Materializing Hyperbolic Spaces with Gradient-Index Optics and One-Way Mirrors

Burning Man is one week away, so I figured I would share a neat idea I’ve been hoarding  that could lead to a kick-ass Burning Man-style psychedelic art installation. If I have the time and resources to do so, I may even try to manifest this idea in real life at some point.

Around the time I was writing The Hyperbolic Geometry of DMT Experiences (cf. Eli5) I began asking myself how to help people develop a feel for what it is like to inhabit non-Euclidean phenomenal spaces. I later found out that Henry Segerman developed an immersive VR experience in which you can explore 3D hyperbolic spaces. That is fantastic, and a great step in the right direction. But I wanted to see if there was any way for us to experience 3D hyperbolic geometry in a material way without the aid of computers. Something that you could hold in your hand, like a sort of mystical amulet that works as a reminder of the vastness of the state-space of consciousness.

What I had in mind was along the lines of how we can, in a sense, visualize infinite (Euclidean) space using two parallel mirrors. I thought that maybe there could be a way to do the same but in a way that visualizes a hyperbolic space.

One-Way Mirrors and 3D Space-Filling Shapes

Right now you can use one-way mirrors on the sides of a polyhedra whose edges are embedded with LEDs to create a fascinating “infinite space effect”:

This works perfectly for cubes in particular, given that cubes are symmetrical space-filling polyhedra. But as you can see in the video above, the effect is not quite perfect when we use dodecahedra (or any other Platonic solid). The corners simply do not align properly. This is because the solid angles of non-cube Platonic solids cannot be used to cover perfectly 4π steradians (i.e. what 8 cubes do when meeting at a corner):


This is not the case in hyperbolic space, though; arbitrary regular polyhedra can tesselate 3D hyperbolic spaces. For instance, one can use dodecahedra by choosing their size appropriately in such a way that they all have 90 degree angle corners (cf. Not Knot):

Gradient-Index Optics

Perhaps, I thought to myself, there is a way to physically realize hyperbolic curvature and enable us to see what it is like to live in a place in which dodecahedra tesselate space. I kept thinking about this problem, and one day while riding the BART and introspecting on the geometry of sound, I realized that one could use gradient-index optics to create a solid in which light-paths behave as if the space was hyperbolic.

Gradient-index optics is the subfield of optics that specializes in the use of materials that have a smooth non-constant refractive index. One way to achieve this is to blend two transparent materials (e.g. two kinds of plastic) in such a way that the concentration of each type varies smoothly from one region to the next. As a consequence, light travels in unusual and bendy ways, like this:

Materializing Hyperbolic Spaces

By carefully selecting various transparent plastics with different indices of refraction and blending them in a 3D printer in precisely the right proportions, one can in principle build solids in which the gradient-index properties of the end product instantiate a hyperbolic metric. If one were to place the material with the lowest refraction index at the very center in a dodecahedron and add materials of increasingly larger refractive indices all the way up to the corners, then the final effect could be one in which the dodecahedron has an interior in which light moves as if it were in a hyperbolic space. One can then place LED strips along the edges and seal the sides with one-way window film. Lo-and-behold, one would then quite literally be able to “hold infinity in the palm of your hand”:


I think that this sort of gadget would allow us to develop better intuitions for what the far-out (experiential) spaces people “visit” on psychedelics look like. One can then, in addition, generalize this to make space behave as if its 3D curvature was non-constant. One might even, perhaps, be able to visualize a black-hole by emulating its event-horizon using a region with extremely large refractive index.



I would like to conclude by considering some of the challenges that we would face trying to construct this. For instance, finding the right materials may be difficult because they would need to have a wide range of refractive indices, all be similarly transparent, able to smoothly blend with each other, and have low melting points. I am not a material scientist, but my gut feeling is that this is not currently impossible. Modern gradient-index optics already has a rather impressive level of precision.

Another challenge comes from the resolution of the 3D printer. Modern 3D printers have layers with a thickness between .2 to 0.025mm. It’s possible that this is simply not small enough to avoid visible discontinuities in the light-paths. At least in principle this could be surmounted by melting the last layer placed such that the new layer smoothly diffuses and partially blends with it in accordance with the desired hyperbolic metric.

An important caveat is that the medium in which we live (i.e. air at atmospheric pressure) is not very dense to begin with. In the example of the dodecahedra, this may represent a problem considering that the corners need to form 90 degree angles from the point of view of an outside observer. This would imply that the surrounding medium needs to have a higher refraction index than that of the transparent medium at the corners. This could be fixed by immersing the object in water or some other dense media (and designing it under the assumption of being surrounded by such a medium). Alternatively, one can simply fix the problem by using appropriately curved sides in lieu of straight planes. This may not be as aesthetically appealing, though, so it may pay off to brainstorm other clever approaches to deal with this that I haven’t thought of.

Above all, perhaps the most difficult challenge would be that of dealing with the inevitable presence of chromatic aberrations:

Since the degree to which a light-path bends in a medium depends on its frequency, how bendy light looks like with gradient-index optics is variable. If the LEDs placed at the edges of the polyhedra are white, we could expect very visible distortions and crazy rainbow patterns to emerge. This would perhaps be for the better when taken for its aesthetic value. But since the desired effect is one of actually materializing faithfully the behavior of light in hyperbolic space, this would be undesirable. The easiest way to deal with this problem would be to show the gadget in a darkened room and have only monochrome LEDs on the edges of the polyhedra whose frequency is tuned to the refractive gradient for which the metric is hyperbolic. More fancifully, it might be possible to overcome chromatic aberrations with the use of metamaterials (cf. “Metasurfaces enable improved optical lens performance“). Alas, my bedtime is approaching so I shall leave the nuts and bolts of this engineering challenge as an exercise for the reader…

Why don’t more effective altruists work on the Hedonistic Imperative?

By David Pearce (in response to a Quora question)


Life could be wonderful. Genetically phasing out suffering in favour of hardwired happiness ought to be mainstream. Today, it’s a fringe view. It’s worth asking why.

Perhaps the first scientifically-literate blueprint for a world without suffering was written by Lewis Mancini. “Brain stimulation and the genetic engineering of a world without pain” was published in the journal Medical Hypotheses in 1990. As far as I can tell, the paper sunk almost without a trace. Ignorant of Mancini’s work, I wrote The Hedonistic Imperative (HI) in 1995. I’ve plugged away at the theme ever since. Currently, a small, scattered minority of researchers believe that replacing the biology of suffering with gradients of genetically preprogrammed well-being is not just ethical but obviously so.

Alas, perceptions of obviousness vary. Technically, at least, the abolitionist project can no longer easily be dismissed as science fiction. The twenty-first century has already witnessed the decoding of the human genome, the development and imminent commercialisation of in vitro meat, the dawn of CRISPR genome-editing and the promise of synthetic gene drives. Identification of alleles and allelic combinations governing everything from pain-sensitivity to hedonic range and hedonic set-points is complementing traditional twin studies. The high genetic loading of subjective well-being and mental ill-health is being deciphered. The purely technical arguments against the genetic feasibility of creating a happy living world are shrinking. But genetic status quo bias is deeply entrenched. The sociopolitical obstacles to reprogramming the biosphere are daunting.

You ask specifically about effective altruists (EAs). Some effective altruists (cfEffective Altruism: How Can We Best Help Others? by Magnus Vinding) do explore biological-genetic solutions to complement socio-economic reform and other environmental interventions. Most don’t. Indeed, a significant minority of EAs expressly urge a nonbiological focus for EA. For example, see Why I Don’t Focus On The Hedonistic Imperative by the influential EA Brian Tomasik. I can’t offer a complete explanation, but I think these facts are relevant:

1) Timescales. Lewis Mancini reckons that completion of the abolitionist project will take thousands of years. HI predicts that the world’s last unpleasant experience will occur a few centuries hence, perhaps in some obscure marine invertebrate. If, fancifully, consensus existed for a global species-project, then 100 – 150 years (?) might be a credible forecast. Alas, such a timescale is wildly unrealistic. No such consensus exists or is plausibly in prospect. For sure, ask people a question framed on the lines of “Do you agree with Gautama Buddha, ‘May all that have life be delivered from suffering’?” and assent might be quite high. Some kind of quantified, cross-cultural study of radical Buddhist or Benthamite abolitionism would be interesting. Yet most people balk at what the scientific implementation of such a vision practically entails – if they reflect on abolitionist bioethics at all. “That’s just Brave New World” is a common response among educated Westerners to the idea of engineering “unnatural” well-being. Typically, EAs are focused on measurable results in foreseeable timeframes in areas where consensus is broad and deep, for instance the elimination of vector-borne disease. Almost everyone agrees that eliminating malaria will make the world a better place. Malaria can be eradicated this century.

2) The Hedonic Treadmill. In recent decades, popular awareness of the hedonic treadmill has grown. Sadly, most nonbiological interventions to improve well-being may not have the dramatic long-term impact we naïvely hope. However, awareness of the genetic underpinnings of the hedonic treadmill is sketchy. Knowledge of specific interventions we can plan to subvert its negative feedback mechanisms is sketchier still. Compared to more gross and visible ills, talk of “low hedonic set-points” (etc) is nebulous. Be honest, which would you personally choose if offered: a vast national lottery win (cfHow Winning The Lottery Affects Happiness) or a modestly higher hedonic set-point? Likewise, the prospect of making everyone on Earth prosperous sounds more effectively altruistic (cfCan “effective altruism” maximise the bang for each charitable buck?) than raising their hedonic defaults – even if push-button hedonic uplift were now feasible, which it isn’t, or at least not without socially unacceptable consequences.

3) The Spectre of Eugenics. Any confusion between the racial hygiene policies of the Third Reich and the project of genetically phasing out suffering in all sentient beings ought to be laughable. Nonetheless, many people recoil at the prospect of “designer babies”. Sooner or later, the ”e”-word crops up in discussions of genetic remediation and enhancement. If we assume that bioconservative attitudes to baby-making will prevail worldwide indefinitely, and the reproductive revolution extends at best only to a minority of prospective parents, then the abolitionist project will never happen. What we call the Cambrian Explosion might alternatively be classified as the Suffering Explosion. If we don’t tackle the biological-genetic roots of suffering at source – “eugenics”, if you will – then pain and suffering will proliferate until Doomsday. Without eugenics, the world’s last unpleasant experience may occur millions or even billions of years hence.

4) Core Values. Self-identified effective altruists range from ardent life loversfocused on existential risks, AGI and the hypothetical Intelligence Explosion to radical anti-natalists and negative utilitarians committed to suffering-focused ethics (cfWhat are the main differences between the anti-natalism/efilism community and the negative utilitarian/”suffering-focused ethics” wing of the effective altruism community?). There’s no inherent conflict with HI at either extreme. On the one hand, phasing out the biology of suffering can potentially minimise existential risk. Crudely, the more we love life, the more we want to preserve it. On the opposite wing of EA, radical anti-natalists oppose reproduction because they care about suffering, not because of opposition to new babies per se. Technically speaking, CRISPR babies could be little bundles of joy – as distinct from today’s tragic genetic experiments. In practice, however, life-loving EAs are suspicious of (notionally) button-pressing negative utilitarians, whereas radical anti-natalists view worldwide genetic engineering as even more improbable than their preferred option of voluntary human extinction.

5) Organisation and Leadership. Both secular and religious organizations exist whose tenets include the outright abolition of suffering. EAs can and do join such groups. However, sadly, I don’t know of a single organisation dedicated to biological-genetic solutions to the problem of suffering. Among transhumanists, for instance, radical life-extension and the prospect of posthuman superintelligence loom larger than biohappiness – though article 7 of the Transhumanist Declaration is admirably forthright: a commitment to the well-being of all sentience. Also, I think we need star power: the blessing of some charismatic billionaire or larger-than-life media celebrity. “Bill Gates says let’s use biotechnology to phase out the genetic basis of suffering” would be a breakthrough. Or even Justin Bieber.

For my part, I’m just a writer/researcher. We have our place! My guess is that this century will see more blueprints and manifestos and grandiose philosophical proposals together with concrete, incremental progress from real scientists. The genetic basis of suffering will eventually be eradicated across the tree of life, not in the name of anything “hedonistic” or gradients of intelligent bliss, and certainly not in the name of negative utilitarianism, but perhaps under the label of the World Health Organisation’s definition of health (cfConstitution of WHO: principles). Taken literally, the constitution of the WHO enshrines the most daringly ambitious vision of the future of sentience ever conceived. Lifelong good health (“complete physical, mental and social well-being”) for all sentient beings is a noble aspiration. Regardless of race or species, all of us deserve good health as so defined. A biology of information-sensitive gradients of physical, mental and social well-being (HI) is more modest and workable thanks to biotech. Optimistically, life on Earth has only a few more centuries of misery and malaise to go.

The Appearance of Arbitrary Contingency to Our Diverse Qualia

By David Pearce (Mar 21, 2012; Reddit AMA)


The appearance of arbitrary contingency to our diverse qualia – and undiscovered state-spaces of posthuman qualia and hypothetical micro-qualia – may be illusory. Perhaps they take the phenomenal values they do as a matter of logico-mathematical necessity. I’d make this conjecture against the backdrop of some kind of zero ontology. Intuitively, there seems no reason for anything at all to exist. The fact that the multiverse exists (apparently) confounds one’s pre-reflective intuitions in the most dramatic possible way. However, this response is too quick. The cosmic cancellation of the conserved constants (mass-energy, charge, angular momentum) to zero, and the formal equivalence of zero information to all possible descriptions [the multiverse?] means we have to take seriously this kind of explanation-space. The most recent contribution to the zero-ontology genre is physicist Lawrence Krauss’s readable but frustrating “A Universe from Nothing: Why There Is Something Rather Than Nothing“. Anyhow, how does a zero ontology tie in with (micro-)qualia? Well, if the solutions to the master equation of physics do encode the field-theoretic values of micro-qualia, then perhaps their numerically encoded textures “cancel out” to zero too. To use a trippy, suspiciously New-Agey-sounding metaphor, imagine the colours of the rainbow displayed as a glorious spectrum – but on recombination cancelling out to no colour at all. Anyhow, I wouldn’t take any of this too seriously: just speculation on idle speculation. It’s tempting simply to declare the issue of our myriad qualia to be an unfathomable mystery. And perhaps it is. But mysterianism is sterile.

Qualia Computing at Burning Man 2018: “Consciousness vs Replicators” talk

I’m thrilled to announce that I will be going to Burning Man for the second time this year. I will give a talk about Consciousness vs. Pure Replicators. The talk will be at Palenque Norte‘s consciousness-focused speaker series hosted by Camp Soft Landing.

The whole experience last year was very eye-opening, and as a result I wrote an (extremely) long essay about it. The essay introduces a wide range of entirely new concepts, including “The Goldillocks Zone of Oneness” and “Hybrid Vigor in the context of post-Darwinian ethics.” It also features a section about my conversation with God at Burning Man.

If you are attending Burning Man and would like to meet with me, I will be available for chatting and hanging out right after my talk (call it the Qualia Research Institute Office Hours at Burning Man).

Here are the details of the talk:

Andrés Gómez Emilsson-Consciousness vs Replicators

Date and Time: Wednesday, August 29th, 2018, 3 PM – 4:30 PM
Type: Class/Workshop
Located at CampCamp Soft Landing (8:15 & C (Cylon). Mid-block on C, between 8 and 8:30.)


Patterns that are good at making copies of themselves are not necessarily good from an ethical point of view. We call Pure Replicators, in the context of brains and minds, those beings that use all of their resources for the purpose of replicating. In other words, beings that replicate without regards for their own psychological wellbeing (if they are conscious) or the wellbeing of others. In as much as we believe that value is presented in the quality of experience, perhaps to be “ethical” is to be stewards and advocates for the wellbeing of as many of the “moments of experience” that exist in reality as one can. We will talk about how an “economy of information about the state-space of consciousness” can be a helpful tool in preventing pure-replicator take-over. Lastly, we will announce the existence of a novel test of consciousness that can be used to identify non-sentient artifacts or robots passing for humans within the crowd.