<table><tr><th>From:</th><th>Joscha Bach</th></tr><tr><td>Sent:</td><td>Monday, February 19, 2018 9:25 PM</td></tr><tr><td>To:</td><td>Jeffrey Epstein</td></tr><tr><td>Subject:</td><td>Re:</td></tr><tr><td>Attachments:</td><td>signature.asc</td></tr></table>

Yes, our universe is reversible, i.e. each state seems to have exactly =ne possible preceding state, and history is being preserved.

This means that it is probably deterministic, because it is hard to =ecover reversibility from probabilistic computation. (Conversely, there =re many ways in which we can get apparent stochasticity from a =eterministic universe.)

We can implement reversible computation on an irreversible computer, but =ach operation that deletes a bit will have to store it somewhere: there =s going to be an accumulation of entropy, of garbage bits. We can also =mplement reversibility on an irreversible computer by simply not =erforming any of the operations that delete bits (if we want to, we can =eep an undo history).

It is possible to build reversible Turing complete automata.

On the other hand, if you take an irreversible finite deterministic =utomaton (like Game of Life) and let it run for long enough, it will =lways become periodic. In the worst case, the period is 1, i.e. every =ynamic structure is dead, but the period can also be extremely long. =nce the automaton has entered a loop, it is reversible.

I don't hold a strong ontological belief in computationalism. I am just =urprised that it seems to work so well as a possible candidate theory =f everyhing, and it seems to work much better than all the competitors, =ike string theory. Both are stubs that cannot yet recover our =bservables, but as far as I can see they hold the promise of doing so. =heories based on computation have one big burden: I don't know how they =ould explain what process leads to the emergence of the primary =utomaton. This first automaton can be extremely simple, as long as it =s Turing complete, but it is not nothing, and it cannot bring itself =nto existence.

Theories based on classical math are much more liberal when it comes to =reation, because they can postulate the existence of things that have =ot been computed. Their burdens are that they are computationally =often even uncountably) infinitely more expensive, i.e. God needs to =uy an infinitely or even uncountable infinitely more expensive computer =o run what amounts to be the same universe. And perhaps more dooming, =omputationalists can tell God how to make a computer, but =ypercomputationalists cannot tell how to make a hypercomputer, because =ypercomputation is not constructive.

If there are metacomputational operators, they are outside the realm of =nalytical description, because all analytical description ultimately =elies on computational languages and tools. Contrary to what Penrose =opes, our mathematical creativity seems to rely entirely on Turing =omputable functionality. This does not mean that such a =etacomputational operator as he intuits does not exist, but it means =hat we probably cannot discover its existence. I will give a talk about =he idea of metacomputational operators at the Science of Consciousness =onference; perhaps James Tagg will get something out of it :)

I am not aware of fudge btw., and will appreciate if you point it out.

On Feb 19, 2018, at 06:55, jeffrey E. <jeevacation@gmail.com> wrote:

> reversibility, the theory should cohort with the evidence. I am =ware of your beliefr structure the god of zero and one plus =omputablity. but it seems fillled with fudge. ?:)/ if it doesnt fit =he model take it out . stringtheory had the same flaw, in reverse , =f it didnt fit , add more.

>

On Mon, Feb 19, 2018 at 6:24 AM, Joscha Bach <Joscha.Bach@...> wrote:
As you may have noticed, my whole train of thought on computationalism =s based on the rediscovery of intutionist mathematics under the name =computation".
=tp://math.andrej.com/wp-content/uploads/2014/03/real-world-realizabil
> ity.=df

>

> The difference between classical math and computation is that =lassically, a function has a value as soon as it is defined, but in the =omputational paradigm, it has to be actually computed, using some =enerator. This also applies for functions that designate truth. For =omething to be true in intuitionist mathematics, you will always have =o show the money: you have to demonstrate that you know how to make a =rocess that can actually perform the necessary steps.

>

> This has some interesting implication: computation cannot be =aradoxical. In the computational framework, there can be no set of all =ets that does not contain itself. Instead, you'd have to define =unctions that add and remove sets from each other, and as a result, you =ight up with some periodic fluctuation, but not with an illegal state.

>

> Intuitionist math fits together with automata theory. It turns out =hat there is a universal computer, i.e. a function that can itself =ompute all computable functions (Turing completeness). All functions =hat implement the universal computer can effectively compute the same =et of functions, but they may differ in how efficiently they can do it. =fficiency relates to computational complexity classes.

> The simplest universal computers known are some cellular automata, =ith Minsky and Wolfram arguing about who found the shortest one. =oolean algebra is Turing complete, too, as is the NAND gate, the lambda =alculus, and almost all programming languages. The Church Turing thesis =ays that all universal computers can compute each other, and therefore =ave the same power.

>

> I suspect that it is possible that the Church Turing thesis is also a =hysical law, i.e. it is impossible to build physical computer that can =alculate more than a Turing machine. However, that conflicts with the =raditional intuitions of most of physics: that the universe is =eometric, i.e. hypercomputational. The fact that we cannot construct a =ypercomputer, not just not in physics, but also not mathematically =where we take its existence as given when we perform geometry), makes =e suspect that perhaps even God cannot make a true geometric universe.

>

> How can we recover continuous space from discrete computation? Well, =pacetime is the set of all locations that can store information, and =he set of all trajectories along which this information can flow, as =een from the perspective of an observer. We can get such an arrangement =rom a flat lattice (i.e. a graph) that is approximately regular and =ine grained enough. If we disturb the lattice structure by adding more =inks, we get nonlocality (i.e. some information appears in distant =attice positions), and if we remove links, we get spatial superposition =some locations are not dangling, so we cannot project them to a single =oordinate any more, but must project them into a region).

>

> On the elementary level, we can define a space by using a set of =bjects, and a bijective function that maps a scalar value to a subset =f these objects. The easiest way of doing might be to define a typed =elationship that orders each pair of objects, and differences in the =calar are mapped to the number of successive links of that relationship =ype. We can use multiple relationship types to obtain multiple =imensions, and if we choose the relationships suitably we may also =onstruct operators that relate the dimensions to each other via =ranslation, rotation and nesting, so we derive the properties of =uclidean spaces.

>

>

>

> To get to relativistic space, we need to first think about how =nformation might travel through a lattice. If we just equalize value =ifferentials at neighboring locations, we will see that the information =issipates quickly and won't travel very far. To transmit information =ver large distances in a lattice, it must be packaged in a way that =reserves the value and a momentum (in the sense of direction), so we =an discern its origin. A good toy model might be the Game of Life =utomaton, which operates on a regular two dimensional lattice and =flows the construction of stable, traveling oscillators (gliders). In =ame of life, only the immediate neighbor locations are involved, so =liders can only travel in very few directions. A more fine grained =omentum requires that the oscillator occupies a large set of adjacent =attice locations. SmoothLife is a variant of Game of Life that uses =ery large neighborhoods and indeed delivers stable oscillators that can =ravel in arbitrary directions.

> I think I have some idea how to extend this toy model towards =scillators with variable speed and more than two dimensions. It may =lso possible to show that there are reasons why stable traveling =scillators can exist in id, 2d and 3d but not in 4d, for similar =easons why stable planetary orbits only work in 3d.

>

> To give a brief intution about a traveling oscillator as a wavelet: =hink of a wavelet as two concentric circles, one representing the =eviation above zero, the other one the deviation below zero. They try =o equalize, but because the catch up is not immediately, they just =witch their value instead. (This is the discretized simplification.) =ow displace the inner circle with respect to the outer one: the =rrangement starts to travel. Making the pattern stable requires =istorting the circles, and probably relaxing the discretization by =ncreasing the resolution. The frequency of the wavelet oscillation is =nversely related to how fast it can travel.

>

> You can also think of a wavelet as a vortex in a traveling liquid. The

> =ortex is entirely generated by the molecular dynamics within the

> liquid =which are our discrete lattice computations), and it does not

> dissolve =ecause it is a stable oscillator. The vortex can travel

> perpendicular =o the direction of the fluid, which is equivalent to

> traveling in =pace. It cannot go arbitrarily fast: the progression of

> the liquid =efines a lightcone in which each molecule can influence

> other =olecules, and which limits the travel of every possible vortex.

> Also, =he faster the vortex moves sideways, the slower it must

> oscillate, =ecause the both translation and state change depend on

> sharing the same =nderlying computation. It will also have to contract

> in the direction =f movement to remain stable, and it will be

> maximally contracted at the =order of the light cone. (The contraction

> of a vortex is equivalent to =iving it a momentum.)

>

> An observer will always have to be implemented as a stable system =apable of state change, i.e. as a system of vortices that interact in =uch a way that they form a multistable oscillator that can travel in =nison. From the perspective of the observer, time is observed rate of =tate change in its environment, and it depends on its own rate of =hange, which in turn depends on the speed of the observer. This gives =ise to relativistic time. Also, the observer does not perceive itself =s being distorted, but it will normalize itself, and instead perceive =ts environment around itself as being distorted. As a result, the =bserver will always have the impression to travel exactly in the middle =f its light cone. This model seems to recover Lorentz invariance, but =ith a slight catch: it seems to me that while speed of light is =onstant and there is no preferred frame of reference wrt acceleration, =he resolution of the universe changes with the speed of the observer. =o idea if this is a bug or a feature, or if it will be neutralized by =omething I cannot see yet before I have a proper simulation.

>

> Obviously, all of the above is just a conjecture. I can make a =onvincing looking animation, and I am confident that many features like =imultaneity etc. will work out, but I don't yet know if a proper =umeric simulation will indeed work as neatly as I imagine.

>

>

>

On Feb 18, 2018, at 09:00, jeffrey E. <jeevacation@gmail.com> wrote:
i want to hear more on your views on projection spaces. . also =eel free to put some more meat on the bones of the thinking re lorentz =ransformations

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please note
The information contained in this communication is confidential, may be attorney-client privileged, may constitute inside information, and is intended only for the use of the addressee. It is the property of JEE Unauthorized use, disclosure or copying of this communication or any part thereof is strictly prohibited and may be unlawful. If you have received this communication in error, please notify us immediately by return e-mail or by e-mail to jeevacation@gmail.com, and destroy this communication and all copies thereof, including all attachments. copyright -all rights reserved

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