The last scattering horizon

(In memory of Andrew Lange)



In cosmology, the surface of last scattering is the "wall of light", the last horizon from which the CMB, the cosmic microwave background we measure today comes to us from the depth of cosmic time, when the photons of the microwave background radiation decouple from matter. In more metaphorical terms, people too have their own last horizon, a boundary of the observable universe, beyond which one cannot directly probe and which represents that external surface from which all information we can access is collected, shielding away a core destined to remain forever out of reach. One tries to guess shapes and structures hidden beyond the horizon through the feeble signs that emerge, inscribed on that last scattering surface.

Some of the most exciting discoveries that brought cosmology to a central role at the frontier of science have come from probing the cosmic microwave background. We recently learned that the global geometry of the Universe is flat, or nearly so. A natural question that scientists and philosophers have pondered about at least since the times of Giordano Bruno, but which, until so very recently, appeared to be completely out of reach of any experimental verification. Now, for the first time in history, we know. This amazing piece of knowledge came to us through the so called Boomerang experiment (Balloon Observations Of Millimetric Extragalactic Radiation and Geophysics, that is). The suborbital balloon flights of the telescope in the Boomerang experiment provided a precise measurement of the angular diameter distance to the surface of last scattering. Combined with data on the Hubble constant, these sufficed to pin down the constraints on the geometry of the Universe. A most beautiful story.



I have never known much about cosmology. It was only in the past year that I made a first attempt at wandering about this glorious landscape, with small uncertain steps. A case of peer pressure probably, given where I am now working. I still know very little, naturally, I am just a silly mathematician borrowing other people's toys and foolishly playing around with them. I enjoyed it, though: it gave me an excuse to begin to learn something completely new to me, and also a way to begin to feel somewhat more at home in my new surroundings, to start creating that sense of belonging I had missed so much for so long. On a more personal level, engaging in the act of learning something new and different from anything I had been doing before was also a way for me to try to get out of a creepy depression I have been trying to come to terms with for several months.

When I first got here last year, to my new job, to the tragic beauty of California and its morbidly sensuous breathtaking landscapes, one of the first people to welcome me into the local scientific community was that same cosmologist responsible for the Boomerang experiment and the discovery of the flat geometry of the Universe: Andrew Lange was also the head of our division, in charge of the Physics, Mathematics, and Astronomy section of Caltech. I was not a close friend of Andrew's, I did not have the time to get to know him well enough, but we exchanged thoughts several times, on mathematics and theoretical physics, on mundane matters of everyday concern, hiring, such things. I told him one day that I was thinking of submitting a grant proposal on some admittedly very weird mathematical thoughts about cosmology: I felt awkward about it, as if I had been in the process of trespassing on someone else's territory. There is always that fear we carry around in our work, of publicly exposing our inadequacy. And yet, he listened to me and he was very encouraging. Not much came of my work, one new paper, big deal. No major breakthrough to write home about, I know, but the encouragement that he offered at that time did matter a lot to me, when so many things had seemed suddenly so difficult to cope with. It helped.



Andrew killed himself last night. We were all informed today during an emergency faculty meeting. He, we learned, had been struggling with mood disorder and a severe depression. And yet, all along, he was always there: for his research group, for the pressing demands of his administrative job, for all the needs and duties. He had nice words to offer, thoughtful scientific comments to make. Helpful, considerate, understanding. How much did it cost him, I wonder, to maintain all that intact until the very last? I know something about those dark psychological spaces, of what it feels like inside: it is the growing weight of the soul that drags you down, the endless pain that keeps exploding in the mind and never stops, the shadow that walks with you, and yet every day one needs to find the strength to live another day, to appear as the world expects you to appear. To act as your role demands. To live up to all the expectations, to be better and more efficient than ever until all the inner strength and resilience is consumed. In truth, I know nothing about what happened to him, I was not close enough to know. We only ever saw the smooth reassuring appearance of his last scattering surface, beyond which we could not probe. Perhaps, we should have paid closer attention to the feeble warning signs inscribed on that horizon: we should have searched it for clues to the inner core of suffering, to the hidden geometry of that very personal universe.





Andrew Lange's Segre Lecture: How did the universe begin? Berkeley, November 9, 2009.

The raft of the medusa

"No time, no space
another race of vibration,
the sea of the simulation"
(Franco Battiato - "No time, no space")



There are strange moments in life when, all of a sudden, one finds oneself writing a paper about loop quantum gravity. No, not even that. Mostly I am just drifting along the currents of the open sea, waiting for an improbable sighting of a distant shore or a passing ship. With no goal at hand, time passes in a mesmerizing dilation of slow movement and thoughts fail to coalesce around any solid object. Like the survivors portrayed in Théodore Géricault's "Le Radeau de la Méduse", I feel like I am ready to resort to cannibalizing my own work, just to get going with one apparent step in some random direction, while waiting for the shipwreck to run its course, back to firm land or to the ocean depths. So I am trying to get by these days, by reformatting in the language of loop quantum gravity some old thoughts. What for? Nothing, letting time pass.



In the loop quantum gravity approach, space-time is quantized by a procedure that encodes it in a discretized structure, consisting of spin networks and spin foams. A spin network consists of an oriented embedded graph in a 3-dimensional manifold with edges labelled by SU(2) representations and edges labelled by intertwiners between the representations attached to incoming and outgoing vertices. These representations relate to gravity in terms of holonomies of connections, and the formulation of Einstein's equations in terms of vierbein, or tetrads, and dual co-tetrads. Thus, to a spin networks, or the 1-skeleton of a triangulation by tetrahedra, one assigns operators of quantized area and volume, coming from counting intersection points of a surface, or 3-dimensional regions, with the edges or vertices of the spin network with a multiplicity given in terms of the spin representation attached to the edges and the intertwiners attached to the vertices.



This quantized version of embedded graphs and tetrahedra of a triangulation, developed within loop quantum gravity, gave rise to very interesting topological applications, such as the Turaev-Viro invariants of 3-manifolds. A spin foam is a 2-dimensional simplicial complex, which gives a geometric transition amplitude between two spin networks, and provides a "sum over histories" approach to loop quantum gravity. Like spin networks provide a formalism for quantized versions of 3-dimensional geometries, spin foams are the discretized version of 4-dimensional spacetimes. A "sum over geometries" weighted by the Einstein Hilbert action, as in a semiclassical Hartle-Hawking approach, becomes in this point of view a sum over spin foams, weighted by a "group field theory" type of action.





So far so good, and then what? I mean, what am I doing with all this other than trying to keep the raft afloat? I still don't know, mostly just playing around with it. I'll see where the flow goes, whether it is rip currents or peaceful stream. For those who seek a milder type of entertainment with the ideas of loop quantum gravity, there is always Greg Egan's novel "Schild's ladder", an action-adventure story of quantum gravity vacua and dynamical triangulations. Not a typical sci-fi bestseller, and sufficiently unusual to be genuinely entertaining.

Man and history

"It is man and man alone who creates history" (Jyoti Basu, 1914-2010)

It is appropriate to pay respect to the departed comrades: Jyoti Basu, who passed away yesterday in Kolkata at the age of 95, was a historic figure of the communist movement worldwide. I will not be getting into an analysis of what his tenure as the longest serving head of a democratically elected communist government achieved in West Bengal. There are people who are more expert and closer to the local reality to judge. It is clear, however, that the fact itself that a state with a population of over 80 millions, which makes West Bengal larger than any single one of the main European nations, had been governed for half a century by a democratically elected communist party, is a fact of crucial significance in world history. Too often the dominating Cold War propaganda, which dragged on, in Europe and elsewhere, well beyond the end of the Cold War era, had tried to persuade the general public that a Marxist version of Communism would be strictly incompatible with a political system based on an elective democracy. Well, perhaps the biggest contribution of Jyoti Basu to world history lies in having proven that this claim is simply wrong. Basu served as Chief Minister of West Bengal from 1977 to 2000, the longest-serving Chief Minister of India, and a record time in office compared to any democratically elected leader worldwide. What made the fortune of the Communist Party of India (Marxists) and its Left Front government coalition was a mixture of massive land reforms, the general support with the population gained after the difficult experience of West Bengal in the 1970s, torn by the experience of war, of the refugee crisis and of the Emergency. The two states of India with the strongest communist tradition, West Bengal and Kerala, have also the highest literacy rate, the lowest incidence of communal violence, and the best profile on issues such as women rights. West Bengal has additionally retained its leading role in culture and the arts, as well as a rapidly expanding presence on the scene of the current Indian scientific blooming. The CPI(M) has its opponents, to the right and to the left: among the latter, most prominently, a very composite archipelago of Maoist movements. Nonetheless, Basu has been highly regarded as a political figure by supporters and opponents alike.



The historic heritage of communism around the world is very diverse and very fragmented. Perhaps the most serious criticism that communist intellectuals can raise against what they would regard as their own political culture is this tendency to continuously split along the fault lines of ideological differences: Marxists-Leninists, Trotskyists, Maoists, Anarcho-Socialists, and so on. The label of "Revisionist" has been thrown infinitely many times at one or another target, akin to "traitor" or worse. In the end, these endless cracks opening up in the body of the international workers movement have only had the effect of weakening it, diluting it to an impotent homeopathy of ideology. The reaction, which efficiently created all the monstrous European and South American Fascisms of the 20th century, all finding their "justification" of existence in the need to stop the advancing of Communism, does not waste time in debating subtle ideological differences: they just go in straight for the kill, while we waste most of our energies deciding whether an already minuscule communist faction in this or that country should further split into two even more ineffective groups over a difference of interpretation of a line in the Grundrisse. The communist leaders who really make history are only those who have the intelligence to adopt an inclusive viewpoint on ideology. This is not the much feared "revisionism", comrades, it is reality knocking loudly at the door!



The international workers movement has a rich tradition which encompasses Anarchy, various version of 19th century Socialism, Marxism and all its historic derivatives throughout the 20th century, as well as the practical, empirical, experience of trade unions, women rights activism, the civil rights movement, the students movement of 1968. We come from very far and if we want to have a fighting chance to keep going very far, we better accept that all of these experiences are with us to stay and they do not have to form a water tight package of ideological consistency in order to be effective. There will always be contradictory stands anyway, there is no way to avoid it, except the repressive one which does not lead anywhere. Our strength is in unity, but "unity in diversity". The experience of India can hopefully teach something to the rest of the world, which is struggling with the burden of being unaccustomed to diversity. This is why the Indian experience of Communism is so relevant to the world. There is no perfect solution, no silver bullet, not even the Revolution and the "final struggle" our fathers sang about. The Bengali solution is also, like everything, a compromise, one that works and doesn't work, one that has good sides and bad ones. We are not building a workers paradise, nor are we seriously changing the deeper nature of humankind, not as our culture had once hoped to do. The youth of ideology is a landscape of dreams, but the struggle that matters in our everyday life is the one that diminishes exploitation of the poor by the rich, that contributes to give to all human beings equal dignity, regardless of their race and gender, that broadens people's access to good education, to good medical care, it is the act of standing up against wars, against brutality and oppression wherever they manifest themselves. These are not secondary tasks, this is the essence of what makes us "progressive", a progress conquered step by step, with the burden of all our contradictions.
The struggle carries on.

Golem XIV

This is a continuation of my previous blog Welcome to the machine. I decided to stop that blog and restart it under a new heading to mark the turning point I have come to and restart my cybernetic life again as a blank slate. I should have given it a phoenix inspired title perhaps, so why Golem?



When Stanislaw Lem wrote "Golem XIV", collected in English as one of the stories in "Imaginary magnitude", he envisioned a sentient machine that grows to transcend the human nature. Built by humans with warfare applications in mind, Golem quickly dismisses its intended task and moves forward, gradually increasing its own intellective capacity, until it loses all possibility of communication with human beings, evolving into an entirely new life form. Just before disappearing out of the cognitive range of humanity, the machine delivers a series of lectures, in which it philosophizes upon human nature, evolution, and intelligence. Golem is the self consciousness of our scientific and technological world, which speaks about itself, its origins, its future. We are there to listen. I called my new blog here "Listening to Golem" because there are times in life when one reaches a profound state of disillusionment about the human nature and, at those times, one should pause and listen. The shortcomings of human hubris and pretension slowly disappear, when projected against the larger landscape which is the greatest of human creations: our science, like Lem's Golem, takes up a life of its own and, dismissing the base motivation of self gratification that guided the human beings who initially attended to it and transcending their smallness, it takes on a cognitive life beyond the reach of any single individual. Our science, our golem, lives on as our collective consciousness, and we the human, the scientists, listen on. Like the golem of Prague legends, our collective golem also bears Emet, truth, written on its forehead. What will restart in us the process of creativity and guide us safely back to the road of life is the awakening of our creature of stone and mud, its capacity to take on life and awareness.



Listening to Golem is what I will be doing in the near future. The capacity to listen is the key to human sensitivity, but nature, which as Heraclitus pointed out loves to hide, talks to us mostly in whispers. A golem is not a large frightening monster, it is a creature of stone alright, a creature as old and slow moving as a geological phenomenon, echoing into the depth of the world's past existence, and yet the golem is a stone that comes alive and moves forward into the future. A metaphor of evolution, slow in its process but of marvelous complexity in its outcome. So is Lem's Golem whose final evolution brings it to disappear into the distant future of humanity: from the stones to the stars, a path precluded to individual human beings but walked upon by our collective endeavor, which we call civilization.