Every man needs a hobby. I have a family so I don’t get much hobby time. Actually, I have 3 families; mine, my wife’s, and my wife’s former sister-in-law’s (long sorted story). Between the kids, parents, grand parents, and politics there isn’t much room to stabilize a consistent hobby, so I just choose random projects and see how far I can go with it. I was in the midst of choosing another project when I was reminded of “affectance” and the infamous James S Saint. So I looked to see if I could find him and do a personality research dossier. And here I am swimming through reams of thoughts and exploring the depths and breaths. Everyone should do that to another person sometime (if they learn to be responsible about it). An older relative would probably be best. It’s better than collecting stamps or watching the political news.
I don’t really know what I will do with the data. I enjoyed professionally collecting and correlating such, but it’s different now. So I’m not sure how far I’ll take it, nor where or when it will end. It wouldn’t be the first time I just tucked a completed project away in a bin, long to ever be seen again.
Even if I knew what that meant, I’m pretty sure that I’m not there yet.
My question pertained to multiplying numeric sets. I have posted it twice. You have ignored it now twice. Then, as predicted, tried to change the subject.
And “May I query this explanation?” does NOT equate to “I disagree”. If anything it would be "May I query into THAT explanation (learn the difference - “this here” vs “that there”). But in reality you merely chose to argue about a different subject:
No it doesn’t. I said that you add 1 to your position. I did not say that you add 1 to the value that is at your position. So more like this:
Infinite set represented as: {…, x, Y, z, …}
Add 1 TOposition y:
New set looks like: {… x, y, Z, …}
The set itself doesn’t change, merely where you are located in or pointing to within the set.
So the rest of your post is nonsense and you still haven’t addressed the issue of your lack of adding the subtotals in order to get the proper product of multiplied sets infA * infA = InfA^2
Like I said, just because “you don’t see the connection yet, don’t presume there is none, let me explain it to you” - do you agree that “presumption is the seed of all sin” like you said, or not? You’re so convinced of some combination of malevolence, incompetence, psychological or political compromise on my part that you refuse to see other quite obvious explanations as to how hard it seems to be to have a simple discussion. Stop presuming so I can unpack this for you, and it will all come together for you unless you don’t want to see it do so, which won’t be my fault.
We calm now? Great. We can continue
To briefly address this one before we get to the actual content, I thought it was fairly straight forward, but as before I have simply been misinterpretted and presumed to be distracting. People ask if they can query something if they think they see the source of some disagreement in said something, no? I proceded to that source, to query whether it shined any light on what’s going on here. Like I said, there’s a connection between all the things I’m saying that I’m trying to bring together in a way that gets to the bottom of our disagreement. If you’d let me explain it to you, you’d see it too. I apologise for not being as literal and concise as you seem to need me to be, ok? I’m trying.
Right, great. Query answered! Easy, right?
Let’s ride this momentum, shall we? It doesn’t mean the rest of my post is nonsense, it just means it doesn’t necessarily get to the bottom of things as directly as I suspected and wanted to test.
I felt I had, you disagree. This is fine, don’t flip the fuck out.
To be clear, I’ve been well aware of the formula (x + y)^2 = (x^2 + 2xy + y^2) since I learned and repeatedly applied it correctly while at school.
You took my method of expanding (x+y)^2 as something like just “2xy”, or just “x^2 + xy” - only part of the full process at any rate & missing “subtotals” as you say, which makes sense from the way you’ve perfectly correctly presented it.
May I please request, at this point, for you to agree or disagree whether this adequately encapsulates where you think I went wrong? May I also please request if you think I’ve sufficiently acknowledged and shown understanding of the point of your contention?
If so, I invite you to consider the scenario where x = y, as done all the way back on page 4:
Using the same form as I did above just now, we now get (x + x) * (x + x) = (x^2 + 2xx + x^2)
Do you agree that this can also be written as (x^2 + 2xx + x^2) = (x^2 + x^2 + x^2 + x^2)?
More specifically, on page 4 we were covering the case that x = y = 1
so since (x + x) * (x + x) = (x^2 + x^2 + x^2 + x^2)
we have (1 + 1) * (1 + 1) = (1^2 + 1^2 + 1^2 + 1^2)
this can be written as (1 + 1)^2 = (1 + 1 + 1 + 1)
Am I right? Do you agree there has been no funny business or “switching up” so far?
A similar thing occurs when you have (1+1+1)^2 = (1^2 + 11 + 11 + 1^2 + 11 + 11 + 1^2 + 11 + 11)
Obviously the right hand side can be expanded to (1+1+1+1+1+1+1+1+1)
As I said in this post: "Consider the example (1+1+1+…+1), is it agreed that the “…” represents an endless string of “1+1"s?”
We covered the examples of (1+1)^2 = (1+1+1+1) and (1+1+1)^2 = (1+1+1+1+1+1+1+1+1). I’m sure you don’t need any more examples of adding an extra 1 each time to solve (1+1+1+1)^2 and so on?
So we ought to be able to jump all the way to (1+1+1+…+1)^2, I feel.
Each time we progress towards this from (1+1)^2, through (1+1+1)^2, through (1+1+1+1)^2 and so on, we get an answer that can be written as (1 + “some finite number of zeroes” + 1)^2 = (1 + “some other finite number of zeros” + 1)
I want to stress that in these finite examples, I acknowledge that “some finite number of zeroes” on the left hand side is not the same as “some other finite number of zeroes” on the right hand side.
Are we in agreement that I acknowledge this and there is still no funny business or “switching up” so far?
The problem is once you transcend these finite examples to the infinite, by the definition of infinity you can no longer bound “some finite number of zeroes” or “some other finite number of zeroes” - they are both endless. There is not an end to either, such that one’s end can be longer or further than another.
Are we in agreement that this is where you think the funny business happens?
My argument is that if you stick strictly to the definition of infinity, (1+ "infinite zeroes +1)^2 = (1+ "infinite zeroes + 1)
That is to say, (1+1+1+…+1) * (1+1+1+…+1) = (1+1+1+…+1)
As I understand it, you distinguish infinite, endless strings of 1s being added up from other infinite, endless strings of 1s being added up. Are you in agreement with this?
You represent the rationale by showing the relation that finite examples show as you tend towards infinity, which is correct.
You represent the rationale by showing the construction of the infinite examples and how they are constructed differently, which is also correct.
Do you agree that I acknowledge your rationale fairly and accurately?
Do you agree that I understand where our arguments diverge?
Do you agree that infinity, by definition has no bounds in order to say one is larger or goes further than another?
Do you agree that this on topic and relates to where you think I made a mistake here:
Why is it so hard to read what I’m saying, instead of forcing it all into something that sounds like a loaded question, under the guise of "well it’s just a simple yes or no question "
Why does it feel like you’re trying to trick me into warping what I’ve said into something you can dishonestly and dismissively construe as either dumb/malevolent/corrupt, when the reality is far from that?
Everything you need to know about what I’ve actually said is in my words. Excuse my suspicion of you, but it’s firmly justified by how you’ve been treating me so far. You haven’t presented yourself as trustworthy or honest one bit so far - can I trust that this has changed?
To be clear what I’m answering, I’m assuming that by “Sum the products”, you mean in calculating (1+1+1+…+1) * (1+1+1+…+1), yes?
In full answer, in case you’re trying to trick me:
At every step so far in this discussion I have calculated (1+1+1+…+1) * (1+1+1+…+1), where “…” is FINITE as (1+1+1+…+1)^2
At every step so far in this discussion I have calculated (1+1+1+…+1) * (1+1+1+…+1), where “…” is INFINITE as (1+1+1+…+1)
In both cases I have properly performed the calculation and did not make the mistake you thought I made.
To also clarify just in case, for the sum of: (1+1+1+…+1) + (1+1+1+…+1), where “…” is INFINITE, I used one method of adding term by term to get (2+2+2+…+2), which can both be presented correctly as 2 * (1+1+1+…+1), and again, where “…” is INFINITE and since “2” can obviously be presented as “1+1”, it can also be presented correctly as (1+1+1+…+1), again, where “…” is INFINITE. Hilbert’s Hotel was set up nearly 100 years ago to visualise these exact kinds of paradoxes when dealing with infinity, I am not communicating anything new or controversial here.
This is in contradiction to where “…” is FINITE, in which case (1+1+1+…+1) + (1+1+1+…+1) = 2 * (1+1+1+…+1), always.
Assuming what you mean is contained in the above, which sums up everything I have been saying in relation to mathematically operating on “infA”, at every step so far in this discussion, then I have properly “summed the products” every time so far in this discussion.
Now, are you going to disregard the correct distinctions that I’ve been making, in order to make out like I’ve said something obviously mistaken, even to me this whole time, which I’ve not actually done, and explained why several times?
Again, excuse me if you’ve taken a turn and are no longer trying to misrepresent me. It’s perfectly understandable if you thought I said something that I didn’t - there’s always room for improvement in everyone’s wording including my own, and I’m sorry if I’ve ever misled you - I’ve done my best to prevent this and rectify it where it appeared to me to be needed. At every step I’ve wanted to hear what others have to say about mistakes they think I’ve made and with 100% honesty I have always willed to accept them if they’ve validly been pointed out. Of course, if they’ve been incorrectly pointed out, I have done nothing but try to correct this with 100% honesty and with no intention to distract, or deny any truth at any point, even if anyone has believed this is not the case. Quid pro quo, to check if you’ve actually read any of this, let me ask you a question: have you read and understood everything I’ve said? This is a separate question to whether you agree with it, which you can answer too if you want, separately.
Because 3 times now I have asked for the very simple conformation, “I disagree” but you insist on the obfuscating tactic of dodging and trying to rewrite the narrative. It only sounds like a “loaded question” because you are trying so hard to divert from it. Grow a couple.
Yes, I am referring to your 3rd grade arithmetic error that you refuse to correct.
That wasn’t your argument, but that is what you did in effect.
And that is where you go off the track.
I showed you a pretty simple rule to follow. The question is, “why do you think that the rule has to change just because you no longer can see the end of the chain?”
So far, you have presented nothing at all, even in your added faux pas that justifies changing how to multiply merely because you don’t think that the chain has an end.
Which was just Sil-ly.
Hilbert’s Hotel is a joke for the simpleminded.
I explained your 3rd grade issue with this:
Simple question
Simple Question
SIMPLE QUESTION:
What is the first line in that explanation, given long ago, that you see to be in error?
“omg. if you read Aristotle’s poetics you’d recognize the peripety there. Duh. The comic tells a joke which isn’t funny at all, and in making a histrionic display of appreciation for telling it, he doubles his idiocy and becomes the brunt of the joke himself, thus creating the sense of the comic.” - prom75
for all this technical talk, the moral of the story is really rather simple. wittgenstein is suggesting that we are bewitched ‘metamathematically’ when we take an otherwise perfectly sensible language of rule governed abstract symbols - in this case numbers - to use for quantifiying our experiences of things, processes, events, durations, etc., … all of which are finite and limited experiences - and naturally mistake the intensional use of the language as a proper representation (or i should say evidence for) of an actual, extensional instance of an ‘endless’ experience (e.g., counting infinitely). we extend the rule beyond our experience of what the rule can yield as extension in normal experience, and imagine that to simply continue to follow the rule would necessarily result in an extension of the infinite. but he points out that endlessness can’t be done, and is therefore a senseless notion despite it being perfectly logical that the rule (intension) should produce an infinity if it is simply followed through endlessly. it’s that concept of ‘endlessly’ that gets us all befuddled. we are writing a list… and we stop. we’ve created a set. but why should’t we be able to list without ever stopping? it’s here that the intensional and the extensional intersect and create the confusion. the extension of the list is completed whenever the listing stops. it reaches an extensional terminus, so to speak, while its still possible to continue with the rule indefinitely. therein lies the bewitchment.
so think about that quote above, again. he says ‘no such thing as all numbers’. you will never complete a finished set of all numbers… but what you can experience directly is applying the rule. following the rule in a direction toward infinity is only ever an ‘approach’, as sil put it. if one insists that an ‘actual’ infinity can exist, well this is some kind of quasi-platonic realism so far divorced from empiricism that it’s… well it’s just fucked up, man. wtf.
I disagree that it is merely language and “abstract notation” that brings the conclusion that there are things (although not objects per se) that have infinite qualities, such as distance. To suggest that what is true is ONLY what we have experienced directly is to say that we have NO capacity for conscious awareness beyond our eyes and ears, that we are but forest animals.
It appears that Wittgenstein is denying that at least some people can reason. And I must point out that he, himself, is using that very same reasoning in defense of the notion that it shouldn’t be used as reliable evidence.
I am really getting the impression that the guy wasn’t all that bright. And I will say again that it is politics that dictates reputation, not performance. Perhaps the politics of that era had incentive to promote the lack of effort to believe in reasoning and science. In fact, I have little doubt of that.
What religion was Wittgenstein? I could look it up, but the question is mostly rhetorical. I think about such things before taking anyone’s reputation and their preaching very seriously.
When you hear something that seems to not make sense and you have to rely on thier reputation, you must then examine their politics and religion.
I don’t think that philosophy should be a product of ad hom. But reputation IS ad hom. If you say that because he has such a strong reputation he should be believed (which you have done) then you have already invoked an ad hom argument, merely in his favor rather than against him.
His reasoning or logic should stand alone. But it doesn’t appear to do so. He seems (by your own account) to be proposing the axiom that unless we directly experience something, it doesn’t exist. And that presumes complete inability to logically project. Science is a demonstration that logically projecting works extremely well when carefully checked for errors.
As it stands, what is said about him testifies that his words are contrary to the evidence that we have directly experienced (technology). His argument is defeated by his own proposition.
very nice, 524, and indeed true. the ad hom works both ways, and i do brag on W quite often, but i’d never encourage anyone to take his word just because he’s like grease lightening. i’d expect people to also notice and give some consideration to the peer review his ideas have received by other major philosophers, typically in the analytical tradition. but therein lies the rub; if you aren’t big on the analytical tradition and its history, you’d probably not find the significance of his thought.
That’s some hobby you got there.
I do think your analysis of JSS is correct… his arrogance on his own ideas hindered him from listening to others… because he was right. Were his theories ever peer reviewed or proven?
Politics? I dabble too, but on the fence between volunteer and career.
Ah some content, I knew I could find some somewhere in amongst the accusations - got faith in ya, buddy!
Who said the rule changed? The rule is the same, but the result it would get to, if it could, is not. One endless string of "1+1"s is not endless more than another endless string of "1+1"s. They’re both endless…
I get your simple mistake, instead of concluding that infinities result in paradoxes, you represent infinities paradoxically. Endlessness going on further than endlessness? - nice try, but no.
No. It’s amazing how you don’t see the connection here…
Like I just said, the rule doesn’t change for how you construct these sums, but what you get differs depending on whether they’re sums of a finite or infinite series:
This method is fine while “…” is a finite number of "1+1"s. Agreefor finites, but disagreefor infinites - like I already covered - not because the construction is different, but because what you tend towards defies this [n] structure you’re imposing on it. That structure is valid for finites because by definition they have ends to distinguish [n] from [n+1] but infinites by definition do not…
You’re distinguishing one endless string of "1+1"s from another during the course of the same summation i.e. imposing a bound: a finitude - to separate an endlessness in the middle of its endlessness.
It’s as though you’re saying that continuing an endlessness on a new line makes the endlessness different. New steps in the same endless process don’t give ends to an endless process.
Again, the method you’re using is fine while “…” is a finite number of "1+1"s that justifies a distinction that could be validly represented by the structure of [n] followed by [n+1] and so on.
More of the same.
More of the same - building contradictory assumptions to produce a contradictory result.
It’s like, because you don’t understand the basic distinction I’m making in your third grade elementary maths, you don’t think I get the elementary maths… even though I keep saying I agree with the elementary maths only for finites. I’ve been saying all along you’re using your intuitions about finites to apply to infinites. But somehow, because I’m showing you something you don’t seem to understand, “I’m distracting” from what you understand. So, to you, my explanations of what you don’t understand have been attempts to “forget” that we need to stick to your elementary mistakes. When you graduate from third grade elementary maths and eventually get to infinites you’ll see the difference (clue: it’s in the name!)
The alternative that you’re completely missing, that there’s something you’re missing, is what I’ve been covering all this time - but it all just completely bypasses you… how are you ever going to grow? At this point you’re making it very clear that learning and growing is not your intention. All I can do is continue to try and show you where you’re going wrong and put up with the presumption that if someone else is seeing something that isn’t covered by your understanding, they either don’t understand your understanding or are trying to distract from it. Your lip service to finding presumption “sinful” and understanding infinities is just that: lip service.
That was almost a definition. One times ANYTHING is that same thing. It doesn’t matter what that thing is. There is no “approaching”. It is a simple defined concept times one.
Now build on that simple definition to the point you’re missing that I’m trying to explain: is (1 * ) more or less endless than (2 * ), or even (n * ) ?
For finites it’s obvious: the ends of a series that equals “2n” get to twice the finite quantity more than the ends of “n”.
For infinities the paradoxes emerge: there are no ends of “2n” to be quantitatively twice as endless as the ends of “n”.
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