jwilzewske: entropy

Showing posts with label entropy. Show all posts

Saturday, December 24, 2011

Hans Zimmer & Co. save Holmes, entropically

I t’s the furiously melodic likes of Gladiator, The Lion King, Inception, Batman Begins, Dark Knight Rises, Pirates of the Caribbean, Kung Fu Panda, and Sherlock Holmes that’s elevated film music to a thing of rocking beauty, as Zimmer and his team have employed every oddball instrument and influence from Gustav Holst, Lebo M. and the sound of bat wings into percussively thematic adrenalin.”
— Daniel Schweiger, 2011.

I f you ask me, Zimmer’s score rescues Sherlock Holmes (and Guy Ritchie et al.) in the new ‘A Game of Shadows’ film.

Z immer and his composer-orchestrator colleagues at Remote Control Productions created a beautiful and varied score that augments the color and vista of the film, lending atmosphere, scope, and interest to what otherwise could seem predictable. Never gets in the way of what the script and imagery are doing, but never merely reinforces or sonically reiterates what’s been said or shown.

B ut more than this, I am really thrilled with the tempi and the rhythmic architecture of this score. I got the soundtrack and listened to it several times, measured the tempi bar-by-bar in each of the cues, and created a spreadsheet of the values (see jpeg above). I also put an EKG on myself and digitized my heartrate during each listening. Not only did my heartrate adapt to each of the tempo changes, but the heart rate variability (HRV, using the simple RMSSD metric) also synced with Zimmer’s music. Empirically, I suspect that that “N-of-1” experiment is indicative of why this music “works”—physiologic response “pulls” cognition, rather than the other way around.

S ee the book by Bacci and Melcher (link below) for more on phase-locking and rhythmic ‘entrainment’ of breathing, heartbeat, and other physiologic rhythms, syncing with music.

S ince I’d captured the tempo timeseries, I decided to do some other calculations on it, too. I used the open-source R system’s package ‘entropy’ (link below) to calculate the Miller-Madow, James-Stein, Tsallis, Chao-Shen, and Shannon/Jeffreys entropy values. The entropy of the timeseries of tempi for these 18 cues is H = 2.72... pretty high... indicating a substantial amount of variability/unpredictability/interestingness. If you do entropy calcs for “bad” or ineffective film scores (as I happened to do several times last summer), you get much lower values, H between about 1.10 and 1.90.

M ost film schools don't even mention music, much less compare examples of good and bad scoring.”
— Richard Bellis, 2006, p. 8.

T he cues’ titles (track-names) collect words and phrases from the screenplay that are cadential—perfect rhythmic-harmonic demarcations of the narrative arc and plotting. It’s clear that Zimmer applied an admirable amount of objectivity in the spotting session, to inject material that adds considerable depth to the character or the story without the material asserting itself as a vehicle for his own ego.

T he score (Die Forelle; The Red Book; Moral Insanity) makes Robert Downey Jr’s Holmes more alert and angry when he is facing Jared Harris’ Moriarty. The score (He’s All ‘Me! Me! Me!’) makes Jude Law’s Dr. Watson all the more hapless as he gets unwillingly caught up in the plot.

T he producers and Guy [Ritchie, the director] and Jude [Law, co-star] and I got together and tried to have it feel like an extension of what we think brotherhood is—the bickering and miscommunications are part of something that aspires to something higher.”
— Robert Downey Jr., Scotland BigIssues Magazine 05-DEC-2011.

A Game of Shadows’ stands as a valentine to the public-school buccaneer. It provides Ritchie with a licence to run wild with Gypsies, trade punches with cossacks, or just generally arse about in expensive hotels. It gives us anarchy as panto and global espionage in the guise of a homoerotic stag weekend.”
— Xan Brooks, The Guardian.

I n other words, Zimmer’s score truly ‘services’ the film’s narrative, neither over-writing nor under-writing. Naturally, given the big-action subject matter in this film, there are lots of huge orchestral cues. But there are more than half of the cues that are intimate, chamber-like pieces.

M any think that what we do is ‘Art’. I disagree. Music is an art form. Film music is a craft with its roots in art. Art is a form of self-expression, and the last thing a director wants is some composer coming in and expressing him/herself all over the director’s film.”
— Richard Bellis, 2006, p. 69.

F olk idioms in the Romani melodies (doina repeated-note gesture of lament), pentatonicism, Phrygian scale with the second and third scale degrees raised when ascending, and fraigish harmonic minor, flying-staccato, alla zingarese poco a poco accelerandos “hallgató/lassú-közép gyors-friss" (e.g., Kesergö or or verbunkos or csárdás style in ‘It’s So Overt, It’s Covert’; ‘Romanian Wind’) to breakneck speeds, acrobatic violin with pitches bending and glissing, and the tone growling and crying ... great colla parte tempo-leading.

T he Hungarian hallgató of the ‘Did You Kill My Wife?’ brass band is superb.

G ee, this soundtrack is an admirable thing! The tremolos begin slowly, and the accelerandi melt into the flourishes so that they sound like one gesture—far bigger ones than you imagined when they began. The playing and conducting are excellent throughout. Precisely nailing the tempo variations, yet sounding totally organic while remaining faithful to meter. Very, very nice!

Friday, June 17, 2011

Minimalism/Designing Simplicity: Jordi Savall’s Celtic Viol

S hort motifs predominate... any feeling of meter is, basically, ‘local’. The majority of sections are only 8 bars long, with strong downbeat emphasis. Each section/variation offers new and different kinds of transparency, some more arpeggiated, some less so. The music may be Irish and Scottish in origin, but through this 2-hour recital I am drawn more than anything toward comparisons with Indian ragas—evolutions of a series of waves progressing over the ocean’s surface for hundreds of miles.

C omparisons with other kinds of minimalist music, a la La Monte Young, Reich, Nyman, Riley, and others seem apt as well.

[50-sec clip, Jordi Savall, ‘Macpherson’s Lament’; 2011, 1.4MB MP3]

I n Savall’s conception of the Scottish folk tune ‘MacPherson’s Lament’, the prospect of being hanged focuses the mind wonderfully. [The prisoner condemned to die requested the privilege to play one last tune, and this is the tune that he performed. Many fast trills, initiated on downbeat and then tapering—little symbolisms of trembling, waning life. After finishing the last note, the prisoner smashed the fiddle: the fiddle would die with him, a second homicide, violating the personhood of the instrument and compounding whatever other crimes MacPherson may have committed.]

T here are surely many musicians who have continued playing up to within a short while before their deaths, usually from cancer or other chronic illness. Consider the gesture as a form of palliative self-care. This is terminal abjection. The music is not meant to be salvific or curative, like a Tarantella! The musician knows full-well that s/he is about to die, and that there will be no reprieve, no escaping this fate. If anything, we hear a brave, dignified aesthetic of fast-approaching doom. [Did Shackleton’s Expedition have amateur musicians abord, I wonder? If so, what did they play toward The End?] All told, the repertoire of those whose lives are ended by the State must be a very small and specialized one. Savall’s performance suggests that jewish musicians of the Theresien (Terezin) Holocaust prison camp do not have a world monopoly on this literature. But I digress.

T he feature of the Jordi Savall-Paul O’Dette-Shane Shanahan performance last night that most fascinated me was the minimalism of it—and how this music (which is ordinarily performed in a freewheeling, raucous manner—at noisy dances with liberal imbibing, lots of stomping and shouting and carrying-on) resembles error-correcting codes in communications and software. The intermittent loss of phase-lock (due to signal attenuation, or multi-path reflections and other interference, or fluctuating changes in signal-to-noise ratio in the communications channel) in ballads and dance music is rapidly detected, the parts (treble viol in Jordi’s lap; Paul’s cittern/lute; Shanahan’s bodhran) are de-skewed, and phase-lock is recaptured, in large part due to the structure of these low-entropy framing “packets”, these 8-bar phrases.

H ave a look at Prof. Hartmut Obendorf’s recent computer science book (link below) to see what I mean.

I wish that Paul O’Dette and Shane Shanahan had had more substantial parts to play during the Celtic Viol concert last night, parts more illustrative of their expressiveness and musicianship. But despite their relegation to low-key ‘accompaniment’ roles, O’Dette and Shanahan seemed to enjoy themselves a great deal on-stage. Accompanists manifest a unique dignity arising from modesty, nurturing, and support—another species of minimalism, I suppose, providing the ‘canvas’ for the soloist’s artistic vision. It was all pretty cool.

Sunday, April 5, 2009

James Mulcro Drew, Chamber Music at Extreme Temperatures

James Drew, amid instruments made by sculptor Lin Emery

T he work’s timeless quality draws attention to a spatial world not unlike the movement within an Alexander Calder mobile, or parallel forms found in Asian court music ... a protest against the flow of musically-experienced time, rather than a space-drama imaginatively constructed from one fragment of a micromusical idea.”
— James Drew, program notes, Manhattan School of Music, 1970.

I aspire to incorporate spiritual immensities in my music through masses of sound which intensifies by the process of refraction or blurring, while allowing submerged melodic lines to appear and disappear. It’s like painting with a very large brush. Like those old fresco guys—or like Asian calligraphy on a massive scale—even with one tone. You know ... like a big swipe with a very loaded brush.”
— James Mulcro Drew.

I n thermodynamics, an adiabatic process is any thermodynamic process in which no heat is transferred to or from the surrounding space. The term ‘adiabatic’ literally means impassable, coming from the Greek roots ἀ- (‘not’), διὰ- (‘through’), and βαῖνειν ("to pass"). It means a total absence of heat transfer.

A t temperatures near 0°K, nearly all molecular motion ceases and the entropy change ΔS = 0 for any adiabatic process. Pure substances can (ideally) form perfect crystals as T→0.

Entropy change, adiabatic process, in the limit at absolute zero

[50-sec clip, Drew et al., Animating Degree Zero, ‘Animating’, 1.6MB MP3]

[50-sec clip, Drew et al., Animating Degree Zero, ’12 Centers Breathing’, 1.6MB MP3]

[50-sec clip, Drew et al., Animating Degree Zero, ‘Solemn Acts in Rain’, 1.6MB MP3]

I n this wonderful recording we have members of the Barton Workshop performing several works that James Drew composed between 2001 and 2005.

A t very low temperatures in the vicinity of absolute zero, matter exhibits many unusual properties including superconductivity, superfluidity, and Bose-Einstein condensates.

A t [musical] temperatures close to absolute zero, quantum [musical] particles begin taking on new ‘collective’ properties. Delinquent waves begin to act in concert. At low temperatures where everything occurs in slow-motion, the true nature of the most basic constituents of the ensemble are revealed. I wonder whether it could be measured... wonder whether quantum phenomena like the ‘observer effect’ occurs outside the subatomic world, in the world of macroscopic processes like human beings playing and listening to music. According to the second law of thermodynamics, all physical processes in the Universe can naturally flow only from a state of greater energy to lesser energy.

T hrow a stone into a lake, and the ripples it makes eventually die out. My cup of hot coffee can [left by itself in a setting where the ambient temperature is lower than the coffee] only get cooler, not hotter.

B ut near absolute zero the particles comprising an object behave differently. Although the ensemble ‘atoms’ are still part of a ‘gas’, they behave more like atoms of a metal—like one smeared-out single entity, similar to experiments with rubidium gas by Eric Cornell and Carl Wieman at the University of Colorado Boulder in 1995, for which they won the Nobel Prize for Physics in 2001. The James Drew expressions form what I think is a musical equivalent to a Bose-Einstein condensate—a peculiar property of atoms slowing down so much that they are zen-like, almost at rest.

T he sonic attributes that I’m referring to can be heard in each of the compositions on this disc... the ‘direct sound duration’ of each note, as contrasted with indirect sounds and their durations and decay. Listen to the sympathetic resonance between notes and the quadratic effect, especially in the piano part [when applicable].

I n the piano, a very high soundboard Q-factor shortens high frequencies’ durations. The piano’s soundboard mechanical impedance affects the global sound duration of the instrument, and, for the instrument performed and recorded on this disc, the high impedance yields longer-duration sounds, slower decays. The tones ‘blossom’ after the initial attack, and sympathetic resonances bring the ensemble of waves in-line. Electron-cloud-like, metallic.

O n hard [piano key; viola; etc.] attacks, the nonlinear part of the string response increases, producing frequencies with twice the values of the normal ones. The quadratic effect influences the loudness of this nonlinear response, and, when the score has such low entropy [close to musical absolute zero], the nonlinearities are very prominent—and are probably related to the superfluid Bose-Einstein condensate-like quality of the collective, coalescing, long-range musical effects that are created here. Similarities to quantum software algorithms (see writings by Matt Hastings at LANL, and others), in terms of process and in terms of how you go about measuring statistical physics properties of music like this...

D rew was born in 1929 and studied with Wallingford Riegger and Edgard Varèse. He taught at Northwestern University, Yale University, UCLA, Cal State, and other institutions. He has performed with and co-founded several musical groups, including the Crossfire Mission Orchestra in the late 1960s in New Haven (radical performances, often behind barbed wire), the Mysterious Traveling Cabaret, the American Music Theater in California, the Blast Opera Theater. In his quasi-retirement he has undertaken concerts and arts education work with the Grey Wolf Project. Barton ‘Zero’ disk is simply excellent.

Wednesday, November 5, 2008

Change We Can Believe In: Sofia Gubaidulina’s Mathematics of Physical and Religious Time

Co•na•tiv•i•ty (kō-nā-tiv'-ə-tee)
n. The aspect of mental processes or behavior directed toward change, including impulse, desire, volition, and striving.”

To-date, the analytical attention that’s been paid to Fibonacci series and other mathematical constructs in the compositions of Sofia Gubaidulina (София Асгатовна Губайдулина) has mainly concerned the role of mathematics in devising her melodies and harmonies and in guiding her voice-leading. Actually, it’s unclear whether Sofia actually uses the words ‘numerology’ or ‘gematria’ in discussing her own compositional methods. Her methods are in any case deeply associated with her Russian Orthodox religious beliefs and spiritual practices.

But besides the mathematical origins of her choices of pitches, she also creates ‘ambient’ fields of multi-rate polyrhythms that are based on the recursive Fibonacci and other mathematically derived series. Becomingness. ‘Change we can believe in,’ to borrow a phrase from the just-completed political election process in the U.S. I’ve recently been exploring recordings of Gubaidulina’s compositions, to discover Fibonacci-accelerando and Fibonacci-ritardando patterns—rhythmic counterparts to her number-theory-based polyphony. This CMT post is meant to tell you a little about what I am finding so far.

T hree hippocampal rhythms: theta rhythms (4-10 Hz), gamma rhythms (30-80 Hz), and a fast oscillation (140-200 Hz). These rhythms are independently generated; we have observed that gamma oscillations persist without theta and compete with fast oscillation... There is a definable relationship among all brain oscillators: a geometric progression from band to band with a roughly constant ratio of e— the natural (Naperian) logarithm. Since e is an irrational number, the phases of coupled oscillators of the various frequency bands will vary on each cycle forever, resulting in nonrepeating, quasi-periodic, or weakly chaotic pattern: this is the main characteristic of the EEG. [But] why are there so many oscillators [in the brain]? Why can the brain not use a single, fixed-frequency clock for all of its computing functions? There are multiple answers to these questions... Once a slow oscillator appeared in simple animals, faster ones could be added as needed in subsequent evolutionary stages [for controlling functions on faster timescales]. We observe the continued coexistence of all of those independent clocks in the neurophysiology and neuroanatomy of brains today. The brain is not like a single, precise, fast clock and time-division [to produce a series of slower clock rates from the fast master clock] as is seen in digital computers. [‘Intelligent Design’ zealots notwithstanding,] the human brain did not appear de novo. The myriad independent clocks are the residue of evolution of the brain over many millennia. There is extra resilience and survival fitness that comes from the multiplicity of biological clocks, from the N-fold redundancy”
— Gyorgy Buzsaki, Rhythms of the Brain, p. 113.

O nce the hippocampus has been primed by stimuli that come down the perforant pathway, its own subsequent responses are greatly enhanced. Three seconds after granule cells in the hippocampus receive their first priming burst from above, they open up the ‘gates’. They transmit impulses much more efficiently across their synapses. This enhancing effect rises to its peak 15 to 20 seconds later. What is the most effective rate at which to deliver these brief trains of potentiating stimuli? Stimulating at the natural theta frequency: 5-7 Hz. Why is the result called ‘long-term potentiation’? Because transmission remains increased for as long as three weeks after the stimulation. Where does the theta rhythm come from? Chiefly from the medial septal region. Medial septal cells are ‘pacemaker’ cells. Their temporal pattern of acetylcholine release drives theta rhythms throughout the hippocampal formation.”
— James Austin, Zen and the Brain, p. 181.

Since the 1980s Gubaidulina’s work has been deeply informed by her Orthodox faith and her ‘zahlenmystik’, or the use of gematria, numerology, mystical mathematical formulae such as the Fibonacci series and the Golden Ratio. Sofia began to use the Fibonacci sequence as a way of structuring the form of the work. The sequence was especially appealing because it provides a basis for composition while still allowing the form to ‘breathe’—the naturalism referred to above. It plays a prominent role in such pieces as ‘Perception’, ‘Im Anfang war der Rhythmus’, ‘Quasi hoketus’ and the symphony ‘Stimmen... Verstummen...’ ). Later the Lucas series and Evangelist series, sequences derived from that of Fibonacci, were added to her repertoire. These compositional devices and effects are easiest to study in Gubaidulina’s chamber works.

There’s a naturalness ... an innate and almost inevitable quality to Gubaidulina’s rhythmic structures. The proportions of the durations and the statistical distributions of the durations of notes feel like ratios and distributions that we are deeply familiar with from phenomena that occur in Nature. When things ‘wind-up’ toward a climax in a Gubaidulina composition, they wind-up in the manner that we see when gravity accelerates a falling object. When things ‘wind-down’, they wind-down in a progressively diminishing pace that we see in dissipative processes in Nature. The music of Sofia Gubaidulina imparts a distinct impression that it complies with the Laws of Thermodynamics and other physical principles. Mass and Energy are conserved, neither created nor destroyed in the course of performing the music. Entropy increases slightly from the beginning to the end of each piece. It can be measured, if you are inclined to do so. But even if you don’t measure it, you feel it. The Universe is proceeding as it should.

Apart from the Orthodox spirituality that Gubaidulina intended to confer on her compositions, all listeners can at least apprehend the ‘organic’ cosmology that her compositional designs embody—the internal consistency and balanced energy and entropy budgets.

Okay. Measure it? Sure. Take one of her simpler pieces, like ‘Serenade’—the Swedish guitarist Mats Bergström (jpeg above) has a nice recording of this piece. It’s clear and the polyphony and rhythmic complexity are not too daunting. The Gibbs-Shannon entropy of a random variable that takes on values i with probability p_i is defined as:

If the rhythmic lines’ clock-rates are arranged so as to be Poisson-distributed, then the entropy of the Poisson distribution is given in terms of an infinite sum:

where λ is the time-constant of the distribution. For long values of λ, the asymptotic form of this expression is:

Or, in a slightly different formulation, the Renyi entropy of order α where α varies between 0 and 1 is defined as:

Obviously, if a composer sticks scrupulously to a mathematical construct in devising rhythms and orchestration, the result may be too complex to be playable. So there are compromises and simplifying decisions to make—collapsing the complexity into something that retains the feel of the programmatically-generated structure but omits things that inject too much variability or impose cognitive demands that are excessive. There’s a need to write forms that support ‘mutual entrainment’ of the disparate rhythms, re-syncing them on some regular basis. I try computing statistical copulas, to do multivariate measurement of synchronization/association between clocks...

Sofia Gubaidulina, Serenade, Fibonacci-beamed 10:3, 11:3, 12:3

C ommunities of Clocks... ‘Mutual entrainment’ is a theme that recurs again and again throughout the physiology of coupled rhythmic systems... [The systems’] ‘phase-scatter’ is altered in proportion to the derivatives of new clock-phase with the old phase and the magnitude of the perturbing stimulus, as characterized by the following differential equation:
— Arthur Winfree, The Geometry of Biological Time, p. 119.

Winfree, Clock-phase ‘mutual entrainment’ of two coupled biological clocks

Based on my measurements thus far, it looks like Gubaidulina’s ‘Fibonacci N-tuplets’ (? Fib-tuplets) and other rhythmic figures are hard for humans to play in a perfectly Fibonacci-timed way. With the note-durations normalized to the duration in milliseconds of each N-tuplet, the 10:3, 11:3, and 12:3 Fib-tuplets in ‘Serenade’ have as-written theoretical Shannon entropies of -2.06, -1.78, and -1.58, respectively.

As performed by Bergström, we get average values of -2.11, -1.85, and -1.72——entropy values slightly lower (more ‘ordered’) than the theoretical as-written values, owing to the [neurophysiology of entrainment that gives the--] plateauing of durations in the middle. (N-tuplets comprised of notes of perfectly identical durations would have Shannon entropies of -2.30, -2.18, and -2.07, for the 10:3, 11:3, and 12:3, respectively.) Interesting...

The ‘clocks’ in our brain that control our muscle function evidently tend to rush the accelerando beginning and ritardando ending just a little, and have a rate ‘plateau’ in the middle where the durations of the notes do not change as much from note-to-note as they should if they were strict, perfect Fibonacci.

It’s just how we're ‘built’, part of our innate physiology—beyond our interpretive control, really. What Gubaidulina reveals in these Fib-tuplets is a boundary between our humanity and our animality; between our conscious, sapient nature and our unconscious, instinctual nature; between things under our control and things that are beyond the possibility of human mastery. It is a fine and beautiful thing she does, reminding us performers and listeners of these things—we are stewards, not owners, of our mortal, animal bodies; we should be mindful of other animals with whom we share the planet; and so on. The Fib-tuplets induce a rhythmic meditation on humility, a spiritual posture that is receptive to grace... Have a listen to the MP3 clip below and you will see what I mean.

MetanoiaMind.com ‘EEG rhythms and states of consciousness’

And the spiritual effect of these naturalistic, physiologically propelled rhythmic structures is what I would say is this: ‘instantaneous epiphanies’ during neural pulse-entrainment. Maybe not on the first performance or the first casual listening. But if you do these pieces with intensely focused repetition, as part of a meditative practice? Wow! How long does an epiphany take to reach? And, once arrived, how long does the moment last? Try it and see!

So Gubaidulina’s music can induce dramatically altered perceptions of time, and transport the listener or performer to ecstatic, mystical, sufi-like states. Try it when you’re alone with your ‘significant other’. Maybe you will get to some exotic tantric, transfigurational, mutual-entrainment place you’ve never been to before. Change you can believe in! The tantric, ecstatic quality of Gubaidulina’s writing is maybe related to ‘theosis’ or the ‘Doctrine of Deification’ and ‘participatory union’ with God in the orthodox patristic tradition (see Russell, Tatakis, and Zizioulas links below).

Mats Bergström is a graduate of the Royal University College of Music (RCM) in Stockholm and Juilliard in New York. He made his recital debut at the Wigmore Hall in London in 1983 and has since pursued a career as soloist, accompanist and ensemble player in various genres. In 2006, he was elected member of the Royal Swedish Academy of Music. He performs solo recitals as well as the standard works for guitar and orchestra, and collaborates with artists such as singers Malena Ernman, Annika Skoglund, Olle Persson and Mikael Samuelson, flautist Anders Johnhäll and violinist Joakim Svenheden. He stretches the concept of chamber music in much of his work. Beautiful, fascinating. Mats currently lives with his wife and 3 kids in an old schoolhouse 30 km northeast of Uppsala.

[50-sec clip, Mats Bergström; Sofia Gubaidulina, ‘Serenade’, mm. 22-35 1.2MB MP3]

Here is a little spreadsheet I put together, which shows the Fibonacci-prescribed accelerando and ritardando timings for Gubaidulina Fib-tuplets that appear in ‘Serenade’ and other of her compositions. You can click on the screenshot to explore or download a copy to play with. Enjoy!

A student doing a practicum in a nursing home reported to me an incident. She was walking with a resident along the hall where there were pictures of various bucolic, relaxing, unobtrusive scenes. One was a painting of a blacksmith shoeing a horse while a small boy looked on. The patient stopped at this picture and told the student, ‘This is a picture of me and Dad.’ The student asked me if, in fact, the picture was of the resident and his father. I told her that the patient's father had indeed been a farrier and that when he was young the son had often helped his father, but this was merely coincidental. The mid-19^th Century Currier & Ives ‘Village Blacksmith’ picture was certainly not a depiction of this particular man and his father in 1925.”
— Allen Edwards, A Psychology of Orientation: Time Awareness Across the Life Stages and in Dementia, p. 208.

[This moment was for the elderly man ‘epiphanic’. And his fugue-like behaviors and experiences were these days continuously filled with small epiphanies. How brutal it would be to dispute his statement. How utterly awful to try forcibly to ‘correct’ the patient’s ‘mistake’ by compelling him to acknowledge it is Currier & Ives’s picture of some generic blacksmith, as a part of a cruel regime of medicalizing and treating the patient’s ‘confusion’ or ‘disorientation’. The old man’s variant, epiphanic reality must be permitted to stand——must be allowed anyhow if one cares a jot about his psychological condition and spiritual future.
—— dsm.]