You get at the degree to which all human knowledge is limited by the central nervous system that humans possess. There must be some finite number of axons and dendrites that can be stuffed into the cranium of a human, and even if there is a sophisticated system of compression and/or multiplexing in use, we can probably assume that a finite amount of axons and dendrites can only carry a finite amount of information.
Thinking of the physical limits on human knowledge leads to a model of knowing that puts the central nervous system at the center of our our experience of the universe. There may be an absolute reality that exists outside of us, but since all of us are human (I assume) we must admit that our knowledge of that absolute reality will forever be shaped by that central nervous system.
The limits of the central nervous system cause humans to look for models of reality that fit well with those limits. For instance, there is The Magical Number Seven, Plus or Minus Two:
Because of the (very very finite) limits on working memory, the human mind leans heavily on heuristics that allow simple models to stand in for the complexity of reality. No human being could easily work with a physics model that had 1 million variables: therefore we tend to look for models that have a handful of variables, yet still give us reasonably good estimates.
Just yesterday there was posted to Hacker News an article about a slinky, and that article contains a good demonstration of the kind of simplifying assumptions we often make to reason about problems that are too complex to approach directly:
"I decided to idealize the problem like this: the slinky is an ideal spring with mass distributed uniformly throughout. It is also a spring that can pass through itself. These assumptions make analyzing the problem easier."
And of course, we often present students with problems where the difficulty of achieving perfect measurements of variables is simply assumed away. For instance in this exercise:
The important things to measure are: force, deflection, torque, moment of inertia, stress and strain. Often, in real life situations, engineers have no way to perfectly measure these things. Large engineering projects proceed with various methods for getting reasonable estimates: known upper and lower bounds, prototypes, isolated testing of particular connections, etc.
The smartest people alive never get to the point where they really know reality, they only know estimates. I do not mean to make this point overly philosophical, I am talking about practicalities here: there may be an absolute reality that we can know directly, but when it comes to doing anything useful, we develop estimates using fairly simple models, models which are well suited to the limits of our minds.
In some sense, the models we build about the world are always simplified models that make it easier for our limited central nervous systems to make estimates about the world.
I just offered a physics examples of simplifying assumptions, but I could also focus on the humanities. Perhaps your life's goal is to figure out the "real" reasons why the French Revolution happened, or why Communism was so popular for so long, or why the Industrial Revolution happened -- the possibilities are as limitless as the combination of all the variables in action over the course of centuries, the psychology and biology of billions of people, and the technology that existed at the time, and the weather and the crops and the economy and the religions and the amount of sunlight reaching the earth and everything else, combining exponentially to some very large sum. You might research the issue for 40 years, but in the end, if you want to draw some useful conclusion, something that others can benefit from, something that might influence policymakers in the future, you will need to come up with a simplified model that focuses on the handful of variables that you regard as the most important.
There is another model of knowing, which takes for granted the absolute reality outside of us. That model is well summarized by this XKCD comic:
In that model, biology is a sub-branch of physics, which is a sub-branch of math. However, if you focus on the limits of the central nervous system as the practical limit of human knowing, then you end up with a model where physics and math (and everything else) is a sub-branch of biology, specifically, a sub-branch of neurology. Even the two models of human knowing that I describe in this post to Hacker News can be thought of as sub-branches of neurology. All human knowing is, in some sense, a clever hack of our neurology, and certainly all heuristics and models are hacks which adapt to the limits of that neurology.
There is nothing wrong with simple models, so long as they allow us to get useful work done. But I think our reliance on simple models tells us why specialization is so important. If a person can study a subject for 40 years and, having read tens of thousands of documents, still distills the data down to a small handful of variables, a model that gracefully adapts to the limits of the human mind, then we must admit that it is the rare human being who goes much beyond simple models. In those cases where simple models don't work, and where there only thing that works is a model with hundreds or thousands of variables, then clearly, achieving an understanding of such models must surely be the work of a lifetime. You need to get to studying when you are 20, and you need to specialize, because when you are 50 you will still be only approaching the ideal, never quite there, only approaching it, still learning more.
> You get at the degree to which all human knowledge is limited by the central nervous system that humans possess.
I think that our current revolution, the Internet and computers in general, is allowing us to overcome these limits.
The question is how to integrate them better, how to improve the link between humans and computers, and how to improve our own cognition in the most natural, most human way to get the most out of the whole of human knowledge that is now available everywhere.
Don't forget writing. Before writing (in some form or another), humans just had to remember things. Writing allowed them to recall things over a much greater period of time, as well as share them.
I don't think the question is about how much we can store in our brains, but rather how much we can cram in there within a lifetime. I think we'll always reach death before we fill our brains. Of course, if we ever reach a true singularity, transfer our consciousnesses into robots, and live forever, the one question becomes the other.
Thinking of the physical limits on human knowledge leads to a model of knowing that puts the central nervous system at the center of our our experience of the universe. There may be an absolute reality that exists outside of us, but since all of us are human (I assume) we must admit that our knowledge of that absolute reality will forever be shaped by that central nervous system.
The limits of the central nervous system cause humans to look for models of reality that fit well with those limits. For instance, there is The Magical Number Seven, Plus or Minus Two:
http://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_...
Because of the (very very finite) limits on working memory, the human mind leans heavily on heuristics that allow simple models to stand in for the complexity of reality. No human being could easily work with a physics model that had 1 million variables: therefore we tend to look for models that have a handful of variables, yet still give us reasonably good estimates.
Just yesterday there was posted to Hacker News an article about a slinky, and that article contains a good demonstration of the kind of simplifying assumptions we often make to reason about problems that are too complex to approach directly:
"I decided to idealize the problem like this: the slinky is an ideal spring with mass distributed uniformly throughout. It is also a spring that can pass through itself. These assumptions make analyzing the problem easier."
And of course, we often present students with problems where the difficulty of achieving perfect measurements of variables is simply assumed away. For instance in this exercise:
http://www.uta.edu/ce/nsf/ret/docs/lesson-plans/reynolds08-5...
The important things to measure are: force, deflection, torque, moment of inertia, stress and strain. Often, in real life situations, engineers have no way to perfectly measure these things. Large engineering projects proceed with various methods for getting reasonable estimates: known upper and lower bounds, prototypes, isolated testing of particular connections, etc.
The smartest people alive never get to the point where they really know reality, they only know estimates. I do not mean to make this point overly philosophical, I am talking about practicalities here: there may be an absolute reality that we can know directly, but when it comes to doing anything useful, we develop estimates using fairly simple models, models which are well suited to the limits of our minds.
In some sense, the models we build about the world are always simplified models that make it easier for our limited central nervous systems to make estimates about the world.
I just offered a physics examples of simplifying assumptions, but I could also focus on the humanities. Perhaps your life's goal is to figure out the "real" reasons why the French Revolution happened, or why Communism was so popular for so long, or why the Industrial Revolution happened -- the possibilities are as limitless as the combination of all the variables in action over the course of centuries, the psychology and biology of billions of people, and the technology that existed at the time, and the weather and the crops and the economy and the religions and the amount of sunlight reaching the earth and everything else, combining exponentially to some very large sum. You might research the issue for 40 years, but in the end, if you want to draw some useful conclusion, something that others can benefit from, something that might influence policymakers in the future, you will need to come up with a simplified model that focuses on the handful of variables that you regard as the most important.
There is another model of knowing, which takes for granted the absolute reality outside of us. That model is well summarized by this XKCD comic:
http://xkcd.com/435/
In that model, biology is a sub-branch of physics, which is a sub-branch of math. However, if you focus on the limits of the central nervous system as the practical limit of human knowing, then you end up with a model where physics and math (and everything else) is a sub-branch of biology, specifically, a sub-branch of neurology. Even the two models of human knowing that I describe in this post to Hacker News can be thought of as sub-branches of neurology. All human knowing is, in some sense, a clever hack of our neurology, and certainly all heuristics and models are hacks which adapt to the limits of that neurology.
There is nothing wrong with simple models, so long as they allow us to get useful work done. But I think our reliance on simple models tells us why specialization is so important. If a person can study a subject for 40 years and, having read tens of thousands of documents, still distills the data down to a small handful of variables, a model that gracefully adapts to the limits of the human mind, then we must admit that it is the rare human being who goes much beyond simple models. In those cases where simple models don't work, and where there only thing that works is a model with hundreds or thousands of variables, then clearly, achieving an understanding of such models must surely be the work of a lifetime. You need to get to studying when you are 20, and you need to specialize, because when you are 50 you will still be only approaching the ideal, never quite there, only approaching it, still learning more.