Happy Leap Day everyone. We have a tradition of giving little gifts involving leaping things to each other to celebrate this day. I thought this post on Safari Ecology was kind of apt. So, if you really want to get into the spirit of leaping, then make like a lion and leap onto a wildebeest, wrestle it to the ground and well, then let it go because wildebeests are kind of fun. Wildebeest wrestling–not just fun but good for you.

*The Throne of the Crescent Moon* is the debut novel by Saladin Ahmed is a well told fantasy that takes its roots from the Middle Eastern world.

In addition to the Middle Eastern setting, Ahmed shakes up the typical fantasy tale by having the core characters be somewhere in their 60’s.

Doctor Adoulla Makhslood, “The last real ghul hunter in the great city of Dhamsawaat,” would really like to retire from having adventures and quietly drink cardamom tea (which sounds good.) However, events rapidly transpire to force the Doctor and his assistant, Raseed bas Raseed–a Dervish warrior sworn to a holy path, to face a dark sorcerer worse than any the Doctor has faced before.

To aid them in this, the Doctor recruits his two old friends Dawoud and Litaz. Dawoud is a mage whose spells draw upon his own life energy and Litaz (his wife) is a highly skilled alchemist.

The final member of their band is Zamia, a young Badawi tribeswoman who has been gifted with the ability to take a lions shape and whose band has been slain by the sorcerer.

In addition to the magical plot, there is political trouble brewing in the city as the mysterious Falcon Prince foments revolution against the cruel Kalif.

The story is pretty quickly paced and quite enjoyable to read. I had a good time reading it. If you like this tale then you will probably also enjoy The Desert of Souls.

The Coldest War by Ian Tregillis in audiobook form came out on January 17 and I snapped it right up. It is the first audiobook I have ever listened to but I didn’t want to wait until July when the book form comes out (although I’ll buy and read that also) before finding out what happens in this, the second book of the Milkweed triptych.

I don’t want to say anything spoilerish about the contents since the actual book form isn’t out and I’ll do a more thorough content review then. For now, let me say that I really really enjoyed it. It is a very worthy successor and isn’t just a middle volume, but moves the story along nicely. Here are a couple of lines that stood out as I listened (and I had some paper handy):

… like rose petals on a virgin’s grave.

… like music written by a spider.

Good job Ian!

It took me a month to listen to–14 hours, 7 minutes long. I discovered that I can’t put an audiobook on in the background like TV or music. I have to pay attention or I end up missing things and have to go back. So, that was interesting to find out about myself.

I really enjoyed the narrator–Kevin Pariseau. He has a very nice voice to listen to and did the various character voices well. He also did a really good job at pronouncing some of the longer German phrases–now I have an idea at a correct pronunciation for them. Ian included quite a lot of good scenic detail in the prose that worked well in this audio format.

*The God Engines* was an enjoyable fast paced novella by John Scalzi. It begins with the intriguing line, “It was time to whip the god.”

Scalzi has created a very interesting universe here. In it, starships are powered by the coercion of beings who are termed “gods.” These beings have been defeated by the “god” of the humans who operate the ships and provide all of the energy and motive force for the vessel.

The ships “god” is held captive within bonds of iron and by the collective faith of the crew in the power of their own god.

The pov character is Captain Tephe of the starship Righteous. Captain Tephe is somewhat conflicted but his faith is strong. There appears to be somewhat the same conflicts between officers and priests as between officers and political officers in the Soviet Union.

This was fairly different than Scalzi’s usual books–a darker tone in general, but well worth the read. It will be interesting if he returns to this universe at some point.

*Awakenings * is the very good debut novel by Edward Lazellari and is the first book of what promises to be a very fun and interesting series.

The story begins with Colby Dretch–a somewhat down on his luck PI who receives some visitors at his office. They want him to look for a boy. The case seems simple enough and Dretch doesn’t much care about any legalities and is quite willing to take their money. They want a little more than his word for loyalty and take his heart as a guarantee while leaving him “alive.” And, thus we are informed that we aren’t just in a PI story.

We are then introduced to Cal, a NY cop who quickly meets some thugs who aren’t quite the type you would normally see and Seth a stoner/”photographer” who is also jolted out of his normal life as his apartment is bombed and he is on the run. Both Cal and Seth share the trait that they don’t recall anything beyond thirteen years ago.

Lastly, we meet Daniel. Daniel is a thirteen year old boy with troubles at home and more at school. His stepfather is abusive and his adoptive mother spends most of her time in a haze of Valium. Daniel spends most of his time daydreaming and trying to avoid the wrath of his stepfather.

As the title implies, this volume of the story is about the awakenings these characters undergo as they realize their parts in the story to come. The reader is gradually introduced to where the characters come from and some of the things they need to be doing. I liked that the needs of their current lives weren’t just thrown aside or overlooked and the characters had a good amount of depth to them.

The book was nicely written and quickly pulled me along into the plot. I look forward to the next volume.

The paper “On computable numbers, with an application to the Entscheidungsproblem” by Alan Turing was published in 1936 and in addition to having a really cool title is a cornerstone piece of computational theory. Before we get to the paper, though, first we need to go over a a bit of background.

The Entscheidungsproblem was proposed by David Hilbert in 1928.

Hilbert asked if it was possible to create an algorithm that would take as input a statement in a formal language and answer whether that statement was true or false. In other words the algorithm would provide an answer as to the decidability of the inputted statement. Entscheidungs is German for decision and Hilbert was German himself, and so entscheidungsproblem was the term given to his question. This was all in parallel and partly in response to Russell and Whitehead’s work on the *Principia Mathematica* in the earlier part of the century. It appears that Hilbert believed that the answer to his question would be yes and set about trying to create a foundational system that would meet his requirements. This effort in mathematics was known as the Hilbert Programme.

The main goal of Hilbert’s program was to provide secure provable foundations for all of mathematics. Hilbert proposed the creation of a finite, complete set of axioms, and provide a proof that these axioms were consistent. Hilbert then further proposed that the consistency of more complicated systems could be proven in terms of these simpler systems. The basic steps for doing this would include:

- There would need to be formalization system for all of mathematics. Every mathematical statements should be able to be written in this formal language. This formal language would need to be able to be manipulated according to well defined rules. (No step such as–“and then something magic happens.”)
- Completeness: There would need to be a proof that all true mathematical statements can be proven in the formal system.
- Consistency: The formal system would need to be consistent with itself. This means that there would need to be a proof that no contradiction can be obtained in the formal system of mathematics.
- Conservation: There would need to be a proof that any result about “real objects” obtained using reasoning about “ideal objects” (such as uncountable sets) can be proven without having to use ideal objects to obtain the proof.
- Decidability: This gets to the well established rules. To satisfy this requirement there should be an algorithm for deciding the truth or falsity of any mathematical statement within the formal system.

In 1931, Kurt Gödel produced the paper “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I”, Monatshefte für Mathematik und Physik, 38: 173–198. Here’s a link to an english translation–On formally undecidable propositions of Principia

Mathematica and related systems. This is another truly amazing paper and I may do a whole post about it sometime. For now, lets just summarize and say that it deals with points 1 – 4 above. Basically, Gödel showed that in any system of mathematics sufficiently powerful to describe itself it was possible to create propositions that were inherently contradictory. The propositions may be thought of as being of the form “This statement is false.” In particular, Gödel used a very clever technique to encode propositions in a formal language into numbers. These numbers are called Gödel numbers. Gödel didn’t, however, say anything about the decidability question. That (finally) brings us to Turing in 1936.

Continue reading »