# The Fine-Tuning of the Universe for Scientific Technology and Discoverability Slides are good until at least 21.

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The Fine-Tuning of the Universe for Scientific Technology and Discoverability
Slides are good until at least 21.

PART I: BACKGROUND

Review of Anthropic Fine-tuning evidence
The anthropic fine-tuning refers to the fact that the basic structure of the universe must be precisely set for life to exist, particularly embodied conscious agents (ECAs). The fine-tuning comes in three types: Fine-tuning of mathematical form of the laws of physics Fine-tuning of the fundamental parameters of physics Fine-tuning of the initial conditions of the universe Most of the discussion in the literature has been on (2), the fine-tuning of the fundamental parameters of physics.

Fine-tuning of Fundamental Parameters
Question: “What are the fundamental parameters of physics?” Answer: They are the fundamental numbers that occur in the laws of physics. Many of these must be precisely adjusted to an extraordinary degree for ECAs to exist.

Example: Gravitational Constant
The Gravitational constant – designated by G -- determines the strength of gravity via Newton’s Law of Gravity: F = Gm1m2/r2, where F is the force between two masses, m1 and m2, that are a distance r apart. Increase or decrease G and the force of gravity will correspondingly increase or decrease. (The actual value of G is 6.67 x Nm2/kg2.) m1 r m2

Dimensionless Expression of Strength of Gravity
The gravitational constant G has units (e.g., in the standard international system it is G is 6.67 x Nm2/kg2 ). Physicists like to use a measure of the strength of gravity that does not have units. A standard choice is: αG = G(mp )2/ℏc, where mp is the mass of the proton, ℏ is the reduced Planck’s constant, and c is the speed of light. Other parameters are also usually expressed in dimensionless form.

Example of Fine-Tuning: Dark Energy Density
The effective dark energy density helps determine the expansion rate of space. It can be positive or negative. Unless it is within an extremely narrow range around zero, the universe will either collapse or it will expand too rapidly for galaxies and stars to form. How fine-tuned is it?

Answer: In the physics and cosmology literature, it is typically claimed that in order for life to exist, the cosmological constant must fall within at least one part of – that is, 1 followed by 120 zeros -- of its theoretically natural range. This is an unimaginably precise degree of fine-tuning.

Dark Energy Density: Radio Dial Analogy
WKLF: You must tune your dial to much less than a trillionth of a trillionth of an inch around zero. +15 billion light years. -15 billion light years.

Summary of Evidence Biosphere Analogy: Dials must be perfectly set for life to occur. (Dials represent values of fundamental parameters. Illustration by Becky Warner, 1994.)

Summary-continued

Review of Multiverse Explanation
The so-called “multiverse hypothesis” is the most common non-theistic explanation of the anthropic fine-tuning. According to this hypothesis, there are an enormous number of universes with different initial conditions, values for the fundamental parameters of physics, and even the laws of nature. Thus, merely by chance, some universe will have the “winning combination” for life; supposedly this explains why a life-permitting universe exists.

Observer Selection Effect
The Observer Selection Effect is crucial to the multiverse explanation. According to this idea, observers can only exist in universes in which the laws, constants, and initial conditions are life-permitting. Therefore, it is argued, it is also no coincidence that we find ourselves in an observer-permitting universe.

Multiverse Hypothesis
Humans are winners of a cosmic lottery:

Many Planets Analogy Given that the universe contains a huge number of planets, it is no surprise that there is a planet which orbits just the right star and is just the right distance from the star for life to occur. Further, it is no surprise that we find ourselves on such a planet, since that is the only kind of planet creatures like us could exist on.

Testing the Theistic Explanation against the Multiverse Explanation
Features of the universe that confirm divine purpose over a naturalistic multiverse will consist of features of the universe that meet the following conditions: (1) We can glimpse how they could help give rise to a net positive moral value – and hence it would not be surprising that an all-good God would create a universe with these features; (2) They cannot be explained by an observer-selection effect . (3) They are very coincidental (surprising, epistemically improbable) under the non-theistic multiverse.

Discoverability Our ability to discover the nature of the universe, which prominent scientists such as Albert Einstein and Eugene Wigner considered to border on the “miraculous,” seems to meet the three criteria: Criterion (1): We normally take discovering the nature of our universe to be of value – either as intrinsically valuable or because it helps us develop technology. Therefore, it would not be surprising under theism that the universe would be structured so that it exhibits a high degree of discoverability.

Criteria (2) – (3) Criteria (2) – (3): There seems to be no necessary connection between a universe being life-permitting and its being discoverable beyond that required for getting around in the everyday world. Thus if the proportion of life-permitting universes that are as discoverable as ours is really small, it would be very improbable under a multiverse hypothesis that as generic observers we would find ourselves in such a universe. I will provide quantitative evidence that this proportion is small.. Life-permitting universes that not highly discoverable. A life-permitting universe that is highly discoverable

PART II: CASES OF DISCOVERABILTY
In the following slides, I will focus on the cases of discoverability involving the fundamental parameters of physics since we can potentially get a quantitative handle on the degree of discoverability in these cases. However, a significant case for discoverability can be made from the fact that the laws of nature have the right form so that we can discover them. This has been pointed out by Eugene Wigner in his famous piece “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” (1960), and recently elaborated in some detail by Mark Steiner in his Mathematics as a Philosophical Problem (1998).

Examples of Fine-tuning of Laws
Hierarchical simplicity Quantization Technique Gauge (local phase) invariance technique 4. Structure of quantum mechanics itself (complex numbers, measurement rule, etc.) Eugene Wigner: “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve” (1960). Einstein: “The most incomprehensible thing about the universe is that it is comprehensible."

Two Types of Fine-tuning for Discoverability
To get a quantitative handle on how coincidental the discoverability of the universe is, for each fundamental parameter of physics, I consider the effects on discoverability of varying it. By doing this, I have found that there are two types of fine-tuning for discoverability:

Type 1: Livability/Discoverability-Optimality Fine-tuning
Livability/Discoverability-Optimality Fine-tuning. This sort of fine-tuning of a parameter occurs if given the basic overarching principles of physics and the current mathematical form of the laws: (i) the parameter is within its livability-optimality range (the range between the thin solid vertical lines); (ii) The parameter falls into that part of the livability-optimality range that maximizes discoverability (range between thin dashed lines). This is shown in the figure below, with the star representing the actual value of the parameter in question: Note: The region between the two thick black lines is the life-permitting range. As far as I can tell, all fundamental parameters seem to be fine-tuned in such a way as to satisfy Livability/Discoverability Optimality.

Example 1: CMB The most dramatic case that I have discovered of this kind of fine-tuning is that of the Cosmic Microwave Background Radiation (CMB). The CMB is microwave radiation that permeates space. It was caused by the big bang.

Basic Idea Behind Big Bang
The visible universe began in an explosion in which all its matter and energy was condensed into a volume less than the size of a golf ball. It consisted mostly of very intense light in the form of photons and particle/anti-particle pairs. Since that time, the universe has been expanding, causing it to cool. Status: Finished

As the universe expands, a photon’s wavelet is stretched because of the expansion of space between the beginning and end of the wavelet. This causes the distance between the crests to get longer and longer. Thus if a photon of light starts off with a wavelength (~450nm) corresponding to blue light, it’s wavelength will get longer and longer. If the universe expands enough, the wavelength will be stretched into the microwave region of the spectrum (~1mm – 10mm). Blue wavelength Microwave Wavelength

Significance of the CMB
The CMB tells us critical information about the large scale structure of the universe: “The background radiation has turned out to be the ‘Rosetta stone’ on which is inscribed the record of the Universe’s past history in space and time.” (John Barrow and Frank Tipler, The Cosmological Anthropic Principle, 1986, p. 380).

Optimizing CMB Much of the information in CMB is in very slight variations in its intensities of less than one part in 100,000 in different parts of the sky. Since it is already fairly weak, this implies that within limits, the more intense it is, the better a tool it is for discovering the universe.

CMB and Baryon/Photon Ratio
Intensity of CMB depends on baryon to photon ratio: ηbγ = (#baryons/#photons) = (#protons + #neutrons per unit volume)/(#photons per unit volume). Prediction of Livability/Discoverability-optimality Fine-tuning: Within the range that ηbγ does not influence livability or other types of discovery, its value is such as to maximize the intensity of the CMB since this would maximize discoverability.

Prediction Correct! Note that the intensity of the CMB is maximal when ηbγ/ηbγ0 = 1: that is, when the baryon to photon ratio is the same as in our universe. Plot of the intensity of the cosmic microwave background radiation (CMB) versus the baryon to photon ratio. CMB/CMB0 represents the intensity of the CMB in the alternative universe compared to our universe, and ηbγ/ηbγ0 represents the baryon to photon ratio in the alternative universe compared to that in our universe.

*Example 2: Weak Force (α w)
The primary role the weak force plays in the universe is the interconversion of protons to neutrons. Potassium 40 (K40) and Carbon 14 (C14) both form the basis of two important dating techniques. Both decay via the weak force. Their decay rate ∝ α w2. Thus, increase the weak force by ten-fold, the decay of rate of potassium-40 would be one hundred times as large, making the amount of K40 in the earth far below the range of detectability; this would render K40 dating useless for dating. Further, the life-time of C14 would be 57 years, instead of 5,700 years. This would make C14 dating useless for artifacts much older than 300 – 400 years old. Note: Particularly in the case of C14, decreasing the weak force does not allow any new dating technique that could replace C14 to become available.

Weak Force -- Continued
The neutrino interacts with other particles via the weak force. Because of this interaction is so weak, neutrinos are very difficult to detect. However, neutrinos carry important information about nuclear processes in the interior of the earth and stars, information that no other known form of radiation carry. Decrease weak force by 10-fold, it would be virtually impossible to detect neutrinos from the earth, sun, and supernovae. Already, detectors are very expensive and the number of neutrinos detected is barely above background noise. require an enormous amount of fluid. Thus, when both radioactive dating and neutrino detection are taken into account, the weak force seems to fall into the discernible-discovery-optimal range.

Type 2: Tool Usability Fine-tuning
The second type of “fine-tuning” is that for having enough usable tools to make the universe as discoverable as our universe is. To explicate this fine-tuning requires defining some terms.

Tools and Discoverability Constraints
A Tool of Discovery is either some artifact or feature of the universe that is used to discover the domain. For example, a light microscope is a tool used to discover the structure of living cells. A Tool Usability Constraint is a non-anthropic/livability constraint that must be met in order for the tool to be usable. These constraints constitute necessary, though not sufficient, conditions for usability. For example, a necessary condition for the use of potassium-argon dating is that there be detectable levels of radioactive potassium 40 in the earth.

Tool Usability Constraint Range and Bounds
A tool usability constraint bound on a parameter is the range of values that the parameter can have for which the tool is usable.

Two Illustrations of Concepts
1. Wood fires and the fine-structure constant. 2. Light microscopes and the fine-structure constant.

Fine-Structure Constant (α)
The fine-structure constant, α, is a physical constant that governs the strength of the electromagnetic force. If it were larger, the electromagnetic force would be stronger; if smaller, it would be weaker.

Example #1: Fires and α A small increase in α would have resulted in all wood fires going out . . .

Civilization and Wood Fires
. . . but harnessing fire was essential to the development of civilization, technology, and science – e.g., the forging of metals.

Explanation Why would an increase in α have this result? Answer: In atomic units, everyday chemistry and the size of everyday atoms are not affected by a moderate increase or any decrease in α. Hence, the combustion rate of wood remains the same. In these units, however, the rate of radiant output of a fire is proportional to α2 . Therefore, a small increase in α – around 10% to 40% -- causes the radiant energy loss of a wood fire to become so great that the energy released by combustion cannot keep up, and hence the temperature of the fire must decrease to below the combustion point. .

Conclusion for α and Wood Fires
Upper Bound on α: The ability of embodied conscious agents (ECAs) to build open wood fires, and hence forge metals,drastically decreases if α is greater than 10% to 40% of its current value. This is represented in the figure below: the actual value of α is represented by the star. The star must fall below the dashed vertical line in order to have open wood fires. Tool = open wood fires for forging metals. Tool usability constraint –ability to ignite and maintain open wood fires. Tool usability constraint range for α – range of α for which it is possible to have open wood fires (all the values for α below the thick vertical dashed line).

Example 2: Microscopes and α
A relatively small decrease in α would decrease the maximum resolving power of microscopes so they could no longer see cells – thus severely inhibiting, if not rendering impossible, advanced medical technology (such as the development of germ theory). As is, α is just large enough to allow us to see of 0.2 microns, the size of the smallest living cell.

*Why this Effect? In atomic units, the speed of light = c = 1/α. Decreasing α, therefore, increases the speed of light without affecting everyday chemistry or the size of atoms. Thus, the world would look mostly the same. The energy of a photon = E = hf, where h is Planck’s constant and f is the frequency of light. (h = 1 in atomic units). A photon of visible light cannot have more energy than the bonding energy of typical biochemical molecules, otherwise it would destroy the molecules in an organism’s eye. This requires that for light microscopes, f < 800 trillion cycles per second. Wavelength of light = λ = c/f. In our world, the above restriction on frequency means that λ > 0.35 microns. Since c = 1/α, as α decreases, c increases, which causes the minimum wavelength of light for a light that can be used without destroying an organism’s eye; this in turn means that the resolving power of light microscopes will decrease since their maximum resolving power is half a wavelength (λ/2).

A “Second-Order” Coincidence
The only alternative to light microscopes for seeing the microscopic world is electron microscopes, which can see objects up to a thousand times smaller than can be seen by light microscopes. Besides being very expensive and requiring careful preparation of the specimen, electron microscopes cannot be used to see living things. Thus, it is quite amazing that the resolving power of light microscopes goes down to that of the smallest cells (0.2 microns), but no further. If it had less resolving power, these cells could not be observed alive.

Summary Top Figure: The star represents the current value of α and thin dashed line represents the lower bound of α for which the light microscope would be usable for seeing all living cells. Bottom Figure: Combines the wood-fire upper bound and the light microscope lower bound for α. The coincidence is that the wood-fire upper bound falls above the actual value of α and the light-microscope lower bound falls below.

Main Argument Define {Ti0} as the set of tools that we use in our universe to discover various physical domains. Given this definition, the main argument can be summarized as follows: It is highly epistemically improbable (i.e., very surprising) under naturalism that every member of {Ti0} is usable It is not surprising under theism that every member of {Ti0} is usable. Therefore, by the likelihood principle of confirmation theory, the usability of {Ti0} strongly confirms theism over naturalism.

. FURTHER EXAMPLES

Example 3: Electric Transformers and α
In atomic units, the strength of a magnetic field produced by a current or magnetic dipole in a ferromagnetic substance is proportional to α2. One Consequence: Decreasing α would require that transformers be proportionally larger; this would cause a proportionate increase in loss of energy by hysteresis – already a limiting factor.

Example 4: Length of Year and α
1. Length of year determines length of seasons. 2. Importance of seasons: (a) instills planning for future; (b) allows for dating by means of stratigraphy (tree rings, lake beds, coral reefs, ice cores, etc.); (c) helps in keeping historical records. To be effective in the above ways, the seasons must not be too short or too long.

Length of Year and α -- continued
L(year) ∝ α-11/2 (Lightman, 1984, Eq. 22, p. 213). Increase α by a factor of 3, a year becomes less than an earth day. Decrease α by a factor of 5, a year becomes greater than 10,000 earth years. Both cases would eliminate usefulness of seasons mentioned above, without giving rise to anything to replace their role in discoverability.

*Example 5: Parallax and α
By measuring the angle p’’, one can determine the distance to a star using the formula: 1au = distance from sun to earth = dsin(p’’). Therefore, d = 1au/sin(p’’).

*Parallax and α -- continued
Distance of habitable planet from its star ∝ α-4 (Lightman, 1984, Eq. 21, p. 213). With a three-fold increase in α, a habitable planet would be 81 times closer to its star, and thus parallax would be good only to 1/81 the distance given the same atmosphere. With the best ground-based telescopes on earth, parallax can only be used to for stars within a 100 light years. The nearest star is Alpha Centauri, approximately 4 light years away. Thus a three-fold increase in α would eliminate the usability of ground-based parallax measurements for any stars.

Summary Diagram for α The star marks the current value of α, which is approximately 1/137. Usability Constraint Bounds: Upper Usability (thick dashed): wood fires; parallax; seasons; Lower Usability (thin dashed lines): light microscopes; electric transformers; seasons.

Importance of Naturally Occurring Radioactive Elements for Discoverability. Use for discovering atom. Radioactive dating. (An irreplaceable means of dating).

Dependence on Strength of Gravity, αG
If αG is decreased more than a billion-fold, the amount of naturally occurring radioactivity in a planet as livable as earth would be less than 1/10,000 of what it is in the earth. This would severely hamper, if not render impossible, radioactive dating. It would also at least hamper the discovery of the nature of the atom.

*Why? Basic Explanation
If αG is decreased, to retain an atmosphere, the radius of a habitable planet must increase. Now, the ratio of volume to surface area of a planet is proportional to its radius. Since the amount of heat produced in a planet via radioactive decay is proportional to the volume of the planet, unless the density of radioactive elements decreases with a decrease in αG, the amount of heat energy per unit area going out through the planet’s surface – and hence the amount of volcanic activity – will increase as αG decreases; at some point this would drastically decrease the planet’s livability. Fairly simple calculations show that for there to be even 1/10,000 as much radioactive elements in a planet’s crust, a planet as livable as ours requires that αG >

*More Detailed Explanation

Optimality The level of natural radioactivity is about as large as it could be without causing a health hazard to any carbon-based life form as complex as us. Since the higher the level the better for radioactive dating, it seems adjusted to be nearly optimal for livability while also optimal for discoverability.

Diagram The star (αG ~ 10-38)represents the actual value of αG (and the dashed vertical line ((αG ~ ) represents the lower usability bound for non-C14-radioactive dating. 1

Example 7: Dimensions of Space
Using the constraint that the mathematical form of the law of gravity be maximally discoverable, it is possible to derive both that gravity obeys an inverse square law and that space is three dimensional. We will show this on the next two slides, starting with Newton’s shell theorem.

*Newton’s Shell Theorem
Discoverability Constraint. The gravitational force obeys Newton’s shell theorem, which says that (i) for an object located outside a spherically symmetric shell of mass, all the matter in the shell can be considered to be at the center of the shell; and (ii) if an object is inside a spherically symmetric shell of mass, the net force on the object is zero. This theorem greatly simplifies calculations of gravitational force – for example, it allows one to consider all the mass of the earth to be at the center; without the theorem, to calculate the force of gravity on the surface of the earth, one would have to know how the density of the earth varies with radius. The theorem is only true if Fg ∝ 1/rN-1 , where N is the number of spatial dimensions. Figure: A uniform shell of mass with a center marked by the star. The attraction of the shell on the object inside is zero; the force of attraction on the object external to the spherical shell is Fg = G x (mass of shell x mass of object)/r2, where r is the distance from the object to the center of mass of the shell.

*Final Step in Derivation
Anthropic Condition: Given that F ∝ 1/rN-1 as required for Newton’s shell theorem, it is well known that stable planetary orbits require that the N – 1 < 3. Since N > 0, this means that either N = 2 or N = 3. A 2-dimensional space is highly unlikely to allow for the kind of complex neuron-like interconnections that ECAs require, and even it did, a 3-dimensional space would be far superior for the existence of ECAs that could discover the universe. Thus, discoverability requires that N ≠ 2. Therefore: If the form of the law of gravity is to be maximally useful for discovery, space must be 3-dimensional and gravity must approximately obey an inverse square (1/r2) law.

Example 8: Low Entropy of the Universe
The universe started with an exceedingly low entropy. This low entropy state is a special, highly ordered, state that is extraordinarily improbable. This improbability is illustrated in the next slide, taken from a book by one of Britain's leading theoretical physicists, Roger Penrose:

From Roger Penrose, The Emperor’s New Mind, p. 343.

Cannot be Explained by Multiverse
This low entropy cannot be explained by a multiverse hypothesis since it is enormously more probable for a random fluctuation to give rise to a small low-entropy region – such as the size of the solar system -- in which observers can exist than for it to give rise to a region of low entropy the size of the universe. Thus, under the multiverse hypothesis, the vast majority of observers should expect to find themselves in a small region of low entropy. Analogy: If a hundred coins in a row are shaken, it is vastly more likely that five coins would all come up heads in a row (local region of order) than for all the coins to land on heads (a large region of order). In fact, the former is virtually certain to happen at least once in the entire row whereas the latter has a chance of less than one in 1030 of occurring.

Explained by Discoverability
Low entropy of entire universe makes it more discoverable for at least two reasons: A universe that has a low entropy throughout is necessary for us to observe other stars and galaxies, and thus to understand the origin and nature of our own planet and sun. (The existence of stars and galaxies requires low entropy.) To apply general relativity to the cosmos – which is central to doing cosmology – one must assume that the distribution of matter is nearly uniform at large scales. This would not be true if the universe started in a high entropy state.

*Other Cases 1. Earth’s Magnetic Field – allows for naturally occurring magnets; used for navigation; helps determining position of continents. Puts a lower bound on the strong nuclear force and a lower bound on the electron to proton mass ratio. 2. Existence of supernovas and Cepheid variable stars at time ECAs exist. (Important for determining distances to other galaxies.) Puts constraints on several parameters, such as the strength of gravity and the photon to baryon ratio. 3. Planets too far away to observe (or reach and communicate by satellites). Places lower bound on strength of gravity. 4. Conditions for workable satellites – atmosphere not too thick; satellite not too far away. Places lower bound on strength of gravity. 5. Existence of enough copper for an advanced civilization that uses electronics. Puts a lower bound on strength strong nuclear force; requires the existence of weak force.

PHILOSOPHICAL ANALYSIS AND THEOLOGICAL IMPLICATIONS
PART III PHILOSOPHICAL ANALYSIS AND THEOLOGICAL IMPLICATIONS

Is it Coincidental? Next I will indicate why we should find it highly coincidental (epistemically improbable) under naturalism that the tool usability bounds presented above are met.

Coincidences for α The star marks the current value of α, which is approximately 1/137. Discoverability Constraints: Upper Discoverability (thick dashed): wood fires; seasons; parallax Lower Discoverability (thin dashed lines): seasons; light microscopes; electric transformers. In order for the discoverability constraints to all be met, all the thin dashed lines must fall below the star and all the thick ones above the star. Since the upper end of the scale is far above 1, and the star is at ~1/137, using α itself as the natural probability measure, it is extremely unlikely by chance for all the thin lines to fall below the star and all the thick ones above the star.

Radioactivity and Strength of Gravity Coincidence Analysis
The theoretically possible range of the strength of gravity, αG, is 0 to 1. Let the star represent its actual value, αG ~ A conservative estimate of the usefulness of radioactivity requires that αG > This lower bound is represented by the thin dashed line. If we think of this lower bound as having an equal probability of falling anywhere in the theoretically possible range, the chance of its falling below is one part in 1038. 1

Unknown Tools Objection to Argument
This objection is that there are other possible tools for discovering the physical domains in question. Given enough other potential tools that would be as good for discoverability, it is likely by chance alone that one of their tool usability ranges will overlap the value of the parameter. This would undermine the argument. To answer this objection, we first must articulate it by considering a fictitious illustration.

Illustration Let the star represent the value of some fundamental parameter, say αq . Suppose its range is 0 to 10, and the star is located at 1. Finally, let each dashed line represent the lower bound on αq for the usability of some possible tool to probe the microscopic world. Finally, let the first dashed line represent the lower bound on αq for the usefulness of light microscope. One might then say that there was a 1/10 chance that the lower bound of light microscopes would be below the star. But, because there are so many possible usable tools, the chance that one of them would be usable is close to 100%. Hence, we should not be surprised that some tool as good as a light microscope is usable.

Response In most cases, there are no other good alternatives to the tool in question. Consider the case of light microscopes. Within the types of worlds we are considering, apart from extrasensory perception, creatures of our size can only gain information via taste, touch, sound, and light. The first three do not have the ability to resolve objects the size of cells. That leaves only light, and hence light microscopes, or something like electron microscopes that generate an image that can be seen. Electron microscopes, however, require light microscopes to construct them; also they are limited – for example, they are very expensive and you cannot see a living cell with them. Thus, light microscopes are irreplaceable. Another Example: Radioactive Dating.

*Fine-tuning of Underlying Laws
Given the value of the parameter is almost fixed by the anthropic range, then the fine-tuning is at the level of underlying laws. To see this, note that: Since the mathematical form of the laws of nature determine the tool usability constraint ranges, given the underlying laws, it is no coincidence that the usability constraint ranges fall where they do. What is coincidental, however, is that our universe has these underlying laws instead of laws in which the usability ranges do not overlap the value of the parameter in question. So, the fine-tuning is at the level of the fundamental laws, not the values of the parameters. Using the parameter itself, or some natural function of it, as a probability measure for the overlap will allow us to obtain a quantitative handle on the degree of coincidence.

Define {Ti0} as the set of tools that we use in our universe to discover various physical domains. It is highly epistemically improbable (i.e., very surprising) under naturalism that every member of {Ti0} is usable It is not surprising under theism that every member of {Ti0} is usable. Therefore, by the likelihood principle of confirmation theory, the usability of {Ti0} strongly confirms theism over naturalism. Discoverability, therefore, gives us evidence in favor of the theistic explanation of the anthropic fine-tuning over that of the multiverse hypothesis.

Primary Theological Implication
If the above argument is correct, this provides good evidence that it was one of God’s primary purposes to create a highly discoverable universe, instead of being a bi-product of some other aim of God’s. Wartime Analogy: If on a bombing run, the bombs landed in such a way as to maximize the killing of civilians, and this required considerable fine-tuning, that would be strong evidence that the civilians were intentionally targeted. Why? Because if they were dropped to achieve some other goal -- such as destroying military targets, one would not expect them to land in just the right way as to maximize the killing of civilians – unless achieving that other goal implied maximizing civilian deaths.

Possible Secondary Theological Implications
If one of God’s primary purposes was to make a discoverable universe, that raises the question as to why God would want such a universe. Some possibilities: Such a universe allows for technology and hence gives us the resources to make our lives better and help one another. Can this idea be generalized? Suggests that reality is constructed to be morally and spiritually discoverable.

Theological Implications -- Continued
3. By being discoverable, the world is structured in such a way that it both trains our reasoning capacities and greatly amplifies the value we place in reason. Is there some important divine purpose for this? 4. Science, which depends on discoverability, also gives us new conceptual resources for thinking about theological and spiritual matters. Is there something particularly important about this? 5. Discoverability raises the question: is there something spiritually important about discovering the structure of the universe?

Best of all Possible Worlds?
6. The data so far also indicates that for the variations we can look at, the universe seems to be the most conducive for the flourishing of ECAs. Does this suggest that structurally, our world might in some ways among the best of all possible worlds?

Final Implication If technology and discoverability are part of God’s purposes, it would be a good bet to invest in technology stocks.

End of main presentation

EXTRA SLIDES

Categorizing Tools An absolutely critical tool or means is one that is central to all of advanced science and technology. The ability to forge metals is an example of an absolutely critical tool. An irreplaceable tool is one such that the ability to discover a domain of physical reality will be severely degraded, if not rendered impossible, without the tool. For example, light microscopes are irreplaceable tools for cell biology. An important tool is one that plays an important, but not irreplaceable, role in discovering some domain. For example, carbon 14 dating is an important, but probably not irreplaceable, tool for archeological dating.

Further Hypothesis: Tool-Near-Optimality Hypothesis
The Tool-Near-Optimality hypothesis is the hypothesis that the level of usability of the tools is such that cultural factors – such as the ability of societies to organize and develop mathematical thought –are the major limiting factor for the development of science, not the quality of the tools.

Technical Stuff Odd’s form of Bayes’ Theorem: 𝑃 𝑇│𝐸 & 𝑘’ 𝑃 𝑁│𝐸 & 𝑘’ = 𝑃 𝑇 𝑘’ 𝑃 𝑁 𝑘’ 𝑥 𝑃 𝐸│𝑇 & 𝑘’ 𝑃 𝐸│𝑁 & 𝑘’ T = Theism N = Naturalism E = C1 & C2 & Ck Where Ci is the claim that the ith tool usability constraint is met.

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