I have a cold, so you get a super-sized word salad.
How can I effectively approach presenting her with opposing facts?
You got to be more subtle than simply present facts. Read: How to Convince Someone When Facts Fail. In case of TL/DR I will make a quick summary:
- The more a fact challenges our world view (or worse, religion or identity), the harder it is to accept it.
View this as investment: if we invested a large part of our time and/or identity into something, acknowledging it is wrong means all this investment is lost, and that feels bad. If the belief is part of our identity, then we have to kill a part of ourselves, which is painful. Thus we choose the easier way out: ignore it, rationalize it away, shoot the messenger, etc.
Example: Galileo. He didn’t just challenge the Church’s worldview, but also their power. This ended with him having a chat with the Inquisition.
Example: it is difficult to convince someone they are in an abusive relationship, and often they will defend the abuser. Facing the truth would require lots of effort and pain: acknowledging that they wasted X years of their life in a toxic relationship, that they love someone who is toxic, then breaking up, being single, etc. Also realizing they have agency and could end it at any time can paint them as a consenting victim instead of a defenseless victim. So the easy way out is to deny everything and hold on to the hope that it will be fine someday. It's logical in its own way, but results in more suffering.
- The backfire effect "in which corrections actually increase misperceptions among the group in question."
Logical consequence of the above. If you challenge their identity/worldview, they may reinforce it as a defense mechanism.
Example: an Apple fanboy purchases a $2700 laptop, which then dies because of bad design or inadequate weatherprooging. At this point, if I laugh and remind them that my 5 year old Thinkpad which is spill-proof and dented all over the place from various falls still works fine, and is cheaper, more practical and just as powerful than their piece of junk, they will simply get pissed, fangirl over Apple for 20 minutes, and purchase another $2700 piece of garbage because owning Apple makes them special. It's identity, it is completely irrational, good luck challenging it. Also it is a social status symbol (see below) which signals their belonging to a smarter class of discriminating geniuses, so its performance doesn’t actually matter. Fashion accessories are not judged by CPU power.
Now, if you are an Apple sheep, you should be angered by the above paragraph and inclined to shoot me, and thus not inclined to hear about how the Thinkpad is a much better engineered product. Thus not only did I fail to convince you, but I also reinforced your pro-Apple bias. This is a quick example of how not to convince someone. (Side note: customers are in an abusive relationship with Apple. They will blame themselves when their junk hardware fails due to bad engineering. For example if their phone doesn't take calls, it's because they're holding it wrong, not because the designers put the antenna in the wrong spot. Gaslighting, anyone?)
Among her beliefs, challenge the one that will least upset her worldview and identity. Don't set out to demonstrate that her father is a nutcase, that's too big a challenge, it’s a direct attack on her family. Instead, pick something really tiny. The more insignificant, the better. You know her, so it's up to you to choose.
Besides, you say she is the only one her father talks to about this (which is unsurprising). This may mean that he wants to keep her that way, in order to have an audience, and you will have to indirectly fight his influence. At some point you will have to help her realize that she can still get along with her father without believing all his theories. Tread lightly.
You also have to pick a belief that you can actually challenge. So, on to part two, about how to disprove conspiracy theories.
You can't prove something doesn't exist. It is well known that politicians are actually reptilian aliens wearing skin suits! Actually, bugmen are way cooler, so it’ll be bugmen. If you catch one and dissect it though, it 'll probably be just a human. That does disprove the assertion “all politicians are bugmen” but doesn’t disprove “some politicians are bugmen in skin suits”. You just caught the wrong one, it was a fluke, the real ones are still out there! And since they’re part of the super-duper-secret conspiracy that rules the world, then by definition, you don’t know which ones. They’re hidden in a secret bunker under Area 51, and you can’t prove it doesn’t exist unless you dig a very deep hole. And even if you dig, the tinfoils will say you dug in the wrong place. I can feel their mind control waves sneaking into my brain!
Therefore, don't challenge unfalsifiable beliefs right now. It is better to challenge an easily falsifiable claim. For example, flat earth: there is only one earth, which dodges most of the “all are/some are” silliness above. Also, we know where it is. It is a positive, thus provable/falsifiable. And Eratosthenes did it with a stick, so you should be able to do it. Stock up on arguments online first. Basically, first understand who you are convinced that the earth is not flat, using observable facts and not argument of authority. These days a simple argument would be the existence of satellites. Having her explain how to hang a satellite in the sky above a flat earth should be an interesting question, depending how gravity works on a flat earth. Besides, if the aliens from the space cigar land on the wrong side of the flat earth, will they fall down? This question needs more beer.
Anyway. You can (and should) flip the script and have her try to convince you that the earth is flat. Frame it as an open-minded discussion, start on equal terms. This is a lot less aggressive than dumping arguments on her and expecting her to believe you out of authority.
You need to pretend and act like she could convince you, so she feels you are on equal grounds. She won't be able to convince you of course, which should be enough to make her doubt this particular belief. But don't push it too far, or expect success after one conversation. If she leaves with doubts, like saying “Hm, you have a point”, she'll think about it later and this is a good thing.
You might even make a few concessions. For example you cannot disprove that Vladimir Putin (who is also an alien) secretly rules over the bugmen. So you could concede it is extremely unlikely but not rigorously impossible (this assertion is true, btw). It costs you nothing but she’ll probably like it. On second thought, astrology would perhaps be a better subject to make concessions on (it is impossible to prove it does not work after all). Or some other junk like numerology. Make sure to remind her that if you can’t prove it’s wrong, that doesn’t mean it’s actually true.
It should be effective to teach her a bit of scientific mindset: Okay, let's seriously consider the flat earth hypothesis, have HER list arguments for and against. Time travel back in high school when you wrote dissertations. You can help, but don't act like a teacher yet. Let her weigh the arguments and try to prove/disprove them, write stuff down, etc. Your real goal is not to teach her that the earth is round, it is to teach her how to debunk the rest of her conspiracy theories by herself. Teach someone to fish, you get the idea.
I have posted some information asking for facts on now 5 forums (how does the Teslas material hold up in space, how are cameras able to stream from space, etc)
Bad choice, this one is too scientific and complicated. Also these questions are legitimate engineering questions that you don't have answers for. For example I wondered if the lithium cells pressure relief safety valves would hold in vacuum, which is not answered by handwaving. Tesla engineers probably tested all this and rmeoved anything unsafe, but you don't have proof. I posted the question here.
It will be interesting to see the answers, or lack thereof.
Now, the article I quoted gives a few hints, most of which are covered by the above approach, which leaves...
1 keep emotions out of the exchange
6 try to show how changing facts does not necessarily mean changing worldviews.
Besides the obvious (don’t get angry), the most important thing to avoid would be shaming. This would be "you're an idiot for holding such beliefs" or outright laughing at her. While shaming is one of the most popular tools to make someone conform to a worldview/culture, as in telling your daughter "how dare you get out dressed like that!" in this case it will backfire.
The purpose of shaming is to outgroup the target. Basically it is a threat of casting someone out of the safety of the tribe, onto the outside where they will be devoured by saber tooth tigers (like back in the day, you know). Its effectiveness rests on the target’s lack of other options: it’s “this society's way or the highway”.
However your friend has options: she is already out of your tribe and belongs to her own conspirationist tribe which is closer knit together than yours. Thus, if you shame her, she will retreat back towards her tribe and you will not only fail in convincing her right now, but also reduce your future chances by reinforcing the bond between her and those who enable her by feeding her wacky theories.
Thus, you can laugh at her ideas only if she laughs about them first (but make sure you laugh less than she does). And you should admit that she will laugh about some of yours at first, and you will promise not to get butthurt and whiny and defensive about that, and above all you will not use words like “uneducated” or say “I don't understand how you can think this!”, rather say “what are the reasons behind your thinking?”
The word “uneducated” hits back. Smart/educated people can be better at rejecting fake news, but they can also better rationalize fake things as true if it confirms their biases, or if it makes them feel unique. Many scientists pursued crackpot theories hoping for celebrity...
Obvious example: "Daughter! How dare you get out dressed like that!" -- Daughter is outgrouped from your tribe, but she joins another tribe, screams "I'm a feminist! No slut shaming! Grrl Power!" so your persuasion effort fails. Shaming tactic backfires. Same for hardcore bible thumpers trying to shame the gay away from their children: it attacks identity, thus it is worse than “not working”, it backfires, makes everyone unhappy, etc.
Another one: the Apple fanboy I quoted above. They also have another option. If you shame them, they can join the fanboys tribe where their fellow worshippers will fawn over their shiny overpriced garbage which makes them feel so warm and good and special inside. Until the next model comes out, at which point the fanboys will shame each other into buying it.
This example illustrates another important point: the macbook can be an entry ticket into an exclusive social space, like “professional video editors”. Likewise, a belief can be a requirement for belonging to a tribe, and holding contrary views (even if they are true) will get you kicked out, or at least criticized. Thus is it important to start small and go slow. Challenge one simple innocuous belief, and wait for her to notice that the sky doesn’t fall on her head, and her fears of no longer belonging to her “community” were unjustified. She can still stay friends with her tinfoil buddies, still have a good relationship with her father, she simply needs to be more critical. In other words, study what James Damore did, and do the opposite. A huge dump of rational arguments does not work in this case.
Now, let’s fire the big guns: you asked for it by mentioning the name of the Orange Beast at the end of your original post.
Liberals shame conservatives all the time for being all kind of deplorable uneducated redneck whatever-ists, in a misguided attempt to out-group them. Notice how this is basically doing everything wrong with respect to what I wrote above, it checks every box to trigger a massive backfiring. As expected, this causes the target of such shaming to retreat back into their own tribe, then radicalize and respond to the perceived aggression, and then Trump gets elected. It's very simple. I watch it happen from the other side of the Atlantic and giggle.
Likewise, the worst possible thing to do if you want to convince someone is to shame them for something they can’t change about themselves (like skin color, sex, birth place, sexual orientation, and of course being an idiot). In this case, since they can't stop being what you same them for, their only two options are either to take the shame, or more likely, decide you are the problem… Thus, don't shame her because of her father: she can't change who her father is.
This last example emphasizes that you’re not in this to prove her she’s wrong in order to feel good about yourself or virtue-signal, which is the wrong attitude. As you said in your question, you do it to help her, and therefore your personal feelings are less important than your mission objective.
One last thing: we tend to prefer clear-cut opinions (be they right or wrong) because they are simple, don’t need too much thinking, and many people hold the same opinions, so it is easier to join a tribe and make friends. See collective hysteria.
Saying “I don't know” takes more effort, and alienates everyone who is absolutely sure things are one way or another… but when you don’t actually know, it is the only correct choice. This isn’t about the flat earth, but about some of the other stuff. It is likely that some beliefs she holds are simply placeholders in order to avoid answering a question with an uncomfortable “I don’t know”. So, if you don’t know about something she’s asking, don’t make a big deal out of it. Show her it’s fine to now know about something and that you don’t feel the need to invent something just to plug the hole.
If you convince her to switch from “secret alien bugmen rule the world” to “I don’t know who rules the world” then that’s already a good step in the right direction, perhaps next month she’ll make another step…
Here’s a specific example. I’m aiming high for this one. This is the boss fight at the end of the last level!
Thus, I present you the most famous twin conspiracy theories: in the left corner of the ring, the Trump-Russia collusion. In the opposite corner of the ring, the other side has their own counter-conspiracy theory with intricate plots involving the FBI, NSA, and possibly Jack Bauer. Both sound like Tom Clancy on LSD. Hard evidence is pretty scarce, but that never stopped a true believer, right?
Is it true? Who wins? I don’t know! This will take years before the jury’s out… but what I want you to do is to pick one of the two conspiracy theories (if you haven’t already) and try to picture someone trying to convince you that yours is fake news, and the other is true, definite 100% since they heard it on CNN/FOX.
This should be a pretty funny (and quite challenging) thought experiment. It will also allow you to understand how she feels when you tell her the earth is round, which I think should definitely help you help her.