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On Intelligence” fulfills Jeff Hawkins‘ dream to encapsulate a basic theory of intelligence in a straightforward plainly written book. Written with science writer Sandra Blakeslee, “On Intelligence” combines Mr Hawkins’ motivational autobiography, a review of natural and artificial intelligence, and a philosophical discussion delivered in a no-nonsense, unembellished, yet stimulating narrative.

At its core, “On Intelligence” postulates that all higher cognitive functions are built on a single relatively simple algorithm replicated across the neocortex. This hypothetic “basic cortical algorithm” is described as a predictive autoassociative hierarchical network. Left to its own devices, such a neural network should spontaneously generate stable invariant representations of regularities in the environment giving birth to perception, behavior, thoughts, consciousness, and imagination. If we could only mimic Nature and build such a network in silicon, we should be able to make computers that learn, think, and imagine. Mr Hawkins admits that most of these ideas are not original and his contribution is to organize them into a coherent hypothetical framework.

How credible is Mr Hawkins’ hypothesis? How do we know the brain does this? How do we know that such an artificial model would exhibit animal-like intelligence? Mr Hawkins’ answer is: be optimistic — we are way overdue for some kind of a general theory of the brain. In a break from scientific form, Mr Hawkins does not seek out contradictory evidence. The autobiographical sections carry an air of a quixotic struggle against the errors and prejudices of the scientific and corporate establishments of the past and present, who lack the audacity to imagine that a comprehensive theory of intelligence could be within reach. In its more technical sections, the book identifies specific cortical structures responsible for these computations in rather computational than biological terms. No experimental evidence and no working computer models are described or reviewed critically. Instead, the key premises derive from introspection and personal interviews with authorities on the subject, e.g. “I had spoken to several … experts and asked them to explain…” Mr Hawkins mixes experimentally supported findings with speculation and swiftly decides standing controversies without identifying them as such, leaving a casual reader with an exaggerated impression of how much is understood about cognition. In this way, the book often reads rather like marketing material for a specific approach than a thoroughly researched thesis presenting latest scientific findings.

Every neuroscientist strives to intuit a fundamental principle behind the ocean of facts about the nervous system and every computer scientists dreams of creating systems that could develop intelligence. Yet Nature is slow to give up its recipes. By helping envision what the answers could be, “On Intelligence” stands to inspire the budding scientist and engineer with the confidence to probe into the most daunting natural phenomenon that is intelligence. And it is for its enthusiasm and inspiration that “On Intelligence” earns my four stars.

“How Round Is Your Circle” by John Bryant and Chris Sanguin has been delighting my mathematical senses for two nights straight with a collection of counterintuitive, paradoxical, and insightful geometrical toys. Try this: What three-dimensional shape has the same width in all directions (other than a sphere)? My most mathematically-minded friends could not believe that such a thing could exist. Turns out there are many of them.

The authors have created a website illustrating some of the objects from the book, but the book has many more.

There seems to be a category of problems that most people get wrong when they first hear or see them. It takes a second deeper look to get the right answer. Here are a few examples that come to mind:

  1. When the Space Shuttle transfers from a higher orbit into a lower orbit, it fires its engines in reverse to slow down twice on opposite sides of the planet. Will the shuttle be moving faster or slower at the end of the maneuver? (faster)
  2. During descent, commercial airplanes often raise spoilers on top of their wings to increase drag and reduce lift so that they can steepen their approach. Will the airplane slow down or speed up as the result? (speed up)
  3. As the ice melts in Antarctica and Greenland, ocean levels rise across the globe. Will the average ocean depth increase or decrease as the ocean levels rise? (probably decrease)

To illustrate this last problem, can you imagine a bowl that has the following wonderful property: as you add more soup to it, the average depth of the soup in the bowl stays constant? Magic? Not really? I have just whipped up just such a bowl in Matlab:

Once you fill the initial cylindrical portion with water, adding more water will leave the average water depth in the bowl the same: h0. The Great Salt Lake probably has this property: as it gets more water, it gets shallower (on average).