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Joscha Bach <joscha.bach@gmail.com>
Monday, February 19, 2018 9:34 PM
Jeffrey Epstein
Re:
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Computation itself does not cost energy, only the deletion of bits in a =eversible universe does. Energy is preserved because after the universe =s reversible, the amount of information in it is constant.

> On Feb 19, 2018, at 16:11, jeffrey E. <jeevacation@gmail.com> wrote:

>

> Energy comes from?

>

> On Mon, Feb 19, 2018 at 3:58 PM Joscha Bach =rote:

> In the computational oscillator universe, energy has two forms: there

> =s the information contained in the oscillator pattern itself, which

> to =e looks like its mass: how much information fluctuates in each

> step? =Mass is basically displacement of information in time.) And

> there is =omentum, which is the amount of information that gets

> translated along =he computational graph. (Momentum is displacement of

> information in =pace.)

## >

> If we look at the relationship between the locus of computation and =he global state, a number of variants are possible:

> - global calculation advances all bits in the state vector at the same

>=ime

> - single bit local calculation advances one one bit at a time

> - multi-local calculation has a number of individual "read/write

> =eads" that weave simultaneously

>

> All variants can be realized so that the resulting dynamics are the =ame, which means that they would be independent from the perspective of =n observer. However, variants B and C could also be implemented in such = way that the outcome of the computation depends on the order in which =ocations of the universe are touched. I doubt that this is the case, =ecause it might make the universe look for stochastic than it does.

>

> On Feb 19, 2018, at 06:49, jeffrey E. <jeevacation@gmail.com> wrote:

## >>

» Energy? Unlimited? Equal per computation ? Non local ? Two places

» =t once? Distributions. Field effects time to compute / all the

>> same =ime? Synchronized

>>

>> On Mon, Feb 19, 2018 at 6:24 AM Joscha Bach |

=rote:

>>

>>

> > As you may have noticed, my whole train of thought on =omputationalism is based on the rediscovery of intutionist mathematics =nder the name "computation".

\( >>=\mathrm{tp}: / / \mathrm{math} \). and rej.com/wp-content/uploads/2014/03/real-world-realizab

> > ility.=df

## >> (cont.)

>>

> 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 = physical law, i.e. it is impossible to build physical computer that =an calculate more than a Turing machine. However, that conflicts with =he traditional 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.

## >> (cont.)

» 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.

» =he vortex is entirely generated by the molecular dynamics within

> the =iquid (which are our discrete lattice computations), and it

» does not =issolve because it is a stable oscillator. The vortex can

> travel =erpendicular to the direction of the fluid, which is

> equivalent to =raveling in space. It cannot go arbitrarily fast: the

> progression of =he liquid defines a lightcone in which each molecule

> can influence =ther molecules, and which limits the travel of every

> possible vortex. =lso, the faster the vortex moves sideways, the

> slower it must =scillate, because the both translation and state

> change depend on =haring the same underlying computation. It will

> also have to contract =n the direction of movement to remain stable,

> and it will be maximally =ontracted at the border of the light cone.

» (The contraction of a vortex =s equivalent to giving 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> =rote:
>>>
>>> i want to hear more on your views on projection spaces. . =lso feel free to put some more meat on the bones of the thinking re =orentz transformations
>>>
>>> --
>>> please note

## >> (cont.)

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