Maths and Hallucinations

Thought this was an interesting read that supports some of my own beliefs regarding the origin of certain universal hallucinations during the psychedelic experience:

Uncoiling the Spiral: Maths and Hallucinations

Please share any thoughts, whether you agree or disagree makes no difference to me.

Er... disagree with what?

Thanks for the article though, it's some of the most fascinating and beautiful research I've ever seen, and the article's very well written... I'm going to have to check out the rest of that website now.

The stuff about Turing was mentioned in the Chaos documentary I posted a week or two ago... I love how the intricate patterns of life can arise from such simple rules. There is a Java app in that article for playing around with, too.

This reminded me vaguely of a well-known phenomenon I read about recently, which is an example of how biology can create intricate structures with very simple actions (presumably governed by a small number of simple genes), namely how the retina builds a one-to-one correspondence with cells in the midbrain (this is before they get transformed in V1 as the article talks about):

"The synaptic network that finally emerges is only partly determined by genes, though. In many parts of the brain, axons initially "overgrow", and then are "pruned" by mechanisms that depend on neural activity.[54] In the projection from the eye to the midbrain, for example, the structure in the adult contains a very precise mapping, connecting each point on the surface of the retina to a corresponding point in a midbrain layer. In the first stages of development, each axon from the retina is guided to the right general vicinity in the midbrain by chemical cues, but then branches very profusely and makes initial contact with a wide swath of midbrain neurons. The retina, before birth, contains special mechanisms that cause it to generate waves of activity that originate spontaneously at some point and then propagate slowly across the retinal layer.[55] These waves are useful because they cause neighboring neurons to be active at the same time: that is, they produce a neural activity pattern that contains information about the spatial arrangement of the neurons. This information is exploited in the midbrain by a mechanism that causes synapses to weaken, and eventually vanish, if activity in an axon is not followed by activity of the target cell. The result of this sophisticated process is a gradual tuning and tightening of the map, leaving it finally in its precise adult form."

All it involves is 1. waves of activity slowly diffusing through the retina, and 2. axons strengthened if they connect two active neurons and weakened if they connect an active and an inactive one.

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Originally Posted by Xei

Er... disagree with what?

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I mostly meant that for anyone still choosing to subscribe to the belief that these hallucinations are the result of some spiritual or otherwise unexplained phenomena. I thought it would be interesting to have discussion from both ends of the spectrum. If more people approached the psychedelic experience more objectively as a means to explore the inner workings of the body rather than as merely a spiritual or recreational activity, I honestly think that the scientific advances in this area would increase dramatically.

It was during one such trip that I was able to fully appreciate the hallucinations I was experiencing were clearly a direct result of neuronal spatial orientation (as explained in the article), and the strobing effects from waves of excitation of neural ensembles oscillating in sync (this was before ever researching such things). When you're tripping I guess you don't stop to think about things like this, but I wish more people would. I realize they have technology that can achieve this, but I still think it could be useful to cognitive neuroscience if they attempted to gain such information from individuals. It's at least a nice jumping off point to make new hypotheses, which can then be tested with appropriate technology.

Anyways, sorry I got a bit off topic...fascinating stuff you posted. I'm curious how finite that precise adult form is and how long it takes to fully develop? Does this imply that visual stimuli will be received very differently in young children than in adults?

Here's a good article on form constants:

Selective 5-HT2A agonist hallucinogens: A review of pharmacological interaction and corollary perceptual effects

In short, 5HT-2a agonism associated with classical psychedelics, combined with an understanding of the feedback mechanisms in the visual cortex, can explain the particular hallucinations one sees on these drugs.

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Originally Posted by cmind

Here's a good article on form constants:

Selective 5-HT2A agonist hallucinogens: A review of pharmacological interaction and corollary perceptual effects

In short, 5HT-2a agonism associated with classical psychedelics, combined with an understanding of the feedback mechanisms in the visual cortex, can explain the particular hallucinations one sees on these drugs.

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Nice, thanks...looks like an interesting read. Bookmarked. This stuff fascinates me. The human mind is amazing enough in its own right, there's no need to come up with magical explanations to attempt to better understand such experiences.

I think that's a really good article. Even tho i don't understand the working and details of it. Especially the first parts. The fact that we can generate pictures with mathematical models that correspond with the actual visuals we see shows how much we already know about the brain. And i see loads of potential in this kind of stuff. It was definetly a good read. And i'm glad you shared it.

The first thing that popped up in my mind after reading this is that it explains some geometric patterns that are seen in different states. It tells us nothing about all the other things that accompany a psychedelic experience. Like the rapid thoughts. Or tendency to get into certain thought patterns. Which then open doors to whole new levels of experience.
And what about the open eye hallucinations of clouds transforming into fully 3 dimensional spaceship resembling flying objects. And sometimes an actual reverse or loop of space and time. Where you can walk the same path 5 times in a row and keep getting back at ur starting destination. Usually accompanied with the alien contact or flying saucer experience. Also it does not explain the psychological methamorphosis that some people undergo in long-term relationships with selective 5-HT2A agonists. That is so eloquently described in the last alinea just before the conclusion of the article that Cmind posted. If i may quote :P ;

"In the case of maladaptive psychedelic programming, one would expect to see the subject crafting self-referential occult belief systems based on ambiguous or archetypal symbols over a period of many months, weeks, or years. These occult belief systems would become more complex over time, relying on a hyper-articulated network of connections between language and symbol systems, thus creating eccentric logic pathways that grow so tangentially elaborate they eventually eclipse common rationality. A person suffering from this syndrome may also exhibit messianic or megalomaniacal tendencies, such as the belief that their occult system was derived from divine origin, along with the urgent need to spread a paradoxical prophecy of doom and transcendence. This syndrome is not symptomatic of neural damage or breakage, it is symptomatic of wholly unique logic pathways forged through obsessive self-referential feedback ideation, facilitated and reinforced through repeated high-dose application of selective 5-HT2A agonists."

I really like ur approach to psychedelics too. And i totally agree that if more people that choose to dive into these things go into the experience with that mindset is a most useful approach to gain more facts about the drugs , our own psyche and our own bodies.

Nice topic and nice replies. I hope i didn't go into to much off-topic. But since you mentioned the spiritual and unexplained. I thought it was appropiate altho maybe a bit much.

Dthoughts, the non-visual effects of 5HT-2a agonists were beyond the scope of the articles just because they were primarily studying the visual cortex. Obviously, if we can get all this interesting stuff happening in one part of the brain, then similarly interesting things can happen in other parts too :)

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Originally Posted by nina

I mostly meant that for anyone still choosing to subscribe to the belief that these hallucinations are the result of some spiritual or otherwise unexplained phenomena. I thought it would be interesting to have discussion from both ends of the spectrum.

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but anyone who has read this would already understand that no matter what they have to say to you about the spiritual side of these experiences, you wouldn't believe, nor would you even try. you've made it clear that the hallucination is just that

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It was during one such trip that I was able to fully appreciate the hallucinations I was experiencing were clearly a direct result of neuronal spatial orientation[...]When you're tripping I guess you don't stop to think about things like this, but I wish more people would.

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most people would rather not, and i can only assume it's because once the magician has reveled his trick, an encore would only seem cruel

Dthoughts, the reason you notice these thing whilst in altered states of consciousness is probably because your brain is deceiving you. You THINK you are walking the same path, but in reality you are walking a different path, you are just getting "rogue" signals as neural communication is altered by the serotonin system navigation. This is also the same for when something highly illogical seems logical while tripping, because your neurons are communicating more, but not in the same fine-tuned ways of normal consciousness. That is my take on this though, and just a theory.

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Originally Posted by Dthoughts

It tells us nothing about all the other things that accompany a psychedelic experience. Like the rapid thoughts. Or tendency to get into certain thought patterns. Which then open doors to whole new levels of experience.
And what about the open eye hallucinations of clouds transforming into fully 3 dimensional spaceship resembling flying objects. And sometimes an actual reverse or loop of space and time. Where you can walk the same path 5 times in a row and keep getting back at ur starting destination. Usually accompanied with the alien contact or flying saucer experience. Also it does not explain the psychological methamorphosis that some people undergo in long-term relationships with selective 5-HT2A agonists.

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But cmind's article does provide an explanation for these phenomena.

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Originally Posted by cmind's article

The Corticocortical Feedback Loop

Moving onward from the visual cortex to higher processing centers along the visual pathway, Layer V pyramidal neurons are once again responsible for mediating corticocortical circuits along both dorsal and ventral streams, all the way up to the multi-modal sensory convergence areas in the pre-frontal cortex (PFC). Destabilization along this all-important binding pathway would allow for a multi-layered cascade of top-down excitatory feedback loops with extreme perceptual results. This is where 5-HT2A selective agonists stop being strictly perceptual and begin to affect the entirety of consciousness. Cross-lobe reciprocal pathways are essential for mediating our real-time multi-modal awareness of reality and the self. When these pathways become excited and begin to destabilize the perceptual effect goes beyond visual hallucination and becomes profoundly disorienting. A subject with heightened excitation along these pathways would experience very complex and disturbing changes in reality, such as visual frame-skipping; memory loss; memory gaps; temporal distortion; time lags; obsessive thought loops; logic traps; the inability to match words to objects; the inability to maintain a train of thought over a few seconds long before it repeats itself; the simultaneous “filling up” or overload of all senses; and the overwhelming urge to shut-down, hide, or recede from reality.

In contrast, once these cortical feedback circuits are fully interrupted and decoupled the subject loses all sense of self, time, and place; becomes profoundly quiet and peaceful inside; becomes infinitely large; floats through an idealized spirit world; and finds existential oneness with the universe. This state is often referred to in psycho-mystical terms as ego-death, the no-mind state, or transcendence. While in this state the subject is perfectly fine and appears to be meditating or in a light trance. The subjective experience of this state is similar in many ways to classic descriptions of out-of-body (OBEs) or near-death experiences (NDEs).

The subjective hallucinogenic and mystical effects of cortical decoupling are best demonstrated in emergent ketamine-induced states, where the visual cortex decouples from external reality and a boundless, formless dream-space appears to open. The mystical effects of cortical decoupling are described in similar terms by stroke victims, epileptics, meditation gurus, drug users, and people who use other technology such as transcranial-magnetic stimulation (TMS) to interrupt phase-coupled cross-lobe activity. At high doses 5-HT2A agonists can create similar decoupling results, yet not as quickly or drastically as the anesthetic ketamine. With orally-ingested psychedelics the journey through excitation to network destabilization to feedback overload to complete decoupling is a long and arduous journey taking many hours to reach full effect. In contrast, smoked or IV DMT administration can compress this process into about five minutes, with another ten or so minutes for the drug to metabolize and the process to entirely reverse itself. This rapid shifting through multi-phase brain states in such a short period of time is perhaps why DMT is considered so dramatic.

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There is more to quote but that was the most pertinent section. I don't feel like there is all that much to discuss here personally, but I must thank nina and cmind for the great and interesting reads.

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Originally Posted by nina

This stuff fascinates me.

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Me too.

I looked into this a little bit, and turns out there's an actual mathematical theory of hallucinations out of the biophysics and theoretical biology department at the University of Chicago. It seems relatively accessible on a conceptual level but still fairly complicated in its mathematical description (differential equations [bifurcation] and abstract algebra [groups]). I'm surprised I've never come across this before, you're like my compass. Here's the abstract, and a link to the article itself:

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Abstract. Neuronal activity in a two-dimensional net is analyzed in the neighborhood of an instability. Bifurcation theory and group theory are used to demonstrate the existence of a variety of doubly-periodic patterns, hexagons, rolls, etc., as solutions to the field equations for the net activity. It is suggested that these simple geometric patterns are the cortical concominants of the "form constants" seen during visual hallucinations.

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A Mathematical Theory of Visual Hallucination Patterns

Looking back on this, I'm familiar with this website now. It's a maths magazine written at Cambridge, and it's really fantastic, it contains some of the coolest articles I've ever read. I'd recommend you check out all the archives, Phion.

I love the overarching message behind this article, which is that the mysteriously ubiquitous forms in hallucinations all correspond to simple alterations of our visual neural apparatus.

It's also very interesting how we can decode shapes such as spirals and the like, in the sense that we can actually find a spacial representation of the shapes in the brain. The really mysterious question is how these shapes are then 'understood' and 'symbolised' by 'the mind'. As far as I know the conceptual paradigm required to answer such questions is still completely undeveloped; we don't understand how to even go about starting to answer these questions. We can trace shapes into the brain only as long as they maintain a simple spacial correspondence to the shapes in the real world; as soon as they go past this stage, the trail goes cold.

I would love to learn more about how the intricate geometrical patterns that you see after taking psilocybin are produced, they're absolutely stunning.

I still hate to say that the psychedelic experience isn't spiritual. It's profoundly spiritual. It's a misunderstanding of spirituality to say that something amenable to scientific explanation can't be spiritual. It's as if it were an either/or proposition. It's not. Real life is just as deeply spiritual as the craziest DMT trip you can imagine. This is another example of new-agers (a.k.a spoiled brats who think they're the center of the universe) poisoning the well of spirituality for the rest of us by setting up some false dichotomy between the "real" world and the "spiritual" world. There's no such separation and there's no need for competition.

So there is a very spiritual explanation for trips. We are inseperable from our bodies and our interpretation of reality is inseperable from our brain chemistry. When we modify our brain chemistry, we modify our interpretation of reality. Hopefully we learn something about how we interpret reality when we're doing this. If learning to understand how we interpret and hence literally create reality isn't spiritual then I don't know what is :)


Great thread though. Very nice.