Monday, October 26, 2015

The Blinding Sun

I recently published this poem on Rational Faiths under the title "Growing Doubt". I need to publish it here, and I just encountered a famous sonnet that uses the same imagery. The messages are both the same and contrary. I will let you enjoy and judge them as you wish.
I was once told. . .


I was once told there’s danger in a question—
Faith and doubt cannot live in one mind,
And doubt leads men to shun the truth and fight
Their God—so I was told. I also learned
Truth shines eternal in the Son, and that is
All the light we need—straight from the source—

But I’ve seen mortal eyes fixed on the sun
Now following his brightness filtered through
Closed eyelids, doing good and seeing the world
As this light tells them it must look. Then when
Night comes they work to morning, filling their call
And telling those who stand in darkness what
The sun is like—the joys of fixing on his light.

They have forgotten that the child of night
Is not the child of darkness. There is truth
At night. The moon and wandering stars reflect
That same sun closed eyes preach, but no closed eyes
Will find these lights; and stars we cannot see
Give still more light than the sun that leads the blind.

I was told I’d built a tower to see the heavens,
And the Lord would cast it down and show
The foolishness of men. Maybe it is so,
But truth is good and light, and I will love it.
And from Joseph Blanco White (1775-1841)
To Night

Mysterious Night! when our first parent knew
Thee from report divine, and heard thy name,
Did he not tremble for this lovely frame,
This glorious canopy of light and blue?
Yet 'neath a curtain of translucent dew,
Bathed in the rays of the great setting flame,
Hesperus with the host of heaven came,
And lo! Creation widened in man's view.
Who could have thought such darkness lay concealed
Within thy beams, O Sun! or who could find,
Whilst fly and leaf and insect stood revealed,
That to such countless orbs thou mad'st us blind!
Why do we then shun Death with anxious strife?
If Light can thus deceive, wherefore not Life?

A Mathematician's Apology -- notes and quotes

After listening to The Man Who Knew Infinity, a biography of Ramanujan, I was inspired to read A Mathematician's Apology by G. H. Hardy. I remember my dad mentioning it many years ago. It's only 90 short pages, and here are a few highlights, for me. It's worth noting, I think, that this was written in 1940 by a man who had spent his entire life at the most prestigious university in England and almost literally without women, except for his sister. If you can enjoy it despite his elitism and sexism, it's a fun read.
Exposition, criticism, appreciation, is work for second-rate minds.
Did I just hear someone say my name? ;)
I write about mathematics because, like any other mathematician who has passed sixty, I have no longer the freshness of mind, the energy, or the patience to carry on effectively with my proper job.
Good work is not done by 'humble' men. . . . He must shut his eyes a little and think a little more of his subject and himself than they deserve. This is not too difficult: it is harder not to make his subject and himself ridiculous by shutting his eyes too tightly.
'I do what I do because it is the one and only thing that I can do at all well.'
most people can do nothing at all well. . . . perhaps five or even ten per cent of men can do something rather well. It is a tiny minority who can do anything really well, and the number of men who can do two things well is negligible. If a man has any genuine talent, he should be ready to make almost any sacrifice in order to cultivate it to the full.
Thankfully, I lack the genius to require that kind of sacrifice. (I think the gifted teacher must be the counterexample to Hardy's 'second-rate minds' barb.) Or perhaps instead of doing math because you are good at it, you do it because it came your way and you might as well:
'There is nothing that I can do particularly well. . . ' . . . most people can do nothing well . . . it matters very little what career they choose.
Approximately what Hardy is going to argue:
  • Math is worthwhile even though it isn't practical (despite his recognizing practical applications of some math).
  • People who are better at math than anything else should do it even if it ends up being a waste of time.
  • Doing something of permanent value, even if it is small, is worthwhile and unusual. Most people don't do anything of permanent value.
The ambition to leave something permanent behind is the greatest ambition, and his target audience is those who agree with this. I once would have. Now I view it as one admirable thing, when balanced with other ethical considerations.

Three driving motivations for research:
  • Intellectual curiosity
  • Professional pride
  • Desire for reputation, power, and/or money
I encountered a recent news article that cited research claiming that science is a reputation economy. Scientists are more interested in reputation than money or power (on average), and I can believe that. Of course, it's a sliding scale.

Math is perhaps the most permanent achievement, since languages die, but math remains. And math is pretty good about giving credit to the people who really did it.

Now for Hardy on art:
A painting may embody an 'idea', but the idea is usually commonplace and unimportant. . . . the importance of ideas in poetry is habitually exaggerated. . . . The poverty of the ideas seems hardly to affect the beauty. . . .
Math lasts longer, but
there is no permanent place in the world for ugly mathematics.
Chess problems are the hymn-tunes of mathematics. [low level of beauty]
As regards applied math:
The 'seriousness' of a mathematical theorem lies, not in its practical consequences, which are usually negligible. . .
Serious math connects many, complex mathematical ideas. Other traits that make math meaningful are depth, beauty, generality, unexpectedness, inevitablity, and economy.

Most useful math is boring, small, and mathematically unimportant. I can concur with this, since my field uses quite a lot of math, but it really is mostly boring, small, specific applications of ideas with much broader mathematical richness. Unexpected pieces of "pure" math do at times become useful, at times, but they are still small pieces.

Hardy closes equating the value of math with the value of art:
The case for my life, then, or for that of any one else who has been a mathematician in the same sense in which I have been one, is this: that I have added something to knowledge, and helped others to add more; and that these somethings have a value which differs in degree only, and not in kind, from that of the creations of the great mathematicians, or of any of the other artists, great or small, who have left some kind of memorial behind them.
I had expected to resonate with Hardy's apology more than I did, but some parts of it rang very true to me. I do aspire to leave something behind. I do hope that it will be unique and beautiful in its sphere. And I feel like I have had only one idea that even approaches the category of mathematical thought. It was the question I asked when I imagined, what if Gods evolved? It's an idea so inevitable that atheists like Richard Dawkins and Sam Harris admit the possibility, but reject it's importance and miss its implications. Yet it is an idea that ties together Mormonism and Transhumanism, religion and science, faith and the future of humanity. It accepts that Gods are limited, but goes beyond to reveal what some limits are. It answers the problem of evil--maybe not as anyone would wish, but very cleanly. It claims an empathetic middle ground between arbitrary universalism and eternal damnation. It leaves a place for God to act and to be hidden. It brings atonement into the realms of nature, and makes salvation about relationships, not satisfying unchanging justice. It creates Gods in our own image, but not falsely idealized. It may come to nothing--there's no eternity for bad philosophy--but it is surprising and beautiful to me.

Monday, October 12, 2015

SURT notes I.1.3 p.30

The Singular Universe, Roberto Unger 

Ch 1 p.30+

The two cosmological fallacies are closely connected. They reinforce each other. They make each other seem to be unavoidable conceptions--indispensable to the practice of scientific inquiry--rather than the contestable options that they in fact are.
Your certainties are disposable options.
The second cosmological fallacy limits our understanding of the variations of nature.
Artificial limit.
The first cosmological fallacy presupposes a view of the workings of nature that makes any other conception of how nature works seem to be incompatible with the requirements of science.
Another artificial limit. Hiding in the unknowable infinite instead of seeking deeper explanations. This is the same false hiding place of the theology of unknowable Gods.
The first cosmological fallacy commits a mistake of method, with empirical assumptions and implications. The second cosmological fallacy amounts to a mistake about the facts of the matter, with wide consequence for the practice of science. The matter that it mistakes is the most important in science: the nature and history of the universe.
. . . there is already more . . . in what science has discovered about the universe than our established natural philosophy . . . is willing to countenance.
There is more. As Unger says we need a science that can proceed without absolute, timeless laws to rely on, we need theology and salvation that can proceed without an omnipotent, transcendent God and infallible revelation. Mormonism has them if we Mormons will accept them.

If cause and effect is an illusion, it can be represented by timeless natural law (and thus math). If time is real, we have to work harder to explain the connection between math and nature.
Causal connections . . . form a real feature of nature.
Previous events actually matter for current events, not simply initial conditions and timeless laws. We can't simply decide that nature obeys laws. We have to measure what happens and only generalize as far as is justified. Laws will vary over time.

Relationships shape subsequent events in law-like ways, despite there being no eternal laws. Relationships govern the cosmos. Many are predictable.
The preceding contrasts show that the reality of causal connection is closely or internally related to the reality of time.
Time and causation are both real. This differs from the deterministic, block universe models of string theory.

Time and relationships are eternal. Laws exist because of regularities in relationships, not vice versa.
[The reality of laws], however, is a derivative reality by contrast to the primitive and fundamental reality of causal connections.
Laws are derivative from agency (that defines relationships) from the bottom to the top (since elementary particles have aency).
These [timebound] ideas do their work at the cost of attacking the foundations on which much of our thinking about causes and laws has wrongly come to rest.
Can't make an omelette . . . 

Emergent phenomena can be truly novel. Not just rare, novel, quantum entangled states that Smolin proposes searching for to prove the principle of precedence. I think this supports my view that human choice is incompletely predictable. It's mostly predictable because relationships behave in predictable ways, but when there are emerging problems with unprecedented solutions, there is incompletely predictable agency at play. Otherwise, we are observing predictable agency, but it's all agency.
Cosmology affirms its ambition to be the most comprehensive natural science when it understands itself as a historical science first, and as a structural science only second.
This strikes right at the core of arrogant, deterministic certainty.
. . . we allow a historical explanation to count as a causal account in cosmology and physics . . .
Historical explanations are real science, and emergent phenomena can't always be predicted.
. . . a state of affairs is the way it is because of the influence of an earlier state of affairs, not because it conforms to timeless and invariant regularities. We shall not always be able to account for the influence of the earlier on the later by invoking such regularities. . . . [we must] pay the price of a practice of historical explanation that is not subordinate to structural explanation.
Law is subordinate to cause, and that comes at a price.
Time . . . is not emergent.
Time goes all the way back.
. . . we have reason to resist accepting either that change of laws of nature is governed by higher-order laws or that it is not.
It's a false dichotomy to require a choice between nature governed by laws or lawless nature. Neither one is the best model, but something in between. I think he is saying that discarding the idea of transcendent law is not the same as saying that anything goes.

SURT notes I.1.2 p.18

The Singular Universe, Roberto Unger

The First Cosmological Fallacy

[in the Newtonian paradigm] The observer stands, both in principle and in fact, outside the configuration space. Conceptually, his relation to it resembles the relation of God to the world, in the Semitic monotheisms . . . : not as creator but as observer. He looks upon it, to use an astronomical metaphor, from the vantage point of the stars. The laws go together with this ideal observer. They govern what happens inside the configuration space. They have, however, no history of their own within that space--or anywhere else.
This is the understanding of science that has led people of my acquaintance to see God as equivalent to the laws of nature. It is also the understanding of science that leads Alvin Plantinga and others to claim that mysteries of science are evidence of God. The failure of cosmologists to truly explain things like fine tuning (instead of explaining they create unobservable values and universes) is easily co-opted as support for the kinds of Gods that are outside of time. All this confirms my long held prejudices against believing in such a God.
Deaf to Newton's warning no to feign hypotheses, we may appeal to the idea of multiple, parallel universes in an effort to rescue the cosmological uses of the Newtonian paradigm. . . . this conjecture will amount to no more than a vain metaphysical fantasy disguised as science.
Unger really isn't nice to multiverse interpretations of cosmology.

[in real time] The observer can no longer stand outside the configuration space, and claim to adopt the godlike view from the stars; all the stars, and everything around them, are dragged down into the field of explanation.
Transcendent science and religion both set arbitrary limits beyond which humanity may not pass without departing from nature. While I believe in an (at least effectively) infinitely complex nature, I don't like the imposition of untested limits.
Thus, every feature of the Newtonian paradigm fails when its subject matter ceases to be a region of the universe and becomes the entire universe. The denial of this failure . . . corrupt[s] the practice of scientific inquiry and prevent cosmology from remaining faithful to its vocation to be a master science rather than a sideshow.

It is as if the jump from the finite to the infinite provided a generic license for the ideas that, in the absence of such license, would readily be dismissed as untenable.
I'm pretty sure he is referring specifically to infinite energy density--the mathematical singularity we know as the Big Bang, or as black holes. He later claims no beginning to time, so some quantities may be infinite without creating the logical license he says others have taken. I need to check this and see if my arguments using infinities hold up or can be replaced with large and growing quantities.

The Second Cosmological Fallacy

Presentism is a problem in cosmology, not just history. Pastism is a problem in assessing the progress of evolution as influenced by humans. Assuming that technology cannot or should not influence evolution at rates beyond what was effected by nature in the past is misguided.
The discovery that the universe has a history, and so therefore must everything within it be historical, has implications for the practice of science. We have so far failed to acknowledge them.
The same is true of theology. Joseph Smith started us (in modern times) with thinking about God as being historical, but we've largely lost it even in Mormonism. It is a big deal.

Accepting singularities as real (the Big Bang had infinite energy density, as do black holes) makes them beyond exploration or explanation (at least in some important ways). Believing these energy densities are large but finite implies "no insuperable obstacle of principle exists to investigating and explaining" the Big Bang or black holes. A singular God (omnipotent, omniscient, etc.) is closed to exploration. A large but finite God we may be able to understand.
The second cosmological fallacy is the disposition to take account of only the [current] state of nature while disregarding the [big bang], and to do so in our methods as well as in our theories. When we succumb to this fallacy, our conception of how to practice science, as well as our view of the workings of nature, allows itself to be shaped by an intellectual engagement with only one set of the variations of nature. It becomes in a sense the science of a special case. It consequently remains limited in the reach of its insight even into that special case. The deepest enigmas of nature escape it.
I am placing Gods into a broader state of nature than our current one, and even into a state beyond our (currently) observable universe, but not beyond nature.
everything is emergent--everything comes and goes--except time.
Gods are emergent. From what? How?
[In] many of the most influential cosmological theories . . . the alternative traits of nature remain hidden under the veil of the infinite.
An infinite God is unknowable unless we are infinite in the same way god is.
Such a science--the science that we in fact have--will be bereft of the cosmological equivalent of the physics of phase transitions: an account of the transitions from one state of nature to another.
Special case science with assumed transcendent laws is incapable of speaking to the reproduction of universes.

Friday, October 9, 2015

SURT notes I.1.1 p.5

The Singular Universe notes and quotes, Unger and Smolin 2015

The science of the one universe in time

In this book we argue that the evidence of science--the deliverances of the science of today, viewed in the light of its recent history--does not entitle us to circumscribe the reality or the reach of time. Our causal judgments cannot indeed be anchored in immutable laws and symmetries.
However predictable, life simply isn't certain.
. . . [laws] may derive from [causal connections] rather than the other way around.
Laws depend on relationships and not the other way around. Corollary: God's laws depend on relationships, not the other way around. Thus, grace and atonement are the features that define law, not repairs to fix broken laws.
It is one thing to respect the inability of science to show that the universe must be what it is. It is another thing to reduce science to a body of precise laws, symmetries, and constants that are unable to account either for themselves or for the initial conditions of the universe.
Real limits vs. self-imposed limitations.
An initial objection to this approach is at once methodological and moral. It invents imaginary entities--all the other unobserved and unobservable universes (in cosmology) or states of affairs (in particle physics)--to save itself from having to confront, in either particle physics or cosmology, the failure of its theoretical conceptions to account for nature as we encounter it. In this way, it wastes the treasure of science, its enigmas.
Enigmas aren't wasted by answering them, they are wasted by saying that they can never be answered. This is the same moral sin engaged in by those who would claim that God is ultimately unknowable, or that a doctrine is an inexplicable mystery. In pretending to embrace the mystery, they waste it, while those who seek to demystify the mysterious, who seek to know God, are the truest lovers of the mystery.
At the end of the day this approach evades the work of explanation. It subsumes the unexplained laws and initial conditions under a vast framework of possible variations of nature, all but a tiny number attributed to unobservable universes and unknown states of affairs.
All possibilities exist as unobserved actualities. Unger and Smolin reject this, and in doing so support an open, evolving, and undetermined cosmos.
Structure results from history more than history derives from structure.
Natural laws are consequences of regularities resulting from cosmic history, not the other way round.
[while there are limits to it, this inverted approach] vastly enlarges the field of causal inquiry. As a result, it suggests an agenda of empirical research that communicates with the major discoveries that cosmology has made over the last hundred years and continues to make now.
Putting the Gods into the cosmos, rather than as the transcendent causes of it, does the same for theology and religious experience. Questions defined as untestable and unanswerable by a transcendent view of God are made tangible, hopeful, and fruitful.
The relations between mathematical and logical propositions are, however, timeless: the conclusion of a syllogism is simultaneous with its premise. They are timeless, even though we reason them through in time, and use them in the analysis of events in time.
Logic and math hold true independent of evolving natural law. So when they are appropriately applied, they do describe nature even if we reject that they define nature.
. . . effacement of particularity goes together with denial of time.
One reason math fails to perfectly describe the world.
However, its selectivity--its disregard for time and particularity--is the source of its usefulness.
This power perennially tempts us to succumb to two connected illusions. The first illusion is that we have in mathematics a shortcut to indubitable and eternal truth, somehow superior to the rest of our fallible knowledge. The second illusion is that, as the relations among mathematical propositions are timeless, the world itself must somehow participate in the timelessness of mathematics.
Mathematics, however, is smaller, not greater, than nature. It achieves its force through a simplification that we can easily persuade ourselves to mistake for a revelation and a liberation.
I know no greater feeling of revelation than what comes with math. The only problem is when we mistake the import of the revelation. This is the same problem of revelation that those who seek to follow the Holy Spirit face every time the seek revelation--the reality of revelation is not in question, but the interpretation is hard.

Monday, October 5, 2015

Singular Universe and the Reality of Time (SURT) notes part 1

Notes and quotes from The Singular Universe and the Reality of Time by Roberto Mangabeira Unger and Lee Smolin, 2015

The nature and scope of this work

To think of the universe as a whole . . . we soon reach the limits of what we know and even of what we can ever hope to know. We press science to the point at which it passes into philosophy and philosophy to the point at which it easily deceives itsolf into claiming powers that it lacks.
Yet we cannot cast this topic aside. . . . we should not seek to escape it because no one can develop and defend ideas about parts of natural reality without making assumptions, even if they remain inexplicit, about nature as a whole. . . . Part of the task is to determine what science has actually found out about the world from the metaphysical commitments for which the findings of science are often mistaken.
I certainly get tired of interacting with critics of God and religion who are expert at pointing out the mistaken metaphysical commitments of religious people (usually incorrectly as applied to me), but view their own understanding as assumption free, or as nearly so as to not matter. I find some glee in the barbs of Unger and Smolin toward these people from the perspective of physics and philosophy.
[regarding the reality of time] By implying the mutability of the laws of nature, the idea of the inclusive reality of time contradicts a dominant interpretation of what the physics and cosmology of the last hundred years teach us about the workings of nature.
Physics and cosmology have assumed an invariant background of time (even if it is somewhat relative), but this is about to go. We're about to see any simple kind of determinism disappear. That makes me happy.
[This work] seeks to distinguish what we in fact know--the hard empirical residue of scientific discovery--from the lens of assumptions through which we are accustomed to see the larger significance of these factual findings.
Smolin and others have been inspiring me to do this with my religion for several years now. It's quite the journey.
It will sometimes happen that no fundamental progress can be achieved in science without dissolving this marriage between the empirical residue and the philosophical gloss. Once the marriage is dissolved, it becomes possible to see the discoveries of science with new eyes. It is never possible, however, to do so without changing some of our beliefs about how nature works.
I'm attempting to separate the experience of God and of the world from the theological gloss. As noted, it can't be done without changing some of our beliefs about how God works.

There are two philosophies followed by Unger and Smolin:
. . . the relational approach to nature and the priority of being over becoming. . . . The case for them here lies in the insights that they together make possible.
In theology, following these philosophies has led me to a new conception of God that I think gives insights on Gods, the meaning of life, the nature and purpose of revelation, free will, universalism and exclusivism, and other significant theological topics. Yet it is a battle to have the ideas heard after more than a century of an unchanging God being the dominant view in Mormon thought. Notwithstanding a changing God seeming to have been the view of Brigham and Joseph.
Timeless versions of relational space-time leave inexplicable basic features of nature such as the choice of laws and of initial conditions. . . . The result may be to substitute a mystical notion for a scientific program by invoking an external force or entity that produces becoming in an otherwise passive universe.
The timeless God of the gaps can live in these features forever without fear of being disturbed or deposed. There will always be room for the First Great Cause, the Prime Mover. But such a being is both protected and curtailed by this position.

They propose a new natural philosophy, "temporal naturalism". Natural philosophy is needed to inspire and enhance normal science to engender revolutionary science.
It is an effort that can succeed because the mind is what it is. We can always see and discover more than any set of methods and presuppositions, in any discipline, can prospectively. Vision exceeds method, and reshapes the practice and discourse, according to its needs.
I want visionary religion in a church that has largely been practicing normal religion for more than a century.
Cosmology is not just one more specialized science. It is the study of the universe as a whole, beyond which, for science [and for Mormonism], there lies nothing.
All our ideas about parts of nature will be influenced, whether knowingly or not, by our assumptions about the whole universe.
I'm trying hard to make the influence of my assumptions knowing.