Let's talk about uncertainty, and its related concept error. You might think that science has got nothing to do with uncertainty or error. Science should be about knowing things and being sure of things, and indeed scientists are confident about many of the theories they have and are very accurate in many of the observations they make. But scientists are always wanting to be aware of the limitations of their theories and the limitations of their data. So good science depends on understanding uncertainty and error. These concepts are distinguishable. Uncertainty involves inevitable, uncertainty involve with the measuring apparatus, the theoretical framework for an observation, or the physical universe itself. An error is something a little different. Usually when scientists talk about an error they're not talking about mistakes as we might do in everyday life, they're telling you about errors associated with measurements or observations, that are to do with limitations of the measuring apparatus or the telescope site. So we can distinguish these two things. They're built into science and they're completely unavoidable. Science is never perfect, and science is never absolutely confident 100 percent of its conclusions. This level of contingency is unavoidable and it's not a problem, it just means we move towards greater certainty and we must always pay attention to the errors. Astronomy is in a particular situation within the fields of science, because astronomy does not work as a laboratory with direct control of the experiment. Experiments astronomy take place trillions of miles away at the minimum, that's one light year. So astronomy is based on remote situations and remote sensing of those situations. As a result, the uncertainties in astronomy or perhaps larger than in other scientific fields or laboratories involved. In some situations in astronomy, we are quite unsure especially in a new regime. We talk about an order of magnitude uncertainty, which means a factor of 10. The answer could be 10 times smaller or 10 times larger than our first guess. This seems almost like we don't know anything at all, but in a new regime and in a universe that spans dozens of orders of magnitude of scale sometimes this is where we start. As astronomers refine their measurements, in many cases they're quite happy with a factor of two or 50% uncertainty. For an observation such as the number of stars in a galaxy or the size of a star, this is a reasonable estimate it can tell us quite a lot. It's hard to do much better. In many fields of astronomy something with 10 percent precision or accuracy is is about as good as we can get. Remember, we're dealing with limited amounts of information from objects that are very faint or very far away, and so 10% or 5% percent accuracy such as for the expansion rate of the universe involves an enormous amount of work even to reach this level. These are the realms of accuracy in astronomy, and we are gradually moving towards precision. There are some measurements in astrophysics where the accuracy is a percent or two, the edge of the earth for example is known with a precision of less than one percent. We can talk in general about three different forms of uncertainty or limitations that occur in science, in all fields of science not just astronomy. The most important and perhaps the trickiest to diagnose is the conceptual limitation of science, for example, we might make a false premise about a theory or an observation. We might confuse causation with correlation, something we'll talk about more, or are powerful pattern recognition apparatus might lead us to infer a pattern where none actually exists. Remember, we're conditioned to do this, if we were hunter-gatherers and we thought we saw a pattern of a leopard hiding in the underbrush and we were wrong, then we just got a fright. If we didn't see the leopard when the leopard was there we were lunch. So we're built to recognize patterns very powerfully, and sometimes in science this can lead us astray. The second level of limitations in science are macroscopic, associated with our observations or measurement apparatus. There is no perfect set of data and science, simply doesn't exist. Every measurement has limitations. Every dataset is finite, and so there was uncertainty associated with those limitations. We can do our best to improve the observations, to improve the instrument, the apparatus, make a bigger telescope or more accurate detector, but we can never completely overcome those limitations. The third level of limitations in science are microscopic, and these are profound because they're associated with the quantum uncertainty in the microscopic world. About a 100 years ago, innovations in physics led to an awareness that there was a fundamental imprecision with which we can measure the physical world of sub-atomic particles. This limitation has nothing to do with our measuring apparatus. No amount of ingenuity or money can overcome this limitation. It's built into the quantum nature of reality, and so it forms a profound limitation on our knowledge of the microscopic world. But when we're dealing with large macroscopic objects of humans and objects that contain trillions and trillions of atoms, these uncertainties become insignificant. The quantum uncertainty in particular is a very strange beast, and physicists continue to debate a 100 years after these theories were invented what their philosophical implication is. Einstein for example, was extremely uncomfortable with these limitations in nature these absolute obstacles to our understanding, and he thought it was just a matter of ingenuity before we develop a deeper theory that could explain everything. At the moment, we think Einstein was wrong on this matter, and there is no perfect theory of nature at the subatomic level. It upset Einstein very much all that damned quantum jumping. It spoiled his idea of God which I tell you frankly is the only idea of Einstein's I never understood. He believed in the same God as Newton, causality nothing without a reason but now one thing led to another until causality was dead. Quantum mechanics made everything finally random. As it could be this way or that way the mathematics deny certainty, they reveal only probability and chance and Einstein couldn't believe in a God who threw dice. He should have come to me, I would have told him. Listen Albert, he is for you. Look around, he never stops. Some principles in science are so foundational that we rarely think about them or question them,even working scientists are rarely questioning these ideas. One of the most important for astronomy is causality, the idea that effects have causes, that nothing happens for no reason. This sounds simple but it's very important. We have to operate as if causality applies. If causality doesn't apply, then effects could happen before their causes which clearly makes no logical sense. But this is a foundational principle because in every situation in astrophysics that we've encountered, when we observe a phenomenon, we imagine that there is a cause of that phenomenon, that nothing occurs without a reason. So far that's been validated. Determinism is the idea in philosophy for this concept and it applies in everyday life too. Let me tell you a story. Imagine you get up in the morning and your car doesn't start. You check your car, there's nothing wrong, the key isn't broken, there's no wires under the dash that are disconnected, the lights haven't been left on all night, the battery seems fine but your car just won't start. It's frustrating, but you've get your friend out of bed your roommate. He knows about cars more than you do so you get him to look at the car. He does things that you can't do. He goes under the hood, checks more wiring, looks at your key, looks at the ignition. After working for an hour, gets exasperated and says, "I can't see anything wrong, your car just won't start." You're not very happy with this explanation so you call the dealer and because your car is still under warranty, they show up in an hour with a fancy van and a lot of high-tech equipment. The dealer wearing his fancy uniform with a logo spends at least an hour on your car. He's testing this and he's testing that. At the end of his time with his hands dirty and some frustration on his face too he says, "I'm sorry I have tested everything. I can't find anything wrong. Your car just won't start." What I'm asking you is to imagine you're in this situation, how would you react to this information? I think you, like most people, like me, would say that's unacceptable. That's wrong. There's obviously something wrong with your car and this person is just not smart enough to find it. It's unacceptable for us to think that situations arise for no cause or for no reason. So we all in fact operate as determinists in our everyday life. Science uses as a foundational principle. In the realm of philosophy however, determinism has a dark side. Determinism means that every effect has a cause. The logic of this means that things are predictable because an a cause has an effect and so on. Newtonian gravity and the mechanics of everyday objects that Newton developed into mathematical theories were presumed to be able to predict the behavior of everything in the universe. So mechanical or mathematical determinism is an idea that came about in the 17th century, the idea that we live in a clockwork universe where if we could calculate the theory of gravity or the theories of atoms accurately enough, we could predict with perfect precision the behaviors of those atoms or of the universe as a whole. Now, we've never shown any sign that we can do this but at the time philosophers rebelled strongly against Newton's theories. They consider that this might rob us of freewill because if the universe is completely deterministic, everything is preordained and there is no free choice and there is no freewill. This profound philosophical debate has not entirely disappeared but it dissipated of course when we realized that the quantum world has uncertainty built in on the ground floor. For a more routine everyday example of this, let's look at the distinction between causation and correlation. We think that things happen for a reason, and it's the job of science to find out that reason and make a physical explanation. But we start by dealing with data and data is not always obvious when it speaks to us. Let's look at a graph where we're plotting data of two quantities that we can measure. It doesn't even really matter what these quantities are. We put them in a scatter plot on a graph. As we make more observations, each observation becomes a point or a data point on this graph and we're looking for a pattern. We might have a pair of observations where it's a scatter plot. It's thrown down at random. There seems to be no rhyme or reason, no pattern to this set of dots. But perhaps as we gather more data, it seems that they follow a straight line. There's a slope we can fit through this straight line and we would say that these quantities are correlated, that they seem to be mathematically related. If it's a straight line, it's a linear relationship. But perhaps we gather more data and the graph suddenly changes to the point where we can no longer fit a straight line through the points. At this point we have to reject that model, a linear relationship between the two quantities in favor of a different model a nonlinear relationship, a different form of mathematics that relates to them, and presumably a different physical theory underlying that mathematical relationship. But notice how difficult and subtle this process is. How do we decide in the absence of a final answer how much is enough data to test for a correlation, and the distinction between correlation and no correlation at all? How do we decide we've explored enough range of the parameters to encompass the possibility that the relationship might not be the simplest one we can fit through the data? When you fit more complex relationships or curves through data points, you have more variables, what scientists will call degrees of freedom and there are more different models you can fit to your data making you less certain that any one of those models is correct. So these are all issue scientists have to deal with when they make observations of the world and explore their data which is how they do it in graphs like this. Science isn't perfect and can never be perfect. There is no such thing as perfect data and there's no such thing as absolutely certain conclusions to be drawn from a scientific theory. The limitations of science occur at different levels. One level is conceptual, where we might confuse correlation with causation, or we might not justify the premises that underlie a theory. The second level is operational based on our measurements. There's no such thing as a perfect measurement. Scientists always want more and more measurements because there are errors or uncertainties attached. When scientists talk about an error, they're not meaning a simple mistake. They're talking about a limitation of the observation based on the measurement apparatus itself. This is true whether it's in the lab or using a telescope. The final level of uncertainty is a floor of uncertainty applied by the quantum theory as it applies to individual atoms. In most aspects of astronomy, we're dealing with such large objects and such large number of atoms that these quantum uncertainties don't apply.
