Comments by "MC116" (@angelmendez-rivera351) on "Rationality Rules"
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To be fair, these mutually exclusive deities are only mutually exclusive if you include some minor petty details about the what defines the deity. It is possible to define the concept of deity such that it encompasses every deity in every currently existing religion, without also being unreasonably broad and including mundane concepts, though constructing such a definition is a different story. Religions differ not very significantly with regards to deities, just with regards to other theological and metaphysical aspects. Of course, the names given to the deity in each religion are different. For example, Judaism and Christianity and Islam all worship the same deity, categorically, even though each religion gives a different name to the same deity. But it would be unreasonable to say that the deity in all three religions are mutually exclusive to one another. In fact, the three religions differ not in who the deity is, but what the deity did. In this regard, it is unsurprising that a theological argument for deities is unable to actually distinguish between those deities.
Of course, the arguments are absurd, but their inability to distinguish petty details concerning deities is not what makes them absurd.
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The cardinality of the two planets' orbit sets being equal isn't the same as the number of orbits being equal.
It is the same. It is the same, by definition.
If the first elements of the sets are 1 and 30, respectively, and in both sets, the value of the successive elements increases at fixed but different rates, then at what point do the values of elements become equal?
Firstly, the premise of your question is wrong, because there is no such a thing as a "successive" element in a set. If you want a notion of next element in a set, or a successive element in a set, then you need not just a set, but a partial order on that set. A partial order is a binary relation on a set that is reflexive, transitive, and antisymmetric. You can induce a partial order on a set by having a sequence from the set of natural numbers to it, and the partial order is induced by making the sequence monotonic with respect to that partial order. Consider the set of natural numbers N, and consider the set 30·N := {n natural : n = 30·m, m natural}. You can take the standard partial order of N, restrict it to 30·N, and this forms a partial order on 30·N.
Secondly, by asking about different rates of increase, you must be talking about functions. However, there are problems with this consideration, as you shall later see.
The answer is that the values are never equal, the later will always be greater than the former as time trends towards the infinite.
Yes, if I have a function f of real numbers with f(x) = x, and a function g of real numbers with g(x) = 30·x, then it is true that for every 0 < x, f(x) < g(x). It also is true that the functions f and g diverge unbounded as x grows unbounded. However, this is completely irrelevant to the scenario being discussed. The question being asked is not "what happens to the number of orbits as time gets bigger?", the question being asked is "what is the number of orbits for each planet after an infinite amount of time?" The answer to the question is that, for both planets, Aleph(0) units of time have passed. This is not a contradiction or an absurdity.
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@frede1905 Surely you can vary the value of some parameter, keeping the other parameters the same, and then use the laws of physics to predict how the universe would evolve with that other value.
Mathematically, yes, you can do that, but there is no evidence that this is physically meaningful at all. There is no evidence that there exist any undetermined parameters which could have been different than what they are, and there is no evidence that, even if they could have been different than what they are, that it changing would not somehow lead to changes in all other parameters. The claim that these things are true is fundamentally unfalsifiable. Also, again, there is no reason to assume a universe different than ours has to obey the same laws than ours does, so this talk about considering different universes as being just variations of our own universe with different is, again, unfalsifiable. There is no evidence of such a thing, and there will not be such evidence in the near future, probably. Playing around with the mathematics of our current laws is physically meaningless, if we cannot confirm that a different universe could have existed, instead of our own, satisfying such mathematics.
Plug a different value for the cosmological constant than that which is observed into the Friedmann equations, for example.
There is no evidence that the cosmological constant could have been any different than what it is, or that if the universe had been any different than it is, that it would still have satisfied Friedmann's equations. These assertions are, again, unfalsifiable.
If fine tuning appears in the model, then as mentioned before, there would appear to be something suspicious in the model, and the better, revised model (which surely must exist, as our models are incomplete, as you say) should somehow resolve it.
The "if fine tuning appears" part is the problem here, since any assertion that there is fine tuning is necessarily unfalsifiable, due to things I have mentioned above. Yes, it is true to say that a model having fine tuning is a problem, I am not denying this. However, you can never actually establish that the model has such a problem, because in order to so, you have to make unfalsifiable assumptions.
That's the fine tuning argument in physics anyway.
In the assumption that there really do exist undetermined parameters in our models (as is the case with the current models), we want to find new models which do not have such undetermined parameters. It is true to say that this is a real problem that is being attempted to solve, but this has nothing to do with the notion of whether the universe could have actually been different than what it is, and how different it would be if it were. At best, this concept of "what if the value of this parameter were different?" is just an inaccurate simplification presented to laypeople in order to basically answer the question "why do we care that there are undetermined parameters?"
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@yohanessaputra9274 Firstly, I didn't insult you.
Yes, you did. You told us to "read the literature", presupposing that we have not read it before this discussion, and that we are thus ignorant on it.
I was merely responding to what Alan Animus said about his dislike about the term "timeless".
He adequately had already explained that his dislike of the term has nothing to do with the neutrality of the term, which you should have known, had you bothered to carefully read the conversation before trying to butt in. Your response was to deliberately ignore that, and then tell us to "read the literature", with implications that I already explained.
Secondly, you exchange with me by Ad Hominem and you presupposed me a theist.
At no point in this conversation have I presented any ad hominem to you. I have also not presupposed you a theist. I said your comment makes you look like an ignorant theist. I never said I believe you are a theist. The fact that you do not know the difference proves my point about your arrogance.
That's a one way to have an exchange lol.
It is the way of exchange that you chose.
I feel of things we will talk is probably just insulting each other, so good luck with your life
You wanted to insult us, so I decided to reply accordingly. If you want to stop being called out for insulting people, then you need to stop insulting people. The fact that you are even pointing this out exposes you as a troll. You know what would be conducive to a productive conversation where I would glady be discussing time and philosophy, instead of your own insults? A conversation where you do not begin by insulting people perhaps. Anyway, I will not waste my time having any further interactions with you, because I have been on the Internet for a long time, and I know that feeding trolls is a bad idea. Farewell.
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@Melesniannon What you are appealing to is a different concept altogether, a concept from measure theory, which is not about determining the number of elements in the set, but measuring the length of the sets. Namely, there is a function called the Lebesgue measure, which, when applied to a set, gives you the length, area, or volume, or the set, depending on whether the set has dimension 1, 2, or 3. Since the intervals (1, 2) and (1, 3) are one-dimensional sets, they have lengths, and the Lebesgue measure, when applied to these sets, gives their lengths, namely 1 and 2. In general, if you have an interval (a, b) with a =< b, and the Lebesgue measure λ, then λ((a, b)) = b – a. So λ((1, 2)) = 1, and λ((1, 3)) = 2. However, even though the Lebesgue measure of the sets is different, their cardinality is the same.
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@Melesniannon I think you misunderstood my example, it's not about length, it's about being able to understand the set in a second dimension which leads to the understanding that even though they are infinite in one way, one infinite set will, given the same parameters, always be larger than the other.
I disagree. This absolutely is about length. You are talking about meter sticks, and comparing an interval of length 1 cm with an interval of length 2 cm, and claiming that while both intervals are infinite, the latter is larger than the former. Meter sticks are precisely about lengths of intervals, not about the number of elements that are members of the intervals. Of course, if you intended to imply something different, then your analogy does not work for your purposes.
A 2 cm wide line extended infinitely is always twice the area as a 1 cm wide line given that they are both extended towards infinity equally.
Yes, it has twice the area, but it also has exactly the same amount of area. This is because Aleph(0) = 2·Aleph(0), so if they both have Aleph(0) square units of area, then one has twice the area of the other, and they have the same area. I am unsure if you are meaning to imply they do not have the same area, but they absolutely do.
A planet that revolves 30x every time another planet revolves 1x, always makes 30x more revolutions, even when time is extended infinitely.
Mm, no, not quite. For every real number x > 0, it is true that 30·x > x, so 30·x and x are unequal. However, this does not hold for x being an infinite quantity.
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@andresvillarreal9271 The claim that the infinite cannot be traversed is something that you have to discuss with mathematicians, not with philosophers.
Thank you! This desperately needed to be said.
In fact, there are a gazillion ways in which, through artifacts of language and not of science, mathematics or good philosophical reasoning, you end up treating infinity as a number, and not a cardinality.
This may just be unnecessary nitpicking, but as the connotation of the conjunction "and" in the English language is more ambiguous than it is in formal logic, I should remark that a cardinality is a number. It is unclear whether your comment is meant to imply otherwise or not, but just in case, I wrote this clarifying remark.
You can add an element to a set that has a cardinality of infinity.
Infinity is not itself a cardinality, though infinite cardinalities do exist. It would be more accurate to say that you can add an element to a set with infinite cardinality. This may seem like a pedantic distinction, but actually, it is quite an important one.
And the new set also has a cardinality of infinity, creating the apparent contradiction that infinity plus one is infinity. But there is no contradiction because infinity is a cardinality, not a number.
This is incorrect, and there are a few misconceptions to unpack here. As I clarified earlier, a cardinality is a number. Every cardinality is a von Neumann ordinal number, and every von Neumann ordinal number is a hyperreal number. As I also clarified earlier, infinity is not a cardinality. Infinity is the property of a set S of there existing an injective function f : N —> S, where N is the set of natural numbers. Infinite sets are said to have infinite cardinality, but different infinite sets have different infinite cardinalities, which is why infinity cannot be called a cardinality itself. The set of natural numbers has cardinality Aleph(0), which is the smallest infinite cardinality. Aleph(0) satisfies the property that Aleph(0) = Aleph(0) + 1, and Aleph(0) = 2·Aleph(0). The set of real numbers has a larger cardinality, the cardinality 2^Aleph(0), which is not equal to Aleph(0), but is larger instead. Assuming the continuum hypothesis, this means the set of real numbers has cardinality Aleph(1).
As for the equation that Aleph(0) = Aleph(0) + 1, it seems to be an apparent contradiction due to our preconceived, erroneous intuition, regarding cancellability. When we work with a commutative algebraic structure (S, +), where S is nonempty, we say that an element x of S is +-cancellable if x + a = x + b. If every element of S is +-cancellable, then we say that + is a cancellable operation. Every algebraic structure you learn about in primary schools, and even in undergraduate colleges, is a structure where + is cancellable. So by intuition, we tend to assume that every algebraic structure in mathematics must satisfy this property. So when we encounter Aleph(0) = Aleph(0) + 1, we immediately assume that cancellability holds, and so we conclude from this that 0 = 1 must be true. However, we know that 0 = 1 is false, so we believe there is a contradiction. Since most people are non-mathematicians, they lack the training to recognize that the problem is not with Aleph(0), but with our cancellability assumption. In fact, historically, it was impossible to know this was the case, because the study of non-cancellative algebraic structures did not develop until many centuries after the topic of infinity had become already controversial. This is where the apparent contradiction comes from.
When you say that the infinite cannot be traversed you are declaring that infinity is a number, and everything you do from that point onward is pure garbage.
I disagree. I would argue that the word "traversing" is not sufficiently well-defined for this conversation to hold, but even if we hold on to just intuition, saying "the infinite cannot be traversed" reasonably translates to "infinite objects do not exist", which in modern terms, is understood as simply rejecting the set-theoretic axiom of infinity. Historically, this makes sense, since axiomatic set theory did not exist until Georg Cantor came along, and it was he who provided a framework for working with infinite sets in seriousness and good faith, by way of equivalence classes and functions, and this happened centuries after the infinite was already controversial.
The answer to everything in the first minutes of your video is that those philosophers did not know much about mathematics.
This much is very true, though, in their defense, neither did anyone else, at least prior to Leonhard Euler.
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@TheWrongBrother The reason for philosophical assessment other than mathematical stems from the ambiguity of results from mathematical operations on infinity when viewed either as a cardinality or a natural number
Prior to the 19th century, you would have been correct in stating that the results of operations with the infinite would have ambiguous and with many apparent absurities. However, we live in the 21st century, and von Neumann-Bernays-Gödel set theory is a tentative foundational theory of mathematics that exists. Rigor for the infinite is well-understood now, and there is nothing ambiguous about operating with the infinite.
♾ + 1 = ♾
Here is where you are relying on an outdated idea of infinity. Infinity is a property of sets. Specifically, a set S is called infinite if and only if there exists an injective function f : N —> S, where N is the set of von Neumann natural numbers. Infinity is not a direct description of the size of a set, let alone a number. For example, the set of natural numbers has cardinality Aleph(0). The set of real numbers has cardinality 2^Aleph(0). Both sets are infinite, but it is false that Aleph(0) = 2^Aleph(0). In fact, according to Cantor's theorem, Aleph(0) < 2^Aleph(0). Aleph(0) and 2^Aleph(0) are numbers, and are infinite cardinalities, but neither of them is called "infinity", and "infinity" is not a number. So what you should have written is that Aleph(0) + 1 = Aleph(0), which is indeed correct.
since the mathematical size of the infinite quantity has grown by one, its logical size has not been impacted in any way and still remains infinity.
Wait, what? Your sentence is extremely confusing. You are making a distinction between mathematical size and logical size, but in reality, you have defined neither. Also, because you wrote "since" at the beginning of your intended sentence, you are indicating that the logical size of the infinite quantity not changing and remaining infinite is a necessary consequence of the mathematical size being increased by 1. However, the meaning of this, and therefore, its truth, is far from obvious.
If two separate events added to the infinite quantity, how would you know the size difference from two separate view points?
I am not sure I understand your question, but if there exists a bijection f between an infinite set X and an infinite set Y, then the two sets, by definition, have the same cardinality, i.e, the same number of elements. This is true, regardless of whether there are elements of Y that are not elements of X, or vice versa.
Hence philosophical assessment bodes better for this analysis...
What your comment has demonstrated seems to be the opposite of this. Philosophical assessment of the infinite is inadequate to understand the infinite, which is why no good understanding of the infinite existed historically until mathematicians took it upon themselves to set the theory of sets on top of a rigorous foundation. To put it more succintly: the ontology of infinite objects is the theory of sets. There is no other way to do it.
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@TheWrongBrother The usual assumption is that the variable V(N0) is linear and the observer assessing it is 1.
No. There are no linear variables required in this discussion. There are no observers required either.
At the end of the set...
There is no end to such a set. If a set has order type ω, then there is no such a thing as its last element.
If the V(N0) is moments in time with the assumption that there have been infinite moments in time till then, can you get to the present?
Yes, you can.
as the last element, if another moment is added, you immediately become the past and are excluded from the state of the present and by that it becomes impossible to get to the present.
This is nonsensical, since (0) time does not work that way, time is a coordinate in spacetime, (1) there is no last element in such a set.
its logically impossible to observe the last moment since new ones are added every 'time'.
No, observation is completely irrelevant here.
If you take an infinite crowd concert (non linear set with infinite elements).
There is no such a thing as a linear set. Stop saying nonsense and inventing terminology that means nothing.
how would you establish that everyone in the set has their lighters on?
Via a bijection.
Traversing a set with Aleph-Naught cardinality is logically impossible and absurd from a math/philosophy point of view.
No, it is not. Your understanding of mathematics and set theory is just REALLY bad.
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Also, saying they are of the "same infinity", is not accurate, or rather, it is imprecise. The set of real numbers has a larger cardinality than the set of integers, while the set of integers has the same cardinality as the set of natural numbers. In other words, the cardinal number corresponding to the set of real numbers is larger than the cardinal number corresponding to the set of integers, which also corresponds to the set of natural numbers. Specifying that you are talking about cardinal numbers here is important, because a more fundamental type of infinite number are the ordinal numbers, but even though the set of integers and the set of natural numbers have the sams cardinal number, they do not have the same ordinal number. The ordinal number for the set of natural numbers is ω, while the one corresponding to the integers is ω + ω. The ordinal number corresponding to the real numbers is some ordinal number greater than or equal to 2^ω, possibly ω(1).
You also would be better of explaining why a pair of sets have the same cardinality or a different cardinality. If there exists an injective function f from a set X to a set Y, then the cardinality of X is less than or equal to the cardinality of Y. This defines a well-order on the class of cardinal numbers.
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@fokocrispis4036 If we say that existence is "something with qualities", nothingness would...
"Something" is not a well-defined metaphysical concept either, so trying to piggy back off "something" to get to a well-defined metaphysical "nothing" is not going to work. Appealing to common sense is also not going to do you any favors.
Nothingness would lack all qualities.
This statement is nonsensical, since, at least in the context of how "quality" is defined in essentially every context, "lacking all qualities" is itself a quality. What you are doing is akin to saying that there is a set of all sets, which is known to be impossible, as it is a logical contradiction. Besides, what does "lacking a quality" even mean? In a formal context, it means literally nothing, since if you "lack" a quality, then you have the opposite quality, hence you still have a quality.
If your nothingness has 0% of events happening, you are not talking about nothingness in the first place.
Exactly. Somehow, you missed the point of the comment, though, and failed to use this as the key premise to conclude that nothingness is incoherent as a concept, which is precisely what the comment set out to prove in the first place. You disagreed for no reason. And ultimately, nothing that you have described in your reply is a sensical definition of "nothing" either, so you have sort of reinforced the point. "Nothing" is not a coherent idea, it is merely a flawed intuition that humans naturally have.
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@fokocrispis4036 but the important part there is that everything in existence has a quality.
That begs the question of what "existence" is. Because, as pointed out in the video, "existence" is not really well-defined idea either. And if it was, then it would no longer really be a matter of ontology. Besides, I can make the claim that "there exists one entity such that this entity has no properties", and I do not think you can prove that this statement is false. This makes your definition of "nothing" inadequate.
Lacking all qualities is a contradiction because of language but it is by itself not a quality.
No, this has nothing to do with language. The contradiction would remain if I used formal logic to state this instead of a natural language. So it is, in fact, a quality.
Lacking a quality also doesn't mean you have the opposite. Lacking size doesn't make something big or small, it just doesn't have size.
This is a bad analogy. Lacking quality would better be compared with lacking bigness, or lacking smallness. Also, if you lack size, then you are sizeless, the opposite quality of being size-having or "sizeful". Of course you do not become big or small if you lack size: I never claimed you do, because those are not "opposites" of "sizelessness". This is a misrepresentation of my point.
I disagreed with the original comment, because I don't see that as nothingness.
The original argument does not claim to see that as "nothing" either. So you did miss the point.
The point in the original comment was nothingness negates itself, therefore it is an incoherent concept.
This is indeed the thesis of the comment, and this is a different claim than claiming that nothingness is probability.
But my point was that nothingness is a viable state, but there is no actual way to describe it as there is no actual contrast to even identify it.
If there is no identification for nothingness, then it is not a viable state. Well-definedness requires that there be precisely something that identifies the thing being defined, even if the identification cannot be put into words. Otherwise, it is not a "thing" in any meaningful sense of the word. It is a non-concept.
I don't believe there is a coherent definition of nothing, though, but that doesn't mean that reinforces the impossibility of nothing as a state,...
It absolutely does reinforce it. If there is no coherent definition of it, then it is undefined, by definition. That is just how it is. Undefined things are not concepts, let alone states. This is a lot like calling "Undefined" a number. It just does not work like that.
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Infinite is a vague and general statement without reference points.
No, it is not. Infinity is a precisely well-defined property of sets, based on the axiom of infinity. A set S is an infinite set if and only if there exists an injective function f : N —> S, where N is the set of natural numbers.
The numbers between 1 - 2 are infinite,...
Which kind of numbers are we talking about? Because, for example, there are infinitely many real numbers r satisfying 1 < r < 2, but there are no natural numbers r that satisfy it. I will assume that you are talking about real numbers here, though, so in this case, yes, you are correct. The interval (1, 2) is an infinite set.
...but not as infinite as the numbers between 1-3, as it contains both the subsets 1-2 and 2-3.
No, this is incorrect. (1, 2) and (1, 3) are sets of the same cardinality, because there exists a bijection from (1, 2) to (1, 3). If you want a specific construction of the bijection, then consider, f0 : (1, 2) —> (0, 1), (f0)(x) = x + (–1); f1 : (0, 1) —> (0, 2), (f1)(x) = 2·x; f2 : (0, 2) —> (1, 3), (f2)(x) = x + 1. Now consider g = (f2)°(f1)°(f0) : (1, 2) —> (1, 3), such that g(x) = (f2){(f1)[(f0)(x)]} = (f1)[(f0)(x)] + 1 = 2·[(f0)(x)] + 1 = 2·[x + (– 1)] + 1 = 2·x + 2·(–1) + 1 = 2·x + (–1). It can be proven quite easily that g is a bijection, and so (1, 2) and (1, 3) have the same infinite cardinality. Yes, it is true that (1, 2) is a proper subset of (1, 3), but this only implies that they have different order type, not different cardinality. In fact, the set difference (1, 3)\(1, 2) of (1, 3) and (1, 2) is [2, 3). (1, 2) and [2, 3) have cardinality Beth(1), while the set of natural numbers has cardinality Aleph(0) = Beth(0). As it happens, the union of (1, 2) and [2, 3) is (1, 3), and that all three sets have the same cardinality reflects the fact that Beth(1) + Beth(1) = Beth(1). For the record, Aleph(0) < Beth(1).
I think this is why infinities are argued against so vehemently.
The reason infinity is argued against so vehemently is because our understanding of infinity via set theory is extremely recent for humanity, and transfinite set theory is so counterintuitive, that some people just reject it. For example, as I already clarified, if we have a set X that is a proper subset of Y, it is still possible for X and Y to have the same cardinality, because it is possible that there exists some f : X —> Y that is a bijection. This is counterintuitive, because intuition tells us that if X is a proper subset of Y, then Y should have a larger cardinality than X, and so such an f should not exist, yet we can prove that such an f can exist. Again, what this reveals is that the subset relationship only gives information about the order type of a set, not the cardinality of a set. For finite sets, order type and cardinality just so happen to align and be equivalent, which is why our intuition fails when this equivalence no longer holds if infinite sets are introduced. This is why the movement called finitism, the rejection of the axiom of infinity, has become so popular. Together with finitism, there is also the intuitionist movement and the constructionist movement.
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@anghusmorgenholz1060 My previous comment was deleted, so I should say this again: I at no point presented 0 as being infinity. You did. You have poor reading comprehension skills. Your original comment asked for a definitive infinite numeral to be talked about in this discussion. I replied by saying that the video is using the numeral Aleph(0). For some reason, you are now insisting that I am instead talking about the numeral 0. I am not. The numeral Aleph(0) is a different numeral than the numeral 0, and I only talked about the former, not the latter, so you need to stop being a lying piece of garbage, and stop pretending that I ever talked about the latter as being representative of infinity.
Using the infinity in mathematical terms to prove a religious or philosophical claim without using actual math doesn't work.
Once again, you display your idiocy, and your lack of reading skills. I never presented any religious or philosophical claims here. I only answered your comment, by explaining that the video did use a definite infinite numeral in its discussion, like you wanted them to. As for using actual maths, the video also did that. It is called set theory.
Anyway, you have exposed yourself as a t-r-o-l-l. I will no longer be interacting with you. I will no longer be reading your comments.
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@EskChan19 It's not quite a code in the general meaning, but it's similar to a code how it's used in computer science.
No, it is not, and this much is common knowledge among geneticists and computer scientists alike. You can even search explanations on Google for why they are only superficially similar at best, if at all.
ASCII for example is a good analogy, in that this really isn't language, it's just more a codec, a way to store and parse data.
No, it is not a good analogy. DNA does not store data anymore than any arbitrary molecule does (yes, all molecules store data, this is a basic fact of thermodynamics), and it certainly is incapable of parsing data, which requires a parsing algorithm. The fact that DNA does not store data any more than any other molecule already disproves your thesis.
And it works similar to an extent, in that certain patterns of base pair 'codes' yield certain results, and the same pattern would theoretically result in the same pattern for people.
No, it would not. Again, every geneticist knows. The reason the discipline of epigenetics exists is precisely because genes do not work this way. Gene expression has an effect on whether a given string of base pairs will give a codon for a protein strand or not. Also, there are a number of other factors that can alter the result that have nothing to do with that particular string itself. Then, there is also the issue of thermodynamic entropy changing the interactions, something that does not exist with actual code.
And just like an ASCII, if it corrupts, it can change all of it.
And unlike an ASCII pattern, a "corruption" can result in no changes at all.
DNA is not a code. It is a molecule.
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@lurch666 If you have infinite time then your past is infinite.
Yes. This is a tautology, so there is nothing to discuss here. Proceed.
So say you wait 10 billion years to do something. Since your time has no start (because you have an infinite past) there's no time to start counting your 10 billion years.
No. Having an infinite past does not imply your past did not have a start. If my time coordinate is t = ω, then because ω is infinite, my past is infinite. However, my past still did have a start, because t = 0 is the minimum time coordinate. Time starts, then ω years pass, then I start counting, until I reach ω + 10 000 000 000 000 years. So I have now counted 10 000 000 000 000 years, which is a finite amount of time, but I still have an infinite past with a beginning.
Because you have an infinite past, you can't start counting from the start like with finite time so like I said any finite amount of time is swallowed by your infinite past.
Why exactly am I obliged to count from the beginning? Just because I cannot count from the beginning, it does not mean there was no beginning. You may just be confused as to what exactly "counting" entails.
The problem with infinity is that it makes no sense.
Wrong. Infinity makes perfect sense. Zermelo-Fraenkel set theory has an axiom dedicated just to infinite sets. von Neumann-Bernays-Gödel set theory goes further by introducing the axiom of global choice, and by being able to quantify over proper classes, rather than just sets. Really, it should just be called von Neumann-Bernays-Gödel class theory. Anyway, infinity is well-studied and well-understood by mathematicians, and it works just fine. It even has applications in physics.
But if time is infinite that now needs an infinite amount of time to pass before it can happen so we never reach it.
You keep insisting that if something takes an infinite amount of time to be reached, then it cannot be reached, but you have not actually explained why this is the case. To me, this just sounds like an unnecessarily elaborate way of saying "infinite sets cannot exist".
Infinity causes paradoxes...
No, it does not. Before the 19th century, when set theory was developed, people had a really poor understanding of the concept of infinity. As such, it did cause paradoxes, though the paradoxes actually originated from wrong intuition, rather than from infinity itself. However, we live in the 21st century. There exists an entire super-discipline of mathematics called transfinite mathematics dedicated to studying infinity. We understand infinity so well today, that it is actually shocking in retrospect how bad we used to be at handling infinity as a concept in the past.
Obviously we have reached now. But if time stretches back into infinity then an infinite amount of time has to pass to get to now.
Yes, an infinite amount of time has to pass to get to now, if the past is infinite. What is the issue? Are you implying that an infinite amount of time cannot pass, so therefore, an infinite past cannot exist? This just sounds like you are saying infinite time cannot exist, which is the conclusion you are trying to prove in the first place. Why is it that infinite time cannot pass?
Because infinite time doesn't get us to now-it gets us to the future.
If it gets us to the future, then it necessarily gets us to now, because now precedes the future. So your claim is wrong. Also, infinite time does not necessarily get us to the future. So your claim is also wrong. If my time coordinate is ω, and I have a time machine, and I set my time coordinate to 0, and then I let my time run for ω units, I am back when I started, and this true, in spite of the fact that ω is infinite. No future required.
Imagine a sea with infinite depth under a sky with infinite height. The surface of the sea is now, under the sea is the past, so the deeper you go the further into the past you go and the sky is the future, the higher you go the further into the future you go.
Yes. Your scenario is reasonable so far.
Now how long of a stick would you need that could stand on the bottom of that sea so the tip of the stick just reaches the surface?
An infinite stick. Specifically, if the sea has depth ω units, then my stick needs to be ω units long.
Any stick of a finite length wouldn't reach the surface because the bottom is an infinite distance away.
Correct. The bottom is an infinite distance away. Please remember this for the next sentence.
Any stick of infinite length would reach the surface but because it's infinite, it would keep going into the sky.
No. In order for it to keep going into the sky, the stick would have to have a length larger than the length from the surface to bottom of the ocean. If both lengths are infinite, then it is not warranted for the stick to have such a larger length, and so it is not warranted that the stick would continue into the sky. If the ocean depth is ω meters, and my stick measures ω meters, then my stick will just reach the surface, and not go into the sky, but the ocean will still have infinite depth, and my stick will still have infinite length.
So there is no length of stick that can just reach the surface (now).
I have just proven otherwise. Such a length of stick does exist.
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@homotheticwren So instead of saying that if infinite time precedes an event, you will never reach the event, it might be helpful to think about infinite in a more numerical sense.
Yes, please. Are working with surreal numbers, hyperreal numbers, ordinal numbers, or just cardinal numbers?
take the set of natural numbers, for example; this is, I think, is the kind of thing you're imagining, where you could theoretically count to an arbitrarily large element in the set.
Yes, although I am not sure how counting to an arbitrarily large finite number is relevant here.
However, what about the set of real numbers? If you tried to count the set of real numbers, or even just the real numbers between 0 and 1, you would never reach even an arbitrarily low number, because where do you even start?
The set of real numbers is known as a dense set. What this means is that, for any two real numbers x and y, there exists many real numbers r such that x < r < y. Density is a property that you can have even with a countable set, such as the rational numbers. 0 is a rational number, but there is no "next" rational number, because for any rational number 0 < q, there are rational numbers r with 0 < r < q. However, the set of rational numbers is a countable set, because there exists a bijection f from the set of natural numbers N to the set of rational numbers Q. This means that every rational number can be written in a list, even though there is no "next" rational number. However, the interval of real numbers (0, 1) is not countable, because there is no bijection from N to (0, 1), so it is not possible to write the real numbers of the interval in a list. What this demonstrates is that density and uncountability are different properties that are not equivalent. I think you may be confusing one for the other.
Also, while it is true that the cardinality of (0, 1) is larger than the cardinality of N, this does not prove that an infinite amount of time cannot pass to reach a point in time.
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@lurch666 But infinity + infinity is still infinity.
Yes, if α and β are infinite numbers, then α + β is also infinite. How is this exactly relevant to what I said?
When you say the depth of the sea and the stick are the same length, then of course the stick would just reach the surface, but since infinity (depth) + infinity (sky) is still infinity then the stick would also reach the sky because the stick has a length of infinity.
No, that is not how that works. I wanted to avoid correcting you explicitly with your previous paragraph, but I have no choice now: "infinity" is not a number. Infinity is a property of sets, and therefore, of numbers, and other mathematical constructs. There are finite numbers, and there are infinite numbers, but infinity is not itself a number, infinity is simply the property of a number being infinite. When you talk about the ocean and sky having some kind of infinite depth or height, you need to specify what kind of infinite number you are working with. This is why in my arguments, I specified a size ω. ω is an infinite number, but it is a different infinite number than ε(0) or ω(1). More importantly, ω is different from ω + 1, and different from ω + ω. What you are doing here is giving the ocean a depth α (which is infinite), the sky a height β (which is infinite, and which may or may not be equal to α), and the say that the stick must have length α + β, which is not true: there is no logical necessity for the stick to have the sum of the lengths. Of course, if it does have length α + β, then of course it will reach into the sky forever and ever. But this is cheating: you are conflating various different quantities and treating them as being the same quantity solely because they all share the same property of being infinite. That is simply not how the infinite works.
That's why infinity doesn't make sense
No, that is why your incorrect understanding of infinity does not make sense. Treating infinity as a number does not make sense. Treating infinity as a property of a class of numbers, however, does make sense.
because when you think about infinity you get contradicting results and math falls apart.
Oh, yeah? Tell that do the the hundreds of thousands of mathematicians studying transfinite set theory, right now. Tell them that if they continue developing transfinite set theory like they have been doing for 150 years, their mathematics are going to fall apart. Please do that, then come back to me and tell me, how the mathematicians took that. Good luck.
Got to admit I don't know infinity from any deep learning this is just what I have figures out myself so I've make some big errors that's down to this being a difficult subject
I would very much argue set theory is not a difficult subject. Only the theorems that are counterintuitive are the difficult ones.
but an infinite past can't have a start.
It absolutely can. I just demonstrated how it can. There exists a smallest ordinal number: the empty set, also called 0. However, ω is an infinite ordinal (the smallest infinite ordinal). So if my time coordinate is ω, then I have an infinite past (because ω is infinite), but said past has a beginning, because 0 is the smallest time coordinate. Are you going to tell me that mathematicians are wrong on this?
but if you have existed for an infinite time then you would never reach the point where you can start because it would take an infinite amount of time to get there.
No, you are wrong. You saying "an infinite amount of time must pass to reach point A" does not demonstrate that "point A cannot be reached." You need to prove it. You keep insisting that it is true, but it is not.
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@homotheticwren I genuinely don't mean to be rude,...
Ah, yes, the classic "I don't mean to be X, but..." only to follow up with a remark that fits exactly the defining characteristic of X, except this time, you wrote said remark before saying. I am sorry, but I cannot take this seriously when say this immediately after saying "it's both utterly irrelevant and unnecessary". It would have been better if you had simply called it unnecessary, irrelevant, and then left it that. The feigned humility in your comment is devoid of meaning, and leaves me unimpressed.
...I don't think what you said has any bearing on the purpose of my comment.
If so, then that is your own failure, not mine. Your comment, by your own admission in your first paragraph, was an attempt to help illustrate Lurch's claim that infinity cannot be traversed or reached. My reply was a direct sentence-by-sentence response explaining why your comment does not help illustrate the point you intend to illustrate, by mentioning the fact that the phenomenon you appealed to has little to do with infinity itself, and more to do with the density property of some sets. If my response somehow has no bearing on the purpose of your comment, then neither does your comment itself. Though, I would also argue, as I indicated at the end of my reply, that much of what you said in your comment had little relevance to Lurch's claim anyway. What you and Lurch argued were effectively two completely separate topics.
Anyhow, I will not be replying to you any longer. This response of yours has made it evident than trying to correct you on your own mistakes is a waste of time, and is even unappreciated, given the rudeness of your comment. Very well, then. Stay wrong, for as long as you want. I will no longer bother you. Farewell.
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