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Knowledge can be a beautiful thing, and a wondrous thing if you stop and think about it.  How do we “know” something?  We go to school and get fed  information that we retain in our memory but can also apply in situations that we have never faced before.  We know that one and one is two, regardless if it is sheep or potatoes that we are counting.  We know that this little ‘gem’ is true no matter what situation we find ourselves in.  Besides being taught, we also learn from experience.  No matter how many times we are told that a knife is sharp and can cut us, finding out by direct experience is much more memorable.  We learn through observing others, through the culture that surrounds us, we even have instinctive knowledge that is somehow passed on to us through our DNA.

Humans possess a wonder at learning new things. We are happy to invest time in learning new skills, new languages and new facts.  We take things apart to work out how they function.  We send probes to the far flung reaches of the solar system to learn something of our place in the cosmos.

And yet there is a limit to knowledge.  Some people assume that we will continue to learn more and more and so explain all of the mysteries of the universe.  Scientists are more circumspect and know that there is a limit to how much we can actually know.  Besides the fact that there is a percentage of knowledge that we hold to be true now that will be shown to be false  within 12 months, there are some fundamental limits to what we can know.

There are limits to measurement.  Even with the best will in the world, there are limits to our ability to measure certain things.  It could be because of temperature fluctuations in the room, or the speed of light affecting how quickly a transistor can switch but there are physical limits to how accurately and precisely we can measure physical properties.

There are limits set by the laws of Quantum Mechanics to what we can know about a system.  The Heisenberg Uncertainty Principle describes how much information we can determine about a system.  It is not, as some think, a problem with our ability to measure but is more about how much information the system is able to give up.  If we know a particle’s velocity well, then we have little idea about its position.

There are limits to our ability to predict.  Even though our computer models are becoming more and more clever, there are still huge difficulties in predicting the outcome of physical systems due to the non-linear nature of the equations being used.  If a billiard ball strikes another billiard ball then the outcome varies vastly depending on the exact initial positions velocities and angles of impact.  And the problem becomes enormously more difficult if extra balls are added to the table.

There are even limits to what we can decide.  In the highly precise field of formal logic, there are properties that are simply undecidable.  We are limited in what we can determine to be true and false.

So as we approach the new year it is time for me to marvel again at what we have learnt as human beings, and what is still left to be learnt, but also to wonder at all the things that we will never know.