Steps to Nuclear Non-Proliferation:
We have been obsessed for a while with the mysteries of the “en-” prefix, and have come to accept its use as if it were a general principle or remedy for our thought: e.g. enfold, enframe, ensure, embody, engage, envolve, engender, entension, enrich, and so on and so on.
We may jokingly suggest it it takes at least two of Zizek’s humorous “and so on’s” to bring us to the appropriate level of a 2-categorical abstraction. More seriously, upon reaching this powerful idea of “enrichment”, it proves time to speak to our obsession with this prefix itself. We can no longer restrict our attention simply to its positive usage in higher category theory and perhaps even in molecular biology and leave out one glaring exception where the term “enrichment” sticks out like a mushroom cloud: Nuclear Physics.
For all this talk of becoming-plasma, all this talk of dealing with experimental physics generally, there has been no single mention of the kinds of atrocities that have been brought forth as a result. Specifically, we have had a historical tendency to weaponize the concept of “enrichment” to horrific ends. That this term evokes memories of collective trauma and great violences in the dropping of the atomic bombs on Hiroshima and Nagasaki, in the tragedies of Chernobyl and Three Mile Island, and most recently in the earthquake-tsunami in Fukushima speaks also to its deeply peaceful importance when used properly.
Particularly when it comes to nuclear arms, bombs, missiles, and other weapons, we cannot overlook this nuclear side of the category of enrichment in our thorough-going thinking through of non-violence as such. When we meet the concept of “enrichment”, we are almost immediately given to think and to resist the violences which have emerged from it. How is it that a concept which has done much to benefit us thus far, in higher category theory and in developing the mathematics behind the internal conceptual logic of satyagraha, can result also in such a disaster?
What were we thinking? Where did we misstep along our path?
We turn back, back to category theory again. Like conceptual engineers, we look to see where the anomaly could possibly have occurred in our usage. As a general rule of thumb, we know it is most likely to be where we started in our thinking, in our first step. Was there not sufficient quality of thought to begin with? Yes, that is probably it, maybe we made a mistake. We must bring ourselves think-together again and again, forming perhaps a global “nuclear family” in addition to our local one. Aha! Here, it appears the problem arises from the essential definition of “category” itself. Because we are speaking in terms of categorical logic, we effectively enforced a certain ordering between the “source” and the “target” objects in order to proceed any further.
You must begin somewhere, they say. Why not begin with a step along a path, like a step from f:A -> B ?
Yes, that is exactly what we did: We assigned one category as the “source” and created a functor all the way on through to the “target” object.
By no means are we “anti-nuclear”, but this original principle of fixing source/target is precisely what may give rise to the possible weaponization of categories, including “enrichment”. Sometimes we impose or force our own categories into the picture, and they can become like a box which constrains our future thinking. Perhaps this is due to our maintaining an immediate focus in “categories of thought” and how they give rise to the systematic thinking of satyagraha, rather than sustaining an a thoughtful emphasis on a pure and original non-violence plain and simple.
This “first principle” which guides our steps ultimately escapes any such categorization and all forms of conceptual or structural violence. As such, Gandhi rightly took great care to ensure that satyagraha was not a fully-defined term, that it still needed to be explored further. In this way, he allowed for many possible constructive first steps, while greatly preventing and diffusing several violent first steps that might have otherwise taken hold.
For instance, we now realize that the call to return ad fontes, back to the hermeneutic “source” of the things themselves, sometimes launches unexpectedly and then explodes in a foreign “target” site instead of fulfilling its original and pure entension. There is a certain risk that comes with saying anything at all, but silence will not do in times of crisis: Something must be said, so we take a first step. We instead listen to the silence to give us our courage to speak, to give us the right words that they may help others. Immersed in an environment of radical immanence, we listen to the soundscape for its many violences, and it gives rise to useful concepts and steps that may be employed on the path of Truth.
Without this make-shift source/target distinction in categorical thinking, we arguably could not have proceeded much of anywhere in the first place. We may not have been able to have ‘systematized’ our understanding of satyagraha. With it, though, there is still much beneficial that may come so long as we are careful enough in the conceptual steps we take.
At least now the problem has been better understood.
Sikhing Life: Daggers of War and Peace
Especially as we begin, we may need to continuously double-back upon ourselves.
We must repeatedly check over our thought in order to ensure and re-ensure if possible that nothing is causing violence or harm anywhere along the path. If there is, we must try our best to adjust ourselves accordingly — to take a different step along the path. In category theory, this particular dilemma or scenario might be best named by the idea of a “dagger-category”. It seems as though many new and important worlds of study open up alongside it. Since it is an additional structure on top of categories, a dagger-structure is often considered to be evil. To wit, it encodes certain equations on otherwise free-moving objects and in so doing breaks “neutrality” as we begin to think non-violently.
Daggers become increasingly important at this stage as we return to the fundamental facts of non-violence again and again, continually exploring and enlarging the possibilities available to us.
A dagger category is a category equipped with an involutive, identity-on-object functor: .
In detail, this means that it associates to every morphism in its adjoint such that for all and .
A dagger category is a category-with-involution, with envolution contained within itself.
When it comes to satyagraha, the idea of “envolution” is in all actuality better understood as this sort of “pseudo-involution”. It is an involution with certain properties (namely those of identity-on-object) affixed to it. For this reason of (ultimate) identity, is intimately related to Buddhist enlightenment (note, of course, the “en” prefix) and non-dual awareness, and also to the idea of moksha in Hindu traditions, namely Sikhism and Jainism. In particular, these categorical steps approach infinity-categories just as one approaches an infinite number of higher states consciousness made available with extended meditation and yoga. The goal of enlightenment would be such that such a sustained compassion would become a “primary structure” of thought and action in the course of Life.
The normally unspoken difference between a pure envolution (what Grothendieck, himself a Buddhist practitioner, simply calls an “actual involution” at the level of infinity-categories) and a “pseudo-involution” at the level of 2-categories or satyagraha is the same difference arising between Buddhism and Gandhian thought respectively. This difference may sometimes be exploited to the inverse of both in the service of weaponizing the “dagger structure”.
In these instances, like Zen at War or trends of religious violence and abuse of spiritual authority generally, the dagger is taken out of its proper place in the spiritual sheath. Those who are otherwise near to an original understanding of non-violence may conceptually assault one another to an end which forecloses upon Love and therefore also upon Life. Then, the problem of “evil” becomes the justification for future violences, particularly in dominant Christian logics.
Grothendieck recognized this in Pursuing Stacks with his trope of innocence, though here he put it lightly:
There are some choices “neater than others”, indeed.
We find that problem arrives in that the double-structure of the “dagger” is still at work in giving rise to the possibility of a truly non-violent satyagraha. A considerable degree of self-purification must used by the practitioner of non-violence at all times. Ironically, the “dagger” thereby ensures that the concept of satyagraha remains non-violent. It encodes satyagraha with the property of non-violence through a certain self-purification.
Quite literally so: Gandhi’s idea of non-violence was most essentially conceived as a result of his encounters with the Sikhs and Jains in their struggles.
The sixteenth squad of martyrs of five hundred Singhs started from ‘Sri Akal Takht’ on the 17th April, 1925 A.D., Before that Squad had reached Gurdwara Gangsar, Sri Malcolm Heely, the Governor of Punjab gave approval to the Gurdwara Act on the 11th July, 1925 A.D. All the Akalis were released on the 27th July. Freedom to hold ‘Akhand Path’ at Jaito was obtained after one year and ten months.
The struggle ended in 1925 with the passage of the Sikh Gurdwara Act. In the last 5 years of agitation for regaining control of their places of worship, 30,000 men and women had gone to jail. 400 had been killed and over 2,000 seriously wounded. The political results were far reaching. The British lost forever the support and loyalty of the Sikhs. The struggle for independence continued, and Sikhs made a tremendous contribution before independence, the Sikh community was only 1.1% of the total population of India. What they achieved is nothing short of phenomenal.
Gandhi was there, watching when the Sikhs were struggling to regain control of their Gurdwaras, through non-violent means. Indeed he admired their courage and their tactics, sending congratulatory notes on more than one occasion. One such telegram dated Jan. 19, 1922 and addressed to the Sikh leadership, read: “The first decisive battle for independence won. Congratulations.”
Sikhs carry with them at all times a kirpan as a matter of observing one of their five articles of faith.
Etymologically speaking, kirpan has two roots: kirpa means “Mercy, grace, compassion, kindness” and aan, which in turn means “Honor, grace, dignity”. In this way, it notably carries the same hybrid structure as satya and agraha, albeit with a different sense. As a result, Sikhs embody the qualities of the Sant Sipahi or saint-soldier. To carry the kirpan in the proper fashion means to fight first and foremost “the enemy within” ourselves.
Without the origins of satyagraha in this Sikh article of faith in the kirpan, without understanding its profound significance, there was no way for him to ensure that the radical musicology of the hybrid “en-” prefix ever takes hold in the heart. We could not find a way to consider a “generic morphism” in a dual or otherwise synchronous way; we could not be able to take any non-violent first steps at all. In other words, in absence of the dagger there is no way to determine whether our understanding of satyagraha in fact corresponds with Life itself, or if it is just another instance of categorical violence.
Any violence of the dagger is not, as Gandhi wrote, a failure of the law of Love itself, but of the fallible human animal who is prone to act violently. In other words, it is the failure of the one who does not successfully fight off his “demons” as it were. The Sikhs demonstrate a peaceful manner of living with the presence of the dagger, and we must therefore look to them for wisdom in carrying it properly.
Gandhian satyagraha seeks to distance itself from all weaponized language, including the discourses of combating “evil” and “sin”. In doing so, it must recognize that there is a certain kind of violence which can in fact be considered appropriately within the generative ethos of non-violence, as though it were an additional structure of thought. We call this the presence of the “dagger” and it serves as a non-violent pre-condition for the development of the systemic logic of (enriched) category theory and therefore its satyagraha.
Perhaps in most cases, this dagger is in fact carried peacefully like the Sikhs teach us, but whenever there is too much force carried in a given concept or category we may say that this category becomes both wielded and weaponized. It is this idea which prevents a dangerous nuclear enrichment, the dropping of bombs conceptual or otherwise, and
All categories, including weaponization itself, seem to have the ability to become weaponized. However, some categories – like satyagraha - actively seek to resist the possibility of violence due to their internal tension and holding-to-truth, and a more construct aware enaction of a pure non-violence emerges as a result.
It was important at the time of the Indian struggle for independence, for instance, that when Gandhi constructed the term satyagraha it was an entirely new term subject to his own essential definition. Other terms such as “pacifism” or “civil disobedience” were already to some degree or another weaponized in unfortunate ways. Perhaps this came as a natural result of their own expedited thinking and missteps. We have now in our view a certain idea which arises of nuclear disarmament, bomb-diffusion, de-compression or de-escalation of conflict in the world as well as in our categories that they may no longer be loaded.
Let us follow the example of our Sikh friends, and look deeper into the meaning of the “dagger”.
Let us try to look further into the pure source of Gandhian non-violence within us.
The Nuclear Mysticism of the Pants of Life:
What do we do with our recognition of the “dagger”?
How are we to wield this “dagger”? How exactly do we ultimately prevent such a weaponization from occurring? What is it that otherwise escapes higher category theory? It is not something that is exclusively in the domain of mathematics; it cannot be entirely encompassed by any present form of mathematics to my limited knowledge. It persists in the non-mathematical and non-physical side of Life, implicit in the humble doings of, say, thoughtful mathematicians like Zalamea among many others. Is it perhaps Life itself?
What is Life, anyways?
It is a question to be pursued in our greatest humility guided by both Truth and Love, as we come to feel its gravitational pull on us. It is the same question to which Erwin Schrödinger gave the answer: aperiodic crystals. He tried to explain the storage of our hereditary information, in its inner structure. Molecules he understood were simply too small, whereas the “amorphous solids” were far too wild and perhaps we might say chaotic. Thus, he settled on a kind of “crystalline” structure, but specifically one with certain key properties to it. Namely, it had to be a-periodic. The helical structure of DNA was soon discovered, and, although not exactly crystalline in this way, it possessed similar kinds of properties.
Of course! How could we forget our many repeated adventures to the alchemical salt-point! The conceptual primacy of the salt-point!
Yet, this does not answer the question of “What is Life itself?”
We can only hesitantly give, by way of our wandering expedition, a certain salt-like idea which speaks to its forever-emanating Form as we receive it, to its categorical container within our Body as we perceive it, or to our collective experience of it in a generative (en)closure. The idea of salt-point is only there as though it were a thematic feature which serves to remind us to re-direct our focus to the question of Life itself when we are unsure. Contrary to Schrödinger, we recognize that it is certainly not the answer to his question. Nor, therefore, is satyagraha which is the manifestation of the salt-point. Nor, therefore, is category theory which maps its internal logic.
According to Nils Baas, category theory may falter precisely on this question of Life itself. I am inclined to believe him.
Nils Baas has been emphasizing for many years, in print and in private communication, the conviction that the usual notions of n-category, infinity-category, omega-category in higher category theory are not naturally suited for describing extended cobordisms such as appearing in the tangle hypothesis in extended quantum field theory; and hierarchical systems such as appearing in complex systems and biology.
Rosen returned to Schrodinger’s unorthodox text towards the end of his own life and, recognizing the radicality of the question, began his own exceptional piece Essays on Life Itself by suggesting that we need to live in a universe sufficiently large enough to deal with the question. This requires an increase in the number of dimensions open to our thought. In the same way, satyagraha works only when it is enacted in the humble service of Life, when it corresponds frequently with Life. At the infinite boundary of satyagraha, we define the conformal boundary which is Life itself. In a word, satyagraha is like the “space-time” of Life.
As Gandhi writes: Where there is Love, there is Life!
A concrete example of a “dagger” category can be found in the notion of “cobordism” as shown above. The term “bordism” comes from French bord, meaning boundary.”Bordism” is the study of boundaries. At present, we are interested in the boundaries of Life at the limits of satyagraha.
Cobordisms tend to be hyperbolic in shape, as in the above morphing of two circles into one. At the “waist”, its shape is rather like a nuclear cooling tower with its large pant-legs anchoring it below the surface to the fleeting ontological essence of Life. This image reminds us that the weaponization of the “enrichment” process is a bit more remarkable than we had originally imagined, and that discourses of “evil” run contrary to Life as does the dropping of a nuclear bomb.
These extended cobordisms are “compact-closed” categories which occur “in nature” that are not-quite-categories after all. Here, there is certain effacement or fusion of the distinction between “source” and “target”. As a “dagger” category, they break the principle of equivalence-invariance and in so doing give rise not only an originary non-violence in thought, but also the problem of “evil” and its violences if one is not enlightened sufficiently. Thus, in lieu of “enrichment” Life as we experience it in our mind and memories may evolve (or envolve) by way of a certain nuclear fission-fusion hybrid. The Pants of Life gives us to think of our unique circuit-contingent experience in the course of Life itself, which is a measure of the quality and quantity of our personal Experiments with Truth.
Wearing the Pants of Life, we progressively come to engage with the many questions of Life itself. If this engagement were itself a category it might be called the “nuclear ideal” like the fulfillment of Salvador Dali’s impossible dream of nuclear mysticism. This is the abstract matter of Life, with its underlying hyperstructure. Life itself, like a generalized conformal field, the weighted limit of satyagraha, would then be considered a “nuclear functor” in this gravity.
Satyagraha, as a gauge-like concept that is itself perturbative or approximative of Truth and Love, seems to point us simultaneously forward to non-perturbative string theories as well as backward towards early-Hindu, Sikh, and eventually Jain ontologies. Satyagraha and Life thus correspond with one another like the gauge-gravity dualism in AdS/CFT correspondance to ensure the other is continuing and enfolding along the horizon of envolutionary progress.
At last, Life leads us to topological quantum field theories (TQFT) in pursuit of a more clear and complete understanding of the gravity of the ancient Hindu question: What is Life itself?
Jainity of Jainities, all is Jainity!
What is Life itself? In some ways, the answer is on the side of mathematics itself; while in other ways, it is, and it is not entirely on the side of the abstract practices of physics or mathematics. Whether we are string theorists or monks, is it in fact the mystery of Life itself which strikes us the most? In some ways, it is, and it is also not entirely the “mystery” of Life, but rather simply Life itself. Therefore in some ways, it is, and it is indescribable…
Read Gandhi: There is a unity of life and a unity-of-means-and-ends. To him, all life is sacred. Yet, in some ways it is not quite “sacred”, and it is simply indescribable…
Read Feyerabend, who re-states it a bit better: There is an abundance of Life. Yes, we may say that in some ways, it is indeed sacred, that it is indeed not sacred, and that it is indescribable. There is an abundance…
Read also Gregory Bateson, who perhaps said it best:
The point… I am trying to make… is that mere purposive rationality unaided by such phenomena as art, religion, dream and the like, is necessarily pathogenic and destructive of life… it’s virulence springs specifically from the circumstance that life depends upon interlocking circuits of contingency, while consciousness can see only such short arcs of such circuits as human purpose may direct.
Most astonishingly of all, we may experiment to find an extended cobordism which comes to look roughly like what Jain texts describe as the shape of the Universe: “A man standing with legs apart and arms resting on his waist. The Universe according to Jainism is narrow at top and broad at middle and once again becomes narrow at the bottom”
Finally, we are given to think of Jain ontology, just as we had figured out in struggling to answer the question:
- syād-asti—in some ways, it is,
- syād-nāsti—in some ways, it is not,
- syād-asti-nāsti—in some ways, it is, and it is not,
- syād-asti-avaktavyaḥ—in some ways, it is, and it is indescribable,
- syād-nāsti-avaktavyaḥ—in some ways, it is not, and it is indescribable,
- syād-asti-nāsti-avaktavyaḥ—in some ways, it is, it is not, and it is indescribable,
- syād-avaktavyaḥ—in some ways, it is indescribable.
To avoid weaponization, then, we must maintain a robust hybridity that demands we frequently re-trace our steps so as to not lose sight of either satyagraha or Life in the process. We must somehow ensure that they correspond with one another at all times.
From the Sikhs, we may learn that to ensure that this communion happens a certain “dagger” must encode an additional structure of self-purification upon our use of categories to guide the practitioner. From the Jains, we learn more in detail how to actually carry out this process through an extended humility in the face of the question of Life itself. Ultimately, the answer requires that we remember to look into the essence of Life, what it actually is.
At last, we may take this cobordial shape as the last side of our modelization or desired “objective externality” of non-violence from inthesaltmine.