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Can someone give a concise yet simple explanation of this theory? I somewhat understand how a Turing machine works and I also understand that these devices use an algorithm or program to perform certain tasks:
The problem I'm having is how do machine-state functionalists believe these machines relate to our own brains?
Hello! We are being taught about the history of modern PCs, and we just started discussing about Turing Machines.
Our teacher taunted us and said: "Try and write some tuples for Turing Machines which can calculate additions (4+3) and multiple additions ( (4+3)+(5+5) )"
I've been able to write instructions for a Turing Machine able to calculate addition (AKA. transforming 01110110 in 0111110 by replacing the separating 0 with a 1 and the last 1 with a 0) using this:
State | Read | Write | Direction | New State |
---|---|---|---|---|
0 | 0 | 0 | R | 0 |
0 | 1 | 1 | R | 1 |
1 | 0 | 1 | R | 2 |
1 | 1 | 1 | R | 1 |
2 | 0 | 0 | L | 3 |
2 | 1 | 1 | R | 2 |
3 | 0 | 0 | R | Halt |
3 | 1 | 0 | R | 3 |
However my efforts for a machine which can calculate any number of additions ( 5+5 + 2+1 + 3 + 5 ) ended up in failure.
State | Read | Write | Direction | New State |
---|---|---|---|---|
0 | 0 | 0 | R | 0 |
0 | 1 | 1 | R | 1 |
1 | 0 | 1 | R | 2 |
1 | 1 | 1 | R | 1 |
2 | 0 | 0 | L | 3 |
2 | 1 | 1 | R | 2 |
3 | 0 | 0 | R | 4 |
3 | 1 | 0 | R | 4 |
4 | 0 | 1 | L | 4 |
4 | 1 | 1 | R | 5 |
5 | 1 | 1 | R | 5 |
5 | 0 | 0 | L | 6 |
6 | 1 | 0 | L | 7 |
6 | 0 | 0 | R | 7 |
7 | 1 | 0 | L | Halt |
This machine can calculate TWO consecutive additions, but the number of zeroes between each number to sum always increases by one, so it cannot reach any new number.
Any suggestions? What am I doing wrong? It's driving me crazy.
Sorry for eventual typos or grammar errors, English is not my native language.
Best Wishes
Was reading The Emperor's New Mind by Roger Penrose and Chapter 2 is essentially dedicated to explaining what a Turing machine is.
After I watched a few videos I kind of understood what it was but all the videos I watched essentially just sad that any computable problem can be done in a Turing machine and that it was the best computational model we have. However, they don't rly explain it and I got rly confused by this. Why can any problem be done in a Turing machine and why is it the best?
Also, why is it important? What else do I need to know about Turing machines when I go to uni?
This is, to my knowledge, the first spell capable of computing anything, in an imperative programming fashion. It should be Turing Complete. (If it could access infinite memory.)
With an appropriately(1*) set up region of memory, this spell will execute a 2D SubLEQ(2*) program encoded in the world via block placement. It is sustainable with a loop-cast bullet, and can compute any compute-able function(3*). I've tested it on a Fibonacci sequence program, and am working on an array sorting program & a virus. (Self copying program).
It is useful to have looping & regular bullets with the spell to alternate btw stepped and regular execution.
The Spell Requires Random Psideas for its Cross-Connectors and DistanceToGround which allow the spell to be small (Hah!) enough to fit on the grid, and it also uses the Hyper-threaded CAD Core to get enough complexity (45).
Create a flat plane 32 blocks above any other blocks, with 32 blocks of empty space above. Place 1 block 32 blocks above the plane, & {-32,-32} blocks from the center of the plane (in the Negative X, Negative Z direction), and shift click with a vector ruler. (This sets up the memory space.)
Approximately in the center of the space run: https://imgur.com/KoN5PzN
to set the Instruction Ptr to the block you are standing on and check your memory plane is at zero.
Blocks above this represent negative numbers; Below: positive.
SUBLEQ is a one instruction computer. SUBLEQ(A,B,C) Sets A = A-B; and branches to C if the result is <= 0.
Because of the 32 block radius world interaction limit; My version has a 2D memory model to allow it to access more memory. My version also has relative jumps which should allow a program encoded outside the 32 block limit to still run as long as it never tries to WRITE outside it. (memory addresses are absolute.)
SUBLEQ V5 operates such: Mem[a,b]-=Mem[c,d]; If Mem[a,b] <=0 then Instruction Ptr += {e,f} else Instruction Ptr += {STEP}
So the instruction 0,0,0,0,0,0 will set Mem(0,0) = 0 and branch to itself.
Parameters are arranged in the +X direction, and normal execution proceeds in the +Z direction, but these are easy to change.
3)Limits:
Currently the spell consumes a block from your hotbar each instruction while in surv
Hi,
I am assuming this is a very old discussion but I have not been able to find it in the format that I have in mind. I will try to formalize it the best I can.
Please keep in mind that I am a guy from computer science with some background in math but my knowledge of physics stops at classical Newtonian stuff, and I am only very distantly aware of anything beyond such as quantum physics and more recent theories.
Assuming the universe has a finite amount of elementary particles, let's imagine all their relevant properties at a given point in time being recorded in the machine, and running a simulation using the known laws of physics. As for radiation and fields, I am distantly aware that they can also be interpreted as particles, but if I am making an error here, let's assume they are recorded with some kind of sampling.
Assuming that space and time (and whatever other dimensions that are reasonably confirmed to exist, if any) are continuous, the symbolic nature of the machine implies rounding errors that would increase over time due to a positive feedback effect, so no perfect simulation is possible.
Eventually, what I describe here is similar to a weather simulation, but of the whole universe and at precision levels unbounded by practical matters.
My question could then be formalized as the following proposition.
For every certain time bound T and maximum allowed error E on the properties of all particles and fields, there is a Turing machine that produces a simulation where at every instant t<T, errors are within the bounds of E.
Can this be proven true or false given the currently well-accepted model of the universe and its physical laws?
Edit: improved wording
The view that machines cannot give rise to surprises is due, I believe, to a fallacy to which philosophers and mathematicians are particularly subject. This is the assumption that as soon as a fact is presented to a mind all consequences of that fact spring into the mind simultaneously with it. -Alan Turing
challenging words: due, fallacy, subject (adj.), assumption, as soon, spring (vb.)
As inspiration, the Japanese translation of this, word-for-word translated back to English, goes roughly like this:
> Machines surprises give can't view, philosophers and mathematicians particularly exposed mistake due to is I believe. This, fact to heart presented soon, that fact's all consequences simultaneously head to float called assumption is.
On the other hand, the Hebrew translation of this is nearly word-for-word identically to the English.
> The idea that machines can't give birth to surprises stems, I believe, from a mistake that the philosophers and mathematicians exposed to it in special. This the assumption that in the moment that brought fact to mind all the consequences of it fact jump to mind in it temporarily.
(The Hebrew word for "simultaneously", strangely, is the word for "in it" plus the word for "temporarily".)
The same is true of Spanish.
> The opinion of that the machines no can give place to surprises is due, I believe, to a fallacy to it that are particularly subjected the philosophers and the mathematicians. That is the assumption of that as soon as presents a fact to the mind, all the consequences of that fact sprout simultaneously in the mind.
I'm not giving proper glosses because these are just meant to be inspirations, and besides, they're natlangs.
I've found a nice combo panel for pulses and volts from mymodularjourney, But I am kinda drawn to the older Voltages module (which volts kind of replaces), with its LED sliders.
I've searched my usual haunts for a panel for it, but no dice, has anyone seen one? Or, perhaps a single panel that houses the whole shebang?
Iβve seen it often asserted as basically obvious gospel but never seen an actual proof. It also seems inherent to the proof that the bounded halting problem is in exptime, but again that part of the question always seems to be just stated as obvious rather than derived. I understand the inherent unpredictability of Turing machines, like how canβt in general know if a Turing machine ever prints a 1. But you absolutely can know if it prints a 1 in k steps. Whatβs to stop there from being an algorithm that tells you the kth state of a Turing machine in, for instance, log k steps?
Hi, I know this might sound stupid but here goes. I am running a campaign for the first time with some of my friends, we've all played 5e before but this is my first time trying my hand at DMing. Anyway I am thinking about introducing a machine used by the bank in my world to calculate things like annuity price from actuarial tables, mortgage interest rates, etc. and I'm wondering if it is theoretically possible to build a computer using elements from 5e? I know these calculations could probably be done by hand or I could just make up spells that the bankers use but I think it would be way cooler if the bankers in-universe found a way to invent a Turing complete apparatus. Maybe a series of connected sending stones or something? Or if anyone can think of some homebrew magic item that could work like a logic gate, and the npcs could have linked up a few hundred of them to create a calculator?
Any help is appreciated, thanks for reading!
> A Turing machine is an abstract model of a computer developed by the famous computer scientist Alan Turing. From a theoretical standpoint, the Turing machine is useful because it allows you to reason about what can and canβt be computed, not just on a digital computer, but any possible computer. This model also allows computer scientists to show equivalence between computing systems if they can each simulate a Turing machine. You can use this to show, for example, that thereβs nothing that you can compute in Java that you canβt also compute in assembly language
The note about being able to prove equivalencies of languages makes sense, that is the interpretation that I am familiar with. But the author also mentions that Turing machines allow us to reason about what can be computed on "any possible computer". What does this mean? What other computers are possible other than digital computers, and how would Turing machines help us there?
The hypothetical idea was stupidly inspired by the Infinite Monkey Theorem.
>Aliens come to Earth presenting a mathematical-proof that we live in a multiverse with infinite universes.
>
>They even present physical evidence that the Multiverse is real & has an unlimited quantity of universes with different laws of physics.
>
>In one of those unlimited universes, a mathematical model for a universal computer, allows it to always guess YES or NO 100% correctly for any problem.
>
>The Aliens showed us that even, the halting-problem can & will be guessed correctly 100% of the time in this Universe.
>
>Sorta like the Infinite Monkey Theorem, but applied to Universes.
n/a
Title
If I understood it correctly, a universal turing machine can simulate any turing machine with any input. For it to be turing complete, it has to be able to simulate any turing machine, therefore UTM must be turing complete by default?
If that's the case, why have the distinction? Feel like I must be missing something here.
Before reading A Madman Dreams of Turing Machines, a novel, I'd read two of Janna Levin's books: one on the history of LIGO, a project that was the first to "detect" gravitational waves using lasers, and another which is as much astrophysics primer as it is beautiful memoir-qua-epistolary. Levin is a cosmologist who focuses on the shape and size of the universe (which she believes is finite) and a leading theorist in the field. Her writing in the science community is unlike any other I've encountered. Her prose is poetic and brimming with playful, artful and carefully pored over language. It's a prose of someone who knows how to use language to engage and inspire a reader while maybe also teaching them something.
A Madman Dreams of Turing Machines is just as meticulously written, and as drinkably wonderful line-by-line as the other books I've read by her, but ultimately it falls a little flat as fiction. Here's why: we have as our protagonists Alan Turing and Kurt Godel. The book maps out the last 20-30 years of these two men's tortured lives (one for his homosexuality and the other for his struggles with mental illness). They're also two men working in the field of mathematics but never met despite knowing of each other, responding to each other in some ways, and working in the same era.
As Levin puts them both into the same novel, a reader would expect there to be some narrative threads that link and tie them together, that the fiction would create spooky action at a distance between the two characters. Echoes and vibrations, whether literally in the "action" of each character's story, or at least thematically, metaphorically, etc. But, to my mind, I don't think that connexion is there. I absolutely love novels that work on a multi-narrative level--and those different narratives don't need to have literal intersections, but there has to be something more to the telling that puts each story in conversation with the other throughout the work. Unfortunately, I just didn't get there with this book.
However beautifully written Levin's sentences are, the plot, characters and arc of the book feel stagnated and empty. Alan and Kurt don't really live on the page so much as they exist there in black and white text. If I ventured a guess, Levin struggled with how far to go into fictionalizing the everyday lives of these men--obviously in the bounds of fiction there's a risk in taking historical figures outside of their context and making them grotesque or ab
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