Michael Graham Richard

Euler on the left and Diderot on the right.

False Stories With True Lessons
It has been pointed out to me that the story about Pythagoras and Hippasus that I wrote about in my previous post was probably not historically accurate. I certainly hope so for Hippasus… Though the events might never have happened, the moral of the story is true, and you should be careful to keep “truth” as your ultimate goal instead of “being right”.

Leonhard Euler vs. Denis Diderot
There is another fictional anecdote that teachers us a similar lesson: The apocryphal encounter between Leonhard Euler and Denis Diderot.

The French philosopher Denis Diderot was visiting Russia on Catherine the Great’s invitation. However, the Empress was alarmed that the philosopher’s arguments for atheism were influencing members of her court, and so Euler was asked to confront the Frenchman. Diderot was later informed that a learned mathematician had produced a proof of the existence of God: he agreed to view the proof as it was presented in court. Euler appeared, advanced toward Diderot, and in a tone of perfect conviction announced, “Sir, (a+b^n)/n = x, hence God exists—reply!”. Diderot, to whom (says the story) all mathematics was gibberish, stood dumbstruck as peals of laughter erupted from the court. Embarrassed, he asked to leave Russia, a request that was graciously granted by the Empress.

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If anyone who reads this is part of academia and is frustrated by how conservative his chosen field is (”Science advances one funeral at a time”), this story should make you appreciate more the current scientific climate.

From Fermat’s Last Theorem by Simon Singh:

One story claims that a young student by the name of Hippasus was idly toying with the number √2, attempting to find the equivalent fraction. Eventually he came to realize that no such fraction existed, i.e. that √2 is an irrational number. Hippasus must have been overjoyed by his discovery, but his master was not. Pythagoras had defined the universe in terms of rational numbers, and the existence of irrational numbers brought his ideal into question. The consequence of Hippasus’ insight should have been a period of discussion and contemplation during which Pythagoras ought to have come to terms with this new source of numbers. However, Pythagoras was unwilling to accept that he was wrong, but at the same time he was unable to destroy Hippasus’ argument by the power of logic. To his eternal shame he sentenced Hippasus to death by drowning.

The ability to change our minds when presented with evidence that disproves our beliefs - even our most entrenched ones - is a hard habit to acquire, but it is extremely valuable. When you start doubting, don’t turn away. Look into the light until your eyes adjust, and see if there is something there.

As P. C. Hodgell said: “That which can be destroyed by the truth should be.” See the Twelve Virtues of Rationality by Eliezer Yudkowsky.

See also: Untangling the Search for Social Status from the Search for Truth

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Often while looking at random flora and fauna (including humans), I marvel at evolution’s work. To think that all these intricate living systems have evolved without conscious design. The more I learn about biology, the more amazing it seems!

But then, I have to remember that I am an evolved creature myself, and my species has not evolved to be able to easily grasp the levels of complexity involved with the evolution of biological lifeforms (long time scales, interactions of complex systems, etc).

The primeval savanna where selection pressure formed my brain had no need for this; it’s just a lucky side-effect that I’m now able to think about it at all, and in the grand scheme of things, my understanding is superficial and forced. I can’t simply hold all the elements in my head and run simulations in the way that I can effortlessly know where a falling baseball is going to hit the ground. To my limited mind, on some level, it all seems almost impossibly complex, even if I know more abstractly how it happened. It’s like trying to visualize large numbers. You know what a trillion is in the abstract, but you don’t really grasp it.

But that fact says as much about me, about us, as about the phenomenon itself. A higher intelligence (an AI that could hold a whole planet’s worth of quarks in its mind, for example) might not find life (or other complex phenomena) so special. Its reaction might be more like “duh”.

a new study from MIT cognitive neuroscientists [has] shown that given the right setting, the human brain can record an amazing amount of information.

In the study, the results of which could have implications for artificial intelligence and for understanding memory disorders, people viewed thousands of objects over five hours. Remarkably, afterward they were able to remember each object in great detail. [...]

The new results suggest that visual capacity is several orders of magnitude higher than the older study implied. “If you encode a lot of detail for each object, you need a lot more space,” Alvarez said.

Earlier studies had shown that people could remember a lot, but it was assumed that we did it by remembering abstract descriptions without too much details. In this study, people not only remembered thousands of images (success rate of around 90% after seeing each image for 3 seconds), but also many details about them (a kitchen cabinet with the door ajar, a glass of water 2/3 full, etc) and could pick the one they had seen before when also shown a slightly altered version.

According to the researchers, two things helped people perform better: Telling them to actively try to remember details, and showing them familiar objects (a remote control, not abstract art).

The former probably just further confirms our intuition that we remember better when we make a conscious effort, and the latter probably means that we don’t make a completely new memory when we can reuse the invariable parts of already existing concepts. In other words, it seems like memory is modular, making it easier to put a pointer to an existing module for “chair” with extra information for “what type of chair”, “what color”, “seen from what angle”, etc, than to create a whole new memory from scratch (for an abstract painting).

It’s the same reason why it’s much easier to remember what someone said in a language that you understand than in a language that you don’t. In one instance, you just create modules pointing to already existing modules for words and concepts. This is further simplified because we have evolved brain-hardware to make processing language easier (the equivalent of a DSP chip in electronics?). In the case of a foreign language, you’d have to create many more modules to try to remember phonetically all the sounds you heard in the right order, a task for which we don’t seem to have dedicated brain-hardware.

I’m just speculating based on my limited knowledge of cognitive science. I’m sure a lot more is known about the above, and I’m looking forward to reading about it in the neuroscience books in my “to read” pile.

These results establish a new bound on the size of human memory, and give credence to artificial intelligence approaches that depend primarily on a large memory capacity.

This certainly has big implications for those who try to create AI by modeling the human brain. Probably not as much for those who are attempting to design AI from scratch because they have a much larger possible design-space.

Source: MIT News

Google has launched a free and open source web browser, Google Chrome. I haven’t had a chance to try it yet (Mac version should be coming soon), but if it works as advertised, it should be pretty good. It has many interesting features that I hope other browsers will copy quickly.

But what I found most interesting about the launch is the 39-page comic book that was released simultaneously. The words are by the Google engineers that worked on Chrome, and the images are by Scott McCloud. It does a very good job of explaining the browser’s features and architecture to both a technical and non-technical public (though they’re obviously targeting early adopters and not grandmas).

This might actually be one of Google Chrome’s biggest innovations.

The comic book will no doubt be read by more people than standard product documentation, and those who read it have a lot more chances of understanding why Chrome’s new features are worth checking out (who else is getting non-programmers to read about the fine points of HTML rendering engines and memory allocation?). By grabbing more early adopters, Google will probably generate more buzz and increase adoption rate. Even the non-tech traditional media will probably have more accurate stories about the browser, with better narratives and less PR-speak. Very smart. It’s a bit like Apple’s product demos, except that you don’t even need to ask the media to gather in a big room. And more intangibly, it really helps the branding of this product by creating a good first impression.