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There's a lot of good in his response, but I do take issue with two of the concepts: > How do we get on the order of 100 trillion connections > in the

There's a lot of good in his response, but I do take issue with two of the concepts: > How do we get on the order of 100 trillion connections > in the brain from only tens of millions of bytes of > design information? Obviously, the answer is through > redundancy. No. That's called algorithmically generated complexity. It's where the function generates data that's more complex than the function itself, because the function (DNA in this case) is fitted explicitly to match that output. This isn't a complicated idea; stop avoiding the issue. The brain is complicated. > Combining human-level pattern recognition with the inherent > speed and accuracy of computers will be very powerful. No kidding. If we had 'human level pattern recognition' this whole thing would be a lot easier wouldn't it? ...but that doesn't just magically appear from no where. The reality is that most progress follows a log normal curve (http://en.wikipedia.org/wiki/File:Lognormal_distribution_CDF.svg http://en.wikipedia.org/wiki/File:Lognormal_distribution_CDF...); it starts linear, and ends flat. Some times it starts flat, looks like its going exponential and then goes flat... but it always ends up flat. The trick is, does the singularity happen after we hit the flat curve (which means it's going to be some nebulous time in the future that may never arrive) or does it happen while we're still on the 'exponential acceleration' curve (which means it may happen in-this-lifetime). I don't see us on an exponential increase path for cpu power, cost reduction or algorithmic strength at the moment. If anything I see us as passed the main hump of growth and into the 'slowdown' phase for all of these. So, I'm dubious of this rebuttal, which is basically endorsing the stupid 'growth for ever! exponential growth! yay! growth!' idea. -_-

Peaker 14y ago
If you use a Kolmogorov measure of complexity, the complexity of a function and/or its output is defined to be the description of that function using some universal language. So a function cannot, by definition, generate data that is more complex than the function itself. Pi can be described by a relatively small formula/function. It can generate very long sequences of seemingly random digits. The complexity in all of those infinity digits is still just that of the simplest formula that generates Pi.
- shadowmint 14y ago
  Poor phrasing on my part. Pi is a great example. The full length of Pi cannot be compressed using traditional means into the same number of bytes that the algorithm that generates Pi can exist in. The point is that a function can generate a dataset that is complex, without redundant information in the data. A dataset that cannot be reduced to a smaller dataset. The idea that a complex function can only generate a simple data set with 'high redundancy' is obviously nonsense. My point being that the OP is suggesting the DNA that is the functional generator for the brain generates highly redundant physical structures because there is a limited amount of information in the functional generator (DNA). While the DNA may generate redundant or repeated structures, it does so (if it does) because of the function. Not because of the information density of the DNA. As your example of Pi shows, a trivial information density can generate complex datasets without repetition.
  - Peaker 14y ago
    I don't think your argument about "traditional means of compression" holds. The existence of redundant data can be proven by the ability to store the same information with less data. Pi's information density is in fact no larger than the small function that generates Pi's digits -- even if traditional compressors fail to identify it.

Peaker 14y ago

If you use a Kolmogorov measure of complexity, the complexity of a function and/or its output is defined to be the description of that function using some universal language. So a function cannot, by definition, generate data that is more complex than the function itself. Pi can be described by a relatively small formula/function. It can generate very long sequences of seemingly random digits. The complexity in all of those infinity digits is still just that of the simplest formula that generates Pi.

shadowmint 14y ago
Poor phrasing on my part. Pi is a great example. The full length of Pi cannot be compressed using traditional means into the same number of bytes that the algorithm that generates Pi can exist in. The point is that a function can generate a dataset that is complex, without redundant information in the data. A dataset that cannot be reduced to a smaller dataset. The idea that a complex function can only generate a simple data set with 'high redundancy' is obviously nonsense. My point being that the OP is suggesting the DNA that is the functional generator for the brain generates highly redundant physical structures because there is a limited amount of information in the functional generator (DNA). While the DNA may generate redundant or repeated structures, it does so (if it does) because of the function. Not because of the information density of the DNA. As your example of Pi shows, a trivial information density can generate complex datasets without repetition.
- Peaker 14y ago
  I don't think your argument about "traditional means of compression" holds. The existence of redundant data can be proven by the ability to store the same information with less data. Pi's information density is in fact no larger than the small function that generates Pi's digits -- even if traditional compressors fail to identify it.