The Scientific Method:Science as Natural Inquiry

Szydagis01.23.2015

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Test ideas with observations Refine or reject those ideas which cannot explain the real

world The five steps of the scientific method

Make an observation of the world Formulate a *testable* hypothesis (explanation) as to the

“why,” the underlying cause(s), behind what you see Run an experiment to test your hypothesis, to see whether

or not it is true. Your hypothesis must be predictive in some form

Analyze your experimental results. What can you conclude? Confirm, or refine/reject hypothesis, and start the process

over again from the beginning, running further experiments. Round and round the circle goes!

The Basic Principles of Science

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Scientific results must be reproducible/repeatable Both multiple trials of the same experiment, and new

experiments, are useful Classic examples of experiments whose (controversial)

data could not be replicated, or inconsistently so Cold fusion (nuclear fusion at room temperature) Several dark matter discovery claims Studies demonstrating telepathy, telekinesis,

clairvoyance, and similar psychic phenomena “Controls” are very helpful: purposeful omission

For example, give one group a placebo pill in a drug study Not always easy to craft. For instance in astronomy we

can’t have (real) multiple Big Bangs and Universes! Blindedness: either experimenters or human subject

participants purposely unaware of something

The Confirmation of a Result

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Scientists are a lot like these guys from the Discovery channel television show, but there are notable exceptions The mythbusters don’t always bother with a control even if it is

possible to have one easily They often have too few trials to ensure a result is significant

© 2015 Discovery Channel

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When experimenters report an “error bar” that does not mean they think they made a mistake. The more formal term is “experimental uncertainty,” and there are two kinds: statistical, systematic (the latter often forgotten/neglected)

Statistical uncertainty is caused by the simple fact that it is impossible to have an infinite number of data points If you tossed a coin a large number of times, your heads to tail

ratio should approach 1:1, but if for example you only had 10 trials, then having 6 heads and 4 tails is not unreasonable, and the degree of that reasonability is quantifiable statistically

Systematic uncertainty refers to your entire measurement possibly being uniformly “off” due to uncertainty in some calibration constant or other parameter you need to use in reporting the final results, or due to some conversion Wrong assumption about an optical property of your telescope

Error Bars and Statistics

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Example: The Due Date (Birth)

http://spacefem.com/pregnant/charts/duedate0.php

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Presidential election: if Candidate #1 has 46 +/- 2% (+/- indicates the error bar a.k.a. uncertainty) of the vote and Candidate #2 has 44 +/- 2% (there are other candidates with small percentages) then… Concluding Candidate #1 is in the lead is an unscientific

statement to make, though people make it all the time This result is said to *not* be “statistically significant”

Often in physics and astronomy, a discovery/detection is said to not even be statistically significant unless it is at least a 5s result ( s = standard deviation) If the potential outcomes are expected to lie along a

Gaussian function (a.k.a. bell curve or normal distribution) this corresponds to a 1 in ~3.5 million chance of a statistical fluctuation, with error bars most often quoted as 1 sigma

Statistical Significance

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OK to interpolate: estimating values between measured data points

But extrapolation, extending your theoretical functional fit outside the bounds of your data, is dangerous

Observation: Stars twinkle. They appear to change size and shape. (If you are pretty sure you already know the correct answer: ask yourselves instead why they are different colors)

Come up with a hypothesis as to why, and an experiment which could be used to test it Doesn’t have to be an experiment you are

capable of carrying out for yourself: use your imagination

Activityhttp://www.netanimations.net/Blinking-stars-meteors-comets-supernova-pulsars-and-space-animations.htm

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Hypothesis can become theory if repeatedly confirmed with many different experiments, and/or a law or principle if formulatable as a concise mathematical expression encoding/encapsulating a profound, far-reaching generality

A model can be almost the same thing as a theory, but most of the time this term refers to an analogy, like thinking of elastic scattering of subatomic particles as “billiard ball collisions,” or atom = solar system

Theory does not correspond to the popular notion: “That’s just your theory!” (a very common misconception). Connotation and denotation differ

Building Theories and Models

http://www.aip.org/history/einstein/atoms.htm

For instance, difficult to doubt atomic theory these days (we can actually see atoms now with certain types of microscopes) but it is still called a theory

silicon atoms in a crystal

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Empiricism is the art of experimentation as a way of achieving an understanding of the world Empirical refers to hard experimental data, usually

numerical in form, as in “empirical results,” or “this is empirically known”

Observation or observational data more common term in astronomy, where often hard to set up direct experiment

Theoretical refers to theories, as you’d guess Theorists (scientists who do not perform experiments, but

rather only formulate theories, common in physics and astronomy) sometimes come up with new ideas before experiments that may test them directly can be constructed

Other times experimentalists race out in front, with new and puzzling results the theorists must confront and explain

Some More Scientific Terminology

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A precise measurement has a great deal of significant digits: for instance, you measure the mass of something to be 1.23456789 kg. Precise!!

Accuracy refers to how close to the true value you get. So, precision gets you nowhere in above example if actual mass was 2 kg (this ties back into bias and systematic uncertainty). Colloquially accuracy mixed up with precision11/16

Precision vs. Accuracy

http://www.feeltennis.net/wp-content/uploads/2013/02/accuracy-vs-precision-tennis.jpg

Event or phenomenon B following A temporally/spatially does not imply that A leads to B, or that A causes B to occur as its direct effect

Classic jokes on this topic Ice cream causes drowning Having fewer classic pirates (ARR!) leads to an increase in

global warming! This is where controls can help, and logical links using

hypotheses already confirmed elsewhere that can connect your hypothetical cause to the observed effect

But, be wary of “common sense,” which is often misleading. Common sense will tell you that heavier objects fall faster than lighter ones and that rest is the “most natural” state of objects

Correlation vs. Causation

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Generally attributed to William of Ockham (c. 1287-1347), although echoes sentiments of philosophers throughout the centuries

The simplest (i.e., with the fewest number of assumptions) explanations are the most plausible; they tend to most often be ultimately proven correct Did aliens eat your homework or did you just not do it?

Fictional character FBI special agent Fox Mulder from The X-Files called it the “principle of limited imagination” Apparent counter-example: 5 elements in all of nature sounds simple

enough (earth, air, fire, water, aether) but it’s totally wrong. There are 92 naturally occurring “elements” (hydrogen through uranium)

One has to be very careful in applying the “razor,” since one can easily make one’s explanation too simple (failing to successfully describe nature). Also, bad example above (elements are made up of different numbers of protons. Simplicity restored to a degree going deeper…)

Occam’s Razorhttps://watchingthedeniers.files.wordpress.com/2010/04/littlefriend1.jpg

http://www.virginmedia.com/images/X-Files-S1-Fox-Mulder-431x300.jpg

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Science is always digging deeper. The most superficial explanation, even one you are given by a scientist teaching a science course at a particular level, is quite often not the full story, because of how much more there would be to explain, sometimes with great difficulty

As just one example, water boils at 100 oC, right? (~0th order) That’s only at 1 atm of pressure. At high altitude (very low

pressure) boiling point can deviate significantly (e.g., Denver), affecting cooking and tried-and-true recipes (~1st order)

Even at standard sea-level atmospheric pressure, water can be “superheated,” i.e., raised above the boiling point while staying a liquid, not turning into gas/steam/water vapor (~2nd order)

If freezing water makes it ice, then what is snow?

Levels of Explanation

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https://www.youtube.com/watch?v=1_OXM4mr_i0

Fictional character Sherlock Holmes is thought of by many as having a scientific approach, which is at least somewhat true, but what he applies is more often inductive not deductive reasoning Deduction is logically concluding specific properties from general

ones: all humans die, so John Smith (a human) will one day die Induction is just the opposite: a stain on clothing is indicative of

one’s career or where one has been today (Sherlock induces this)

However, science is not always about deductive reasoning. Equally important is inductive reasoning: generalizing the specific results of experiments into universal principles Conservation laws (physics): mass/energy, momentum, charge,

spin Stars of a certain color share other properties (mass, age)

Induction vs. Deduction

http://aiutomutuo.finanza.com/files/2013/11/EPH23-02.jpg

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Homework: Imaging at a trillion frames per second https://www.youtube.com/watch?v=Y_9vd4HWlVA How far away are active invisibility cloaks?

http://www.popularmechanics.com/technology/engineering/news/how-far-away-are-active-invisibility-cloaks-16466686

Why do stars twinkle? http://www.universetoday.com/25345/why-do-stars-twinkle/ Out in space, back in time http://hubblesite.org/hubble_discoveries/dark_energy/de-

out_in_space_back_in_time.php Reading on color & light, part I (also read “Sources of Light” link at bottom) http

://www.asu.edu/courses/phs208/patternsbb/PiN/rdg/color/color.shtml Light as a particle (don’t stress over math, and ignore the “homework questions” at the

end)http://www.lightandmatter.com/html_books/lm/ch34/ch34.html The Structure of Matter (skip down to History of Atomic Structure. Feel free to do questions

at end) http://www.physicsclassroom.com/class/estatics/Lesson-1/The-Structure-of-Matter