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.
Nevertheless it is the case. We think 4, 4 is 0, therefore "0=not what you think" isn't true.
Voyager
1yr ago
Did you just claim less than 0.0001% of people think 2+2=4?
4 is what everyone thinks, 0 is merely a different representation of the same object. So people are giving the correct answer, you're just insisting on a different formulation.
Voyager
1yr ago
Then explain how that's supposed to be a response to my point, please.
My point being that in Z/4Z, 2+2=0 and 2+2=4 are the same statement. Ergo, 2+2=0 is merely another way to write down what we think. We might not literally think it, but we are thinking an equivalent statement.
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
(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 took the liberty of clarifying my position instead of answering the badly posed question. Naturally modular arithmetics is not the same as integer arithmetics.
"2+2=4" is true in both, only in one 2+2=0 is also true.
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.
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
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
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
In your opinion, which isn't infallible.
Is that supposed to be a counterargument?
This is not enough.
Yes it is. Listening to your case and engaging with your argument will make me change my mind if your case is convincing enough.
Therefore it's impossible for you to be convinced of anything (about Alice and even less of Bob), and there's no point in me even trying.
No, it's still possible for me to be convinced of true things.
You'e right there's no point trying to convince me of a false statement about math. Instead you should let yourself be convinced by me.
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
No it won't.
Now you're making an unsupported assumption about my character instead of an argument. Retract it and apologize.
Obvious circular reasoning. You believe X is false, and you say it's possible for you to be convinced that X is true if X were true, but X is false, because you believe X is false.
No, I proved X is false separately. "X is false, because I believe X is false" is not an argument I've made.
Do you accept the possibility that X may be true? Yes or no.
No. X is a mathematical claim, and it's proven false.
Note that if you make a new argument I will consider the possibility again while analyzing your argument.
Voyager
3mo ago
I'm not sure if averages will necessarily be enlightening, because we can easily imagine a multimodal distribution. On one hand, transition doesn't necessarily lead to removal of all biological sex differences, on the other it's a medical procedure that can have negative health effects impacting athletic performance. Both seem very plausible.
If, as an exaggerated toy model, transition half of the time does nothing, half of the time completely cripples the patient, we'd observe it averaging out, but half of transwomen would easily dominate.
We don't need to look at averages when we can look at individuals. If we take a specific individual and compare their relative performance before and after, that tells us what transition did in their case. If Lia Thomas or Laurel Hubbard go from average in the male division to record-breaking in the female division, then clearly transition doesn't guarantee to nullify the sex advantage, and therefore shouldn't allow competing in the female division. It doesn't matter if even 90% of transwomen are average and some have health issues - the women competing against Thomas or Hubbard still got robbed.
(2+2=4 (mod 4)) might be the same statement as (2+2=0 (mod 4)), but not (2+2=4).
So you're now saying that 2+2=4 without further context is not the same statement as 2+2=4 (mod 4)?
Dare I hope you finally saw reason? That you accept that you are not allowed to say "2+2=4" without context and pretend you mean modular arithmetic, and that "2+2=4" is simply true?
(And if you're just going to say the () change the meaning, then you should start off defining your idiosyncratic notation, and by "start off" I mean you should have done it 10 posts ago when you first used it. And then you should retract your argument, since it's a non-sequitur obfuscated by misleading notation.)
Voyager
1yr ago
You just accepted your mind cannot possibly be changed below.
I accepted that my mind cannot be changed on a proven statement. This naturally excludes the possibility of a convincing argument. But in the general case, my mind can be changed.
That's the end of the road then.
No, it remains to convince you that X is false.
Voyager
3mo ago
Since no one has ever demonstrated a statistical advantage in win/loss records and we have weak priors about innate ability, we should assume then null hypothesis for now and let trans women compete.
I disagree. The situation is that normally ineligible people are demanding special allowance, on the basis of arguing that they have a way to nullify the impact of the property that makes them ineligible. The onus is on them to prove that it's really nullified. If we don't know either way, we play it safe.
If they win every contest they ever go to and no one can compete with them, that's probably unfair.
Doesn't need to. If the transwoman only makes 3rd place, then the woman in 4th lost the bronze medal. If that's due to an unfair advantage, that's bad and she was treated unfairly.
There are a trillion local and regional sports records for a trillion things, records get broken literally every day by cis athletes.
But not by mediocre cis athletes.
Hubbard and Thomas perform better than before, by a lot. This shows that transition gave them an advantage.
If we took away entire demographics rights because of 2 anecdotes, we'd be in a lot of trouble as a society.
This isn't a rights issue, there is no right to compete in the women's division with a male body. Cis men don't get to, and no one has a problem with it. The question is whether transwomen should get a special allowance.
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
No, I said (2+2=4 (mod 4)) might not be the same as (2+2=4). I very clearly never said what you claim I'm supposedly "now saying": I said "might not be", never said "is not".
You also said
(2+2=4 (mod 4)) exists, which is not the same as (2+2=4)
So yes, you said it. Do you want to retract that statement now?
YOU claimed (2+2=4) is just another representation of (2+2=0 (mod 4))...
I claimed that 2+2=4 (mod 4) is another representation of 2+2=0 (mod 4). I specified "in Z/4Z" the first time I made my statement, I referred to modular arithmetic the second time, I clarified my statement to the literal same when you asked.
The question I answered referred to 2+2=4 in standard arithmetic(although it took you 5 comments to finally clarify your ambiguous question), which makes it a different question with a different answer.
You're trying to cut out the context, which makes it a misrepresentation of me. Retract and apologize.
I'm willing to engage in open debate with you, and your chance to convince me depends on the correctness of your position. You can't expect to convince anyone if you don't have a point. An open mind does not require me to ignore knowledge I have.*
If you refuse to talk further when you turn out to be wrong, you will never learn anything.
*And you don't see it, but I did some research to verify my position before responding. Do you insist Russell should doubt 1+1=2 after writing PM?
And if you make a new argument, I will do more research to refute it.
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
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
And who decides the correctness of my position?
The correctness of your position is a matter of fact. No one decides it, we research it. I have done so and found out it's not correct. If I happened to be wrong about that, there would be convincing counterarguments you could make, proving me wrong. But I notice you're not even trying to argue X anymore.
How is this not the definition of circular reasoning?
It's the definition of a strawman. I have not made the circle of reasoning you describe. I have proven that X is not true, separately.
Only because 4=0. So 2+2=4 is true, and the central claim of your substack post is wrong.
No. Some basic mistakes:
Isomorphy requires preservation of structure, in our case the structure of respective additions. This is not the case: Addition in
{0,1,2,3}works different than inℤ/4ℤ.We don't say an element in a structure is isomorphic to one in another.
(ℤ/4ℤ)*is an entirely different structure. For starters, it contains only 3 elements. (The*signifies we're excluding the 0.)More options
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