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A natural number can be represented in any number encoding; for example, in binary, every natural number is some sequence of 0s and 1s. In decimal, it's a sequence of the decimal digits (0, 1, ... 9). Depending on which encoding you pick, if you try to enumerate every element in the sequence (0, 1, 2...), you get a sequence that looks slightly different, and you'll notice the length of some strings changes depending on the number of digits you use. However, it cannot be disputed that the encoding does not have any impact on the number of elements in the sequence.

You can think of the "rational" numbers as being the natural numbers, but encoded in a number system wherein there are 11 digits: the 10 digits from (0, ... 9) and an 11th digit for representing fractions, '/'. Seeing as we've stated that it does not matter how many digits you use to represent the natural numbers, it is perhaps unsurprising that there are as many rational numbers as natural numbers. You of course have to add the constraint that '/' can never precede a sequence of all 0s, but that's a relatively minor thing. Even without that constraint they're still the same set.

A natural number can be represented in any number encoding; for example, in binary, every natural number is some sequence of 0s and 1s. In decimal, it's a sequence of the decimal digits (0, 1, ... 9). Depending on which encoding you pick, if you try to enumerate every element in the sequence (0, 1, 2...), you get a sequence that looks slightly different, and you'll notice the length of some strings changes depending on the number of digits you use. However, it cannot be disputed that the encoding does not have any impact on the number of elements in the sequence.

You can think of the "rational" numbers as being the natural numbers, but encoded in a number system wherein there are 11 digits: the 10 digits from (0, ... 9) and an 11th digit for representing fractions, '/'. Seeing as we've stated that it does not matter how many digits you use to represent the natural numbers, it is perhaps unsurprising that there are as many rational numbers as natural numbers. You of course have to add the constraint that '/' can never precede a sequence of all 0s, but that's a relatively minor thing. Even without that constraint they're still the same set.

[QUOTE=Plotato;968274]Your definitions are awful, inaccurate and unhelpful.

A natural number to put it simply is a number represented without fraction or complex numbers. The set of all natural numbers (1, 2, 3, 4,...) is our definitional basis for the countability of infinite sets.

Your third line misrepresents the whole argument because the set of rational numbers are countable and are a certain permutation of the natural numbers. You haven't defined what "certain permutation" means and therefore is moot and your definition of irrational number is also completely unhelpful. Permutation implies a certain order and as far as it goes, the decimal construction of irrational numbers have no order to them (and therefore can't be represented as a fraction).

You can't say it is obvious that there is "more of something". There are no more even numbers than there are natural numbers. There are no more numbers of the Fibonacci sequence than there are natural numbers. Alluded to earlier there is no more fractional numbers than there are natural numbers. Cantor's diagonalization states specifically that such a construction exists where you can generate an entirely new number from an infinite list of numbers that was not previously recorded in an infinite mapping with the natural numbers. This isn't an "inbetween argument" like the way you put it. Infinity does not work the way you describe it like it has a certain scale or something.[/QUOTE]
[B]
The set [/B]of rational numbers is a permutation of the naturals. Yes, hence why the set of rationals is countable. But for irrational numbers, it is every irrational number, itself, that is countably infinite.

Edit: Oh but I wasn't providing a definition though. I was just stating that if you think about it, a natural number is a finite sequence of digits. Not EVERY finite sequence of digits is necessarily a natural number (but can definitely encode [B]any[/B] natural number).

Originally Posted by Plotato

Your definitions are awful, inaccurate and unhelpful.

A natural number to put it simply is a number represented without fraction or complex numbers. The set of all natural numbers (1, 2, 3, 4,...) is our definitional basis for the countability of infinite sets.

Your third line misrepresents the whole argument because the set of rational numbers are countable and are a certain permutation of the natural numbers. You haven't defined what "certain permutation" means and therefore is moot and your definition of irrational number is also completely unhelpful. Permutation implies a certain order and as far as it goes, the decimal construction of irrational numbers have no order to them (and therefore can't be represented as a fraction).

You can't say it is obvious that there is "more of something". There are no more even numbers than there are natural numbers. There are no more numbers of the Fibonacci sequence than there are natural numbers. Alluded to earlier there is no more fractional numbers than there are natural numbers. Cantor's diagonalization states specifically that such a construction exists where you can generate an entirely new number from an infinite list of numbers that was not previously recorded in an infinite mapping with the natural numbers. This isn't an "inbetween argument" like the way you put it. Infinity does not work the way you describe it like it has a certain scale or something.

The set of rational numbers is a permutation of the naturals. Yes, hence why the set of rationals is countable. But for irrational numbers, it is every irrational number, itself, that is countably infinite.

Edit: Oh but I wasn't providing a definition though. I was just stating that if you think about it, a natural number is a finite sequence of digits. Not EVERY finite sequence of digits is necessarily a natural number (but can definitely encode any natural number).

[QUOTE=Plotato;968273]Let's not conflate mathematical definitions with whatever definitions we feel comfortable with, because this is the biggest source of definitional fuckery that goes nowhere. These definitions in math are constructed from the ground up and have no notion of what infinity is. As a result of multiple theorems and proofs, we can show that different kinds of infinities exist, and while some are larger than others, no infinity can be smaller than the set of natural numbers.

The definition of infinite in math is something that is not finite. It's weird putting it that way but it really is; infinity is defined by the not finite state of something. In real analysis this means that there is no bound to a set. Saying that something "never ends" is reductive because depending on how we construct that "never ending" collection we will arrive that the place where there are infinities of different sizes, and as Cantor's paradox comes from the fact that there is no such thing as a "biggest" set, and if we were to assume such a set exists that has infinite cardinality then it would be the "biggest infinity", holding other infinities inside it. When people say infinity is an idea, it is; depending on how you construct it and use it.

Normal parlance can suck it because it makes no sense outside of general conversation and metaphors[/QUOTE]
I disagree, if it "makes no sense" outside of normal parlance, then it is mathematical definitions that do not make sense. People came up with these definitions according to an intuitive understanding of what infinity is. Math is intended to represent some "real" notion, it's not just made up nonsense.

Originally Posted by Plotato

Let's not conflate mathematical definitions with whatever definitions we feel comfortable with, because this is the biggest source of definitional fuckery that goes nowhere. These definitions in math are constructed from the ground up and have no notion of what infinity is. As a result of multiple theorems and proofs, we can show that different kinds of infinities exist, and while some are larger than others, no infinity can be smaller than the set of natural numbers.

The definition of infinite in math is something that is not finite. It's weird putting it that way but it really is; infinity is defined by the not finite state of something. In real analysis this means that there is no bound to a set. Saying that something "never ends" is reductive because depending on how we construct that "never ending" collection we will arrive that the place where there are infinities of different sizes, and as Cantor's paradox comes from the fact that there is no such thing as a "biggest" set, and if we were to assume such a set exists that has infinite cardinality then it would be the "biggest infinity", holding other infinities inside it. When people say infinity is an idea, it is; depending on how you construct it and use it.

Normal parlance can suck it because it makes no sense outside of general conversation and metaphors

I disagree, if it "makes no sense" outside of normal parlance, then it is mathematical definitions that do not make sense. People came up with these definitions according to an intuitive understanding of what infinity is. Math is intended to represent some "real" notion, it's not just made up nonsense.

[QUOTE=DJarJar;968231]hmm did you read the 2nd paragraph of the page you linked?

the paradox applies specifically to set theory because of the way sets and the like are defined. If you try to declare there is some set that contains all other sets - well that's cool and all but i can just make the power set of that set and bam i have a bigger one. hence there's no way you could ever have a "largest" set.

this doesn't necessarily apply to other abstract concepts of infinity, although in pretty much any case where your infinity has some arbitrary rules or bounds to it then we could find a way to break those bounds. Meanwhile a "pure infinity" with no limitations would be a pretty useless concept since there'd be no way to interact with it.[/QUOTE]

It seems to me the definition of infinity in math is slightly different than in normal parlance. As far as I can tell, something is infinite if it "never ends" if you try to list every single element in that "it". But normally when we talk about infinity we mean some abstract thing that is very large in size and which includes "everything" else.

Originally Posted by DJarJar

hmm did you read the 2nd paragraph of the page you linked?

the paradox applies specifically to set theory because of the way sets and the like are defined. If you try to declare there is some set that contains all other sets - well that's cool and all but i can just make the power set of that set and bam i have a bigger one. hence there's no way you could ever have a "largest" set.

this doesn't necessarily apply to other abstract concepts of infinity, although in pretty much any case where your infinity has some arbitrary rules or bounds to it then we could find a way to break those bounds. Meanwhile a "pure infinity" with no limitations would be a pretty useless concept since there'd be no way to interact with it.

It seems to me the definition of infinity in math is slightly different than in normal parlance. As far as I can tell, something is infinite if it "never ends" if you try to list every single element in that "it". But normally when we talk about infinity we mean some abstract thing that is very large in size and which includes "everything" else.

According to [url]https://en.wikipedia.org/wiki/Cantor%27s_paradox[/url], there's no such thing as an infinite set that is larger than every other infinite set. I understand the idea behind it, but the notion sounds ridiculous to me. Surely there [I]has[/I] to be something that is absolutely and totally infinite?

According to https://en.wikipedia.org/wiki/Cantor%27s_paradox, there's no such thing as an infinite set that is larger than every other infinite set. I understand the idea behind it, but the notion sounds ridiculous to me. Surely there has to be something that is absolutely and totally infinite?

[QUOTE=Plotato;942837]i knew you would still be confused about this, oh, how the germans have stumped the french once again

mathematically, countability is defined of whether you can assign 1, 2, etc. to whatever you want to map to on a [B]one-to-one[/B] basis, no element left unjerked. if the list is infinitely long, then, as unintuitive as it sounds, then a countably infinite list is full... matched with infinite elements, on a one-to-one basis.

Cantor's argument comes with the above presupposition that you can build such a list where you can map every integer (1 -> 0.1232, etc) with a real number [I]once[/I] (therefore making it countable). the order of the list doesn't matter. now why wouldn't such a list already have the whatever number produced by diagonalization? no, i can, through diagonalization, come up with a new number that [B]won't have an sole integer assigned to[/B]. i know it sounds unintuitive, but i will make bold the affirmative. the case is: i have produced a new number [B]of which there is not an assignment of an integer[/B], therefore proving my idea that such a list is countable wrong. guess its not countable. this idea also implies the varying sizes to infinity, as we can't match one-to-one every element from one set of numbers to another without leaving something behind...

the thing with math is that you have to explicitly define, prove and state everything in a sheer logical manner. the definition of "countable" is mentioned earlier, and if i, for some reason, can't make that one-to-one complete map from the integers to whatever, the definition is now uncountable by contradiction. intuition doesn't matter. somethings in math are just unintuitively the case. yes, every number that would exist exists between 0 and 1... can you "count" them all, given the definition of "countable"? if you're still thinking that you could always generate a new integer for a new real number produced, well that would just break the definition of "countable" that we have, which is a pretty good one, based off of mathematical reasoning. if we hold the definition of "countable" to be the case, well, you can't have your intuition go your way.

please understand you escargot[/QUOTE]

I have a much simpler explanation.
What is a natural number? It's a finite sequence of digits. What is the totality of natural numbers? An infinite sequence of digits, ordered in a certain way.
What is a irrational number? An infinite sequence of digits. Every irrational number corresponds to a certain permutation of the set of natural numbers. If you take all these permutations together, it is obvious there are more irrationals than naturals. You effectively run into an infinity of infinities

Originally Posted by Plotato

i knew you would still be confused about this, oh, how the germans have stumped the french once again

mathematically, countability is defined of whether you can assign 1, 2, etc. to whatever you want to map to on a one-to-one basis, no element left unjerked. if the list is infinitely long, then, as unintuitive as it sounds, then a countably infinite list is full... matched with infinite elements, on a one-to-one basis.

Cantor's argument comes with the above presupposition that you can build such a list where you can map every integer (1 -> 0.1232, etc) with a real number once (therefore making it countable). the order of the list doesn't matter. now why wouldn't such a list already have the whatever number produced by diagonalization? no, i can, through diagonalization, come up with a new number that won't have an sole integer assigned to. i know it sounds unintuitive, but i will make bold the affirmative. the case is: i have produced a new number of which there is not an assignment of an integer, therefore proving my idea that such a list is countable wrong. guess its not countable. this idea also implies the varying sizes to infinity, as we can't match one-to-one every element from one set of numbers to another without leaving something behind...

the thing with math is that you have to explicitly define, prove and state everything in a sheer logical manner. the definition of "countable" is mentioned earlier, and if i, for some reason, can't make that one-to-one complete map from the integers to whatever, the definition is now uncountable by contradiction. intuition doesn't matter. somethings in math are just unintuitively the case. yes, every number that would exist exists between 0 and 1... can you "count" them all, given the definition of "countable"? if you're still thinking that you could always generate a new integer for a new real number produced, well that would just break the definition of "countable" that we have, which is a pretty good one, based off of mathematical reasoning. if we hold the definition of "countable" to be the case, well, you can't have your intuition go your way.

please understand you escargot

I have a much simpler explanation.
What is a natural number? It's a finite sequence of digits. What is the totality of natural numbers? An infinite sequence of digits, ordered in a certain way.
What is a irrational number? An infinite sequence of digits. Every irrational number corresponds to a certain permutation of the set of natural numbers. If you take all these permutations together, it is obvious there are more irrationals than naturals. You effectively run into an infinity of infinities

[QUOTE=HentaiManOfPeacesGhost;967720]Easiest way to tell everyone you have no credibility.

Jordan Peterson is a tough academic who crushes their debate opposition that young, disenfranchised males look up to because they have no control in their lives. The world needs less of him and more better thinkers who have time to fix bigger challenges than bullying trans people because of their inherent biological gender.[/QUOTE]

Jordan Peterson says stuff that is deeper than it looks. It's not all political
And it's not all for helping young men

Originally Posted by HentaiManOfPeacesGhost

Easiest way to tell everyone you have no credibility.

Jordan Peterson is a tough academic who crushes their debate opposition that young, disenfranchised males look up to because they have no control in their lives. The world needs less of him and more better thinkers who have time to fix bigger challenges than bullying trans people because of their inherent biological gender.

Jordan Peterson says stuff that is deeper than it looks. It's not all political
And it's not all for helping young men

Fun fact: you can extend this indefinitely. There are also "numbers" that have an [I]uncountably infinite [/I]number of digits after the decimal point, in which case this set of numbers has a cardinality that is equal to (N!)!, aka equal to the cardinality of the set of all the subsets of irrational numbers.

Fun fact: you can extend this indefinitely. There are also "numbers" that have an uncountably infinite number of digits after the decimal point, in which case this set of numbers has a cardinality that is equal to (N!)!, aka equal to the cardinality of the set of all the subsets of irrational numbers.

@[URL="https://www.sc2mafia.com/forum/member.php?u=29377"]Marshmallow Marshall[/URL] are you still confused about this, Frenchman? I can offer a more intuitive explanation:

The set of integers are numbers with a distance equal to 1 between them. If you draw a tick at every single natural number along a line, you will see a distance of 1 between each. However, this cannot be done with irrational numbers because every irrational number consists of a countable infinity of digits after the decimal point. This means that in order to reach the immediate neighbour of a given irrational number, you have to add or subtract an amount of the form 0.00000.....01 = 1 / infinity = 0 from each. You cannot do this.

Basically the irrational numbers are an infinity of infinities. In fact, if you were to say that the rational/integral numbers have a cardinality of, say, N, then the irrational numbers have a cardinality that is "conceptually" equal to 2 ^ N: if you were to take the set of all possible subsets (including the whole set) of integral numbers, this set of sets would have the same cardinality as the set of irrationals: basically, there are as many subsets of the integral numbers as there are rational numbers.

This number is bewilderingly large because this infinity is the [B]BINARY POWER [/B]​of another infinity.

@Marshmallow Marshall are you still confused about this, Frenchman? I can offer a more intuitive explanation:

The set of integers are numbers with a distance equal to 1 between them. If you draw a tick at every single natural number along a line, you will see a distance of 1 between each. However, this cannot be done with irrational numbers because every irrational number consists of a countable infinity of digits after the decimal point. This means that in order to reach the immediate neighbour of a given irrational number, you have to add or subtract an amount of the form 0.00000.....01 = 1 / infinity = 0 from each. You cannot do this.

Basically the irrational numbers are an infinity of infinities. In fact, if you were to say that the rational/integral numbers have a cardinality of, say, N, then the irrational numbers have a cardinality that is "conceptually" equal to 2 ^ N: if you were to take the set of all possible subsets (including the whole set) of integral numbers, this set of sets would have the same cardinality as the set of irrationals: basically, there are as many subsets of the integral numbers as there are rational numbers.

This number is bewilderingly large because this infinity is the BINARY POWER ​of another infinity.

[url]https://www.sciencedirect.com/science/article/pii/S0096300305008490[/url]
Here's an article on the topic if you're curious

https://www.sciencedirect.com/scienc...96300305008490
Here's an article on the topic if you're curious

"Understanding" is a word that is hard to define. I'll put it this way: when you feel like you've finally understood something, you possess understanding (some of the time, at least). This is not the same as merely knowing that something. It is not merely a feeling, but the feeling is there when you have understanding.

It follows from this "definition" that computers/algorithms/whatever do not possess understanding. They do not [I]understand[/I] things like we do; they merely use grammatical rules and a set of axioms to derive new propositions from a set of initial statements.

If you want to test this assumption yourself, picture yourself being given a list of instructions to follow. Now picture that these instructions, if performed, do something, but you cannot understand what it is that they're doing. You most clearly do not possess any understanding in this scenario. This is exactly how computers work

"Understanding" is a word that is hard to define. I'll put it this way: when you feel like you've finally understood something, you possess understanding (some of the time, at least). This is not the same as merely knowing that something. It is not merely a feeling, but the feeling is there when you have understanding.

It follows from this "definition" that computers/algorithms/whatever do not possess understanding. They do not understand things like we do; they merely use grammatical rules and a set of axioms to derive new propositions from a set of initial statements.

If you want to test this assumption yourself, picture yourself being given a list of instructions to follow. Now picture that these instructions, if performed, do something, but you cannot understand what it is that they're doing. You most clearly do not possess any understanding in this scenario. This is exactly how computers work

[QUOTE=yzb25;967336]I've seen reference to the notions of "intelligence", "self-awareness" and "understanding" like they have concrete definitions. Is there a well defined definition I am ignorant of?

To clarify about the distinction between "computable" and deterministic - there are classes of problems such that there is no algorithm that can solve every problem in the class, but each problem in the class has a yes or no answer. The most famous example of this is probably the halting problem. It asks if there is an algorithm which, when given an arbitrary computer program, will figure out whether the program terminates or runs indefinitely.

Now, apparently, there are classes of problems in Quantum Mechanics which are undecidable. I do not know much Quantum Mechanics, but I at least know what "decidability" means. That's saying there are classes of problems in Quantum Mechanics for which there is literally no algorithm which can solve them. In fact, [U]there will always be specific instances of the problem which resist a solution, regardless of your particular axiomatization of mathematics[/U] (all sensible modern mathematics is always done by making logical deductions from a consistent set of axioms. That's how we can come to absolute conclusions about truth and falsehood).

This is very different from simply saying "there are systems / models we use in Quantum Mechanics which involve probability and randomness". This is actually a far more damning issue than having a system that involves randomness. If an omnipotent being throws a "perfect die" which is "truly random", we cannot know for sure what number will come up. But I can perfectly model and understand its mathematical structure. It simply has a 1 in 6 probability of showing any particular side. For our purposes, this may be "random", but it is at least "decidable".

Undecidability would be more like if the mathematics involved in modelling what side comes up were so fucked up that I literally couldn't even calculate the probability. And the mathematics is so fucked up I can give a separate mathematical proof demonstrating that I literally cannot mathematically compute it.

p;edit this blog post gives an example of a class of problems in QM which are apparently undecidable. I can't vouch for its authenticity but.. erm... they seem like they know what they're talking about [URL]https://www.i-programmer.info/news/112-theory/9253-quantum-physics-is-undecidable.html[/URL][/QUOTE]
Just to add to your point, it appears the n-body problem may be Turing complete. One could use the n-body problem to make arbitrary computations

Originally Posted by yzb25

I've seen reference to the notions of "intelligence", "self-awareness" and "understanding" like they have concrete definitions. Is there a well defined definition I am ignorant of?

To clarify about the distinction between "computable" and deterministic - there are classes of problems such that there is no algorithm that can solve every problem in the class, but each problem in the class has a yes or no answer. The most famous example of this is probably the halting problem. It asks if there is an algorithm which, when given an arbitrary computer program, will figure out whether the program terminates or runs indefinitely.

Now, apparently, there are classes of problems in Quantum Mechanics which are undecidable. I do not know much Quantum Mechanics, but I at least know what "decidability" means. That's saying there are classes of problems in Quantum Mechanics for which there is literally no algorithm which can solve them. In fact, there will always be specific instances of the problem which resist a solution, regardless of your particular axiomatization of mathematics (all sensible modern mathematics is always done by making logical deductions from a consistent set of axioms. That's how we can come to absolute conclusions about truth and falsehood).

This is very different from simply saying "there are systems / models we use in Quantum Mechanics which involve probability and randomness". This is actually a far more damning issue than having a system that involves randomness. If an omnipotent being throws a "perfect die" which is "truly random", we cannot know for sure what number will come up. But I can perfectly model and understand its mathematical structure. It simply has a 1 in 6 probability of showing any particular side. For our purposes, this may be "random", but it is at least "decidable".

Undecidability would be more like if the mathematics involved in modelling what side comes up were so fucked up that I literally couldn't even calculate the probability. And the mathematics is so fucked up I can give a separate mathematical proof demonstrating that I literally cannot mathematically compute it.

p;edit this blog post gives an example of a class of problems in QM which are apparently undecidable. I can't vouch for its authenticity but.. erm... they seem like they know what they're talking about https://www.i-programmer.info/news/1...decidable.html

Just to add to your point, it appears the n-body problem may be Turing complete. One could use the n-body problem to make arbitrary computations

[QUOTE=oops_ur_dead;967332]Both the examples you've listed are approximations of physical processes and thus aren't really related to the topic at hand.

The question you're posing doesn't relate to the brain, it relates to all of physics. Namely you're trying to ask if it's possible that every physical process can be completely and accurately described by math.[/QUOTE]
But it does. I just gave you an example of a physical process that may not be computable, one that does not have a soul. It seems to me a soul should be something apart from physics; like the place in which a soul could exist would have [I]its own laws.[/I]

Originally Posted by oops_ur_dead

Both the examples you've listed are approximations of physical processes and thus aren't really related to the topic at hand.

The question you're posing doesn't relate to the brain, it relates to all of physics. Namely you're trying to ask if it's possible that every physical process can be completely and accurately described by math.

But it does. I just gave you an example of a physical process that may not be computable, one that does not have a soul. It seems to me a soul should be something apart from physics; like the place in which a soul could exist would have its own laws.

[QUOTE=oops_ur_dead;967299]So you think there are physical laws which apply to the brain which cannot be described mathematically? That sounds like a soul with more steps to me. There is no shame in believing in a soul, most of the world does so.

Unless your point is that computers aren't yet powerful enough to simulate the brain, which is an even less interesting point.[/QUOTE]
Lets say hypothetically that the solution to the 3-body problem is such a function, i.e. a function that cannot be described mathematically. Would you say the 3-body problem has a soul?

I'm speaking out of my ass on this next one because I don't really know, but you could also add the Navier-Stokes equations to this list because AFAIK they also cannot be solved analytically

Originally Posted by oops_ur_dead

So you think there are physical laws which apply to the brain which cannot be described mathematically? That sounds like a soul with more steps to me. There is no shame in believing in a soul, most of the world does so.

Unless your point is that computers aren't yet powerful enough to simulate the brain, which is an even less interesting point.

Lets say hypothetically that the solution to the 3-body problem is such a function, i.e. a function that cannot be described mathematically. Would you say the 3-body problem has a soul?

I'm speaking out of my ass on this next one because I don't really know, but you could also add the Navier-Stokes equations to this list because AFAIK they also cannot be solved analytically

[QUOTE=Helz;967264]It is not a bad breakdown of our conversation and is very concise. Oberon seems to have argued a difference between determinism in thought with some connection to computational thought that I don't understand but outside of that its a good summary imo.[/QUOTE]
Its little to do with determinism. It's about whether or not human minds have capabilities that computers do not possess. To put it plainly, given an infinite amount of time, I believe there are answers that people would be able to reach that computers would not.

Are there still answers that neither can reach? I believe the answer is yes but I am not certain.

Originally Posted by Helz

It is not a bad breakdown of our conversation and is very concise. Oberon seems to have argued a difference between determinism in thought with some connection to computational thought that I don't understand but outside of that its a good summary imo.

Its little to do with determinism. It's about whether or not human minds have capabilities that computers do not possess. To put it plainly, given an infinite amount of time, I believe there are answers that people would be able to reach that computers would not.

Are there still answers that neither can reach? I believe the answer is yes but I am not certain.

This has nothing to do with belief in a soul. If there are physical laws that are deterministic, but which cannot be computed by a given Turing machine (or an algorithm, since they are equivalent), and these laws can be harnessed to perform computations, then it must follow that it is physically possible for computers more computationally capable than the ones we have now to exist.

It certainly seems to me that the mind is such a computer; I do not see where the idealism/dualism comes into play. [I]Certainly[/I] one solution to the problem of a mind that is a hyper-Turing machine involves a mind that is not reducible to the brain, but it isn't necessary.

This has nothing to do with belief in a soul. If there are physical laws that are deterministic, but which cannot be computed by a given Turing machine (or an algorithm, since they are equivalent), and these laws can be harnessed to perform computations, then it must follow that it is physically possible for computers more computationally capable than the ones we have now to exist.

It certainly seems to me that the mind is such a computer; I do not see where the idealism/dualism comes into play. Certainly one solution to the problem of a mind that is a hyper-Turing machine involves a mind that is not reducible to the brain, but it isn't necessary.

[QUOTE=oops_ur_dead;967249]This discussion is complete intellectual masturbation on all sides and the point is entirely inarguable.

The entire thing boils down to a decision tree with two branches

1) Do you think the contents of the universe follow a deterministic set of laws that can be computed and/or mathematically modeled? If no then so-called algorithmic machines do not exist and the whole argument is moot.

If yes, then:

2) Do you believe the human brain is subject to the same rules as all other matter in the universe? If so, then the brain is necessarily a machine per this weird definition of "machine".
3) If no, then you believe in some extra-physical process that comprise human thought, i.e. a soul.

This entire thread, IMO, is the same as asking "Do you believe in a soul?" which is a very uninteresting conversation.[/QUOTE]
3) Does not follow.

Assuming the mind can be reduced to the brain, a physical mind that can "compute" non-Turing computable "functions" [I]has[/I] to be based on physical laws that are not computable. I do not see where the belief in a soul comes into play

Originally Posted by oops_ur_dead

This discussion is complete intellectual masturbation on all sides and the point is entirely inarguable.

The entire thing boils down to a decision tree with two branches

1) Do you think the contents of the universe follow a deterministic set of laws that can be computed and/or mathematically modeled? If no then so-called algorithmic machines do not exist and the whole argument is moot.

If yes, then:

2) Do you believe the human brain is subject to the same rules as all other matter in the universe? If so, then the brain is necessarily a machine per this weird definition of "machine".
3) If no, then you believe in some extra-physical process that comprise human thought, i.e. a soul.

This entire thread, IMO, is the same as asking "Do you believe in a soul?" which is a very uninteresting conversation.

3) Does not follow.

Assuming the mind can be reduced to the brain, a physical mind that can "compute" non-Turing computable "functions" has to be based on physical laws that are not computable. I do not see where the belief in a soul comes into play

[QUOTE=Marshmallow Marshall;967220]@[URL="https://www.sc2mafia.com/forum/member.php?u=29012"]Auwt[/URL] Arise from your slumber, O ye mighty, and come get role madness'd :D[/QUOTE]
Behold, a French summoning

Originally Posted by Marshmallow Marshall

@Auwt Arise from your slumber, O ye mighty, and come get role madness'd

Behold, a French summoning

[QUOTE=Oberon;963957]And yes I agree that thinking is deterministic. I am aware there is little hard evidence out there but I am pretty convinced of this as, the more intelligent people are, you'd expect them to be more random, which is a bit strange. I mean how could something that gets more random be better? Shouldn't it get... worse, approaching a 50/50 split?[/QUOTE]
Just wanted to add that randomness does not [I]require[/I] a 50/50 split. True randomness can come from any distribution - including none - and it is impossible to predict in advance what the sequence will look like.

In fact, a distribution implies some kind of determinism.

Originally Posted by Oberon

And yes I agree that thinking is deterministic. I am aware there is little hard evidence out there but I am pretty convinced of this as, the more intelligent people are, you'd expect them to be more random, which is a bit strange. I mean how could something that gets more random be better? Shouldn't it get... worse, approaching a 50/50 split?

Just wanted to add that randomness does not require a 50/50 split. True randomness can come from any distribution - including none - and it is impossible to predict in advance what the sequence will look like.

In fact, a distribution implies some kind of determinism.

[QUOTE=WrathCyber;967173]You named a lot of nobel laureates there.[/QUOTE]
not on purpose if that's what you're wondering lol

Originally Posted by WrathCyber

You named a lot of nobel laureates there.

not on purpose if that's what you're wondering lol

[QUOTE=Marshmallow Marshall;967161]Literally this lol. And to add something because now I feel cheap: scumchats that aren't 24/7 absolutely can contribute to setups that are "asking questions" such as the ones Lag linked; setups centered around communication and nuances in communication are a perfect example of this.

And I'm totally not repeating what everyone said already but balance is a means to attain fun, not the end goal, no matter how important the means can be.


Yes, we know Lag is cool 8)

That doesn't mean discussions about setups aren't fun, interesting, or productive, though! I really like what I've seen in this thread. Part of the fun in playing Mafia is being a game theory nerd, after all, just like how playing with new people is part of it![/QUOTE]
game theory is cringe

Originally Posted by Marshmallow Marshall

Literally this lol. And to add something because now I feel cheap: scumchats that aren't 24/7 absolutely can contribute to setups that are "asking questions" such as the ones Lag linked; setups centered around communication and nuances in communication are a perfect example of this.

And I'm totally not repeating what everyone said already but balance is a means to attain fun, not the end goal, no matter how important the means can be.


Yes, we know Lag is cool

That doesn't mean discussions about setups aren't fun, interesting, or productive, though! I really like what I've seen in this thread. Part of the fun in playing Mafia is being a game theory nerd, after all, just like how playing with new people is part of it!

game theory is cringe

[QUOTE=Helz;967137]On the most basic level playing games is about having fun. Its usually more fun for a wolf team to have 24/7 on multiple levels but balance is also a big requirement.

If the goal is to bring people here I think a separate conversation should be held about what people consider fun and what this sites 'brand' of fun is.
I like complexity on the mechanical side that enables and drives conversation while allowing for lies, gambits, deception, and analysis.
I dislike functions that remove analysis, games that do not have enough action to maintain interest/conversation or mechanics that can not be countered by play.

At its core I believe the main thing that makes games fun is people being able to influence how they do. At some point I made a bunch of ramblings on some core concepts for setup designing I might try to dig up but thats a bit of it off the top of my head. Also why someday I would like to make something that quantifys a sort of point value for individual measurement removing the social loafing issue that drags some games down.[/QUOTE]
I agree with your point. It seems to me that we should also ask ourselves whether [I]we[/I] find night chats more fun than 24/7; we don't have to change ourselves, and neither do they, necessarily, unless we really want more people to come here.

Do we want more people coming here? Perhaps, perhaps not. More is not necessarily better if it makes games less fun, but it is also true I hardly see having only 24/7 chats from now on as being detrimental in and of itself.

I personally dislike complexity on the mechanical side as I feel it tends to detract from the game (but then again I'm a person who gets [B]obsessed[/B] with all the mechanical possibilities, and not everyone is like me).

Originally Posted by Helz

On the most basic level playing games is about having fun. Its usually more fun for a wolf team to have 24/7 on multiple levels but balance is also a big requirement.

If the goal is to bring people here I think a separate conversation should be held about what people consider fun and what this sites 'brand' of fun is.
I like complexity on the mechanical side that enables and drives conversation while allowing for lies, gambits, deception, and analysis.
I dislike functions that remove analysis, games that do not have enough action to maintain interest/conversation or mechanics that can not be countered by play.

At its core I believe the main thing that makes games fun is people being able to influence how they do. At some point I made a bunch of ramblings on some core concepts for setup designing I might try to dig up but thats a bit of it off the top of my head. Also why someday I would like to make something that quantifys a sort of point value for individual measurement removing the social loafing issue that drags some games down.

I agree with your point. It seems to me that we should also ask ourselves whether we find night chats more fun than 24/7; we don't have to change ourselves, and neither do they, necessarily, unless we really want more people to come here.

Do we want more people coming here? Perhaps, perhaps not. More is not necessarily better if it makes games less fun, but it is also true I hardly see having only 24/7 chats from now on as being detrimental in and of itself.

I personally dislike complexity on the mechanical side as I feel it tends to detract from the game (but then again I'm a person who gets obsessed with all the mechanical possibilities, and not everyone is like me).

13v4 doesn't seem that scumsided to me
Having a large scum team is bad, not good

13v4 doesn't seem that scumsided to me
Having a large scum team is bad, not good

I'm now utterly confused about what you guys want. I can't tell if you want to change this to improve balance or if you want people used to 24/7 to stay

I'm now utterly confused about what you guys want. I can't tell if you want to change this to improve balance or if you want people used to 24/7 to stay

I think that a better idea, since such a default cannot exist (unless you [I]enforce[/I] it as a general site rule, and only allow night chats as an exception), is to [I]ask[/I] people to start making setups that include 24/7 chats in case new people show up who might hate night chats. I think the latter is perfectly reasonable and hence I believe that the discussion can stop here, [I]unless[/I] you're talking about restricting ladder games to solely 24/7 chats.

I think that a better idea, since such a default cannot exist (unless you enforce it as a general site rule, and only allow night chats as an exception), is to ask people to start making setups that include 24/7 chats in case new people show up who might hate night chats. I think the latter is perfectly reasonable and hence I believe that the discussion can stop here, unless you're talking about restricting ladder games to solely 24/7 chats.

[QUOTE=Helz;967117]I don't really understand the point of having a 'default.'

The aspects of 24/7 I do not believe were pointed out is how it allows for stronger puppet shows/coaching upping the overall wolf IQ for the new players. I really like this because wolfing with good wolves really improves newer wolves ability and helps spread strategy.

It also helps prevent the frustration that is inherent to wolfing. When you have a team mate overly bussing, supporting you, or even just making a play you see as bad its not fun. Being able to talk to them about it removes a lot of that frustration.

I think consideration should also be given to the abnormal level of complexity this site hosts. Other sites have grown to accept complicated setups but SC2 still is pretty out there and has some unique day game mechanics that matter when considering 24/7 vs day/night.

As I said in the beginning, I don't see a reason to declare a default at all and it makes more sense to leave it as a balance function. For a parallel it would be like declaring a default night cycle and requiring reasoning to do anything else. I just do not see what that accomplishes.[/QUOTE]
I THINK the idea is that it would attract more people from other sites, since apparently on these 'other sites' 24/7 chats are the norm.

Originally Posted by Helz

I don't really understand the point of having a 'default.'

The aspects of 24/7 I do not believe were pointed out is how it allows for stronger puppet shows/coaching upping the overall wolf IQ for the new players. I really like this because wolfing with good wolves really improves newer wolves ability and helps spread strategy.

It also helps prevent the frustration that is inherent to wolfing. When you have a team mate overly bussing, supporting you, or even just making a play you see as bad its not fun. Being able to talk to them about it removes a lot of that frustration.

I think consideration should also be given to the abnormal level of complexity this site hosts. Other sites have grown to accept complicated setups but SC2 still is pretty out there and has some unique day game mechanics that matter when considering 24/7 vs day/night.

As I said in the beginning, I don't see a reason to declare a default at all and it makes more sense to leave it as a balance function. For a parallel it would be like declaring a default night cycle and requiring reasoning to do anything else. I just do not see what that accomplishes.

I THINK the idea is that it would attract more people from other sites, since apparently on these 'other sites' 24/7 chats are the norm.

[QUOTE=OzyWho;967102]who knows
popular guess is that night only chat is a miserable experience for mafia by comparison[/QUOTE]
Miserable seems too strong a word tbh. I'd play either

Originally Posted by OzyWho

who knows
popular guess is that night only chat is a miserable experience for mafia by comparison

Miserable seems too strong a word tbh. I'd play either

If you really wanna see if more people are gonna join on-site games if 24/7 mafia chats become the norm, try running a few games like those on-site and see if people stay. Or conduct a survey and just ask a lot of people if they'd consider signing for a game on a different site with night-only chats.

PERSONALLY, I would join a game with 24/7 chats as readily as any other game so I kinda doubt people care that much

If you really wanna see if more people are gonna join on-site games if 24/7 mafia chats become the norm, try running a few games like those on-site and see if people stay. Or conduct a survey and just ask a lot of people if they'd consider signing for a game on a different site with night-only chats.

PERSONALLY, I would join a game with 24/7 chats as readily as any other game so I kinda doubt people care that much

[QUOTE=aamirus;967079]With “only night chat”, the strongest scum teams I was in just made up cues to secretly communicate during the day anyway.

Like “I will @ everyone but the third person I @ is who I saw my target visit”

At that point you might as well just give us a 24/7 scum chat.

Also it’s way more new player friendly to have 24/7 scum chat. I feel like playing your first game ever and roleing scum with no ability to get advice is a fast ticket to somebody never signing again


Also I feel like you presented the change the wrong way cuz it’s not like hosts are being forced to use it, it’s just changing the default setting[/QUOTE]
What is the "default setting" tho

Originally Posted by aamirus

With “only night chat”, the strongest scum teams I was in just made up cues to secretly communicate during the day anyway.

Like “I will @ everyone but the third person I @ is who I saw my target visit”

At that point you might as well just give us a 24/7 scum chat.

Also it’s way more new player friendly to have 24/7 scum chat. I feel like playing your first game ever and roleing scum with no ability to get advice is a fast ticket to somebody never signing again


Also I feel like you presented the change the wrong way cuz it’s not like hosts are being forced to use it, it’s just changing the default setting

What is the "default setting" tho

[QUOTE=OzyWho;967087]This should be the only criteria for all I care. A[COLOR=#ff0000][B]nd it's not even a subjective statement because mafiascum have made the research and concluded that statistically there's far fewer replacements in 24/7
mafia chat games. [/B][/COLOR]Though weren't Mafiascum games like a week per game day or something? That's different if so..[/QUOTE]
Why would this be the case

Originally Posted by OzyWho

This should be the only criteria for all I care. And it's not even a subjective statement because mafiascum have made the research and concluded that statistically there's far fewer replacements in 24/7
mafia chat games. Though weren't Mafiascum games like a week per game day or something? That's different if so..

Why would this be the case

[QUOTE=Marshmallow Marshall;966342]Alright, so what is the conclusion of all of this estimated value discussion? That everything is fine, right? lol

Apart from this, please specify the usual stuff under Mechanics: phase lenght, lynch mechanics, etc.[/QUOTE]
Would like to host this in the near future

Originally Posted by Marshmallow Marshall

Alright, so what is the conclusion of all of this estimated value discussion? That everything is fine, right? lol

Apart from this, please specify the usual stuff under Mechanics: phase lenght, lynch mechanics, etc.

Would like to host this in the near future

I would 100% do this again. The only thing I would really change about my play is read more properly when people are as aggressive DoctorZeus was.

I would 100% do this again. The only thing I would really change about my play is read more properly when people are as aggressive DoctorZeus was.

I think everyone mistook my posts as a defense of ceko, which they were not lol. It was an attack on the idea of policy lynching people.

It's basically just setting a barrier past which you do not feel bad if you are wrong. At the end of the day, the fact is, if you lynch town, you're still wrong.

I think everyone mistook my posts as a defense of ceko, which they were not lol. It was an attack on the idea of policy lynching people.

It's basically just setting a barrier past which you do not feel bad if you are wrong. At the end of the day, the fact is, if you lynch town, you're still wrong.

There was no MVP this game, but I would nominate myself if I could

There was no MVP this game, but I would nominate myself if I could

I think the stuff Peterson says is deeper than it looks. Like at first I thought he was just spewing nonsense and branding it off as profound philosophy, but a lot of the ideas he espouses, I've reached myself on my own. He just builds a lot of allegory and uses a somewhat mystical language to explain it

I think the stuff Peterson says is deeper than it looks. Like at first I thought he was just spewing nonsense and branding it off as profound philosophy, but a lot of the ideas he espouses, I've reached myself on my own. He just builds a lot of allegory and uses a somewhat mystical language to explain it

Ozy asked me to post this so here it goes.

I don't think I can come up with 10 but here goes, in no particular order:

Searle
Gödel
Lovelace
Penrose
Schrödinger
Da Vinci
Jordan Peterson
Democritus
some guy in the 18th century who asked what would happen if someone duplicated his brain years after his death

post your own list

Ozy asked me to post this so here it goes.

I don't think I can come up with 10 but here goes, in no particular order:

Searle
Gödel
Lovelace
Penrose
Schrödinger
Da Vinci
Jordan Peterson
Democritus
some guy in the 18th century who asked what would happen if someone duplicated his brain years after his death

post your own list

[QUOTE=Marshmallow Marshall;966342]Alright, so what is the conclusion of all of this estimated value discussion? That everything is fine, right? lol

Apart from this, please specify the usual stuff under Mechanics: phase lenght, lynch mechanics, etc.[/QUOTE]
Done

Originally Posted by Marshmallow Marshall

Alright, so what is the conclusion of all of this estimated value discussion? That everything is fine, right? lol

Apart from this, please specify the usual stuff under Mechanics: phase lenght, lynch mechanics, etc.

Done

no

no

No arguments exist in favour of the brain being computational in nature, other than that it may be. Whenever I tried to envision an algorithm according to which the brain could function, I could never come up with one but told myself there had to be one.

This is all well and good, however when looking at the arguments against, plenty come to mind. Therefore the mind must be non-computational. This seems to be a nearly certain fact.

I challenge someone to come up with argument as to why the brain has to be algorithmic

No arguments exist in favour of the brain being computational in nature, other than that it may be. Whenever I tried to envision an algorithm according to which the brain could function, I could never come up with one but told myself there had to be one.

This is all well and good, however when looking at the arguments against, plenty come to mind. Therefore the mind must be non-computational. This seems to be a nearly certain fact.

I challenge someone to come up with argument as to why the brain has to be algorithmic

[QUOTE=DoctorZeus;966336]Well fuck you then

[B][COLOR=#00FFFF]-daykill @[/COLOR][/B][URL="https://www.sc2mafia.com/forum/showthread.php/member.php/45595-Oberon"][COLOR=#F8F8F8]Oberon[/COLOR][/URL]

@[URL="https://www.sc2mafia.com/forum/member.php?u=15807"]Stealthbomber16[/URL][/QUOTE]
You're a fucking moron lol I wasn't even scum reading you

Originally Posted by DoctorZeus

Well fuck you then

-daykill @Oberon

@Stealthbomber16

You're a fucking moron lol I wasn't even scum reading you

DoctorZeus + MM = scumteam
Get zeus

DoctorZeus + MM = scumteam
Get zeus

[QUOTE=DoctorZeus;966330]How did you do this[/QUOTE]
You're the next one to die. You will die by my fucking hand

Originally Posted by DoctorZeus

How did you do this

You're the next one to die. You will die by my fucking hand

Either that or you're straight up scum or fucking dumb

Either that or you're straight up scum or fucking dumb

[QUOTE=DoctorZeus;966331]Followed by this:[/QUOTE]
You need to up your reading comprehension because right now it's on the level of a monkey

Originally Posted by DoctorZeus

Followed by this:

You need to up your reading comprehension because right now it's on the level of a monkey

Next one to daykill gets killed by me

Next one to daykill gets killed by me

That's all for now, I'll read the game tomorrow morning when I'm less tired.
Don't hammer or you're fucking dead.

That's all for now, I'll read the game tomorrow morning when I'm less tired.
Don't hammer or you're fucking dead.

ALSO we should seriously consider punishing Martin by day killing him today

ALSO we should seriously consider punishing Martin by day killing him today

FOR THE LOVE OF GOD please do not lynch/daykill anyone for 48 hours. I'm planning on reading this entire game in my spyglass mode to detect bullshit
if anyone hammers or day kills before then, I will fucking kill you

FOR THE LOVE OF GOD please do not lynch/daykill anyone for 48 hours. I'm planning on reading this entire game in my spyglass mode to detect bullshit
if anyone hammers or day kills before then, I will fucking kill you

[QUOTE=theoneceko;966222]is this a serious post?[/QUOTE]
No lol

Originally Posted by theoneceko

is this a serious post?

No lol

[QUOTE=Marshmallow Marshall;966227]You may refer to him by the pronoun "asshole" :)[/QUOTE]
No u

Originally Posted by Marshmallow Marshall

You may refer to him by the pronoun "asshole"

No u