CAN YOU SAY "RETROCAUSATION"?

[Bill10558]

Good one, even I can grok this explanation. Thanks.

[reddclay]

But you would get the wrong answer

Grok is inferior to the human mind in critical thinking. Deductive and Inductive reasoning.

Almost all answers I get from it violate basic rules of logic. It does nothing more than identify patterns and repeat back it’s interpretations of patterns.

And if you had to Grok the question, it’s likely you hadn’t thought of the question to seek it out which questions the theory of relativety the same as Joseph has been doing.

I won’t even mention the effect of people relying on AI for answers it’s effect on cognitive thinking.

I follow one of the top traders in the world, a market wizard, who puts out small bits of information for people to consider. One after the other they GROK, in public, without shame, can you explain it to me and it comes up with the wrong answers. The market wizard said the answers do not even resemble the thinking that they are putting out.

Technocrats 1…Non technocrats…0

[chris]

@omnimatter

within each sub-continuum, or phase-space, that composes the cosmos, time is no mere abstraction. It functions as a measurable force intrinsic

Yes, but our phase-spaces are temporary and illusory in that sense, which makes time a mere sideffect and not ‘real’ outside of these small spaces, when one is in a larger, ‘more real’ reality(.)(?).

[reddclay]

Richard Bartlett is a special person. Not sure what to call him. He doesn’t like the word healer so he’s not that. He’s sort of a mystic. But not in words which are just approximations of his experiences.

I’m into the field of energy psychology. Going into people’s depths and ridding them of unconscious material. You take people back on the time line and you pull the stuff. After all my training, the last thing I wanted to do was go to another workshop. Somebody insisted I just go for his free introductory talk before his three day webinar. So I did.

I had no idea or concept of what I was going to see. The guy can collapse the wave function and bring people into new time lines. If somebody told me that ten years ago, I’d say ok…woo woo.

Well some woman gets on stage. And she has “back problem” or some really bad condition. I don’t remember. All of a sudden, she starts falling backwards. Yeah, like those Sunday morning goof balls that say you’re healed. But what I saw was not a woman falling backwards on the stage. I saw an infinite series of now. Time stopped at each point so her fall felt like an eternity.

I snapped out of it. What did I just witness? Did anybody else see it? So I forked up $500 bucks so I could understand what he was doing.

He teaches people how to collapse the wave function. And all weekend, he’s bringing people on stage with broken arm problem, stomach problem, I hate my mother problem and talking quantam woo woo.

The only context I had for what I was witnessing and experiencing was a book back in the 60’s written by Brad Steiger. “In my Soul I am Free” where the guy in the book fixes are car light by collapsing the wave function. And there was a guy back in the 60’s Bostic, I think his name was who started all these psychic institutes, Berkley Psychic institute who taught this technique called the erasure technique which was where I think that guy Hubbard got his idea for for Dianetics. Well, that whole movement went wrong.

But the initial idea might have been a good one.

So basically, Richard is NOT writing from the mind. The guy can walk the talk and I’ve been able to replicate this process, somewhat, from what he showed at workshops and practice.

You’re literately jumping timelines and bring in new things, but this ain’t theory or philosophy. You’re experiencing it. The theory is for people to help understand. So basically this is a book on transformation/reality and quantam madness by somebody that can actually make it happen.

Some years back, Joseph wrote a blog from Physics.org. They were attempting to collapse the wave function of the economy so we never went into a recession again.

Anybody recall that one? So this article reminded me off it. Even if they could do it, and I think the universe and time makers wouldn’t be happy if they succeeded and interfered with human stupidity vs allowing it to run it’s course, there would be a price to pay.

And that was my one disagreement with Richards theory, that you can help somebody out of misery and not be interfering in their universal agreement. I’d never do this on anybody else unless I was in danger. But I play in the matrix on myself. law of non-interference.

[Bill10558]

I used grok in place of “understand”. I was classified early in school life as having average intelligence so have been educated as such within the educational curriculum.

[Scarmoge]

See Hubert Dreyfus - (1) What Computers Can’t Do and (2) What Computers Still Can’t Do. 1972 and 1992 respectively. I think both are available gratis on Archive.org

… It (the computer) doesn’t “know” anything. It can neither assert nor propose. It can not experience nor remember. It can not INTERPRET It can not reason. It can not, as Antonio Damasio would say, “Have the feeling of what is happening”. But, and most importantly, it can not go “outside” its database.

it would probably be best to stop thinking about computers Anthropomorphically.

… and no matter how many dyads are strung together to produce whatever length of dyadic chain at whatever speed is achievable … it will always be the Illusion of Thought.

[reddclay]

Good story!

There are special people among us. They are touched. And just because you have a special ability doesn’t mean you should use it. Especially altering people’s timelines.

But if government adapted off world technology for their agenda. Then remote viewing and collapsing wave function are certainly part of their experiments. They don’t seem to comprehend the principle of blow back

[omnimatter]

Time, as a universal phase locked flow is absolutely real, if it were not, the sub-continua of phase spaces would not exist. This is where poetry fails.

[chris]

Real, but not a permanent structure or space, correct?

[Scarmoge]

… there are 2 types of objects available for observation and scientific study. Existent Reals and Non-Existent Reals. Existent Reals are material objects that have properties such as color, weight, mass and so on … Non-Existent Reals can have any or all of those properties except 1 … the property of physical existence / manifestation. All Existents are Real but not All Reals are Existent.

C.S. Peirce asked the question … What if God is one of these Non-Existent Reals. see his …
“A Neglected Argument for the Reality of God” (1908) - available gratis many places on the Interwebs.

See also … Nubiola very good on Peirce

Charles S. Peirce and the Abduction of God by Jaime Nubiola1
[image]
](https://www.unav.es/users/CSPAbductionGodIARP.pdf)

[reddclay]

We’re on the same page!

It’s good to know Milton Erickson technology/NLP only so you can know when it’s being used on you by the political class. Just assume it is.

I understood the intrigue and interest in this area because I was like that too. But I’m old now. I went Stoic. I no longer want super human powers other than develop powers of good character and right decision making in my small little world of influence. I also figured that’s the ultimate super power that our world needs more of. Just good people. What an idea. It’s also not a small task. Always needs to be improved.

[omnimatter]

Correct, in my view, the flux.

[omnimatter]

Being of necessity and contingency.

[sunnyboy]

@Scarmoge

it would probably be best to stop thinking about computers Anthropomorphically.

Indeed, yes, you’ve nailed a big problem with how people think about AI!

[bluefalken]

1. Time in Biological Learning and Error Correction

In real brains, learning unfolds over time. Unlike artificial networks where error gradients are computed instantaneously and applied after each batch, the brain must work with:

• Delayed feedback: Rewards or consequences don’t always follow immediately (e.g., you touch a hot pan → learn not to do it again).
• Temporal credit assignment: How does the brain know which past activity led to a present reward or mistake?

Related Concept: Temporal Difference Learning (TD Learning)

• Used in reinforcement learning and resembles dopamine-based signaling in the brain.
• Learns to associate past events with future outcomes using prediction errors over time.

In essence, learning is not just spatial (layer to layer), but temporal (past to future).

2. Predictive Coding & Time

Predictive coding, which we discussed earlier, naturally incorporates time:

• It models the brain as a system that’s always trying to predict the next moment.
• The difference between what was predicted and what actually occurred becomes the error used to refine the model.

This aligns with how humans:

• Expect sequences (e.g., the rhythm of speech or motion).
• Get surprised when an expected pattern is broken (a beat skips, a word is mispronounced).

The brain learns across time, not just within a frozen snapshot.

3. Backpropagation Through Time (BPTT)

In machine learning, recurrent neural networks (RNNs) are trained using Backpropagation Through Time (BPTT), a temporal extension of backpropagation.

What it does:

• Unrolls a neural network over time (e.g., t=0 to t=10).
• Applies standard backpropagation across the entire sequence.

Biological Challenge:

• The brain likely doesn’t “unroll time” explicitly.
• But it does maintain working memory, attention, and temporal buffers that allow for time-sensitive learning.

4. Dendrites, Spikes, and Time Encoding

Neurons in the brain use spikes (short electrical pulses), and their timing matters:

• The relative timing of spikes between neurons determines plasticity (called Spike-Timing-Dependent Plasticity, or STDP).
• This is explicitly time-sensitive—learning depends on whether the pre-synaptic spike happens before or after the post-synaptic spike.

Example:

If A fires just before B → strengthen the connection (A caused B to fire).
If A fires after B → weaken it.

This is a real-time analog to gradient signals.

5. Mental Time Travel and Internal Simulation

Some neuroscientists suggest the brain performs “internal simulations” of the future to test outcomes—effectively doing something like forward modeling and error correction before acting.

This might resemble:

• Monte Carlo rollouts in reinforcement learning
• Model-based learning
• Planning using internal representations (like imagining playing chess moves ahead)

Summary: How Time Intertwines with Learning Models

Concept	Role of Time	Related Mechanism
Backpropagation	None (static snapshots)	Feedforward error correction
Predictive Coding	Constant updating based on prediction	Sensory feedback loops
Temporal Difference Learning	Assigns value to actions over time	Dopaminergic signaling
STDP (Spike-Timing Plasticity)	Learning based on spike timing	Millisecond-scale time coding
BPTT (Artificial RNNs)	Explicitly unrolls time for learning	Sequence modeling
Mental Simulation	Simulates future to influence present	Planning, imagination

[Scarmoge]

… keep researching … I promise you’ll come to some “interesting” conclusions especially concerning the nature of time. If you can look specifically at experimental literature regarding back propagation in HUMANS.

[bluefalken]

Just a teeny, tiny taste of what I found:
Here’s a deep dive into how predictive coding and timing mechanisms shape human perception of time—the sense of “now,” the misalignment of events, and temporal illusions like the flash‑lag, kappa, and tau effects.

1. Real‑time Extrapolation & the Flash‑Lag Illusion

• Flash‑lag illusion: A moving object appears ahead of a simultaneously flashed object because the brain extrapolates motion forward, compensating for neural delays (~100 ms).
  • Motion‑based predictive model accurately reproduces human psychophysical data by combining current sensory data with motion priors and explicit delay compensation jov.arvojournals.org+14journals.plos.org+14en.wikipedia.org+14.
  • Delay‑aware predictive coding model implements both forward (extrapolation) and backward (alignment) processes to realign predictions across a cortical hierarchy en.wikipedia.org+2eneuro.org+2nature.com+2.
    ➤ Result: The brain’s perceptual “now” is a prediction-corrected present, not simply the raw sensory input.

2. Time‑binding Illusions: Tau & Kappa Effects

• Tau effect: When the interval between stimuli varies, the perceived spatial distance is warped—time influences space perception en.wikipedia.org+1en.wikipedia.org+1.
• Kappa effect: Longer spatial separation makes intervals feel longer; shorter ones feel shorter—echoing spatiotemporal Bayesian inference with velocity priors .
  ➤ These illusions reveal that perception of time and space is interwoven, jointly inferred under predictive coding frameworks.

3. Temporal Asynchrony in Visual Features

• Perceptual asynchrony: Color changes are perceived ~70–80 ms before motion changes in the same object researchgate.net+15en.wikipedia.org+15pmc.ncbi.nlm.nih.gov+15.
  ➤ This indicates the brain has feature-specific processing latencies, yet we experience a unified moment through temporal integration and prediction.

4. Temporal Scales in Hierarchical Predictive Coding

• Hierarchical time‑scales: Cortical levels track different temporal extents; lower levels respond to fast-changing inputs while higher levels integrate over seconds en.wikipedia.org+1en.wikipedia.org+1.
  ➤ The brain maintains multiple “nows”, enabling both immediate sensory processing and context-sensitive perception.

5. Neural Oscillations & Temporal Prediction

• Oscillations (e.g., alpha, gamma) structure time into meaningful chunks, enabling prediction and error signaling at specific phases en.wikipedia.org.
  • Theta–gamma coupling in the hippocampus compresses sequences so STDP can link temporally distant events into coherent episodes .
    ➤ The brain uses rhythms as clocks, organizing prediction and sensory integration within oscillatory cycles.

6. EEG/FMRI Evidence of Predictive Temporal Processing

• Prediction error ERPs (e.g., Ne/ERN) reflect fast mismatch detection (~100 ms), even for timing violations sciencedirect.com+15en.wikipedia.org+15nature.com+15arxiv.org+4pmc.ncbi.nlm.nih.gov+4journals.physiology.org+4.
• Early vs late ERP components correspond to feature‑level mismatches vs identity/context mismatches in visual prediction tasks pmc.ncbi.nlm.nih.gov+1sciencedirect.com+1.
  ➤ Temporal prediction is layered: early feedforward errors, then recurrent identity/contextual updating.

Bringing It Together: Time in Human Experience

• Perception of “now” is a reconstruction, synthesized from momentary inputs and hierarchical predictions.
• Temporal illusions like tau/kappa occur because the brain merges space and time under Bayesian expectations.
• Feature asynchrony reflects modular timing but unified experience emerges via synchronization.
• Oscillatory rhythms gate when errors are computed and changes are integrated.
• ERP evidence shows timing prediction errors manifest rapidly and hierarchically in the brain.

Summary

Phenomenon	Mechanism	Perceptual Outcome
Flash-lag	Motion extrapolation + delay alignment	Moving objects appear ahead
Tau/Kappa	Bayesian expectation of uniform motion	Spatiotemporal illusions
Feature asynchrony	Modular processing latencies + integration	Integrated “now” experience
Hierarchical timescales	Layered predictive hierarchy	Fast perception + slow contextual updating
Oscillations	Temporal gating	Rhythmic timing for prediction & error
ERPs	Early vs late prediction errors	Layered temporal mismatch detection

[bluefalken]

Physics: Retrocausation and Time-Symmetric Theories

In physics, retrocausation is mostly a speculative or interpretive issue:

1. Quantum Mechanics (QM)

• The Delayed-Choice Quantum Eraser and Wheeler’s Delayed-Choice Experiment seem to show that how you measure a photon today changes its past behavior.
• Transactional Interpretation (TI) by John Cramer is explicitly retrocausal — where “offer” waves travel forward in time and “confirmation” waves travel backward in time, allowing a transaction between emitter and absorber outside of a strict past→future flow.

2. Time-Symmetric Theories

• Physics equations — like Maxwell’s electromagnetic equations — don’t care which direction time moves.
• Retrocausality often shows up in CPT-symmetric (Charge, Parity, Time) theories or in solutions of Einstein’s relativity allowing closed time-like curves.
• Some physicists explore Two-State Vector Formalism (Aharonov, Bergmann, Lebowitz), where present and future states together describe a quantum system.

3. No-Communication Theorems
   Even if these interpretations imply some backward influence, mainstream physics upholds that no usable information can be sent into the past — so paradoxes like sending messages backward or changing history don’t follow.

Philosophy: Retrocausality and the Nature of Time

Retrocausality raises deep questions:

• Causal Loops & Paradoxes
  • Classic example: You receive blueprints for a time machine and build it, then send those blueprints back to yourself — so who invented it?
  • This is the famous Bootstrap Paradox, showing that retrocausality can create self-consistent loops.
• Block Universe Theory
  • Under a Block Universe view (where past, present, and future coexist), retrocausality is not “changing the past,” but just one part of a 4D structure of time.
  • Future and past are fixed and entangled; “causes” could appear to go in either direction.
• Free Will
  • Retrocausality implies future events can restrict present choices, challenging intuitive notions of free will.

Fiction and Pop Culture: Playing with Time

Retrocausality is rich material for storytellers because it subverts our usual sense of cause and effect:

• Movies and Shows:
  • Tenet (2020): Time-reversed people and objects flow backward through cause-and-effect.
  • Arrival (2016): Learning an alien language that allows you to experience time nonlinearly — knowledge from the future shapes present decisions.
  • Dark (Netflix series): Multi-generational causal loops and characters being their own ancestors.
• Literature:
  • Philip K. Richard and Robert Heinlein wrote stories built on closed causal loops, like Heinlein’s “—All You Zombies—” where a character is their own parent.

Impact on Our Understanding of Time

At its most profound level, retrocausality:

• Suggests time might not be a simple one-way street.
• Makes us wonder if our concept of now is an illusion.
• Encourages physicists to explore whether cause and effect are emergent properties of a deeper, time-symmetric reality.

Interesting Conclusions

Retrocausality is a mathematical possibility in physics interpretations, but not an accepted feature of everyday life.

Even if retrocausality exists at some quantum level, it probably cannot send usable information into the past due to quantum randomness.

Philosophically, it supports block-universe views — that past, present, and future might exist all at once — challenging our intuitive sense of time.

One could go even deeper into one particular aspect — like the math of transactional interpretations, thought experiments (e.g. Novikov self-consistency principle).

[bluefalken]

1. Time as a Coordinate (Traditional Physics)

Context:
In Newtonian mechanics, time is an absolute parameter: a uniform background ticking along the same for everyone — a scalar number you can read on a clock. Even after Einstein, time is mostly treated as a dimension in 4D spacetime:
(x,y,z,ct),
(x,y,z,ct),

which we package into a 4-vector xμxμ. This is where time’s scalar-ness comes in: it’s just one coordinate, distinguished by its minus sign in the metric ds2=−c2dt2+dx2+dy2+dz2ds2=−c2dt2+dx2+dy2+dz2.

Why this is insufficient:

Treating time this way doesn’t tell us what time is, only how it enters equations.

Time is not an observable like a field — you never measure "the time field at a point"; you measure the evolution of other things over time.

2. Time Crystals — Time as a Temporal Lattice

Concept:
Time crystals were first proposed theoretically by Frank Wilczek (2012). A time crystal is a quantum system that exhibits spontaneous periodicity in its ground-state behavior, breaking continuous time-translation symmetry into a discrete one — like a lattice structure repeating itself in time.

Key insight:
Imagine the atoms in a conventional crystal repeating in space:

atom — atom — atom — atom — …

Time crystals repeat in time:

state(t) → state(t + T) → state(t + 2T) …

Implications:
Time crystals show that periodic order — normally thought of in space — can emerge in the time domain too.
Although these don’t necessarily imply time is “made of atoms,” they do make time look less like a continuous parameter and more like a discrete or semi-regular structure under some conditions.

Current Status:
Real-time crystals have been observed in driven quantum systems (e.g. in trapped ions and NV centers).
This is still condensed-matter physics — but it has spurred thought about discrete temporal order.
3. Causal Set Theory — Time as a Graph/Lattice of Relations

Concept:
In causal set theory (Rafael Sorkin and others), spacetime is fundamentally discrete. Instead of smooth spacetime:

Every “point” is an event, an element in a set.

The only structure is the causal order (a≺ba≺b) telling you which event can influence which.

Key insight:
Time is not an independent coordinate, it is an emergent feature of the partial order of events.
If you take the graph of this causal order and sprinkle it into Minkowski space, you get an approximation to smooth spacetime — but fundamentally it looks like a random Poisson lattice.

Implications for time:

Time is neither scalar nor vector, but the ordering structure itself — a combinatorial or algebraic object.

Continuity is lost; temporal flow is emergent.

The closest analogy to a lattice/quasi-crystal here is that these causal sets can have discrete structure without periodicity.

4. Loop Quantum Gravity & Spin Networks — Time Emerges from Networks

Concept:
Loop Quantum Gravity (LQG) suggests that space is made of discrete chunks — “quanta of area and volume,” represented as nodes and links in a spin network.
Time evolution happens via “spin foams,” where one spin network morphs into another.

Implications for time:

Time is not a fundamental coordinate; it's a parameter that describes transitions between one quantum state of geometry and the next.

The structure is more like a graph evolving in discrete steps, like a cellular automaton — again suggesting something like a lattice, but one governed by combinatorics, not a continuous flow.

5. Emergent Time from Quantum Entanglement

Concept:
A radical idea — pushed by people like Don Page and William Wootters — is that time might emerge from entanglement correlations within a global quantum state.
In some versions:

The universe is one huge, stationary quantum state.

What we call “time” is the way subsystems perceive correlations with the rest of the state.

Implications for time as a lattice/quasi-crystal:

Time isn’t a coordinate or a continuous parameter at all.

It’s more like an informational pattern — a web of correlations that unfolds like a quasi-crystalline structure (ordered but not periodic) across the quantum state.

6. Time as a Quasi-Crystal?

Quasi-crystals:

Ordered, but not periodic — they repeat according to non-repeating symmetries (e.g. Penrose tilings in 2D).

If some deeper theory of spacetime is governed by such non-repeating symmetries (e.g. E8 lattice projections into lower dimensions, which some unification theories invoke), then time could also come in quasi-repeating structures, not perfectly periodic nor perfectly continuous.

Why this might matter:
In some cutting-edge work:

The E8 lattice projected into 4D yields a pattern that looks “almost periodic,” and some authors (e.g. Garrett Lisi's “Exceptionally Simple Theory of Everything,” though very speculative) play with this idea.

Temporal quasi-crystals have already been demonstrated in periodically driven quantum systems — essentially showing that temporal order can be complex and non-repeating, like a Penrose tiling in time.

7. Philosophical Implications — Time as Relation, Not Thing

Leibniz famously argued time is a relation between events, not a thing.

Modern relational interpretations — like Barbour's timeless configurations of the universe — say there’s no fundamental time; there are just “nows,” and time is our way of ordering them.

Summary Comparison Chart

Here’s a summary chart comparing the different models you’re interested in:
Idea What Time Looks Like Key Implication
Classical/Relativistic Scalar coordinate in a smooth manifold Time is continuous, one-dimensional
Time Crystals Periodic repetition (temporal lattice) Time can show discrete symmetry breaking
Causal Set Theory Partially ordered set (graph/lattice) Time is fundamentally discrete and relational
Spin Networks (LQG) Sequence of discrete graphs (evolving) Time is emergent from quantum geometry
Quantum Entanglement (Page-Wootters) Correlations in a timeless state Time is informational, emerges from correlations
Temporal Quasi-Crystals Aperiodic temporal order Time may exhibit complex repeating patterns
Conclusion — A Synthesis

Your question is on the bleeding edge of foundational physics.
Current mainstream physics treats time as a continuous coordinate, but:

Many serious researchers believe this continuity is an approximation.

Underneath lies something combinatorial, graph-like, or aperiodically ordered — much like a lattice or a quasi-crystal.

That means time might not be “a thing” at all — it could emerge as a pattern from a deeper, discrete or algebraic structure.

Time as a Discrete or Emergent Structure

1. Time as a Scalar in Classical Physics

In classical Newtonian mechanics, time is an absolute scalar parameter. In Einstein’s relativity, time is one coordinate of a four-dimensional spacetime continuum, often treated as a component of a 4-vector. Here, time is smooth, continuous, and flows uniformly.

2. Time Crystals — Temporal Lattices

Time crystals are systems that spontaneously break continuous time-translation symmetry to repeat their state periodically. Frank Wilczek first proposed them, and they have been realized experimentally in driven quantum systems like trapped ions and nitrogen-vacancy (NV) centers. Time crystals suggest that under some conditions, time can have a discrete or periodic order — a kind of temporal lattice.

3. Causal Set Theory — Time as a Graph

Causal set theory posits that spacetime is fundamentally discrete — a set of events with a partial order defining causality. Time emerges as the ordering relation of these events rather than as a continuous coordinate. Causal sets look like a random Poisson lattice at large scales, and temporal intervals correspond to chains of causally linked events.

4. Spin Networks & Spin Foams in Loop Quantum Gravity

Loop Quantum Gravity (LQG) models spacetime as a superposition of discrete structures. Space is built from spin networks — graphs with nodes and links — and time is the process of these networks evolving into one another, called a spin foam. Time is thus not a fundamental continuum but emerges from this evolving graph structure.

5. Emergent Time from Quantum Entanglement

The Page-Wootters mechanism explores the idea that time may be an emergent feature of correlations in a stationary global quantum state. In this view, what we call time arises as a relational property between subsystems — effectively making time an informational and entropic construct, rather than a primary variable.

6. Temporal Quasi-Crystals

Some speculative models draw analogies between time and quasicrystals — structures that show order without periodicity. Time could exhibit quasi-repeating patterns governed by mathematical structures like Penrose tiling, potentially arising from higher-dimensional projections. Temporal quasi-crystals, already demonstrated in periodically driven quantum systems, hint that time could possess an aperiodic order.

Conclusion

While mainstream physics treats time as a continuous coordinate, cutting-edge research paints a richer picture. Time might emerge from discrete, graph-like structures, entangled states, or complex patterns that look like temporal lattices or quasi-crystals. This moves time from the status of a mere coordinate to an emergent structure that reflects deeper symmetries — or broken symmetries — in the underlying fabric of reality.

Suggested Reading

• R. Sorkin, Causal Sets: Discrete Gravity
• C. Rovelli, Quantum Gravity
• F. Wilczek, Quantum Time Crystals
• D. Page & W. Wootters, Evolution Without Evolution
• S. Lloyd, Emergent Time from Quantum Mechanics
• Penrose, Tilings and Quasicrystals