ASTR 2010 Modern Cosmology Professor: James Green
Logistics: Textbook Math Expectations Grading Homeworks Midterm Final Exam Lecture Notes
Cosmology The Scientific Study of the Universe
What is Science? There is not a universally accepted definition Standard definition is that intellectual pursuits adhering to the scientific method comprise science. However, most scientific research today does not adhere to the scientific method I want to take a broader approach
Logic Deductive Logic Inductive Logic Aristotle
Logic Deductive Logic Inductive Logic Aristotle
Logic Deductive Logic Start with an axiom, a statement that is self-evidently true. You can deny, but can t argue axioms. By logical definition, they are irrefutable. Apply the rules of logic to build on the axiom Whatever you deduce is as true as the original axiom Inductive Logic
Logic Deductive Logic Start with an axiom, a statement that is self-evidently true. You can deny, but can t argue axioms. By logical definition, they are irrefutable. Apply the rules of logic to build on the axiom Whatever you deduce is as true as the original axiom The only familiar systems that are pure deductive logic are geometry and mathematics Axioms of algebra, for example include if a = b then b = a or if a = b then a + c = b + c but from these simple beginnings you can derive all of algebra and calculus
Logic Inductive Logic Involves assembling information through observation and measurement, and then assembling a generalized explanation for these phenomena this does not result in truth nor does it necessarily illuminate the underlying causes of the generalization even though the generalization may be accurate and predictive The most famous example of inductive logic is the theory of evolution
Logic Deductive Logic Pseudo-deductive Logic Develop an hypothesis, and assume that it is an axiom Apply the rules of logic as if this were a case of deductive logic, and make testable predictions If any of these predictions fail the hypothesis is refuted and not an axiom. This is not the same as being false or useless The most famous examples would be Newton s Law of Gravity or Einstein s Theory of Relativity This is the strict scientific method. Inductive Logic
Logic Deductive Logic Pseudo-deductive Logic Deductive Paradigm Develop an hypothesis but assume that it is only a generally applicable guiding principle a paradigm and not an axiom. The paradigm is used to make predictions, but it is not expected that these predictions will be 100% accurate, as they are in the case of pseudo-deductive logic. When contradictions between the paradigm and observations arise, the paradigm is modified to include the new observations. In this way, the paradigm evolves and improves, however, it is no longer refutable. As such, it can obtain the aura of an axiom. But it is not. This does not mean it is false, but it is not axiomatic. The most famous example of this are the current explanations of climate change as resulting from human activity. Inductive Logic
Logic Deductive Logic Pseudo-deductive Logic Deductive Paradigm Inductive Logic Correlative Induction This involves the correlation of data (such as lung cancer incidence vs. smoking habits) and inferring a causal relationship from the correlative relationship. This approach has many inherent weaknesses, but is often the only available data due to ethical or physical limitations. Correlation Causation. This is the weakest case, but is most common in medicine and social science because people cannot be ethically used as appropriately controllable test points. Again, this does not mean that conclusions reached by this method are false or useless, but they are frequently reversed by later studies.
Correlation Causation Example 1 What if a study showed that employees who took the highest number of short, outside breaks during a work day had a 50% greater likelihood of developing lung cancer. Should we make people stay inside?
Correlation and Causation When inferring the implied causal reaction from a correlation, one must always consider the inherent axiomatic assumptions that one is applying, often sub-consciously. The data are the data but what do they imply? This depends on the underlying axiomatic assumptions that you make.
Logic Deductive Logic Pseudo-deductive Logic Deductive Paradigm Inductive Logic Correlative Induction All of these approaches are scientific in that they incoporate logical analysis and quantitative analysis, but they are not equivalent.
Brain Break
Definitions? The Universe
The Universe Definitions? My definition: The universe contains anything and everything that was in the past, is now, or will be in the future, within my causal horizon (can effect me). Involves both space and time
The Universe Definitions? Space-Time / Events Causal Connection Horizon Olber s paradox
Aristotle Earth does not move (an unchallengeable premise).. Stars move All things seek their natural location, heavenly objects moves on spheres, heavier objects move more rapidly Motion = force Model is consistent not predictive
Ptolemy
Ptolemaic System Motion on spheres/epicycles/equants Predicts planetary motions reasonable well Earth at center unmoving (not a preferred location) Consistent with lack of stellar parallax
heaven, the dwellingplace of God and of all His elect
Copernicus Sun at center Results in simpler motions for predicting planetary positions (retrograde motion in particular) Prime advantage simplicity Kills Aristotelian principle of no earthly motion
Tycho Brahe
Tycho Exquisite measurement of planetary motions
Kepler Used Tycho s numbers to calculate their motion as perceived from the sun Came up with three empirical laws No underlying principle for these laws was proposed However another Aristotelian principle killed (motion on spheres)
Galileo Dropped balls from tower: Aristotelian motion laws disproved Looked at Moon/Venus/Jupiter/Stars with telescope: Heavenly/earthly separation attacked Venusian phases kills Ptolemaic system Stars at varying distances Proposed concept of relative speed