The Sphere of Knowledge

The more we know, the more we come to see how little we know. I expect this is true in all areas of deep study. Years ago, I came across a wonderful analogy, “the sphere if knowledge,” that I think explains it best. (If you know who came up with this, please let me know so I can acknowledge the source.)

The Sphere of Knowledge.

Imagine a space in which everything you know is packed into the shape of a sphere and everything you don’t know is outside of that. As you pack more and more knowledge into it, your sphere of knowledge grows bigger and bigger. From deep within your sphere, you are surrounded by things you know. The outside edge of your sphere is where you encounter what you don’t know. When your sphere is small, you have a small circumference of ignorance, but as your sphere grows larger and larger, so grows your circumference of ignorance. The larger your circumference of ignorance, the more exposure you have with a whole universe beyond your knowledge. In other words, the more you know, the more things you discover you don’t know.

              Does this mean you should stop learning? Who wants to discover how little they know?

              Uncertainty creates discomfort in all of us, it’s true. Yet it’s this very discomfort that spurs us to learn more, to seek better answers, to grow as individuals. The alternative is to stay comfortable and hold firmly to your beliefs, ignoring all contrary evidence. Of course, beliefs that fit poorly with reality are not very useful, other than to provide comfort. So if your biggest need is for comfort, for heaven’s sake, don’t expose yourself to contrary voices.

              On the other hand, if you thirst for better understanding, seek out the discomfort of uncertainty. We’re human beings. We can’t possibly know everything. Nor should we expect ourselves to. But we can always learn.

Here’s what the world’s leading scientists have come to understand, as exemplified by Heisenberg’s Uncertainty Principle: we can never know reality with certainty. All new information can do is give us better approximations of reality. That’s a useful goal.

Indeed, the fundamental quest of science to not to provide final answers; it’s to discover better questions, questions that might lead us to new insights, which in turn will lead to even better questions. This is the essence of the scientific process. Those who give up on science because it doesn’t provide final answers are those who simply misunderstand the process.

              Here’s the irony. On any given topic, you need to know a lot to realize how little you know. When you find yourself speaking with absolute certainty, let that give you pause to wonder what you’re missing.

              One of the things I like to do in my writing is to challenge readers to look at things from an unfamiliar perspective. Why? Because that’s how we expand our horizons.

“The mind, once stretched by a new idea, never returns to its original dimensions.” Ralph Waldo Emerson

So, what do you think of this “sphere” analogy? Have you heard any other good ones? I’d love to hear what you think.

Seven Billion Worlds

— on one planet.

Want to visit a strange new world? Talk to a human.

Though largely unaware of this fact, each one of us lives in our own little world. (Wait a minute; I guess that’s pretty obvious these days.) Ours is the world constructed by our brain, our own idiosyncratic representation of reality. We’re as unique on the inside as we are on the outside.

We “live in our heads” most of the time. If you are in a familiar place, you don’t have to look around to know what’s around you. Having an internal representation of the outside world is efficient and adaptive. Our brains do it because, like every other human trait, it helped our distant ancestors survive long enough to reproduce. (Traits that weren’t helpful with this way died out. Yea, natural selection.)

As we learn about the world around us, we learn to identify things by sight, sound, smell, touch, etc. Our brains automatically build mental models of these things. Now we can remember and think about them even when they are not present. We can imagine them.

Over time, we build elaborate maps and models of the whole world this way. Our maps and models may match those that others have internally built, or they may not. Everyone has a unique perspective and learns from their own unique experiences. Two people can look at the same thing and perceive, on deeper levels, quite different things.

The bottom line is, each of us lives in a unique world. There may be large areas of overlap, but there will always be discrepancies.

As social primates, we tend to feel safer when we are following the crowd, but we are each unique, with our own inborn biases and preferences. It is the height of folly to expect everyone else to see things the way we do. Some will, and that’s always reassuring. But to demand agreement from everyone is aggressively authoritarian.

The kindest thing we can do is to accept and tolerate the differences between us.

Embrace your uniqueness and, as long as they are doing no harm, let others embrace theirs.

Here’s what I’d love to know. Which fictional character have you most admired for their bold acceptance of being different? Or for their acceptance of differences in others?

Past or Future?

Past or future? Which draws you?

Almost everyone has a preference. 

Science fiction tends to appeal to future-oriented people, as does speculative fiction in general. Other genres tend to be dominated by stories of the past or present. There are always exceptions. Alternative history, time-travel, steampunk, and fantasy often mix time-frames in interesting ways.

Some of us are drawn to the past, some to the future. Our records of the past provide glimpses into the experiences of others, valuable if we learn from them. Our speculations about the future provide goals and warnings, valuable if we heed them.

History is always recorded from a particular perspective. The history we know is a tiny sliver of what has actually gone before, a very incomplete picture. Even our own memories are notoriously unreliable. On a personal scale, the past is as imaginary as the future.

The future is a blank slate. We may assume that current trends will continue, but based on past experience, this is unlikely. Recorded history is essentially the record of events that disrupted the expected flow. Yet we live and plan our lives as if we know what’s going to happen. The future is truly unknowable.


There is nothing we can do about the past, but we can influence the future. The future is a rich playground for imagination, which is why it attracts speculative fiction writers. We can extrapolate from what we know into plausible futures. We can create stories that encourage us to think twice about where we are going, to hopefully plot a safer and more productive course.

The future is where our hopes and fears all reside. Forewarned is forearmed. Progress requires a goal. Let’s look ahead.

When you look to the future, what do you see that doesn’t get enough attention in fiction?