Transcript: The scientific method is a way of gaining knowledge about the world we live in.  Science starts with curiosity about nature, observing the world, but there is a method to science, a way that distinguishes it from other modes of thought.  Science is based upon evidence, upon observations.  Scientists take the evidence, and from that they formulate ideas or hypotheses.  And eventually when those have been sufficiently tested, the hypotheses become turned into theories about the natural world.  It’s important to understand the scientific method because that’s the way we create knowledge.  If I told you a fact it would be as if I gave you a fish to eat.  You have that one fish.  You have that one meal.  But if I gave you a net you could catch many fish.  The scientific method is the net that allows us to catch many fish, to learn many things about the world we live in.

The Scientific Method

Transcript: The bare bones of the scientific method does not encompass the fact that science is done by people.  In the scientific method we have to have someplace for the ideas of luck, serendipity, being in the right place at the right time, persistence, inspiration.  How did these fit into the scientific method?  The stories of science are full of such ideas.  Alexander Fleming, the discoverer of penicillin, itself an accidental discovery, once said “Fortune favors the prepared mind.”  When a scientist makes what seems to be an accidental discovery it’s often because they are doing careful experiments and are noticing something that doesn’t fit a pattern or appears out of the norm.  The discovery of vitamin-C dates back to a scientist noticing that citrus fruit never bruise and other fruit did and wondering why.  The discovery of x-rays occurred because one scientist, Wilhelm Rontgen about one hundred years ago, noticed that certain photographic plates in his lab fogged in the presence of a radioactive source.  It was an accident, but he was able to deduce that invisible rays were traveling from the radioactive source and fogging the photographic plate.  The discovery of x-rays revolutionized modern medicine.  When scientists make discoveries they cannot always tell where they are going to lead.  When Thomas Edison first started using electricity he was asked what possible use is it.  He said “What use is a new born baby?”

The Work of Scientists

Transcript: There’s very little direct evidence in astronomy.  In a few cases we’ve been lucky enough to have meteorites falling from space.  We’ve even had a few free samples of Mars.  But most of the evidence of astronomy is gathered remotely.  We’ve sent spacecrafts to most parts of the solar system, and they’ve sent back images and other information of radiation received.  We’ve used telescopes to explore distant regions of space.  We’ve extended our senses across the electromagnetic spectrum with detectors that can measure everything from x-rays and gamma rays to long wavelength radio waves.  In astronomy we depend on the extension of our senses through technology but must of the evidence of astronomy is indeed indirect, the radiation that reaches us from throughout the universe.

The Evidence of Astronomy

Transcript: How do we test theories?  There are two fundamental ideas.  The first is the idea of induction.  This was put into place by Francis Bacon, sixteenth century philosopher of science.  Induction is the idea that we can generalize from a finite set of observations, or situations, or data, to a much broader range of situations.  Science proceeds by induction but always has to recognize that the amount of data is limited and that data has errors attached.  So induction is a process that can fail with insufficient data.  The second idea is called falsification.  It was put into place by the twentieth century philosopher of science, Karl Popper.  The idea of falsification is that we make a theory or a hypothesis.  We gather as much data as we can, and see if the data is confirming or falsifying the theory.  In principle, if the data is falsifying the theory even by a modest amount or even only using a small amount of the data the theory must fall and must be replaced by a better theory.  Once again observations have errors attached and are sometimes limited.  So the idea of how a theory becomes falsified is a controversial issue amongst philosophers of science.

Testing Theories

Transcript: There are several essential steps in the scientific method.  They apply equally to astronomy and all other sciences.  The first step is gathering data or observations.  In astronomy this is usually not direct evidence.  Usually it’s radiation gathered from space.  The more observations or data the better.  The second process is to analyze the data or look for patterns.  Scientists look for patterns in the evidence or observations as a way of understanding how nature works.   This leads to insights as in the example of the periodic table or the patterns in fossils that might tell how species evolved.  Astronomers also look for patterns.  In the third step astronomers take the patterns they have found and form a hypothesis to try and explain all the observations they have in hand.  They hope this hypothesis will lead to predictions about new situations as yet untested.  And if the hypothesis is successful, they form a theory of nature to try and describe what they’ve been observing.  Science can never guarantee truth, but with sufficiently good observations it can guarantee good explanations of the natural world we live in.

Steps of the Scientific Method

Transcript: Scientific reasoning is an important part of how science works.  You may have your own beliefs or your own faith, and they are your own.  They’re unchallengeable.  But if you make an assertion in a scientific way, you have to be able to back up that assertion.  So when scientists argue about theories and models and data they are using a formal way of arguing about things that can lead to advances in knowledge.  A scientist can only make an assertion if it’s backed up by evidence.  They can only make an assertion if some other scientist could go out and verify the assertion.  That’s the way that science proceeds.  Why then do scientists argue so much?  Often because there are multiple theories or models to explain a given set of data.  Equally data itself is never perfect, is often limited, and sometimes has errors attached.  These uncertainties allow scientists to have room for doubt and lead to the fact that not all scientists agree on every issue.

Scientific Reasoning

Transcript: Astronomers have to deal with very large and very small numbers.  As we deal with things as low density as the vastness of space and as high density as the center of a black hole, as hot as the first instant after the big band and as cold as intergalactic space, we are dealing with very large and very small numbers.  Scientific notation is a short hand for writing very big and very small numbers.  For instance, the nearest stars are about 4 or 5 trillion miles or kilometers away. 4 or 5 trillion is 4 or 5 followed by twelve zeros.  So scientists use a shorthand form of writing this large number, 4*1012 or 4 times 10 with 12 as an exponent.  If the number is very small the exponent has a negative sign in front of it.  In science in general and in astronomy in particular we need scientific notation as a quick and efficient way of writing and manipulating large and small numbers.

Scientific Notation

Transcript; Astronomy spans an enormous range in scales of time as well.  The shortest thing we can measure, 10-23 seconds, is the time it takes light to cross a proton.  Visible waves of light have a frequency of about 1015 Hertz, which means that one oscillation of light as an electromagnetic wave is 10-15 seconds.  In the middle of this huge range are humans; a heartbeat, roughly 1 second.  107 seconds is a year.  1011 seconds is the length of recorded history, and the age of the universe measured since the big bang is 1018 seconds.  The full range of these numbers from largest to smallest is 41 orders of magnitude or powers of 10.

Scales of Time

Transcript: The study of astronomy contains an enormous range in scales of mass.  The lightest thing there is is an electron, 10-30 kilograms.  The heaviest atom, Uranium atom, is 10-25 kilograms.  The tiny living organisms, a bacterium or a virus, about 10-15 kilograms.  Somewhere in the middle of the huge range are human beings with a typical mass of 100 or 102 kilograms.  The entire Earth is 1025 kilograms.  The sun, 1030 kilograms.  And the entire mass of the observable universe, containing some 60 billion galaxies, amounts to 1052 kilograms.  The entire range from the largest to the smallest is 82 orders of magnitude or powers of 10.

Scales of Mass

Transcript: Astronomy contains an enormous range of scales and length as well.  The smallest thing that we can routinely measure is a proton; the diameter is 10-15 meters.  The size of a hydrogen atom is 10-10 meters.  Somewhere in the middle of the huge range are human beings at about 1 meter in round numbers.  The next largest scale we might consider is the size of the solar system or the Earth-Sun distance, 1 Astronomical Units, 1011 meters.  A lightyear, a typical distance to a nearby star, is five orders of magnitude larger, 1016 meters.  The milky way, the system of stars in which we live, is 1021 meters across.  And the observable universe containing billions of galaxies is 1026 meters.  The full range of scales from the largest to the smallest is 41 orders of magnitude or powers of 10.

Scales of Length

Transcript: Another reason that science cannot make statements with absolute certainty is to do with sampling or the limitations of data.  Induction as a tool of the scientific method is based on generalizing from a finite set of observations or situations to a broader conclusion.  If I had ten people in front of me and I asked which hand each of them wrote with and all ten said that their right hand, would I be justified in concluding that all people are right-handed?  You know that the answer is no.  The incidence of left-handedness in the population is about 10%, so with ten people questioned I might just be unlucky and find none that are left-handed.  However with a hundred people, if I question them, I would expect ten of them to be left-handed, and the odds of finding no left-handers would be very small.  Thus our ability to draw a conclusion on the incidence of left-handedness depends sensitively on the number of people asked or sampled.  Astronomy has exactly the same situation.  If I inspected the nearest ten stars to the sun and found them to be all of a certain type, would I be justified in concluding that that was the only type of star that existed?  No, I would probably need to sample space more fully and contain larger samples of stars to make a statistical statement with any certainty.  Astronomy depends on the issues of sampling as many other fields do.  For instance in politics the voting intensions of tens of millions of adult Americans are based on samples of only a few thousand people.  So these techniques can be used with reliability.

Sampling

Transcript: In science we deal with two fundamentally different types of errors.  Random errors are usually associated with limitations in the measuring apparatus.  A random error can displace a measurement either to the high or low side of the true value.  Random errors are fundamental in science and in astronomy, and their theory was put in place by Carl Friedrich Gauss.  Random errors can even apply when we count things.  Although you may be able to count the number members in your family completely accurately, in astronomy we’re not able to count with complete precision.  So we estimate the number of stars in a galaxy or the number of galaxies in the universe, and the count has an error attached to it.  The second type of error is called the systematic error.  A systematic error does not displace equally to the high or low side of the true value.  It represents either a failure in our understanding of how to make a measurement or a flaw in the measuring equipment itself.  For example, if you used a ruler to measure the width of a table and that ruler was either miscalibrated in the way it was a applied the scale when it was manufactured or the ruler had its scale applied at a different temperature from the temperature you are making the measurement, then all of your measurements of distance would be off in one direction.  That’s called a systematic error.  It is one of the most dangerous and tricky things in astronomy or in any science to track down systematic errors.

Random and Systematic Errors

Transcript: Science is and must be objective.  It must be based on observational data and experimentation.  The results must be published so that other people can check or confirm or independently measure the same things.  Science depends on this, but there is a social element to scientists too.  Science is communicated in the public arena, at conferences, and symposia.  Theories become popular and then less popular.  Thomas Kuhn, the philosopher of science, has referred to the idea of a paradigm which is a theory of science that takes hold within a community of scientists such that it becomes the conventional and established wisdom.  The hold that a theory takes place amongst scientists can cause it to be difficult to change the theory which is why we have revolutions in science, but we should not go from this understanding to a belief that science is just one way of knowing about the world and is not objective.  As a philosopher of science recently said, “Anyone who thinks that Newton’s Theory of Gravity is just a social convention, I invite them to step out of my 17th story office window.”

Paradigms

Transcript: Angular measurement is an important part of astronomy.  When you want to quote the position of an object on the sky you give it in terms of two different angles.  The basic unit of angular measurement is a degree.  There are 90 degrees in a right angle and 360 degrees in a circle.  The system of angular measurement dates back to Babylonians over 5 thousand years ago.  On smaller scales then a degree we divide the degree into 60 units called “minutes of arc” and the minute is divided into 60 further units called “seconds of arc”.  One arcsecond is therefore 1/3600 of a degree, a very small angle indeed.  It corresponds roughly to the angular resolution of a telescope on the ground.  One arcsecond is a very small angle.   It’s the angle subtended by the two sides of a quarter seen at a distance of about two miles.

Measuring Angles

Transcript: People make many statements in everyday life.  Some statements are quantitative and some are qualitative.  You might say, “This piece of music is great,” or, “It was cold outside yesterday.”  The first statement cannot be quantified.  It may be true for you and not true for one of your friends.  It’s a purely qualitative statement.  The second statement can be quantified, but we need a system of units.  Scientists only deal with quantitative statements.  Every statement about science that involves a measurement has two parts.  It has a quantity and a unit, and science always deals with these two things coupled together.  So when I say, “It was cold yesterday,” I need a system of units and a measurement.  And even if I say, “Fifteen degrees,” I have to tell you which measurement system I was using, Celsius or Fahrenheit.  If I said, “The Dow fell fifty points yesterday,” that’s a quantitative statement, but you would have to know something about the units; which means you would have to know something about what goes into making a point on the Dow-Jones Industrial Average.  So in general scientists always deal with quantitative measurements, and those measurements must have units attached.

Measurements

Transcript: Scientists use a system of units based on mass, length, and time.  Almost every physical quantity in the world can be reduced to some combination of units of mass, units of length, and units of time.  For example area is length times length.  Volume is length times length times length.  Velocity is a distance or a length divided by a time.  Momentum is a mass times a velocity.  So many of the things you see in astronomy will be simply reducible to combinations of mass, length, and time.  This is the way in which astronomers make sense of a complicated world, and in astronomy as in all science we measure mass, length, and time in units of the metric system: kilograms for mass, seconds for time, and meters for length.

Mass, Length and Time

Transcript: Logic is a fundamental tool of the scientific method.  In logic we can combine statements that are made in words or in mathematical symbols to produce concrete and predictable results.  Logic is one of the ways that science moves forward.  The first ideas of logic using words were put together by the Greek philosophers, especially Aristotle.  The equivalent mathematical formalism for logic was put together about a hundred years ago by the philosopher Bertrand Russell.  The word logic comes from a Greek root “logos” meaning logical, natural order.  The Greeks believed that the universe was a rational place, and in fact the word cosmos, which we take today to mean the universe and everything in it, meant a little bit more to the Greeks.  Cosmos meant natural and harmonious working of all the parts in the whole.  The antithesis of cosmos is chaos, disorder and utter disorganization.  So for the Greeks the universe was a balance between cosmos and chaos, and logic was their way of making sense of the natural world.

Logic

Transcript: Induction is an important tool of the scientific method.  In induction a specific statement based on a limited set of data or observations is generalized to form a very broad conclusion.  Newton, for example, based on limited measurements of orbits within the solar system, hypothesized that his theory of gravity applied to all orbits inside the solar system and outside the solar system, a very broad generalization called the Universal Law of Gravity.  When, subsequently, orbits were measured outside the solar system or new objects within the solar system were discovered such as comets, it turns out that his law applied to them too.  That is a successful use of the inductive method.  Induction tries to gain knowledge by generalization, but is always susceptible to limited observations.  One of the dangers of induction is generalizing based on too few or insufficient quality observations.

Induction

Transcript: Modern science is based on the fundamental idea that we can extend our senses through technology.  If all we could learn of the natural world came through our senses of sight, smell, sound, touch, we wouldn’t know much about how the world works.  We’d know very little about the microscopic world of the atom, and we’d know very little about the universe beyond the Earth.  Physics and astronomy depend completely on the fact that we can extend our senses to detect magnetic and electrical fields, to sense subatomic particles, and to see the universe beyond the solar system.  Astronomers use telescopes to extend the visual sense gaining a light grasp that’s billions of times greater then can be achieved by the naked eye.  And in fact all science depends on the reliability of extending our senses to learn about the natural world.

Extending the Senses

Transcript: Because of the huge range of skills and quantities in astronomy, we often use exponential or logarithmic forms when presenting information.  Exponential growth and exponential numbers are very different from linear growth and linear numbers.  There are three typical forms of exponentials used in science.  The first are exponents or powers of 2, that of course is the basis of the binary counting system and the way computers work, exponents or powers of the natural number “e,” 2.7, which is often encountered in biology, and exponents or powers of the number 10, our familiar powers of 10 way of counting.  There’s a huge difference between linear counting or linear growth and exponential counting or exponential growth.  For example, if you had one dollar on the first day of a month and everyday added a dollar to it, at the end of the month you would have 31 dollars.  If however you had one dollar and everyday doubled that dollar, by the end of the month you would be close to being the richest person on the planet which gives you a good example of the rapid way powers of 10 or powers of 2 can grow.  In astronomy we use exponential or logarithmic forms to compress the huge scales of the universe and make them more accessible and easy to manipulate.

Exponentials and Logarithms

It is a fact that Jupiter and Saturn aligned to begin a new 800 year cycle just before Kepler witnessed the brightest supernova in modern history and the Scientific Revolution unfolded. Whether or not it is a &#34;statistical&#34; fact has nothing to do with the meaning of that fact. Astrology is about meaning -a subject to which Science is devoid. In this sense Science is pseudo-Hermetic, in that it has only explored one of three dimensions of existence -salt or matter. It has relatively little Soulful depth (Psychology is about &#34;mental&#34; health) and absolutely zero Spiritual meaning. You cannot heal people or the world by saying that everything is random electrons. Science has its place but needs to learn it.

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1. Fundamentals of Science and Astronomy

Transcript: The study of knowledge is called epistemology.  There are two fundamental routes or paths for the study of knowledge.  One is the idea of empiricism which dates back to Aristotle 25 hundred years ago.  In the empirical approach to the method of science everything is based on observation or data.  You start by gathering data or observations and then proceed to make a hypothesis which leads to a prediction of other observable phenomena.  Then you make more observations to test your hypothesis and adjust it as needed.  In this view of the universe and how science works everything is based on observations.  The alternative view is called rationalism, and it probably dates back also 25 hundred years to the mathematician Pythagoras.  In the rationalists view of how science works you start by conceiving mentally of models or ways that the world works.  So you start with a mental framework, and then you proceed to derive observational tests of that mental framework and you go from there.  Clearly science as it’s actually practiced by scientists imbeds elements of both ways of doing science.  Science cannot proceed without observation, and clearly scientists have formulated important and sophisticated mathematical models of how the universe works.  Both are required if science is to move forward.

Epistemology

Transcript: Science starts by looking for patterns in data.  Therefore it’s important to understand the distinction between causation and correlation.  Scientists believe in causation, the general idea that events have causes.  However science starts by looking for patterns in observational data.  Typically two quantities may be plotted on a graph against each other.  If there’s a correlation, science tries to look for a cause.  However it’s not always possible to find a cause, or it’s not correct to infer a cause.  For example, it took 30 years of research before the government was sufficiently convinced of the correlation and the causation of smoking and cancer rates to put health warnings on all packets of cigarettes.  So we must be careful of the distinction between two quantities that are correlated and whether one causes the other.  Sometimes there may be an underlying variable or third quantity that relates to the causation.  In astronomy we plot the Hertzsprung-Russell diagram where the luminosity and the effective temperature of main sequence stars are tightly correlated.  However the underlying variable in this case is mass, a quantity not plotted at all.  So scientists must be very careful not to make the jump from causation to correlation without a justified physical theory that makes predictions that can be confirmed.

Causation and Correlation

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