - Because Great Minds Discuss Ideas | Community Blog

Further Details:

I have noticed that every August, hundreds of sparrows in my neighbourhood congregate in a half doze

...

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Warming up 1 Millon Gallons of Water Daily to
76°C

post from CR4 on 24 August 2006 08:37:00 PM. © CR4

Escalante writes: For effects of laundry, we took 1 millon daily of gallons of water of the subsoil (27°C) and we warmed up to (76°C) in a cycle of 24 hours we give it back to the subsoil already treated about (35°C). we used natural gas 20MMBTUS at the moment. We see an improvement opportunity,...

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Church Numerals Rerun

post from Good Math, Bad Math on 24 August 2006 07:33:54 PM. © Good Math, Bad Math

So, now, time to move on to doing interesting stuff with lambda calculus. Tostart with, for convenience, I'll introduce a bit of syntactic sugar to let usname functions. This will make things easier to read as we get to complicatedstuff.

To introduce a global function (that is a function that we'll use throughout our lambda calculus introduction without including its declaration in every expression), we'll use a definition like the following:

square ≡ λ x . x × x

This declares a function named "square", whose definition is "λ x . x×x". If we had an expression "square 4", the definition above means that it would effectively be treated as if the expression were: "(λ square . square 4)(λ x . x×x)".

In some of the examples, I used numbers and arithmetic operations. But numbers don't really exist in lambda calculus; all we really have are functions! So we need to invent some way of creating numbers using functions. Fortunately, Alonzo Church, the genius who invented the lambda calculus worked out how to do that. His version of numbers-as-functions are called Church Numerals.

In Church numerals, all numbers are functions with two parameters:

Zero ≡ λ s z . z
One ≡ λ s z . s z
Two ≡ λ s z . s (s z)
Three ≡ λ s z . s (s (s z))
Any natural number "n", is represented by a Church numeral which is a function which applies its first parameter to its second parameter "n" times.

A good way of understanding this is to think of "z" as being a a name for a zero-value, and "s" as a name for a successor function. So zero is a function which just returns the "0" value; one is a function which applies the successor function once to zero; two is a function which applies successor to the successor of zero, etc. It's just the Peano arithmetic definition of numbers transformed into lambda calculus.

But the really cool thing is what comes next. If we want to do addition, x + y, we need to write a function with four parameters; the two numbers to add; and the "s" and "z" values we want in the resulting number:

add ≡ λ s z x y . x s (y s z)

Let's curry that, to separate the two things that are going on. First, it's taking two parameters which are the two values we need to add; second, it needs to normalize things so that the two values being added end up sharing the same binding of the zero and successor values.

add_curry ≡ λ x y. (λ s z . (x s (y s z)))

Look at that for a moment; what that says is, to add x and y: create the church numeral "y" using the parameters "s" and "z". Then apply x to that new church numeral y. That is: a number is a function which adds itself to another number.

Let's look a tad closer, and run through the evaluation of 2 + 3:

add_curry (λ s z . s (s z)) (λ s z . s (s (s z)))

To make things easier, let's alpha 2 and 3, so that "2" uses "s2" and "z2", and 3 uses "s3" and "z3";

add_curry (λ s2 z2 . s2 (s2 z2)) (λ s3 z3 . s3 (s3 (s3 z3)))

Now, let's do replace "add_curry" with its definition:

(λ x y .(λ s z. (x s y s z))) (λ s2 z2 . s2 (s2 z2)) (λ s3 z3 . s3 (s3 (s3 z3)))

Now, let's do a beta on add:

λ s z . (λ s2 z2 . s2 (s2 z2)) s (λ s3 z3 . s3 (s3 (s3 z3)) s z)

And now let's beta the church numeral for three. This basically just "normalizes" three: it replaces the successor and zero function in the definition of three with the successor and zero functions from the parameters to add.

λ s z . (λ s2 z2 . s2 (s2 z2)) s (s (s (s z)))

Now.. Here comes the really neat part. Beta again, this time on the lambda for two. Look at what we're going to be doing here: two is a function which takes two parameters: a successor function, and zero function. To add two and three, we're using the successor function from add function; and we're using the result of evaluating three as the value of the zero! for two:

λ s z . s (s (s (s (s z))))

And we have our result: the church numeral for five!

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The Politically Incorrect Guide to Darwinism and
Intelligent Design: Chapter 3: Simply incorrect embryology

This article is part of a series of critiques of Jonathan Wells' The Politically Incorrect Guide to Darwinism and Intelligent Design that will be appearing at the Panda's Thumb over the course of the next week or so. Previously, I'd dissected the summary of chapter 3. This is a longer criticism of the whole of the chapter, which is purportedly a critique of evo-devo.

Jonathan Wells is a titular developmental biologist, so you'd expect he'd at least get something right in his chapter on development and evolution in The Politically Incorrect Guide to Darwinism and Intelligent Design, but no: he instead uses his nominal knowledge of a complex field to muddle up the issues and misuse the data to generate a spurious impression of a science that is unaware of basic issues. He ping-pongs back and forth in a remarkably incoherent fashion, but that incoherence is central to his argument: he wants to leave the reader so baffled about the facts of embryology that they'll throw up their hands and decide development is all wrong.

Do not be misled. The state of Jonathan Wells' brain is in no way the state of the modern fields of molecular genetics, developmental biology, and evo-devo.

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Watching televangelists makes you fat

Religious shepherds need to keep better watch over their flocks and add activities to keep from fattening them up, says a Purdue University researcher who has found that some religious activities may promote obesity.

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