It may be represented that way, but they are not the same thing.
4 and 0 are equivalent as representants of the residue class. If you can write down 2+2 where 2 refers to a residue class, the answer can be written down as 4.
your claim that 4 (sa) = 0 (mod 4)
How many times do I have to ask you to stop misquoting me?
Voyager
1yr ago
You are trying to distract from what you said
No, I'm trying to explain what I said, because you keep removing the context:
- 2+2=0 (mod4) is not the same statement as 2+2=0
I said 2+2=4 in standard arithmetic is not the same statement as 2+2=0 (mod 4). I insisted on making this explicit, because it came up on the context of mod 4. And because I suspected you were trying lead me to a contradiction, so I made sure to speak clearly, proofing myself against it.
So if you cut out the important context, and then try to construct a contradiction that doesn't work with the context included, you're misrepresenting me.
Retract and apologize.
(Assuming here you meant to write 4 instead of 0, but otherwise it would just be an even worse misquote, so I'm charitably assuming it's a typo.)
But it's pretty clear that you meant 2+2=4, not 2+2=4 (mod 4), because the former is what most people think is true.
I meant "2+2=4", "in Z/4Z" omitted, as in your original setup*. When it's about people's reaction to the statement, formulation is important.
*But in my case it was available from context, whereas in your example it was deliberate misdirection.
People think it's true, while they're denied the context. But given the full context, which changes the meaning, it's still true.
It's also quite peculiar that you're doing what you're accusing me of: I pointed out you were contradicting yourself, you tried to weasel away, and when I nailed you down, you tried to ignore it. Do you stand by the statement
(2+2=4 (mod 4)) exists, which is not the same as (2+2=4), and you finally accept that they are two different things.
?
Voyager
1yr ago
Really? Wasn't your entire argument relying on the fact that if the arithmetic wasn't specifically specified, then certain arithmetic was always assumed?
It has been specified beforehand:
in Z/4Z, 2+2=0 and 2+2=4 are the same statement.
If in response you talk about standard arithmetic without clearly denoting it, that's just you communicating badly again, which is why I made you add a clarification.
For the record, when I ask ChatGPT if it's always necessarily the case, it answers "no". It says that's not the case in other arithmetics. Weird that it interprets math like me, not like you.
You can get ChatGPT to tell you all sorts of bullshit, including self-contradictions. It's not an authority for anything.
it's standard arithmetic
That makes it a derail, since we were talking about modular arithmetics. But just for the record, the answer is no then.
Voyager
1yr ago
It's a badly posed question because it's not fully specified, namely, you're not stating where (2+2=4) lives.
Normally this wouldn't be a problem, because we can assume it's the default if not otherwise noted, but a) we'e explicitly discussing multiple number systems here and b) you have already proven you can't be trusted not to omit relevant information.
Your question is ambiguously stated. Normally it wouldn't be, but have earned a reputation of communicating badly. Define whether (2+2=4) in your question is integer arithmetics or (mod 4) (or something else) and I'll answer your question.
Voyager
1yr ago
It's a badly posed question. You have been weaponizing ambiguity the whole time, I'm not accepting your framework without adding context.
If you want a question answered, state it clearly.
Voyager
1yr ago
There is nothing to interpret, it's straightforward math. I'm merely writing it down.
Voyager
1yr ago
(2+2=4 (mod 4)) and (2+2=0 (mod 4)) is the same statement. If you omit the (mod 4) part, you're merely communicating badly. Again.
Voyager
1yr ago
I'm not ignoring it, I'm rejecting it has any relevance. Everyone doesn't know a lot of things. This is hardly new or interesting.
But the existence of modular arithmetics doesn't make 2+2=4 incorrect. It merely makes 2+2=0 another representation of the same statement. So "most people" remain correct.
Voyager
1yr ago
But 0 is what we think, because 0 is 4. You're just changing the representation. It's like saying "You think 2+2 is '4', but it's actually 'four'".
Also, the claim in your post was
So there you have it: 2+2 is not necessarily 4.
which is wrong whether or not 2+2=0 can be true.
Voyager
1yr ago
Information is always missing.
Not information that is available and relevant to the argument. I already explained that to you. Stop defending your fallacious argument.
No, you are deliberately not engaging with my argument.
To the degree I am, it's because you're trying to set up a red herring.
Voyager
1yr ago
Yes, but the premise of this line of thought is precisely the opposite: it's not easy to prove Bob isn't racist, other other hand it's extremely easy to prove Alice isn't racist.
That's my exact point. If you prove Alice isn't racist, you haven't proven anything relevant. You're just nitpicking. The actual relevant question of whether Bob is racist is unaddressed.
But discussing is not accepting. You are arguing that Bob is a racist, but you are nowhere near accepting the possibility that he might not be.
I'm accepting the possibility Bob might be racist to the degree I'm required to: I'm listening to the supporting case and engaging with your arguments.
Your arguments that Bob is racist just aren't convincing. You're mainly arguing he's as racist as Alice and I happen to know she isn't. And instead of leaving it at that until you make a better argument, which I could, I'm trying to work out why you think Alice is racist and how it applies to Bob, and arguing against that.
You are not willing to accept […]. Which proves my point.
No, I'm not accepting your point because it's false. You don't get to twist opposition to your argument into support for your point.
Voyager
1yr ago
So it's essential.
No it isn't. You will never encounter it in most math fields. Philosophy mostly is what you do when you aren't busy with concrete problems.
Depends on what you mean by "doubt".
What should an engineer do who needs to calculate 1+1 to design a bridge? I hold that anything but "answer 2 and move on" is wasting time that could be used to build a bridge.
Voyager
1yr ago
If a person says "Bob is as racist as Alice", and I show that Alice is not racist, then says, "OK. Bob is as racist as Mary", and I show Mary is not racist, "OK. Bob is as racist as Linda", Linda isn't racist. Wouldn't it make sense to doubt whether or not Bob is actually racist?
Okay, but if someone says "Bob is as racist as a KKK grand wizard", it would still make sense to doubt it. Conversely, if they say "Bob is as racist as Alice, because he's the author of the bobracial supremacy manifesto", pointing out Alice isn't racist just distracts from the point at hand. Yes, it's a bad metaphor, but the point stands.
Compare this discussion. I have refuted your argument that 2+2=4 is not unequivocally true, but I'm still willing to discuss the point you were trying to make without forcing you to come up with a new example.
Absolutely not. The speaker knows what the statement means, what the symbols mean, in what structure we're operating. The rest is just basic arithmetic over the natural numbers.
Voyager
1yr ago
If IQ does not exist or is not important, why does the left put so much effort into saying it does not matter. What difference would it make if blacks score lower than whites if these tests are meaningless?
That seems unfair in the exact same way as the mirror questions usually leveled in the other direction, that you're indeed arguing against right here.
If IQ is meaningless, that means there's a test that measures nothing important but people use it to judge your capability, in some cases even your moral worth as a person. People argue against helping the disadvantaged citing the meaningless number, arguing it implies they deserve their disadvantage. You also believe that disadvantage is actually due to racism.
If that reasoning is false, it seems very worthwhile to push against, just like "outcome differences between races are due to racism, therefore we need to fight this racism" is worthwhile to push against.
It's probably false, but honestly believing it's true makes speaking for it consequent, maybe even morally imperative. "If you really believed X you would shut up about it" is as unconvincing as always.
Voyager
1yr ago
The OP was definitely talking about "all female or all-Latino trading firms."
OP was talking about undervalued people making their own company. They're all female/minority because that's the reason they're undervalued.
That ain’t happening without selection pressure.
If women are as undervalued as is claimed, the best candidate for a given budget and the cheapest candidate of a given quality will pretty much always be a women. So you don't have commit to only hiring women to end up with all women - it's a natural consequence of optimal behaviour.
Likewise, the “Progressive half” of retail investors would be leaving money on the table if they opted out of the vast majority of the market.
Investors are always opting out of a majority of the market they consider less profitable - profitability just usually isn't as clearly demarcated. The point is that if the claim is true, everyone else is leaving money on the table - so the rational move is to go to the part of the table where the money is lying and pick it up.
Even if you're right, that's a nitpick towards the OP, not a rebuttal. There's still money to be made if you let in the occasional white male who doesn't want more money than he's worth.
Voyager
1yr ago
Some possible changes can only be peaceful to the extent that people submit themselves to victimization without complaint.
Then I think we should enable free speech, so the would-be victims can complain.
That's the flipside: Censorship can be weaponized as well, and the only real protection is free speech. And censorship is less likely to protect the victims, because the group that has the power to enforce societal change against them likely also can apply censorship against them.
Voyager
1yr ago
The subconscious will win out initially if entrenched (if not, it's just "huh, I learned something"), but it will remember the counterargument and be weakened in its conviction. Repeat a few times and you can change the subconscious mind. Adjusting with new information is just how humans learn.
However, I do believe that "You can't reason someone out of an emotion they didn't reason themselves into" is mostly* true, and "Scared of X" is an emotional response. You can potentially reason someone out of a position that incites emotion, but the emotion itself will remain. If I'm worried, then I might be convinced nothing will go wrong, but I will still be worried.
This obviously becomes a problem when, like in OP's example, people make it about the emotions themselves.
- It can be done and is called therapy, but it requires highly trained professionals, lots of time and effort, and the target's cooperation.
Voyager
1yr ago
If you're omitting the information of which week it is because it's not relevant, you're omitting information, and that means you can't use the result to support your argument, because it's missing information.
Voyager
1yr ago
But your clock would read 01:00.
We use this concept in programming all the time. If the week ends in Sunday we don't say that the day after that is Monday the next week, it's Monday
That's merely convention, omitting information that can be derived from context for brevity. If you want to make a formal argument, you need to include that information again. Everyone is aware monday is next week, that's why you don't spell it out if it isn't relevant, but if you're e.g. scheduling business on a weekly base, you might have to say "Tomorrow is monday, which is next calendar week".
Voyager
1yr ago
The right is skeptical of the state's ability to improve test scores and career outcomes for women and (non-asian) minorities but thinks the state is quite capable of convincing people to cut off their own genitals.
I think there's a fundamental difference in that career outcomes are measured over the entire population, whereas "making people trans" only affects a (more suggestible) subgroup of the target group.
The government can convince some people, particularly confused teenagers, to transition, and there are also surely some women who respond to a women-in-tech program.
The government can not convince everyone to cut off their genitals, and equally not convince women as a group to make life choices indistinguishable from men as a group.
As the user in question, I can clear this up: Although I didn't make this clear at the time*, I was referring to the statement "2+2=/=4 (mod 4)" (which was @felipec 's argument in favor of "2 + 2 = 4 is not unequivocally true").
This is a plain mathematical statement which I disproved (I didn't publish the formal proof because I wasn't challenged on the informal rebuttal). I consider mathematical proof adequate justification for certainty.
*Perhaps this led to confusion, I might revisit the thread with that in mind.
Notably, this is not the case, the argument in the original post was flawed and the example does not demonstrate what it was supposed to. I had pointed this out in another comment thread and referred to it.
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