We began course by asking fundamental question
Is there meaning to our existence?
We suggested the related questions
What elements signify meaning, and how do we assign degrees of importance to these elements?
What elements define our existence?
We suggested that human response has been to divide question and devise ways of thinking that we recognize as fields of
Theology, search for meaning in our spiritual existence
Philosophy, search for meaning in our intellectual existence
Science, the search for meaning in our physical existence
Art and literature being expressions of results of quest for meaning
Therefore, we suggest that a subtitle for this course is "the search for meaning in physical existence"
"Science is a very human form of knowledge. We are always at the brink of the known, we always feel forward for what is to be hoped....Science is a tribute to what we can know although we are fallible....We cannot reach certainty because it is not there to be reached....There is no God's eye view of nature...only a man's eye view." Jacob Bronowski
24.2. Thesis of This Course
Thesis of this course has been that science is:
To a great extent, the search for meaning in physical existence
A human effort to devise a way of thinking about the physical aspects of human existence
Utilization of that way of thinking to produce a logical representation of our collective sense experiences
Not something that we do; thus it is not technology, which is about survival
"The effort to understand the universe is one of the very few things that lifts human life a little above the level of farce, and gives it some of the grace of tragedy." Steven Weinberg
24.3. Science - Public and Private
No single method of science exists on individual level
Common elements do exist
"Methods of science" really have meaning at collective or public level, not private
Individual scientists are motivated by variety of issues
Some are even non-rational
Some are mystical
Some are religious
Individual scientists
Are tenacious
Are driven by sense of exhilaration by scientific activity
Are responsive to wonder and beauty
Feel sense of fulfillment when successful
Scientific theories have aesthetic value and qualities which are part of driving motivation
Objectivity is gained at time of absorption of individual science into collective body of public science
Facts, experience, and observation must be interpreted in context of themes that have and continue to thread over time through practice of science
"Since the primary object of the scientific theory is to express the harmonies which are found to exist in nature, we see at once that these theories must have an aesthetic value. The measure of the success of a scientific theory is, in fact, a measure of its aesthetic value...we see that the motives which guide the scientific man are, from the beginning, manifestations of the aesthetic impulse... J. W. N. Sullivan
24.4. Themes or Preconceptions in Science
Themata (Gerald Holton)
Definition: preconceptions or presuppositions that are believed but are not directly derivable from either observation or from analytical considerations
Most of themata are ancient and long lived
Holton suggests that about 50 have been sufficient to understand history of science
Evans and Shumate argue that only 5 primary themes are necessary to understand history of science
Unity theme
There exists a unity in nature deriving from nature's operation through a few simple principles which give rise to the multiplicity and diversity we observe to exist
Implications: simplicity or Occum's Razor
Mathematical theme
These few simple principles are mathematical in nature and they give rise to the mathematical laws that exist between nature's observable aspects and such mathematical laws are independent of any act of human perception
Implications: invariance, symmetry, necessity, and determinism
Transformation theme
Nothing springs from nothing, but all exists as transformations of some fundamental units, not necessarily material, in a multiplicity of ways
Implications: discreteness
Nature of phenomena theme
What exists must have either
Discrete character (locality)
Continuous character (non-locality)
Both continuous and discrete character (both local and non-local)
Neither continuous nor discrete character (void)
Implications: locality from discreteness, non-locality or global from continuous
Inevitability theme
Scientific thinking will inevitably comprehend all as consequence of the fact that directions in nature are not totally random but point toward a certain inevitable conclusion (meaning)--albeit that such a conclusion need not be known until the very end
Implications: causality (Newtonian), completeness
"When judging a physical theory, I ask myself, whether I would have made the Universe in that way, had I been God." Albert Einstein
24.5. Science, A Way of Knowing
Understanding in science presupposes the existence of a mental picture of the relational structure within the scientific enterprise; examples
Pyramid relational model, pure or abstract science flows down pyramid to create applied science and then to lowest level to create technology
Circular relational model, like wedges in a pie, activities in science and technology relate to nearest neighbors both beside and across
Tapestry relational model, threads are various fields of astronomy, physics, chemistry, and mathematics
Threads do not interact with each other at just one point
Are interwoven so that they interact at numerous points
Trying to be selective in what one accepts as valid and what is not valid is to misunderstand this interlocking structure
Any attempt to remove one thread would unravel whole fabric of science
Knowing that you know and how you know are as important as what you know
Technology, in contrast to science, is what human being have done to provide for our existence, and technology is an outgrowth of our instinct for survival
Science is not a process that can be learned devoid of content, i.e., mind does not work like computer with learned algorithms
Science is a human effort to devise a way of thinking
Albeit a very sophisticated method of thinking
About physical aspects of human existence
To use that way of thinking to conceive of theories that are logical representations of our sense experiences
Theories are most logical and economical means of representing past, present, and future events
Business of science is to trace in physical phenomena a consistent structure with order and meaning
In this way to interpret and to transcend our direct experiences
"There is a single general space, a single vast immensity which we may freely call Void: in it are innumerable globes like this on which we live and grow; this space we declare to be infinite, since neither reason, convenience, sense-perception nor nature assign to it a limit." Giordano Bruno
24.6. Incompleteness Theorem
1931, Kurt Gödel, Austrian mathematician, published the following paper in mathematical logic
"Über formal unentscheidbare Sätze der Mathematica und verwandter System, Teil I."
Main points of Gödel's paper
Given a formal, self-consistent, axiomatic system
There are statements that it cannot prove to be true
There are even true statements that it cannot prove to be true
To prove these statements true, must appeal to more encompassing axiomatic system which subsumes original axiomatic system
Implications of Gödel's theorem
Is a unified structure of thought, a cosmology, even possible in light of Gödel's theorem?
additionally one may ask
Has our system of thought, because of its incompleteness, pre-determined the arena in which we may look for answers to cosmological questions?
24.7. Cosmologies
Horizon-Stonehenge Cosmology (???-ca. 1000 B.C.)
A mystic-mythical cosmology
Horizon astronomy of Neolithic monuments
Astronomically significant monuments exist in both the old and new worlds
Babylonian-Egyptian astronomy
Technology, survival
Greek Cosmology (ca. 1000 B.C.-ca. 1500 A.D.)
A geometric-logical cosmology
Theology, philosophy, art, music, science, and mathematics
Thematic concepts - preconceptions or presuppositions - unity, mathematical representation, transformation, phenomena representation, inevitability
Thales, Pythagoras, Plato, Aristotle, Aristarchus, Hipparchus, Ptolemy
Galilean-Newtonian Cosmology (ca. 1500-ca. 1900)
A mechanistic-clockwork cosmology
Based on thematic concepts of Greek cosmology
Arabic-medieval European science
Copernicus, Kepler, Galileo, Descartes, Leibniz, Newton
17th century experimental science
Einstein-Friedmann Cosmology (ca. 1900-ca. 1960)
A mechanistic-mathematical cosmology
Based on thematic concepts of Greek cosmology
Relativity and quantum revolution
Explosion in experimental science
Modern observational astronomy; black holes
Planck, Einstein, Bohr, Friedmann, Lemaitre, Hubble
Modern Cosmology (ca. 1960-present)
A mathematical cosmology
Based on thematic concepts of Greek cosmology
Incompleteness theorem of Gödel
Extension of ideas in relativity and quantum theory; unified theory - theory of all
Missing mass; dark matter universe
Inflationary theory; flatness and homogeneity problem
Particle theories
Bell's theorem and string theory
Hawking, Sandage, Guth
What are the foundations of modern cosmology?
They are the same themes or preconceptions as those of science
Unity theme
Mathematical theme
Transformation theme
Nature of phenomena theme
Inevitability theme
They are certainly very old and by no means modern
They are probably Greek foundations or at least the major portion are probably Greek
They are without doubt controversial foundations in the following sense
Contention by many scientists that such "biases" or "preconceptions" certainly do not exist - objectivity
Contention that even if some preconceptions do exist they of a more recent origin
Contention that even in the worst case of the existence of old preconceptions they are much more diffuse in origin and impact on science or cosmology