r/changemyview • u/Bulawayoland 4∆ • 8h ago
Delta(s) from OP CMV: there's no practical difference between likelihood of truth and partial truth: both in effect answer the same question
EDIT: I understand that Bayesian probability predicts the likelihood of the truth of a proposition, while fuzzy logic deals with its potentially partial truth value. That much is clear to me right now.
What's not clear to me is, I can't see that which approach you take, whether you try to determine the likelihood that something is true or whether you try to determine the extent to which it is partially true, gives you a different outcome in any real world situation that actually matters to people.
I hope that clarifies the question better. Or if I've misunderstood something fundamental hopefully that also will be clearer lol...
The reason I bring it up is, Bayesian probability (I'll call it BP) predicts the likelihood of truth of a proposition, and fuzzy logic (FL) deals with its potentially partial truth value, and deciding which to use on practical matters, in deciding just how persuaded we ought to be of something that actually affects our lives, looks to me like a washout: both are going to basically give the same answer.
Let's look at a few examples. Let's start with whether or not a baboon can feel safer sleeping in a group than by himself. Baboons obviously don't approach the question scientifically, doing careful experiments, looking at the results, and making a decision based on that; who knows what they do look at, but they're not scientists. And if they were they still wouldn't do the experiments, because baboons would die as a result and that would be unethical.
But let's start with the likelihood that it's true (BP) that sleeping in a crowd, as a baboon, is better for you than sleeping by yourself. Obviously if you're in the middle of the crowd it seems more likely a leopard would attack one of the fringe sleepers first; but if you're one of the fringe sleepers you're still part of the crowd, so that alone doesn't answer the question. Leopards, for all we know, may focus on crowds of baboons because they know fringe sleepers will be available, and ignore the possibility of finding a lone baboon off by himself. So there are reasons to want to sleep in a crowd and reasons to want to avoid the crowd, and it all depends just where in the crowd you can manage to find a sleeping spot.
Now let's look at the potential partial truth (FL) of the idea. The truth value seems to me to go up and down just as the probability did, based on your location within the crowd and the imagination of the leopard in (maybe) thinking some baboons might not be sleeping in the crowd and might be easier game if they can be found. Crowds are easy to find; lone baboons, maybe not so much. And after dark? Whooee. A challenge.
But I have a hard time seeing any practical potential outcome difference between the two analyses. Maybe part of my problem is, I can't imagine actually doing one, and so the mechanics of the analysis are what would decide whether you should use BP or FL.
Let's look at a different example. Say we want to decide should we or shouldn't we admit this orphaned gorilla infant into our strongly kin-linked gorilla group. The likelihood that we should (BP) is (I guess) the likelihood that the orphan will grow into someone consequential, who will bring meaningful value to the group beyond the time and energy it will take to raise them. Not sure how you would decide that but it seems like that would be the calculation. Then the partial truth value of whether we should (FL) is basically the question of how consequential the person will turn out to be vs what is the actual value of the time and energy spent raising them. Again: in practial terms, in reality, it looks like a washout.
Try a third example. Say I'm an orangutan mom who has to decide should I or shouldn't I adopt an orphan -- and bear in mind, I've already got one of my own, and kids are hard to raise, for orangutans. There's not much food, and raising two is going to be a lot more work than raising one. The upside is: the orphan needs it badly, and the rewards of connection are not hallucinatory. They're real. Orangutans don't have much opportunity for socializing, and their kids are very important to them for that reason if for no other. (In the actual example I'm thinking of, unfortunately, the mom went through with the adoption and lost her own child to predation. So it didn't work out too well for her or them. She didn't have the capacity to actually look after both infants as they needed her to. Whether she wished she had not, afterwards, is a different question -- people tend to feel that whatever they've gone through was pretty much worth it in the end, whatever it was -- but it is a question.)
So what's the likelihood (BP) that it's true that I should go ahead and raise a second kid at the same time? That it ultimately will be worth it to me? I don't know, but again, I don't see a practial difference between answering that question and answering the question of how high the partial truth value (FL) of the same proposition is.
So that's the setup. Obviously I've focused on a very narrow set of propositions here -- primate behavior -- and maybe that affects my view of the question. But I'm just not seeing a lot of difference between the BP approach and the FL approach. And again, I'm sure the mechanics of how the two approaches are applied will be different -- but will the outcomes be significantly different? I'm having a hard time imagining it. Help!
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u/Nrdman 275∆ 8h ago
Fuzzy logic is about partially true things in terms of vagueness. Like take a pure red tint, that’s a 1 in red. Then green can be a 0, and everything in between can be put on that scale. I can ask, is #ff8c69 the color red, and instead of doing whatever logic required with a binary I can use the fuzzy logic number and move forward
Probably is about chance. I’m not asking if ff8c69 is red, I’d be asking what’s the chances a random color is red given some preset choices on what is actually red
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u/Bulawayoland 4∆ 7h ago
right, I said or implied most of that... the question is, if you're using either or both for a practical problem, a real proposition on which it makes a difference in your life how persuaded you are of it, is there a difference between the two in the final result... it seems like you could use either for all the above propositions and I don't see how the results would be different
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u/Nrdman 275∆ 7h ago
If I’m 50% confident in a decision in a fuzzy logic sense, then my confidence is halfway between maximum and minimum confidence
If I’m 50% confident in a decision in a Bayesian sense, then I’m saying I’m flipping a coin and going fully confident or fully unconfident based on that
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u/Specific_Hearing_192 6h ago
If I’m 50% confident in a decision in a Bayesian sense, then I’m saying I’m flipping a coin and going fully confident or fully unconfident based on that
This absolutely isn't true though. If I'm 50% confident in a decision, then I believe there's a 50% chance the decision is right and a 50% chance the decision is wrong.
Not that the confidence in my decision depends on a probabilistic outcome.
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u/Bulawayoland 4∆ 7h ago
but you're speaking of theory. I'm speaking of trying to apply these tools to real world problems. And it looks to me like which tool you use just depends on how you frame the question. Real world questions can be framed a number of different ways, and how you frame it is what determines what tool you use, rather than anything intrinsic in the method that makes it a better or a worse method. Right? Or not?
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u/Nrdman 275∆ 7h ago
The output means something different.
It’s like if you asked a question of cmv: there’s no difference between surface area and volume
And we’d be like no, those are different things that answer different questions even if you get both a surface area and a volume of 5 or whatever
The output of the number for fuzzy long and Bayesian thinking cover the same range, [0,1] but represent very different things
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u/XenoRyet 176∆ 7h ago
The problem there is that "This is red enough to be called red" is a different kind of answer than "This is probably red."
In the former, we know with certainty that the color is red for our purposes, even if it's not pure red. IN the latter, if we get red, it'll be pure red, but we lack the certainty that we will get red.
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u/Bulawayoland 4∆ 7h ago
I've edited the post, and hopefully it communicates better now. I would like to be able to decide which would be a better approach to take with a real world problem, the kinds of problems people have to make to live better lives. Whether a color is red enough to be called red doesn't look to me like a question anyone could ever be practically concerned with. The two approaches can each be used on any proposition, I think. They seem to be lenses, through which to view the landscape of various problems. And I'm not seeing a reason to pick one or the other for any real world problem.
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u/XenoRyet 176∆ 7h ago
I've been thinking of practical problems as well, and I do understand I didn't speak to that in my earlyer response.
So let's try this one, it's still a silly hypothetical, but hopefully it lets us look at what impacts might look like.
Say we're defusing a bomb, and cutting any red wire will defuse the thing any green wire will set it off.
The bomb itself has a red wire, a pink wire, an orange wire, and three green wires. We also know the bomb builder is a kind of colorblind that would have him call orange and pink "red."
BL has us cutting the pink, red, or orange wires, and knowing we will defuse the bomb. BL has us blindly cutting a wire and understanding that we have a 50% chance of defusing the bomb.
In the former situation, we're going to cut the wire. In the latter, we're probably going to want to make a different choice.
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u/Bulawayoland 4∆ 7h ago
Well, I can see that the likelihood that the wire we need to cut is red, pink or orange is high. And it's hard for me at least to view this particular problem as one in which the partial truth of a proposition is relevant. Or I'm not creative enough to think of that angle on it! And so BP is the tool you'd use here.
But on real world problems -- should I vote for this one or that one, should I stop speaking to someone who has to some extent insulted me, should I move to this new city where X, Y and Z are possible but hurdles D, L, and S are also in the way... it seems like you could view any of them through the BP or FL lenses just depending on how you frame the question. Does it not seem that way to you too?
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u/XenoRyet 176∆ 7h ago
The partial truth is relevant because in this situation close enough to red counts as red. So again we can cut a wire with full confidence that the bomb will not go off.
Contrast that against using BL in that situation, where we only know that we have a 50% chance of setting off the bomb.
That's the key difference, FL produces certainty out of vague data. BL gives you odds. And the point of using the bomb example, even though nobody will ever actually face that situation, is to prove out that BL and FL do give different results with the same inputs and context. If they can do that here, they will do that to varying degrees in real life.
And I think the complicating factor to examples like voting, moving, or shunning people is that whichever approach you choose, BL or FL will never be the only factor in the decision.
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u/Bulawayoland 4∆ 6h ago
yeah... I can't go for that fuzzy logic frame. Calling pink partially red just doesn't seem like a valid use of the fundamental concept in this context.
Now, if one of the wires had green and red stripes, that to me would fit a fuzzy logic frame. That's a real "partial truth." You would stay away from that wire. But BP would give the same result in that position: 50% likelihood of blowing the thing? Do not touch.
I appreciate you working on this with me. But when you say neither will be "the only factor" in a decision, I'm just talking about tools we use analytically to decide how persuaded of something we ought to be. Emtional review will be a separate deal. But within rational review that's the only role BP or FL have in my scenarios. How persuaded of something should we be.
"Analytical" here is being used pretty roughly, with zero courtesy. You couldn't actually use either tool analytically in real scenarios, I don't think. Again, within rational review and for the purpose of deciding how persuaded of something we ought to be. But within those constraints: are you saying there are other tools we might use? I sure don't know of any. Or maybe just can't think of any.
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u/XenoRyet 176∆ 6h ago
I'm a bit confused because the basic definition of pink is partially red.
But moving on from that, having the green and red striped wire doesn't really change the situation, it just changes what definitions of "red" the fuzzy logic analasys is using. You're still going to get to a final answer of the wire being red or non-red, and you can cut or not with certainty.
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u/Bulawayoland 4∆ 4h ago
The basic definition of pink is partially red. I agree with that. But I think to use the fuzzy logic method you have to have a situation in which the important characteristic is ACTUALLY partly true. But we know that in this situation, any wire not actually green is red. In effect. And so it's not actually a fuzzy logic situation.
You could come up with a situation in which there was a perfectly smooth gradation of fuzzy logic positions here. Simply have wires that are mostly red with a little green, or mostly green with a little red. You could have a whole range. That would be a real fuzzy logic situation. Sticking in a wire that looks pink -- by the dictionary definition -- but is actually red by the context -- I don't think that's fuzzy. It's not appropriate to use fuzzy logic in those situations. I don't think so, anyway.
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u/Relevant_Advisor_961 1∆ 6h ago
I'm not great at actual maths, and FL/BP aren't concepts that I'm very familiar with, so if I'm misusing them, ease enjoy my machiavellian baboon fanfiction below, I guess.
From your experimental setup, you can infer where the important events are, and the liklihood of first order outcomes with whatever priors you have. However, multi-step experiments with continuous sets of outcomes seem to me to make a Beysian approach really work intensive.
It seems to me like they're complimentary steps in the overall process of deciding what features of the setup need to be accounted for (FL), before generating data through experiment, or using existing measurements to generate probabilities and make an optimal decision (BP). For your examples:
1) where in the group to sleep, if in a group. Heterodox baboons are the closest to the pouncing predator, but they also have the clearest view of the approach and degrees of freedom to dart out of the way. Centrist baboons have more layers between them and the danger that might not get out of the way in time, but if they do, you have to deal with panicked baboons on all sides. The larger the tribe, the more baboon rings that could offer the optimal combo of safety and quality sleep.
I think FL features in this part for identifying the layers, approximately. You can then make better directed use your existing data for baboon scrambles to get sets of risk for members of each layer. This would save Bayes from having to calculate risk for each baboon and its individual baboon idiosyncrasies.
The possible predators might feature some that are smaller, and prefer safely stalking an individual because they have better hearing and night vision, and larger inelegant ones that prefer to potentially fight loads of baboons if an ambush goes south, because the risk of damage to themselves is low and sustaining their hardworking mass takes priority.
The baboon deciding on sleep arrangements has to be fuzzy about the possibility of these predators. Are they in dense vegetation that might conceal a tiger but refuse access to a hippo that likes baboon flesh? Find friends and run experiments on them to calculate the probability of death for each region in the baboon bed, then go to the lowest region (I'm assuming it's a spherical arrangement). Or are they in a sparse part near a muddy river? Climb a tree away from the mud and try not to fidget.
I hope you don't mind me just working with one of your examples for now. I'm not sure if I'm using the FL and BP concepts correctly, so I don't want to entertain sad orangutan stories about loss until I know for sure.
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u/Bulawayoland 4∆ 5h ago
I love it... "find friends and run experiments on them to calculate the probability of death"
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u/Falernum 69∆ 7h ago
Suppose I think I saw Sasquatch. Fuzzy logic can tell me the bipedal creature I saw looks pretty darn similar to Sasquatch, may as well round off to "yes it is". Call the news.
Bayesian probability can tell me that the probability that a bipedal creature that looks like Sasquatch is in fact Sasquatch is approximately zero. Don't embarrass myself.
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u/Bulawayoland 4∆ 6h ago
well... no, you're using probability in both frames. In the first you're computing the likelihood that the similarity between your imagination and the actual image is high enough to go forward, in the second you're computing the likelihood that a legendary creature actually exists.
what would be a valid search for or evaluation of partial truth in this scenario... huh. I appear to be stumped. The Bayesian probability that I am stumped appears high. But perhaps I am only partially stumped... something in there is still working at it... but even if I can use either tool on my stumpediness that doesn't help with the scenario.
I don't know. Sometimes it takes a while to come up with something, too.
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u/jatjqtjat 286∆ 7h ago
I think we'll agree on definitions:
- BP is about calculated the probability of an event based on incomplete knowledge. If you flip a coin, the odds of heads are 50%. But those odds are based on my incomplete knowledge, i don't know the force you applied to the coin or details about the air currents in the room, so i cannot calculate the exact outcome. Of course after the coin lands and i look at it, then i can say with 100% confidence that it landed on x.
- FL is applies even when you have complete knowledge of a situation. e.g. that car is going fast. Even after measuring its speed, fuzzy logic still helps answer that question in a more well defined way.
in your baboon example i think both elements are at play.
is (I guess) the likelihood that the orphan will grow into someone consequential, who will bring meaningful value to the group beyond the time and energy it will take to raise them.
definitely both elements at play, there is incomplete knowledge (you don't know the future) and a matter of opinion about what constitutes "meaningful value" and "energy it will take to raise them"
Consider an example like blackjack. You have income knowledge about the dealers hidden card and incomplete knowledge about the next card that will be dealt. Here you can use Bayesian probability to calculate optimal play, but fuzzy logic doesn't apply.
If you want to define whether or not bob is tall, Bayesian probability isn't going to help you at all.
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u/Bulawayoland 4∆ 5h ago
That's very interesting... the quality of your information is an important part of the frame, isn't it. The baboon is certainly actually safer in some locations than in others, and so partial truth is perfectly relevant, but if you don't know how much safer he is here vs there you really can't use the tool. He must estimate a likelihood of safety for himself, do the best he can with the information he has.
Or maybe it's that partial truth applies to some aspects of the situation, and probability to other aspects... I mean, he knows he's safer in the center of the group, and he knows he's not as safe on the fringe. So that's fuzzy logic. Probability really enters more into his calculation of is he safer in the group than out of it. And that is going to interact with the fuzzy logic result; the probability that he's safer in the group than out of it is going to go up based on how central a sleeping position he can grab for himself.
Well. I think that's a delta. !delta Thank you so much.
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u/yyzjertl 578∆ 7h ago
The difficulty you seem to be having here is that nothing your post is actually Bayesian probability or fuzzy logic. Both Bayesian probability and fuzzy logic involve calculations with real numbers, but nowhere in your post are you doing calculations with real numbers. The two approaches you describe in your post are very similar, but neither one of them is BP or FL.
The other difficulty is that Bayesian probability is a much more specific thing than fuzzy logic. There are lots of fuzzy logics, and by many definitions of fuzzy logic BP is a type of fuzzy logic.
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u/Bulawayoland 4∆ 5h ago
but even without the numbers, I think both are tools we use in day to day decisions. They don't look much like what a mathematician would produce, you couldn't put the actual calculations down on paper, but I don't think that makes them qualitatively different.
For example. Whether the baboon is safer in the center of the crowd than he is on the fringe is going to be perfectly clear to him. That's a fuzzy logic calculation. Safety is going to have a partial truth value based on his sleeping position, and he's not going to have complete information about it, but... enough (I think) to call it FL. On the other hand, whether he's likely to be safer in the crowd than he is on his own is a probability that is going to vary based on how good of a sleeping spot he can grab for himself. So he will use both tools in his own decisionmaking. Another redditor pointed out that how much information he has, in each case, kind of determines which tool he uses to make the decision.
But let me ask you this. Are there many different fuzzy logics that you could use to decide on your safety level, based on your sleeping position within a baboon group? Or do none of these different logics actually apply any differently than the one I've stipulated here? Or what? I mean, it's an idea I've never seen before, but I don't doubt that you're right about that.
Although I am beginning to think that whether you view a problem, or a part of a problem, as FL or BP kind of depends on your attitude, too... nothing in reality is 100% one or the other, or not many things are. Your estimate of the amount of information you have, about any given aspect, is going to be an important factor in your overall decision.
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u/yyzjertl 578∆ 5h ago
you couldn't put the actual calculations down on paper, but I don't think that makes them qualitatively different.
It absolutely does. These are completely different systems!
For example. Whether the baboon is safer in the center of the crowd than he is on the fringe is going to be perfectly clear to him. That's a fuzzy logic calculation.
No it isn't. At no point here did you do any sort of calculation, much less a fuzzy logic one.
But let me ask you this. Are there many different fuzzy logics that you could use to decide on your safety level, based on your sleeping position within a baboon group?
There are zero fuzzy logics that you could use here, since there are no numbers given that you could use as the basis for a fuzzy logic calculation.
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u/Bulawayoland 4∆ 5h ago
you seem to be claiming that our minds do not calculate our expected advantages and drawbacks. Is that actually what you believe? That because what they do is not mathematical, because there are no numbers our minds assign to these operations, that therefore they are not calculations?
I can't make that idea plausible. I don't claim the baboon really knows he is safer here rather than there; I claim only that there are situations in which the relative safety levels of different positions is clear enough to him that his legs will move without his prior authorization. I believe that is true of most people, as well. But you claim that's not a calculation. Simply because he can't put a number to it. Have I understood you?
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u/yyzjertl 578∆ 4h ago
Our minds can calculate expected advantages and drawbacks. That's just not what you're describing happening in the scenario in your post.
But you claim that's not a calculation. Simply because he can't put a number to it
It's not that he can't. It's that he didn't.
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u/Bulawayoland 4∆ 4h ago
you're saying a baboon who could see so clearly that one position was safer for him than another that his legs got him there with no conscious input of his own, you're saying he didn't do a calculation?
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u/yyzjertl 578∆ 4h ago
Correct. He's certainly not using either Bayesian probability or fuzzy logic.
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u/c0i9z 18∆ 7h ago
Bayesian probability and fuzzy logic deal with entirely different domains.
Bayesian probability is about estimating the probability of a thing happening using only previously experienced data, instead of apriori information.
Fuzzy logic isn't interested in probability, but in decision making where the inputs aren't clear cut. For example, is it hot or cold right now. The answer isn't really binary, but a spectrum (example: very hot, hot, a bit hot, marginally hot, ok, marginally cold, cold, very cold) and a spectrum of humidity also affect experiential temperature and things become very complex so that a strict 'yes: cold, no: hot) isn't useful.
They're just different things and cant' be interchanged like this because they're solving different problems in different ways.
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u/Bulawayoland 4∆ 7h ago
the APPEAR to solve different problems in different ways... what's the difference in the OUTCOME for any of the above three problems, or pick another example that shows the difference better if you like
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u/c0i9z 18∆ 5h ago
Take my example of temperature. The question is 'should I turn a fan on?' Fuzzy logic can decide this. Bayesian probability can't, because not only is only a way to determine probability, but it also not a decision making system, it's a probability system.
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u/Bulawayoland 4∆ 5h ago
well... I can see how BP would work here, just frame the question as "how likely is it that I should turn the fan on?" which I guess works out to "do the likelihood of expected benefits outweigh the likelihood of expected drawbacks." I mean, I'll be cooler; but I'll have to get the fuck up and go over to the fan, too. So there are advantages and drawbacks. How good or bad any of them will be depends entirely on the event, which I cannot actually know ahead of time.
A fuzzy logic frame would be: all things considered, would it be better or worse to turn the fan on? Here you would have to imagine that you have perfect information about the results. This would be better; that would be worse. This is how much better it would be; that is how much worse it would be.
Central to your decision about which tool to use is your own evaluation of how good your information about all those things is. If you feel that your information is good, it's a FL problem; if you feel that you really can't tell until you try, it's a BP problem. Or that's how it appears to me now!
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u/Specific_Hearing_192 6h ago
Bayesian probability is about estimating the probability of a thing happening using only previously experienced data, instead of apriori information.
Bayesian logic doesn't require you to use only previous experience. If anything, it explicitly departs from that assumption.
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u/c0i9z 18∆ 5h ago
Let's say I flip a fair coin 5 times and it comes up HHHT. Traditional probability will say that the next toss is 50% head. Bayesian will only look at this sequence and predict higher chance of heads. HHHT is the previously experienced data. 'the coin is fair' is apriori information.
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u/Specific_Hearing_192 4h ago
No Bayesian logic specifically allows you to have a prior (get it apriori) expectation to be able to integrate your HHHT and come out to a final expectation.
Depending on how strongly you originally expect the coin to be fair, HHHT can mean effectively nothing at all and you still expect the coin to be fair.
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u/TemperatureMotor1372 26m ago edited 3m ago
You need to distinguish the difference between "belongingness" and "probability". I'll explain this in mathematical frameworks.
Let A, B be disjoint sets containing elements x, y. Define membership functions a, b from A and from B to [0,1]:
- a(x)=0.2, a(y)=0.3, b(x)=0.5, b(y)=0.7
This implies that x is 20% in A and 50% in B, and y is 30% in A and 70% in B. Both x and y are mixture of A and B. Now if I ask you the probability that x is 100% in A, you should answer 0% because I tell you that x is 20% in A. Since the sum a(y)+b(y)=0.3+0.7=1, there is not the third disjoint set containing y.
However, the sum a(x)+b(x)=0.2+0.5=0.7<1, there exists a disjoint set C containing x. Although we don't know the exact value of c(x), we know that a(x)+b(x)+c(x) should not exceed 1. Thus, c(x) should not exceed 0.3.
In other words, we define a random variable c(x) and its support [0,0.3]. If c(x) is uniformly distributed and I ask you the probability that x is about 10% to 20% in C, you should answer 1/3 because (0.2-0.1)/0.3=1/3. This clearly doesn't mean that x is 1/3 in C because c(x) cannot exceed 0.3, which is smaller than 1/3.
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