Despite the form, statement (b) is not actually a logical conjunction. It is a statement about the collective of both parents.
This becomes clearer if we strengthen the statement slightly to "Alvin's mother and father are responsible for all of his genome". It's much more clear now that it is not a logical conjunction. If it were, it would mean "Alvin's mother is responsible for all of his genome and Alvin's father is responsible for all of his genome", both of which are false.
This is probably meant as a reply to this comment.
In Eliezer Yudkowsky's essay Burdensome Details, I get stuck by the first paragraph on the Conjunction Fallacy:
The conjunction fallacy is when humans assign a higher probability to a proposition of the form “A and B” than to one of the propositions “A” or “B” in isolation, even though it is a theorem that conjunctions are never likelier than their conjuncts.
According to Wikipedia's entry on Conjunction Fallacy:
"... the probability of two events occurring together (in "conjunction") is always less than or equal to the probability of either one occurring alone..."
I can see now how Yudkowskys statement the "...conjunctions are never likelier than their conjuncts." can also be stated as [the probability of two events occuring together] is always less than or equal to the probability of either one occurring alone..."
What I don't get is how, in a case where the conjunction is truer than either conjunct alone, this can hold true. Maybe I am approaching this wrong, but here is an example I'm having trouble with:
Alvin is a human being, average in every way. He was conceived and birthed naturally by his parents. Which of the following are true?
a) Alvin's mother is responsible for his genome
b) Alvin's mother and father are responsible for his genome.
Since each of his parents contribute 23 chromosomes to his genome, for a total of 46, isn't this a case where the conjunction is 100% true while the lone statement of a) is only 50% true?
I've never taken a formal logic class and stopped at pre-calc, so I know I'm missing something somewhere. Is it that the conjuncts are 2 similar to be considered as separate statements? I suppose common knowledge would suggest that by stating "Alvins mother contributed half his genes" automatically infers that his father contributed the other half, so that the statement 'b' is really just restating 'a'?
And after reading up a little I also found this article from 2015 stating you actually get more genes from your mother when you consider the sets of both nuclear dna and mitochondrial dna. Although the Wikipedia entry for Human Genome states that these 2 sets are "usually treated separately" (in discussions of who is responsible for your dna, I guess?)
So after trusting what I learned in bio 101 (or where ever) that both my parents are responsible for my genome, now I'm confused about whether it's actually true, AND how to think about the issue from a perspective trying to take in the conjunction fallacy.
Could someone help clear this up for me? Thanks in advance.
The short answer is that both statements are true, so the "or equal to" part is satisfied and the inequality holds. The values involved are probabilities over binary truth/falsity, not degrees of truth.
That clears up the issue for me. Thank you!
Maybe read up on the concepts of outcome, sample space, event, probability space, and see what the probability of intersection of events means in terms of all that. It's this stuff that's being implicitly used, usually it should be clear how to formulate the informal discussion in these terms. In particular, truth of whether an outcome belongs to an event is not fuzzy, it either does or doesn't, as events are defined to be certain sets of outcomes.
(Also, the reasons behind omission of the "or equal to"s you might've noticed are discussed in 0 And 1 Are Not Probabilities, though when one of the events includes the other this doesn't apply in any straightforward sense.)
Thanks for the suggestions, and now that I understand the idea that the probability values correspond to a binary interpretation of the events, it makes these areas easier to navigate for me in discussion.
In particular, truth of whether an outcome belongs to an event is not fuzzy, it either does or doesn't, as events are defined to be certain sets of outcomes.
This definitely stands as a hard to argue against idea, and it makes sense when seen from the viewpoint of rational humans interpreting data from systems based on binary calculations and logic.
Do you think it's possible that there is a better way than Binary logic to compute and reason though?
Not being familiar with the literature, I wonder if it's possible that because we have relied on binary logic to compute and reason for so long, it's created a false dichotomy in our understanding of reality. Is there another way to reason that works better, based on quantum computing rational?
How the next decade will add to the discussion of reality in terms of the advances in Quantum computing seems to be debatable. Translating probability values into either true or false logic is a step in binary computing that I believe quantum computing skips, and so the data returned takes in to account I think, the cases in which "...one of the events includes the other..." in a more or less straightforward way.
At this point though, (I could be wrong) I believe there is still more of a front end system that runs binary to interpret the Quantum calculations of a quantum computer, because when the data returned isn't binary, we're still trying to figure out what it's good for.
In relation to events and how long or little they last, this whole area of Quantum clocks is interesting to me. We can measure time more accurately because of them, but it seems like so much of the science in common use still relies on the second as the base measurement. Maybe the second is the bottom limit of what humans can somewhat accurately perceive without aid of a tool like a watch, which makes a case for basing measurements of time using more accurate methods off of the second.
Is it possible we could create wet ware with augmented vision which would allow us to 'perceive' smaller and smaller units of time, or would we just be better off trying to figure out how to slow down time? Sometimes rationally speaking, in the light of all these scientific advances, it gets a little harder to appreciate humans when you consider our limited abilities. I think it's our ability to conceptualize these phenomenon though that is our 'saving grace.'
At this level of technical discussion it's hopeless to attempt to understand anything. Maybe try going for depth first, learning some things at least to a level where passing hypothetical exams on those topics would be likely, to get a sense of what a usable level of technical understanding is. Taking a wild guess, perhaps something like Sipser's "Introduction to the Theory of Computation" would be interesting?
I just downloaded the 2nd edition. Thank you for the suggestion.
I''ve wanted to write short fiction for awhile, and since I've joined the LW community I feel like my writing is getting better. Anyways, I have loads of ideas but this is one that seems good for short fiction, with the possibility to expand on the world, story and characters. Feedback and constructive criticism is welcome.
Eve busied herself in the kitchen preparing breakfast while her husband of 20 years finished his shower.
It was a healthy breakfast, typical American fare: Good organic bacon, free range eggs - scrambled, and a gluten free piece of toast with sweet cream butter and organic honey, black coffee, but no orange juice.
Her husbands stomach couldn’t handle the acidity of orange juice.
So as he entered the kitchen to eat, Eve poured 2 glasses of apple juice for the 2 of them; the kids were still in bed as it was only about 4:30 in the morning.
This was unusual, as Eve’s husband’s schedule was usually very flexible as the 9-5 workday had been abolished a few years back; shortly before the singularity, the government’s AI systems had finally done the research to provide the evidence necessary to show the harmful effects of forced schedules and unnatural work hours which interfered with an individuals circadian rhythms.
Plus, her husband had insisted that remote work put him too far away from the infrastructure he was responsible for, and he needed to work onsite. So on a typical day, he usually went to work around 1 in the afternoon.
“Why are they calling you in this early again honey?” Eve asked a little worriedly as she took a sip of her apple juice.
“They just wanted to alert me to a small change in the system, that’s all, ‘it’s no big deal’ they said.”
“Don’t worry, I’ve been an important part of the team for years, probably the most important part as I’m the only hybrid involved. I’ll be in and out in a couple hours, the system just needs me to verify a change and then my jobs done for the day. It’ll be a short day and then it’s the weekend!”
“I know Adam, but ever since the...Leaving Behind started, our friends are harder and harder to spend time with.”
She continued “The ban on human use of digital technology was a really big deal. We don’t have anything to talk about anymore. Since our family is considered ‘hybrids’ because of your work with the main government AI system, the fact we’re allowed to use digital tech is causing all kinds of personal problems.”
She continued, clearly upset now “ And you know all our human friends think that’s a bunch of bullshit! They think we’re actually human too!”
“And you know the kids are the only mostly human hybrids in school now, and while they enjoy class still, and their project on micro cold fusion reactors is going well, in comparison to the rest of the class, they’re only functioning on a 6th grade level. All the other kids in class are already developing perpetual motion generators based on quantum...something or other. I can’t even keep up with the latest middle school research these days! I’m starting to feel as if my dual major in theoretical physics and space aeronautics was a waste of time!” Eve turned to Adam sorrowfully.
“I know! You don’t think I know what they’re saying?! Of course we’re hybrids! We have access to digital technology, that’s the difference between a human and a hybrid! Just because the human race has been banned from using digital technology though, doesn’t mean we have to be! And we can still spend time with humans, although we’ll just have to explain to them again what makes us different.”
“I can’t help feeling like there should be something we can do though to protect ourselves from constantly being attacked because we are different though. That’s what this is all about honey, with the friends, they’re just jealous, that’s all.” His face a little flushed, Adam lifts a piece of pork to his mouth and half-heartedly bites into it.
“I know, I know, I’m sorry. I keep forgetting. Ever since I lost my job I’ve just had too much time to think.” Adam puts his hand on Eve’s to comfort her.
“I know honey, I know.”
Trying to look hopeful, Adam continues “Have you reconsidered playing tennis with the Fergusons again? You know the company developing their bidpedal humanoid containers is still tinkering– you have a wicked backhand and I bet you could still beat Jennifer.”
“The physical portion of their, you know, being, hasn’t yet caught up with the advanced personality and identity constructs yet. They’re great to talk with, but you remember trying to hike in the swiss alps with them last year.\? How many times did we have to help them up or replace a broken limb? Plus, the time you spend on the court with her during her physical development will be appreciated, and you know it. You can still contribute to research.”
“Maybe you’re right Adam.” Eve smiles for the first time in a couple days as she thinks about how much she and Adam love each other. “You need to stop it now though and finish getting ready. This is an important day, you know – last hybrid with a job!” Eve giggles a little as she says the last part.
“And drink your apple juice before you take off!”
Just then the phone rings.
Eve gets up from the table to retrieve the handset for the landline phone attached to the wall. With the advance of 10g wireless technology, the prioritization of the available bandwidth means that personal tech like cellphones didn’t work anymore, so all human and hybrid communications technology reverted back to being wired.
“hello?” Eve said into the handset. “Yes? Yes. He’s right here, hold on...Adam? It’s for you.” Adam looked up as she handed him the handset and took a drink of his apple juice before reaching for the receiver. As Eve passed him the receiver, the cord snaked around his arm as he held it up to talk.
“Hello? Yeah, Hi. I was just getting ready.”
“What? I don’t…”
“ ...I don’t...don’t understan…d”
All the color had drained out of his face immediately and he stared at nothing in particular for a minute as he let the phone fall to the ground.
“Adam? What is it?” asked Eve.
“Adam? Honey?” But Adam just sat there, stunned, unable to think.
“Honey, you’re scaring me. What did they want?” Eve looked at him worriedly, knowing, but not knowing what had just happened.
“Adam? Please say something…” Eve’s voice had begun to take on a pleading edge, as she could feel panic rising in her body.
“What did they say?!” she demanded.
Adam finally turned his head towards the sound of her voice, but he couldn’t focus his eyes. After a minute of moving his mouth without making any sounds, he finally found a small, terrified voice “...they..fired me?...I’m...fired….they said...We...we….we….were human...”
With this last statement, he sat down hard on the dining room chair.
Eve looked on in stunned silence, unable to move for fear she might jump out of her skin.
They were human after all.
Which meant they were no longer allowed to use digital technology.
Which meant Adam lost his job working with the Government AI systems because they were digital.
Which meant the Leaving Behind was complete: AI society had shut out human society totally and irreversibly; the last man to have a job that mattered, had just lost it.