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## Thread for Non-CA Academic Questions

A forum where anything goes. Introduce yourselves to other members of the forums, discuss how your name evolves when written out in the Game of Life, or just tell us how you found it. This is the forum for "non-academic" content.

### Thread for Non-CA Academic Questions

Have you ever had a big, huge, or deep non-CA question but was/is/are to lazy to post it on some other site? This is the place to post them to get answered!
My question:
Is it possible to grow animal cells inside plants? Like plants with nerve cells or muscle cells?
If you're the person that uploaded to Sakagolue illegally, please PM me.
x = 17, y = 10, rule = B3/S23b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5bo2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo! (Check gen 2) Saka Posts: 2837 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X ### Re: Thread for Non-CA Academic Questions Q:How would the following model evolve?And can you reduce it? I made a model that simulates evolution before. It has a tape. Programs and data are saved on it. There are also many tape readers on it. But unlike Turing machines,the readers execute the programs on the tape(Instead of running the rule saved in the reader),and they can read data or go to lines randomly. Here are the commands. Each command is made of three 16bit numbers. The first one is the command ID. The second and the third are the parameters. They can be values or pointers. 0 x y:Halt whatever x and y are. 1 x y:*x=y 2 x y:*x=*y 3 x y:*x+=y 4 x y:*x+=*y 5 x y:*x-=y 6 x y:*x-=*y 7 x y:*x*=y 8 x y:*x*=*y 9 x y:*x/=y 10 x y:*x/=*y 11 x y:if(x!=0) go to the y th line (aka the 3*y th, 3*y+1 th,3*y+2 th number) 12 x y: make a new reader on the x th line whatever y is. x = 15, y = 36, rule = B38/S23-bo$2bo$3o14$13bo$12bo$12b3o2$11bo$12bo$10b3o4$12b3o$12bo$13bo2$10bo$8bobo$9b2o$6b2o$5bobo$7bo!
72c20e

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### Re: Thread for Non-CA Academic Questions

Wow,a suitable place for the question in my signature:Is there any relationship between the R/S configuration of a chiral carbon atom and the right hand rule?
Welcome to share your ideas about
etymology of names! GUYTU6J

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### Re: Thread for Non-CA Academic Questions

Does the 24-cell function as a caltrop?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: Thread for Non-CA Academic Questions

72c20e wrote:the readers execute the programs on the tape

There is quite an issue on the sequence of executing.
Suppose that reader 1 and reader 2 have the following commands:
reader 1: *x=*y
reader 2: *y=*x
Different sequences of executing gives different results.
Still drifting.
Bullet51

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### Re: Thread for Non-CA Academic Questions

muzik wrote:Does the 24-cell function as a caltrop?

No, cells are opposite cells and vertices are opposite vertices. gameoflifeboy

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### Re: Thread for Non-CA Academic Questions

...then how can it be self-dual?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: Thread for Non-CA Academic Questions

muzik wrote:...then how can it be self-dual?

Well, how can the square be self-dual if vertices are opposite other vertices?

I've touched on this topic before. An n-polytope is self-dual if there exists a transformation composed of rotations and reflections that, applied to the polytope, exchanges d and (n - d - 1)-dimensional elements. As a polytope and its dual must have the same axes of symmetry, the axes of symmetry must remain invariant under this transformation. However, as a convex polytope cannot itself remain invariant under such a transformation, there must be more than one way to mark it with axes of symmetry. Thus, given fixed axes of symmetry, there are two ways to orient the polytope such that it aligns with them. Now a new symmetry is defined, with all the transformations that kept the polytope invariant ("even" transformations) plus all those that transform it to dual orientation ("odd" transformations).

Now choose a point P on an n-D hypersphere. From this point, we can define a set of points, all on the hypersphere, which are equivalent to P under some transformation. This set can be divided into two subsets containing the results of "even" transformations and "odd" transformations. An "odd" transformation on any member of one set produces a member of the opposite set. Transforming the self-dual shape into its "dual" orientation can be done by any "odd" transformation.

For example, doubling tetrahedral symmetry this way produces octahedral symmetry. In this picture, each black triangle can represent an "odd" transformation, and each blue triangle an "even" one: https://upload.wikimedia.org/wikipedia/commons/1/10/Octahedral_reflection_domains.png

In odd dimensions, it seems that turning the shape upside down is always an odd transformation (is there a known proof of this?), and thus turning an odd-dimensional self-dual convex polytope (like the tetrahedron) upside down results in its dual orientation. However, in even dimensions this is not always the case, and in the case of the icositetrachoron (24-cell), turning it by any multiple of 90 degrees is always an "even" transformation that maps the polytope to itself, not to its dual.

An example of an "odd" transformation turning the icositetrachoron into its dual can be realized by rotating 45 degrees in a rotation based on the Hopf fibration of the cube.

TL;DR: Self-dual convex shapes must have self-dual symmetries, which can be doubled by adding transformations that turn the base orientation into the dual orientation. It appears, but I'm not certain, that in odd dimensions, turning a shape upside down is always a transformation of the second type and thus self-dual convex polyhedra are their duals upside-down.

By the way, if anyone knows more about this than I do, I would like to be informed if I have made any flaws in my reasoning. gameoflifeboy

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### Re: Thread for Non-CA Academic Questions

Is there any way to stabilize superheavy elements through metastability? I'm thinking of something like tantalum-180m.
x = 81, y = 96, rule = LifeHistory58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A$4.2A18$4.2A$4.2A2.2A$8.2A! Gamedziner Posts: 678 Joined: May 30th, 2016, 8:47 pm Location: Milky Way Galaxy: Planet Earth ### Re: Thread for Non-CA Academic Questions Gamedziner wrote:Is there any way to stabilize superheavy elements through metastability? I'm thinking of something like tantalum-180m. There have been reports of Ub-292 (unbibinum, element 122) with a half-life of about 7*10^8 years in a thorium deposit. Apparently evidence in the data points to it having an excited state but these results haven't been reproduced. Also, is this formula for the probability an X with half-life y (in seconds) will decay in k (seconds) correct? Pd(k)=1-1/(2^(k/y)) (Pd stands for Probability of Decay, not pentadecathlon) Sketch of proof: The probability that an X will decay in y seconds is 1/2, so Pd(y)=1/2 Ps(y)=1-1/2=1/2. Pd(y)=1-Ps(y)=1-1/2=1/2. Pd(2y)=1-Ps(y)^2=1-1/4=3/4. Pd(3y)=1-Ps(y)^3=7/8 ... and so on. Extrapolation: Pd(cy)=1-Ps(y)^c=1-1/(2^c) Pd(y(1/y)=1-1/(2^(1/y)) Pd(1)=1-(1/(2^(1/y))) Ps(1)=1-(1-1/(2^(1/y)))=1/(2^(1/y)). Pd(k)=1-Ps(1)^k=1-(1/(2^(1/y)))^k=1/(2^(k/y)). Pd(k)=1-1/(2^(k/y)) EDIT: typo Last edited by toroidalet on July 26th, 2017, 9:19 pm, edited 1 time in total. x = 11, y = 5, rule = B2ck3-ij5n78/S01e2ei3-k5ai8b2o$2o3b2o$bo4bo3bo$2bo2b2o$o7bo! (Check Gen 2) toroidalet Posts: 936 Joined: August 7th, 2016, 1:48 pm Location: my computer ### Re: Thread for Non-CA Academic Questions Is it possible to emulate a normal computer in a quantum computer? https://www.youtube.com/watch?v=q6EoRBvdVPQ One big dirty Oro. Yeeeeeeeeee... gameoflifemaniac Posts: 722 Joined: January 22nd, 2017, 11:17 am Location: There too ### Re: Thread for Non-CA Academic Questions You guys know about how a giant centrifuge can make artificial gravity? Isn't that essentially a giant fidget spinnet that spins really fast (that has rooms in it of course.)? If you're the person that uploaded to Sakagolue illegally, please PM me. x = 17, y = 10, rule = B3/S23b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5bo2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2) Saka

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### Re: Thread for Non-CA Academic Questions

gameoflifemaniac wrote:Is it possible to emulate a normal computer in a quantum computer?

Yes, there's a standard trick for this. Given a function f : {0, 1}^n --> {0, 1}^m expressed as a circuit C of classical logic gates, you can replace the gates in the circuit with reversible equivalents to yield a reversible circuit C' (which may have lots of ancillary '0' inputs and some arbitrary messy outputs):

[n input bits][k ancillary '0' bits] --> [m output bits][n+k-m unwanted garbage bits]

Suppose we have another m ancillary '0' bits at this stage. Then we can CNOT the output bits with these ancillary bits to produce another copy of the output, like so:

[n input bits][k ancillary '0' bits][m extra '0' bits] --> [m output bits][n+k-m unwanted garbage bits][m output bits]

Now apply C' in reverse to the first n+k bits to clean up the mess we created:

[n input bits][k ancillary '0' bits][m extra '0' bits] --> [n input bits][k ancillary '0' bits][m output bits]

The upshot of this is that the ancillary '0' bits can be reused in a future computation. This combined circuit, ignoring the k ancillary '0' bits, actually computes the reversible function:

f : {0, 1}^(n+m) --> {0, 1}^(n+m)
(x, y) --> (x, f(x) XOR y)

Now, every reversible classical circuit is a quantum circuit (permutation matrices are unitary matrices), so this can be built out of quantum gates.
What do you do with ill crystallographers? Take them to the mono-clinic! calcyman

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### Re: Thread for Non-CA Academic Questions

I have a conjecture I'd like to prove. Take a k*k matrix P, where every item in P is >0 and less than or equal to b.

Then imagine a function E(k,b) which returns the amount of matrices that exist with those parameters which are antipalindromic. We'll define antipalindromic as meaning the sub-arrays that are the rows, the columns, and the diagonals are all non-palindromes. If you need further clarification and/or discussion, see here.

Now, assuming b is constant, what is the asymptotic behaviour of E(k,b) as k increases? My conjecture states that it tends to 0, and I believe it happens exponentially. Here is my reasoning.

Premise 1: The probability that a length k string is a palindrome goes down exponentially as k increases.
Premise 2: The amount of sub-arrays in P only increaes linearly as k increases (2k+2).
Conclusion: The exponential part of the equation should overpower the linear one, and so palindromes should become less common in big matrices.

This is a rough line of reasoning, not a mathematical proof. I can't really grasp how I'd mathematically prove this when the sub-arrays intersect each other; maybe you could prove they're still independently random despite their intersections. Can anyone prove this?
succ blah

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### Re: Thread for Non-CA Academic Questions

calcyman wrote:
gameoflifemaniac wrote:Is it possible to emulate a normal computer in a quantum computer?

Yes, there's a standard trick for this. Given a function f : {0, 1}^n --> {0, 1}^m expressed as a circuit C of classical logic gates, you can replace the gates in the circuit with reversible equivalents to yield a reversible circuit C' (which may have lots of ancillary '0' inputs and some arbitrary messy outputs):

[n input bits][k ancillary '0' bits] --> [m output bits][n+k-m unwanted garbage bits]

Suppose we have another m ancillary '0' bits at this stage. Then we can CNOT the output bits with these ancillary bits to produce another copy of the output, like so:

[n input bits][k ancillary '0' bits][m extra '0' bits] --> [m output bits][n+k-m unwanted garbage bits][m output bits]

Now apply C' in reverse to the first n+k bits to clean up the mess we created:

[n input bits][k ancillary '0' bits][m extra '0' bits] --> [n input bits][k ancillary '0' bits][m output bits]

The upshot of this is that the ancillary '0' bits can be reused in a future computation. This combined circuit, ignoring the k ancillary '0' bits, actually computes the reversible function:

f : {0, 1}^(n+m) --> {0, 1}^(n+m)
(x, y) --> (x, f(x) XOR y)

Now, every reversible classical circuit is a quantum circuit (permutation matrices are unitary matrices), so this can be built out of quantum gates.

Adam, you are smart as hell.
https://www.youtube.com/watch?v=q6EoRBvdVPQ
One big dirty Oro. Yeeeeeeeeee... gameoflifemaniac

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### Re: Thread for Non-CA Academic Questions

gameoflifemaniac wrote:
calcyman wrote:
gameoflifemaniac wrote:Is it possible to emulate a normal computer in a quantum computer?

Yes, there's a standard trick for this. [...]

Now, every reversible classical circuit is a quantum circuit (permutation matrices are unitary matrices), so this can be built out of quantum gates.

Adam, you are smart as hell.

Wait, I didn't invent the technique; it's well-known: https://en.wikipedia.org/wiki/Uncomputation

According to Scott Aaronson, it was 'proposed by Bennett in the 1980s' (which I assume refers to Charles Henry Bennett).

The best resource for learning about quantum computation is 'Quantum Computation and Quantum Information' by Nielsen and Chuang. I once had an interesting conversation in the Faculty about this, wherein I described it as 'the Kamasutra of quantum computing', only to be informed that the word 'Bible' is more commonly used as a metaphor for its authoritative status.
What do you do with ill crystallographers? Take them to the mono-clinic! calcyman

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### Re: Thread for Non-CA Academic Questions

Are primes computable?
https://www.youtube.com/watch?v=q6EoRBvdVPQ
One big dirty Oro. Yeeeeeeeeee... gameoflifemaniac

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### Re: Thread for Non-CA Academic Questions

gameoflifemaniac wrote:Are primes computable?
not sure what you mean. But yes, there are tons of programs that find primes and you can easily multiply and add primes on a computer.

Is it possible to make a program that evolves itself? For example, it starts out as 1 file. The file is programmed to duplicate itself, but with some random "mutations" every duplication, like adding some specific code to a function wich gets called after a certain condition (Also mutable (e.g. function is called every 2 duplications)) and the worst files, determined by another program, the "fitness tester". Will this file be able to evolve so much with the right fitness tester and become an AI?
If you're the person that uploaded to Sakagolue illegally, please PM me.
x = 17, y = 10, rule = B3/S23b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5bo2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo! (Check gen 2) Saka Posts: 2837 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X ### Re: Thread for Non-CA Academic Questions If two atom-sharp needles were pushed together, would the extremely focused pressure cause nuclear fusion? x = 81, y = 96, rule = LifeHistory58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A$4.2A18$4.2A$4.2A2.2A$8.2A!
Gamedziner

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### Re: Thread for Non-CA Academic Questions

Saka wrote:Is it possible to make a program that evolves itself? For example, it starts out as 1 file. The file is programmed to duplicate itself, but with some random "mutations" every duplication, like adding some specific code to a function wich gets called after a certain condition (Also mutable (e.g. function is called every 2 duplications)) and the worst files, determined by another program, the "fitness tester". Will this file be able to evolve so much with the right fitness tester and become an AI?

Disclaimer: I haven't looked at this topic recently so my observations may be out of date.

What you describe has been explored in a branch of artificial life research. All of the successful research efforts that I am aware of involve running programs in a simulated computing environment similar to a virtual machine. In this case though the architecture of the virtual machine and the instruction set it supports are specifically designed to ensure that "mutations" of a program result in another functional program. Two examples of this line of research are Tierra and Avida. These systems show evolutionary behaviour of the digital organisms which exist within them and all kinds of properties were observed. The result of evolution in these systems often favours smaller program size, because less computation time equals faster replication. In some cases programs analagous to viruses were observed, where the program no longer contained the functionality to replicate itself, but used the replication code from another program in the environment instead. You can find links to other examples of this type of artificial life here: https://en.wikipedia.org/wiki/Artificia ... simulators - look for entries classed as "Executable DNA".

Instruction sets for real computers are not designed to ensure that all or even most valid assembly code will actually result in an executable program. As a result, applying this kind of evolution through simple mutation of functional programs leads to almost all "children" being non-functional programs. This makes it very difficult to observe evolution which leads to any interesting behaviour in the resulting programs. Similarly with a system that tries to evolve programs written in a higher level language like C, nearly all possible "child programs" which are the result of mutations of a functioning C program will fail because the program is very unlikely to even be able to compile.

Maybe someone has tried combining a system like this with some kind of automatic program generator which is much more likely to produce functional programs - something like this RNN trained on the Linux code base (see the section titled "Linux Source Code"). If so, I'd be interested in seeing the results.
wildmyron

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### Re: Thread for Non-CA Academic Questions

How would fractional tetration work?
https://www.youtube.com/watch?v=q6EoRBvdVPQ
One big dirty Oro. Yeeeeeeeeee... gameoflifemaniac

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### Re: Thread for Non-CA Academic Questions

Here is an article about someone's attempts to extend the second argument of tetration to the real numbers. I haven't really tried to understand it but I will probably do so when I am less busy.

A much simpler solution is to just use linear approximation, but this lacks the beauty of the original because the function is not smooth (i.e. cannot be differentiated everywhere an infinite number of times). gameoflifeboy

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### Re: Thread for Non-CA Academic Questions

Would it be possible to make an image of say, 1 city, so detailed, you can clearly see individual people?
If you're the person that uploaded to Sakagolue illegally, please PM me.
x = 17, y = 10, rule = B3/S23b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5bo2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o\$4bob2o2bobobo!

(Check gen 2) Saka

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### Re: Thread for Non-CA Academic Questions

What's the bounding box of the Mandelbrot set?
https://www.youtube.com/watch?v=q6EoRBvdVPQ
One big dirty Oro. Yeeeeeeeeee... gameoflifemaniac

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### Re: Thread for Non-CA Academic Questions

I'm currently trying to figure out how a universe in which Newton's second law is F=mj would behave. So far, I've determined that particles travel in parabolas (possibly degenerate) when not acted upon by any force, objects falling under a constant force with zero horizontal acceleration descend cubic curves, and that colliding objects attracted by a force rebound either superelastically or inelastic with a probability of 1 depending on how the force varies with distance — no kind of energy is in any way conserved, at least if my intuition is correct. I'm wondering what kind of work has been done on this problem.

Also, is there anything known about a two-dimensional universe in which Newton's second law is F=imv? Clearly, systems containing attractive and/or repulsive forces where the law is just F=mv either expand without limit, quickly lead to singularities, or both, but it seems like stable orbits would exist no matter how force varies with distance in the F=imv case. There might be a conserved quantity associated, as well, but I'm not sure exactly what it is.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

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