On the Collective Lacanian Real, some notes to the poem, "the reef of Godel's woe"

In a previous post I uploaded a poem I wrote, "the reef of Godel's woe". This touched on a number of themes, but it hinted, towards the end, of a strange symmetry between two opposes forces so to speak in culture and language. The poem concerned itself with the Lacanian "Real", those places and events, generally traumatic, though not always, where language breaks down. The "Real" in Lacan is not reality (the world described by language) but is rather those places where language breaks down. The UFO hovering over the corn fields. Traumatic events like 9/11. Even at times intense feelings of romantic desire. These things all somehow escape language, and are examples of the "Real". In Lacan's theory, the mind develops coping strategies to deal with this Real, and structures the sub-conscious around sort of "fencing off" the intrusion of the Real, the intrusion of those events where concepts and linguistic systems break down, the "Tower of Babel" events in everyday life so to speak.

The symmetry I hinted at, is that while the Lacanian Real serves as a "Lack" (another Lacanian term), that is, it is the "lack" of the ability of concepts or language to keep up with experience, loosely speaking, there ought to be a countermanding fore to the Real, that is, in psychoanalysis, finding out how the mind has built coping mechanisms to deal with the Real and "re-programming" these coping mechanisms to alleviate symptoms, is how the Real for the subject is dealt with. Culturally and historically, is there a similar antidote so to speak for the Real? That is the issue I wanted to raise most primarily.

These issues sometimes are best approached by way of analogy. In the Tanakh, Israel under Joshua had to deal with a lot of challenges in the conquest of the land of Canaan. Some of these challenges could well be seen as examples of the Lacanian Real. Joshua and his friend Caleb spied out the land of Canaan and reported "giants". The term "giant" is kind of a catch-all phrase in ancient literature for "formidable opponent" but more than that, it is an opponent not normally encountered and one that inspires fear. Today we might call certain paranormal events, like UFO's, as something like this ancient experience of "giants". Canaan had what today we might think of as a paranormal effect on the Israelites, it represented a fear of the unknown, something that did not fit into traditional categories and experience. Surely Israel under Moses had dealt with opponents before (read: the Egyptians) but never such fear-inspiring phenomena as was seen in Canaan. This was a classic example of the Real - where something traumatic breaks in and "disturbs the universe" if one wills. However, Joshua had a secret weapon as it turned out which is known to any Stephen Spielberg fan: the Ark of the Covenant. As Dr. Marcus Brody said to Indy, "An army that carried the Ark before it, would be invincible". And so it was as recorded in ancient tradition. No giants or other such paranormal phenomena could stand a chance against Joshua's armies that had the Ark, and in time Canaan was under control of Israel. The Ark, then, was an "antidote" to the experience of the Real.

I won't get into the ins-and-outs of psychoanalysis in terms of how the "Real" is dealt with, other than briefly to make this point: a fundamental basis for analysis to work is the bond between therapist and subject. The subject needs to form a trust with the therapist in order for therapy to work, and process called technically "transference" though I won't belabor the details here. Suffice it to say that it is the emotional bond that takes place in therapy that enables the subject to "re-program" her subconscious as it relates to the Real. Academic insight into one's problems is not enough, rather, the emotive content of the therapeutic process is what really makes it effective. The subject cannot just "view from a distance" his subconscious but must get into the trenches so to speak, a process made possible by the relationship of trust built with the therapist. This bond with the therapist the subject has becomes the subject's "Ark" which enables her to wage war against her experience of the Real.

Historically and culturally there is also this "Real". Events like Pearl Harbor or 9/11 or more recently with the unspeakable tragedy at Newtown, CT disturb the cultural universe and render the collective subconscious (so to speak) in something of a shell-shocked state. What then, is an "Ark" (an antidote to the Real) to be had on a cultural / socio-historical level? "Society" does not have a "therapist" with whom to form an emotional bond. Indeed, as the late Baroness Thatcher alluded to once, there is no such thing as society, there is only all of us as individuals, individuals frail and frightened at the slings and arrows of outrageous fortune so to speak, and when enough people in a society become "shell shocked" societies crumble into totalitarianism or other forms of chaos. What antidote to the Lacanian Real is there to be had on a societal level? Where is the Ark of the Covenant if one wills?

Carlos Arrendo, an immigrant to the United States from Costa Rica, had a son in the military who died in the Iraq War in 2004, and in wake of this event became known as a peace activist. Tragically, his other son died in 2011 by his own hand, unable to deal with the loss of his brother. A few weeks ago, Carlos, a man who has suffered unimaginable tragedy, was at the Boston Marathon to cheer on a runner who was running in honor of his son lost in the war, and was near the finish line when terrorists detonated bombs, killing and maiming countless people around him. Rather than seeking cover, he ran into the carnage, clearing debris so that emergency personnel could gain access to the victims, and single-handedly helping to tie off arteries to stop the bleeding of people whose limbs had been blown off. His courage became a symbol for the resilient spirit of the people of Boston and America, a people who can endure beyond human understanding, and rise up to aid one another in the darkest hour.

Rabbi Sherwin Wine, the late founder of the Society for Humanistic Judaism wrote a number of poems as part of defining a new liturgy for the contemporary era. This is one:

(in transliterated Hebrew)

Ayfo oree? Oree bee.

Ayfo tikvatee? Tikvatee bee.

Ayfo kokhee? Kokhee bee - v'gham bakh.



Where is my light? My light is in me.

Where is my hope? My hope is in me.

Where is my strength? My strength is in me – and in you.



Returning to the question I metaphorically described as where is there an "Ark of the Covenant" on a societal level to counter the experience of the "giants" of the present time, I would posit that human beings rising above what is normally humanly possible, as Carlos Arrendo did, is what gives hope for the future, gives hope that despite senseless events like the Marathon bombings or Newtown, CT, that human life will continue to flourish, because the good people outnumber the bad, and the interdependent force of people coming together to overcome impossible challenges creates a force greater than the sum of its parts, greater even than any given analysis of this force, even this post. What might one call the name of this interdependent force, driven by a common bond of humanity as great or greater than the bond between subject and therapist, this force that defies all giants, all terrorists, all dark nights of the collective soul? Well, it is a secret. Not really, but it is more fun that way. :-) So I'll just tell you this: Lilith knew it. She called it Arammu. You my friend, well, you can google it.



Francis Erdman

Austin, Texas

April 28, 2013 C.E.

the reef of Godel's woe (a poem)

this is not a poem, this is not a line therein, nor is this a clause

this is not self-referential like Bertrand Russell's Barber of Seville

self-reference is the bane upon which set theory founders, incompletely

so we must build better babels to beguile the reef of Godel's woe

which is to say babel must be abandoned and humbler pursuits obtained

leaving our half-flung edifices incomplete but at least consistent.





in the primordial state before the dawn of word memes there was the Real

not "reality" but an absence, a non-sense, the Lack of any sense

we need today only to look at the skyline of southern Manhattan

to see this Real which exists as two towers which should be there but are not

the Real you see does not exist, it is the lack of that which should exist,

Rachel refusing to be comforted, for Newtown's children are no more.





mathematical set theory is construed to bring order from the void

whereof it holds, reason holds and whereof it holds not let us there tread not

Turing made machines that could compute all but their own innermost workings

and more powerful oracle machines that yet too could not self-reflect

Russell's Sets, Turing's Machines, and Godel's Logic all could not introspect

Platonic objects divining all knowledge except knowledge of themselves.





Cantor's Aleph Numbers first rendered infinity intelligible

and formed the basis for set theory before Godel found limitations

long ago likewise did Moses give us the Law so that humans might live

day to day under the shadow of the Real without casual slaughter

if Math is an enterprise forever beneath the Pall of Incompleteness

so is Ethics an enterprise forever beneath the Pall of the Real.





yet prior to the Law there was the Real as did the Void precede the Light

or as the Sophists preceded Plato or Esau preceded Jacob

but as the Real is Not, but is naught but Lack, it threatens ever the Law

for it is easier to destroy than to build, to murder than to save,

it is easier, so the computer people tell us, to verify

an answer than to find it sometime before Jadis awakens in Charn.





the Real surely is Not but it forever threatens the Law and Reason

but the Law, beleaguered, has an equal and opposite force on its side

another No-Thing, not an object itself, that yet counteracts the Real,

it avoids the self-referential paradox by not having a Self,

Lack-of-Lack, not existing, whose ek-sistence opens the door to the Law -

I don't know what to call it, but they say Lilith knew it as Arammu.





Francis Erdman

Austin, Texas

2013-04-25

On the Ontological Symmetry of the Tegmark Level IV Ensemble

The ontological status of the Level IV ensemble has been a murky issue, and here I suggest a possible way forward. The Level IV ensemble are those mathematical structures that comprise the Level IV multiverse (where the Level III multiverse refers to the quantum multiverse which can be thought of as a vector in Hilbert space, the Level II multiverse as the well-known inflationary model, with the Level I being the multivariate configurations of matter as expressed in an infinite amount of Hubble volumes contained within each inflationary "bubble" of the Level II).

The ontological status of the Level IV relates to the measurement problem, that is, what structures is one likely to find in a "typical" denizen of the Level IV multiverse, which, once known, one could begin to look for these structures within one's own universe, presuming one lives in a "typical" universe. For example, if we determine that the Level IV "typically" produces inflationary-like models, and that, furthermore, these models have say, cosmic strings (string-theory lines of energy that span across light years), then one would know to look for these, which, if found, would provide an indirect confirmation of the Level IV multiverse, in a sort of statistical manner.

However, before the measurement problem can be looked at, the ontological symmetry issue of the Level IV needs at least a passing glance. This issue can be stated simply this way: which mathematical structures correspond to real, physical worlds and which do not, and, having established this, in what sense do these mathematical structures "exist"? Or, as William Jefferson Clinton might put it, this issue comes down to what the definition of "is", is.

I here suggest the following solution to this issue: 1) "Physical" worlds, or, put another way, worlds likely to evolve observers to have these conversations in the first place, correspond to mathematical descriptions which may be said to be computable, that is, the laws of physics of such worlds can be defined / described by a finite and halting computer program, or Turing Machine. 2) Uncomputable descriptions (or Turing Machines running on non-halting input) bear no correspondence with "physical" worlds, and, furthermore, those aspects of mathematics which are not computable (the real numbers, i.e., fractions, for instance) also bear no correspondence with "physical" worlds, however, their ontological status is the same as those aspects of mathematics which could correspond to physical worlds.

(1) above is a rather tame assumption. It is merely restating the Computational Universe Hypothesis (Tegmark, et al) which more or less says that the Level IV ensemble is made up of worlds whose laws of physics can be described by a finite, halting Turing Machine (and thus, in some sense, can be thought of themselves as being "computers" or behaving as such). (2) is perhaps a bit more hard to stomach, but I would suggest is the simplest way out of the conundrum of ontological symmetry.

Concretely, let us take "computable" sets - Aleph_0 in the Aleph set for instance (where the Aleph set ("Aleph numbers") is the set of sizes of infinity, Aleph_0 being the smallest, the infinity of integers, Aleph_1 being the next smallest, including the real numbers, and so on, so the Alpeh set or Aleph numbers is sort of an infinite set of infinite sets, ordered by cardinality, or "size"). So let us say the Level IV ensemble are those worlds that can be described as computable (halting) functions over the Aleph_0 ("Aleph Naught") set, and say that those functions over this set which are not computable (which do not halt or are not well defined) do not correspond to anything in the Level IV ensemble, and we can furthermore say that any sets above Aleph_0 in the Aleph number series are irrelevant insofar as the Level IV ensemble is concerned.

However, and here is the key point, the "ontological status" of (say) the Alpeh numbers (the "set of infinite sets" so to speak) is the same whether we are talking about computable sets or not. The only distinction is that computable sets happen to correspond to worlds where one might happen across a spacetime metric from time to time and perhaps little green men to have these sorts of discussions with. Put another way: the "is-ness" of mathemetical structures (or, here, members of the Aleph set, to give a concrete example) is all the same, and, while computable functions correspond to members of the Level IV multiverse and are unique in that sense, these computable functions do not have more "is-ness" than their non-computable brethren. Hence "ontological symmetry" is preserved while defining the Level IV, that is, we have not "privileged" one or more mathematical structures as having more "is-ness" than others.

To give a rather naive analogy, but by way of explication: in computer programming there are basically two kinds of errors, "compiler" errors, and "runtime" errors. A "compiler" error for non-programmers out there are those errors in which the machine cannot understand the syntax of the code - perhaps one forgot a semicolon someplace for instance, depending on the language - and thus cannot run the program at all. A "runtime" error is an error that happens during program execution - that infamous "blue screen of death", for example, for those long-suffering Microsoft users out there (yes, I am an Apple groupie!). I am here essentially positing that the Level IV ensemble can be thought of as a collection of computable sequences without either type of error. If a sequence ran forever, never halting, that is a "runtime error" (is not computable). If a sequence is not well-defined in the first place (cannot be defined in terms of integers, for example, and needs real numbers - fractions - for instance) that is a "compiler error". However, if I write three programs, A, B, C, where A has a compiler error, B has no compiler errors but has a runtime error, and C has neither kind of error at all, all three are quite "real" but only C has any usefulness. Similarly, if one thinks of the world of mathematics in its various forms, one can think of this as being quite "real", but only a subset - the integers - is well defined when it comes to computability (has no compiler errors, very roughly) and only a subset of that is actually computable (halting in a finite time and giving back an answer). I suggest that the Level IV multiverse is in a sense made up of or defined by computable functions but that these have the same ontological standing as any other well-defined mathematical structure - it just so happens by necessity that only computable functions can describe things we like to think of as "universes".

Thinking along these lines, the pieces snap together rather facilely: what comes to mind when we think of a "universe"? Well, a metric to define space and time, at least. Well a metric itself is just a topology with a few additional properties thrown into the mix, and a topology is a discrete system, easily defined computationally. The Level III ensemble (the so-called quantum "parallel worlds") can be viewed as a vector in Hilbert Space with certain discrete states, a system which is also definable in computational terms.

If on the right track here, we can begin to address the measurement problem by better understanding the nature of computation, the behavior of computational systems, and in particular Turing machines and other "finite state" machines. Because such study would enable us to figure out what "typically" shows up in computational worlds, and knowing that, then we know what to look for in our own world, know what to predict, essentially. Which of course would make discussions of the Level IV ensemble into a real, predictive science, shielding it from the accusation of being so many mathematical parlor games, as does happen from time to time.

It is not lost on me that the issue of Oracles poses potentially some questions for the Computational Universe Hypothesis which I am here supporting. An Oracle Machine is a Turing Machine M, which, for an input, I which is non-computable for M, can nevertheless return an answer by using an Oracle (M sort of takes I, gives it to the Oracle, gets the answer back from the Oracle machine, and then returns back the answer for the input I, where the Oracle machine is just another Turing machine, a "black box" so to speak). So, if the Level IV ensemble is comprised of computable functions, what of functions which have a so-called "Turing degree" of 1? (Where a computable function has a Turing degree of 0, a function computable via 1 Oracle has a Turing degree of 1, a function needing 2 Oracles has a degree of 2, and so on.) This may be a red-herring, given how the same computational sequence can be modeled in multivariate ways, but I only mention it to illustrate the vexing nature of trying to pin down the Level IV ensemble, and related ontological issues. Simply throwing about the term "computable" merely begs the question, how is one using the term, "computable"?

But this I can leave to another day. Here I wanted to simply offer a suggestion to the question of the ontological symmetry of the Level IV ensemble by offering the perhaps unorthodox suggestion that mathematical structures have all the same ontological status (level of "is-ness" so to speak), and the fact that some structures correspond to physical worlds neither elevates these favored few structures, nor degrades the others, insofar as ontological status goes.

It must be left to future researchers to determine the computational model of the sunken city of R'lyeh where dread Cthulhu waits dreaming...

In response to the Connecticut tragedy...

Like anyone else, my reactions to the shootings in Connecticut were shock and horror. After all, one might expect such carnage from, shall we say, more rural parts of the country, but certainly not in "civilized" New England. That such horror should transpire in that august and tranquil region is beyond comprehension. My first thoughts were and still sort of are along the lines of: this is why, along with "the Duke" (Gov. Mike Dukakis), one of my personal heroes, I have always supported gun control, since there is a reason why this sort of tragedy does not transpire in the UK, and it is because, other than, say, fox hunting, in the UK guns are very much regulated.

One thing, however, that someone said, did reach my thinking. At Shabbat services last night, Rabbi Robert Barr of ourjewishcommunity.org, said a very profound thing, in terms of the politics of such tragedies, and that was, that discussing the politics of the thing was one way to avoid dealing with the abject horror and loss of the tragedy. That is, speaking for myself, my first thoughts were about gun control, and I stand by my positions on the matter, but Rabbi Barr had a fair point, in terms of the fact that thinking about the political aspect of things was and is perhaps a "shield" to avoid dealing with the utter insanity of the whole thing. So, fair enough. This is a painful reminder of the uncertainty of life, of the unstable nature of the human race, of the fact that there are no guarantees in life, of the fragility of life. We are painfully reminded how we must always bear in mind those closest to us, for one never knows what may happen. And that is the more important point, rather than the political issues surrounding such a tragedy.

I will let the politics sort themselves out. Personally, for what it is worth, I have no problem with for example fox hunting or target shooting, not that personally I would like to do either, the former because I bloody well like animals too much, ha, and the latter because, well, I think there are more healthy ways to "vent" rather than resorting to firearms, but that is my own personal viewpoint, and I respect the fact that others may have different viewpoints. I do think there is space to be had in the conversation about limiting access to weapons, in terms of increasing background checks and psychological screenings and things of that nature. I am aware of how some folks like to trot out 18th century laws about the second amendment which I would argue dealt with the rights of colonies to defend themselves against the threats of the times such as difficulties with the Native Americans at the time and so on, and is not pertinent to today's world. So these are legitimate conversations to be had, and I think they should be had, but I think the most important thing to be thought of as one deals with such a horror as this is the inherent unfairness and fragility of human existence, and the consequent need for love and understanding for our fellow human beings, knowing that life is an uncertain prospect, and that therefore compassion for one another is not a luxury, but is a requirement, in the otherwise sometimes cruel universe we inhabit, for if we cannot love one another, in the brief time that we have the opportunity to do so, than I would submit that the nihilist position of there being no meaning to life would have been right after all, but, I choose not to believe that such is so. Life is a transitory proposition, and the only meaning to be derived therefrom is the meaning we choose, by, as some philosopher or other once said, loving our neighbor as ourselves.

We all have to deal with these sorts of things in our own way. Personally, although I have always "politically" supported gun control and personally never had a "taste" for firearms of any kind, I think these tragic events have only confirmed my personal belief that guns will never solve anything, and that, as Gail Russell's character in Angel and the Badman might have said, use of force ultimately harms not only others, but one's own soul, however one might define that term. Accordingly, these events only serve to reinforce my utter disgust for anything to do with guns, albeit, again, I respect the fact that complex political issues are going to have a variety of viewpoints surrounding them. All I can do is respond to this tragedy in my own way, and, to my viewpoint, Gail Russell's character was bloody correct, and I only wish in my younger days I had seen that more clearly, but now I certainly do. But, again, folks must deal with this in their own particular ways, and I think we can all agree that we must appreciate more the people we cherish in our lives the most, knowing how fleeting, how very tragically fleeting, is human existence.

As Bobby Kennedy once quoted from the Greek poet Aeschylus: Even in our sleep, a pain which cannot forget falls drop by drop upon the heart, until, in our despair, against our will, comes wisdom, through the awful grace of God.

If a UTM models the universe, the Tegmark Level 3 multiverse is necessitated

Premise: A UTM (universal Turing machine) can model the physical universe.

Known fact: A Turing Machine by definition is Markovian.

Therefore if the physical universe (or, precisely, the inflationary multiverse ) can be modeled by a UTM, then the universe (so defined) also is Markovian.

By definition, a Markov system of state S1 can have the next state S2 predicted using only the information from state S1 and not any previous state, then S1 contains all needed information to be able to predict (or evolve the system to) state S2.

The "information" is contained in the Schrodinger wave equation, but, this must never collapse, for, if it did, the universe ceases to be Markovian (able for the next state to be able to be derived from the current state and the current state alone).

By definition, if the Schrodinger equation never collapses, the universe is described by the Everett-Wheeler many-worlds interpretation of quantum theory (or the so-called "Level 3" multiverse of Tegmark where "Level 1" refers to recurring matter configurations within an inflationary bubble, and "Level 2" refers to the various inflationary bubbles out there each with potentially different string theory dimensionality and different physical constant values).

Thus, by a relatively "safe" or "conservative" premise, that the inflationary multiverse can be modeled by a UTM, the Level 3 multiverse is necessitated.

The ability to model the universe by a UTM is in principle testable, by looking for and studying (for instance) anomalous behavior of high-energy gamma radiation from deep space, and possibly other ways as well. Were this to be supported by experiment, then, that would be a support, not only for the underlying computational nature of the inflationary multiverse, but, by extension, the existence of so-called quantum "parallel worlds" as well.

Schrodinger's beleaguered cat, at least, should be relieved by the notion.