What sophisticated ideas did you come up with independently before encountering them in a more formal context?
I’m pretty sure that in my youth I independently came up with rudimentary versions of the anthropic principle and the Problem of Evil. Looking over my Livejournal archive, I was clearly not a fearsome philosophical mind in my late teens, (or now, frankly), so it seems safe to say that these ideas aren’t difficult to stumble across.
While discussing this at the most recent London Less Wrong meetup, another attendee claimed to have independently arrived at Pascal’s Wager. I’ve seen a couple of different people speculate that cultural and ideological artefacts are subject to selection and evolutionary pressures without ever themselves having come across memetics as a concept.
I’m still thinking about ideas we come up with that stand to reason. Rather than prime you all with the hazy ideas I have about the sorts of ideas people converge on while armchair-theorising, I’d like to solicit some more examples. What ideas of this sort did you come up with independently, only to discover they were already “a thing”?
When I was a teenager, I imagined that if you had just a tiny infinitesimally small piece of a curve—there would only be one moral way to extend it. Obviously, an extension would have to be connected to it, but also, you would want it to connect without any kinks. And just having straight-lines connected to it wouldn’t be right, it would have to be curved in the same sort of way—and so on, to higher-and-higher orders. Later I realized that this is essentially what a Taylor series is.
I also had this idea when I was learning category theory that objects were points, morphisms were lines, composition was a triangle, and associativity was a tetrahedron. It’s not especially sophisticated, but it turns out this idea is useful for n-categories.
Recently, I have been learning about neural networks. I was working on implementing a fairly basic one, and I had a few ideas for improving neural networks: making them more modular—so neurons in the next layer are only connected to a certain subset of neurons in the previous layer. I read about V1, and together, these led to the idea that you arrange things so they take into account the topology of the inputs—so for image processing, having neurons connected to small, overlapping, circles of inputs. Then I realized you would want multiple neurons with the same inputs that were detecting different features, and that you could reuse training data for neurons with different inputs detecting the same feature—saving computation cycles. So for the whole network, you would build up from local to global features as you applied more layers—which suggested that sheaf theory may be useful for studying these. I was planning to work out details, and try implementing as much of this as I could (and still intend to as an exercise), but the next day I found that this was essentially the idea behind convolutional neural networks. I’m rather pleased with myself since CNNs are apparently state-of-the-art for many image recognition tasks (some fun examples). The sheaf theory stuff seems to be original to me though, and I hope to see if applying Gougen’s sheaf semantics would be useful/interesting.
I really wish I was better at actually implementing/working out the details of my ideas. That part is really hard.
I had to laugh at your conclusion. The implementation is the most enjoyable part. “How can I dumb this amazing idea down to the most basic understandable levels so it can be applied?” Sometimes you come up with a solution only to have a feverish fit of maddening genius weeks later finding a BETTER solution.
In my first foray into robotics I needed to write a radio positioning program/system for the little guys so they would all know where they were not globally but relative to each other and the work site. I was completely unable to find the math simply spelled out online and to admit at this point in my life I was a former marine who was not quite up to college level math. In banging my head against the table for hours I came up with an initial solution that found a position accounting for three dimensions(allowing for the target object to be in any position relative to the stationary receivers). Eventually I came up with an even better solution that also came up with new ideas for the robot’s antenna design and therefore tweaking the solution even more.
I came up with the idea of a Basic Income by myself, by chaining together some ideas:
Capitalism is the most efficient economic system for fulfilling the needs of people, provided they have money.
The problem is that if lots of people have no money, and no way to get money (or no way to get it without terrible costs to themselves), then the system does not fulfill their needs.
In the future, automation will both increase economic capacity, while also increase the barrier to having a ‘valuable skill’ allowing you to get money. Society will have improved capacity to fulfill the needs of people with money, yet the barrier to having useful skills and being able to get money will increase. This leads to a scenario where the society could easily produce the items needed by everyone, yet does not because many of those people have no money to pay for them.
If X% of the benefits accrued from ownership of the capital were taken and redistributed evenly among all humans, then the problem is averted. Average people still have some source of money with which they can purchase the fulfillment of their needs, which are pretty easy to supply in this advanced future society.
X=100%, as in a strict socialism, is not correct, as then we get the economic failures we saw in the socialist experiments of the past century.
X = 0%, as in a strict libertarianism, is not correct, as then everyone whose skills are automated starve.
At X = some reasonable number, capitalism still functions correctly (that is, it works today with our current tax rate levels, and hopefully in our economically progressed future society, it provides sufficient money to everyone to supply basic needs).
Eventually I found out that my idea was pretty much a Basic Income system.
Once a Christian friend asked me why I cared so much about what he believed. Without thinking, I came up with, “What you think determines what you choose. If your idea of the world is inaccurate, your choices will fail.”
This was years before I found LW and learned about the connection between epistemic and instrumental rationality.
P.S. My friend deconverted himself some years afterwards.
This is not a direct answer: Every time I come up with an idea in a field I am not very deeply involved in sooner or later I will realise that the phenomenon is either trivial, a misperception or very well studied. Most recently this happened with pecuniary externalities.
Came up with the RNA-world hypothesis on my own when reading about the structure and function of ribosomes in middle school.
Decided long ago that there was a conflict between the age of the universe and the existence of improvements in space travel meaning that things such as we would never be able to reach self-replicating interstellar travel. Never came to the conclusion that it meant extinction at all and am still quite confused by people who assume its interstellar metastasis or bust.
Derivatives. I imagined tangent lines traveling along a function curve and thinking ‘I wonder what it looks like when we measure that?’ And so I would try to visualize the changing slopes of the tangent lines at the same time. I also remembering wondering how to reverse it. Obviously didn’t get farther than that, but I remember being very surprised when I took calculus and realizing that the mind game I had been playing was hugely important and widespread, and could in fact be calculated.
Oh, another thing: I remember thinking that it didn’t make sense to favour either the many worlds interpretation or the copenhagen interpretation, because no empirical fact we could collect could point towards one or the other, being as we are stuck in just one universe and unable to observe any others. Whichever one was true, it couldn’t possibly impact on one’s life in any way, so the question should be discarded as meaningless, even to the extent that it didn’t really make sense to talk about which one is true.
This seems like a basically positivist or postpositivist take on the topic, with shades of Occam’s Razor. I was perhaps around twelve. (For the record, I haven’t read the quantum mechanics sequence and this remains my default position to this day.)
In 6th or 7th grade I told my class that it was obvious that purchasing expensive sneakers is mostly just a way to show how cool you are or that you can afford something that not everyone else could. Many years latter I would read about signalling http://en.wikipedia.org/wiki/Signalling_(economics)
The following are not ideas as much as questions I had while growing up, and I was surprised/relieved/happy to find out that other people much smarter than me, spent a lot of time thinking about and is “a thing”. For example I really wanted to know if there was a satisfactory way to figure out if Christianity was the one true religion and it bothered me very much that I could not answer that question. Also, I was concerned that the future might not be what I want it to be, and I am not sure that I know what I even want. It turns out that this isn’t a unique problem and there are many people thinking about it. Also, what the heck is consciousness? Is there one correct moral theory? Well, someone is working on it.
I had drawn up some rather detailed ideas for an atomic powered future: The idea was to solve two major problems. The first was the inherent risk of an over pressure causing such a power plant to explode. The second problem to solve was the looming water shortage facing many nations.
The idea was a power plant that used internal sterling technology so as to operate at atmospheric pressures. Reinforcing this idea was basically a design for the reactor to “entomb” itself if it reached temperatures high enough to melt its shell. The top of the sterling engine would have a salt water reservoir that would be boiled off. The water then would be collected and directed in a piping system to a reservoir. The plant would then both produce electricity AND fresh water.
Of course then while researching thorium power technology in school I discovered that the South Korean SMART micro reactor does in fact desalinate water. On one level I was depressed that my idea was not “original” however, overall I’m exited that I came up with an idea that apparently had enough merit for people actually go through and make a finished design based upon it. The fact that my idea had merit at all gives me hope for my future as an engineer.
I’m another independent discoverer of something like utilitarianism, I think when I was in elementary school. My earliest written record of it is from when I was 15, when I wrote: “Long ago (when I was 8?), I said that the purpose of life was to enjoy yourself & to help others enjoy themselves—now & in the future.”
In high school I did a fair amount of thinking (with relatively little direct outside influence) about Goodhart’s law, social dilemmas, and indirect utilitarianism. My journal from then include versions of ideas like the “one thought too many” argument, decision procedures vs. criterion for good, tradeoffs between following an imperfect system and creating exceptions to do better in a particular case, and expected value reasoning about small probabilities of large effects (e.g. voting).
On religion, I thought of the problem of evil (perhaps with outside influence on that one) and the Euthyphro argument against divine command theory.
16-year-old me also came up with various ideas related to rationality / heuristics & biases, like sunk costs (“Once you’re in a place, it doesn’t matter how you got there (except in mind—BIG exception)”), selection effects (“Reason for coincidence, etc. in stories—interesting stories get told, again & again”), and the importance of epistemic rationality (“Greatest human power—to change ones mind”).
I’ve found that ideas that affect me most fall into two major categories: either they will be ideas that hit me completely unprepared or they are ideas that I knew all along but had not formalized. Many-Worlds and and timelessness were the former for me. Utilitarianism and luminosity were the latter.
After learning the very basics of natural selection, I started thinking about goal systems and reward circuits and ethics. I thought that all of our adaptations were intended to allow us to meet our survival needs so we could pass on our genes. But what should people do once survival needs are met? What’s the next right and proper goal to pursue? That line of reasoning’s related Googling led me to Eliezer’s Levels of Intelligence paper, which in turn led me to Less Wrong.
Reading through the sequences, I found so many of the questions that I’d thought about in vague philosophical terms explained and analyzed rigorously, like personal identity vs continuity of subjective experience under things like teleportation. Part of the reason LW appealed to me so much back then is, I suspect, that I had already thought about so many of the same questions but just wasn’t able to frame them correctly.
This made me curious enough to skim through my childhood writing.
Convergent and divergent infinite series, quicksort, public choice theory, pulling the rope sideways, normative vs positive statements, curiosity stoppers, the overton window.
My Moloch moment is what led me to seek out Overcomingbias.
Tangent thread: What sophisticated idea are you holding on to that you are sure has been formalized somewhere but haven’t been able to find?
I’ll go first: When called to explain and defend my ethics I explained I believe in “Karma, NO not the that BS mysticism Karma, but plain old actions have consequences in our very connected world kind of Karma.” If you treat people in a manner of honesty and integrity in all things, you will create a community of cooperation. The world is strongly interconnected and strongly adaptable so the benefits will continue outside your normal community, or if you frequently change communities. The lynchpin assumption of these beliefs is that if I create One Unit of Happiness for others, it will self propagate, grow and reflect, returning me more that One Unit of Happiness over the course of my lifetime. The same applies for One Unit of Misery.
I’ve only briefly studied ethics and philosophy, can someone better read point my to the above in formal context.
This seems like a good place to ask about something that I’m intensely curious about but haven’t yet seen discussed formally. I’ve wanted to ask about it before, but I figured it’s probably an obvious and well-discussed subject that I just haven’t gotten to yet. (I only know the very basics of Bayesian thinking, I haven’t read more than about 1⁄5 of the sequences so far, and I don’t yet know calculus or advanced math of any type. So there are an awful lot of well-discussed LW-type subjects that I haven’t gotten to yet.)
I’ve long conceived of Bayesian belief statements in the following (somewhat fuzzily conceived) way: Imagine a graph where the x-axis represents our probability estimate for a given statement being true and the y-axis represents our certainty that our probability estimate is correct. So if, for example, we estimate a probability of .6 for a given statement to be true but we’re only mildly certain of that estimate, then our belief graph would probably look like a shallow bell curve centered on the .6 mark of the x-axis. If we were much more certain of our estimate then the bell curve would be much steeper.
I usually think of the height of the curve at any given point as representing how likely I think it is that I’ll discover evidence that will change my belief. So for a low bell curve centered on .6, I think of that as meaning that I’d currently assign the belief a probability of around .6 but I also consider it likely that I’ll discover evidence (if I look for it) that can change my opinion significantly in any direction.
I’ve found this way of thinking to be quite useful. Is this a well-known concept? What is it called and where can I find out more about it? Or is there something wrong with it?
Imagine a graph where the x-axis represents our probability estimate for a given statement being true and the y-axis represents our certainty that our probability estimate is correct. So if, for example, we estimate a probability of .6 for a given statement to be true but we’re only mildly certain of that estimate, then our belief graph would probably look like a shallow bell curve
I don’t understand where the bell curve is coming from. If you have one probability estimate for a given statement with some certainty about it, you would depict it as a single point on your graph.
The bell curves in this context usually represent probability distributions. The width of that probability distribution reflects your uncertainty. If you’re certain, the distribution is narrow and looks like a spike at the estimate value. If you’re uncertain, the distribution is flat(ter). Probability distributions have to sum to 1 under the curve, so the smaller the width of the distribution, the higher the spike is.
How likely you are to discover new evidence is neither here nor there. Even if you are very uncertain of your estimate, this does not convert into the probability of finding new evidence.
I think you’re referring to the type of statement that can have many values. Something like “how long will it take for AGI to be developed?”. My impression (correct me if I’m wrong) is that this is what’s normally graphed with a probability distribution. Each possible value is assigned a probability, and the result is usually more or less a bell curve with the width of the curve representing your certainty.
I’m referring to a very basic T/F statement. On a normal probability distribution graph that would indeed be represented as a single point—the probability you’d assign to it being true. But we’re often not so confident in our assessment of the probability we’ve assigned, and that confidence is what I was trying to represent with the y-axis.
An example might be, “will AGI be developed within 30 years”? There’s no range of values here, so on a normal probability distribution graph you’d simply assign a probability and that’s it. But there’s a very big difference between saying “I really have not the slightest clue, but if I really must assign it a probability than I’d give it maybe 50%” vs. “I’ve researched the subject for years and I’m confident in my assessment that there’s a 50% probability”.
In my scheme, what I’m really discussing is the probability distribution of probability estimates for a given statement. So for the 30-year AGI question, what’s the probability that you’d consider a 10% probability estimate to be reasonable? What about a 90% estimate? The probability that you’d assign to each probability estimate is depicted as a single point on the graph and the result is usually more or less a bell curve.
How likely you are to discover new evidence is neither here nor there. Even if you are very uncertain of your estimate, this does not convert into the probability of finding new evidence.
You’re probably correct about this. But I’ve found the concept of the kind of graph I’ve been describing to be intuitively useful, and saying that it represents the probability of finding new evidence was just my attempt at understanding what such a graph would actually mean.
In my scheme, what I’m really discussing is the probability distribution of probability estimates for a given statement.
OK, let’s rephrase it in the terms of Bayesian hierarchical models. You have a model of event X happening in the future which says that the probability of that event is Y%. Y is a parameter of your model. What you are doing is giving a probability distribution for a parameter of your model (in the general case this distribution can be conditional, which makes it a meta-model, so hierarchical). That’s fine, you can do this. In this context the width of the distribution reflects how precise your estimate of the lower-level model parameter is.
The only thing is that for unique events (“will AGI be developed within 30 years”) your hierarchical model is not falsifiable. You will get a single realization (the event will either happen or it will not), but you will never get information on the “true” value of your model parameter Y. You will get a single update of your prior to a posterior and that’s it.
I think that is what I had in mind, but it sounds from the way you’re saying it that this hasn’t been discussed as a specific technique for visualizing belief probabilities.
That surprises me since I’ve found it to be very useful, at least for intuitively getting a handle on my confidence in my own beliefs. When dealing with the question of what probability to assign to belief X, I don’t just give it a single probability estimate, and I don’t even give it a probability estimate with the qualifier that my confidence in that probability is low/moderate/high. Rather I visualize a graph with (usually) a bell curve peaking at the probability estimate I’d assign and whose width represents my certainty in that estimate. To me that’s a lot more nuanced than just saying “50% with low confidence”. It has also helped me to communicate to others what my views are for a given belief. I’d also suspect that you can do a lot of interesting things by mathematically manipulating and combining such graphs.
One problem is that it’s turtles all the way down.
What’s your confidence in your confidence probability estimate? You can represent that as another probability distribution (or another model, or a set of models). Rinse and repeat.
Another problem is that it’s hard to get reasonable estimates for all the curves that you want to mathematically manipulate. Of course you can wave hands and say that a particular curve exactly represents your beliefs and no one can say it ain’t so, but fake precision isn’t exactly useful.
I’m referring to a very basic T/F statement. On a normal probability distribution graph that would indeed be represented as a single point—the probability you’d assign to it being true. But we’re often not so confident in our assessment of the probability we’ve assigned, and that confidence is what I was trying to represent with the y-axis.
Taken literally, the concept of “confidence in a probability” is incoherent. You are probably confusing it with one of several related concepts. Lumifer has described one example of such a concept.
Another concept is how much you think your probability estimate will change as you encounter new evidence. For example, your estimate for whether the outcome of the coin flip for the 2050 Superbowl will be heads is 1⁄2, and you are unlikely to encounter evidence that changes it (until 2050 that is). On the other hand, your estimate for the probability AI being developed by 2050 is likely to change a lot as you encounter more evidence.
It wouldn’t be the first time a sport has gone from vastly popular to mostly forgotten within 40 years. Jai alai was the particular example I had in mind; it was once incredibly popular, but quickly descended to the point where it’s basically entirely forgotten.
Taken literally, the concept of “confidence in a probability” is incoherent.
Why? I thought the way Lumifer expressed it in terms of Bayesian hierarchical models was pretty coherent. It might be turtles all the way down as he says, and it might be hard to use it in a rigorous mathematical way, but at least it’s coherent. (And useful, in my experience.)
Another concept is how much you think your probability estimate will change as you encounter new evidence.
This is pretty much what I meant in my original post by writing:
I usually think of the height of the curve at any given point as representing how likely I think it is that I’ll discover evidence that will change my belief. So for a low bell curve centered on .6, I think of that as meaning that I’d currently assign the belief a probability of around .6 but I also consider it likely that I’ll discover evidence (if I look for it) that can change my opinion significantly in any direction.
But expressing it in terms of how likely my beliefs are to change given more evidence is probably better. Or to say it in yet another way: how strong new evidence would need to be for me to change my estimate.
It seems like the scheme I’ve been proposing here is not a common one. So how do people usually express the obvious difference between a probability estimate of 50% for a coin flip (unlikely to change with more evidence) vs. a probability estimate of 50% for AI being developed by 2050 (very likely to change with more evidence)?
I believe you may be confusing the “map of the map” for the “map”.
If I understand correctly, you want to represent your beliefs about a simple yes/no statement. If that is correct, the appropriate distribution for your prior is Bernoulli. For a Bernoulli distribution, the X axis only has two possible values: True or False. The Bernoulli distribution will be your “map”. It is fully described by the parameter “p”
If you want to represent your uncertainty about your uncertainty, you can place a hyperprior on p. This is your “map of the map”. Generally, people will use a beta distribution for this (rather than a bell-shaped normal distribution). With such a hyperprior, p is on the X-axis and ranges from 0 to 1.
I am slightly confused about this part, but it is not clear to me that we gain much from having a “map of the map” in this situation, because no matter how uncertain you are about your beliefs, the hyperprior will imply a single expected value for p
I believe you may be confusing the “map of the map” for the “map”.
If I understand correctly, you want to represent your beliefs about a simple yes/no statement. If that is correct, the appropriate distribution for your prior is Bernoulli. For a Bernoulli distribution, the X axis only has two values: True or False. The Bernoulli distribution will be your “map”. It is fully described by the parameter “p”
If you want to represent your uncertainty about your uncertainty, you can place a hyperprior on p. This is your “map of the map”. Generally, people will use a beta distribution for this (rather than a bell-shaped normal distribution). With such a hyperprior, p is on the X-axis and ranges from 0 to 1.
I am slightly confused about this part, but it is not clear to me that we gain much from having a “map of the map” in this situation, because no matter how uncertain you are about your beliefs, the hyperprior will imply a single expected value for p.
What sophisticated idea are you holding on to that you are sure has been formalized somewhere but haven’t been able to find?
The influence of the British Empire on progressivism.
There was that book that talked about how North Korea got its methods from the Japanese occupation, and as soon as I saw that, I thought, “well, didn’t something similar happen here?” A while after that, I started reading Imagined Communities, got to the part where Anderson talks about Macaulay, looked him up, and went, “aha, I knew it!” But as far as I know, no one’s looked at it.
Also, I think I stole “culture is an engineering problem” from a Front Porch Republic article, but I haven’t been able to find the article, or anyone else writing rigorously about anything closer in ideaspace to that than dynamic geography, except the few people who approach something similar from an HBD or environmental determinism angle.
Well, this isn’t quite what you were asking for, but, as a young teenager a few days after 9/11, I was struck with a clear thought that went something like: “The American people are being whipped into a blood frenzy, and we are going to massively retaliate against somebody, perpetuating the endless cycle of violence that created the environment which enabled this attack to occur in the first place.”
But I think it’s actually common for young people to be better at realpolitik and we get worse at it as we absorb the mores of our culture.
In middle school I heard a fan theory that Neo had powers over the real world because it was a second layer of the matrix—the idea of simulations inside simulations was enough for me to come to Bostrom’s simulation argument.
Also during the same years I ended up doing an over the top version of comfort zone expansion by being really silly publicly.
In high school I think I basically argued a crude version of compatibilism before learning the term, although my memory of the conversation is a bit vague
This happened when I was 12 years old. I was trying to solve a problem at a mathematical contest which involved proving some identity with the nth powers of 5 and 7. I recall thinking vaguely “if you go to n+1 what is added in the left hand side is also in the right hand side” and so I discovered mathematical induction. In ten minutes I had a rigorous proof. Though, I didn’t find it so convincing, so I ended with an unsure-of-myself comment “Hence, it is also valid for 3, 4, 5, 6 and so on...”
When I was in high school, creationism seemed unsatisfying in the sense of a Deus Ex Machina narrative (I often wonder how theists reconcile the contradiction between the feeling of religious wonder and the feeling of disappointment when facing Deus Ex Machina endings). The evolution “story” fascinated me with its slow and semi-random progression over billions of years. I guess this was my first taste of reductionism. (This is also an example of how optimizing for interestingness instead of truth has led me to the correct answer.)
Cartesian skepticism and egoism, when I was maybe eleven. I eventually managed to argue myself out of both—Cartesian skepticism fell immediately, but egoism took a few years.
(In case it isn’t obvious from that, I did not have a very good childhood.)
I remember coming close to rediscovering pseudoformalism and the American caste system, but I discovered those concepts before I got all the way there.
I remember being inordinately relieved/happy/satisfied when I first read about determinism around 14 or 15 (in Sophie’s World, fwiw). It was like, thank you, that’s what I’ve been trying to articulate all these years!
(although they casually dismissed it as a philosophy in the book, which annoyed 14-or-15-year-old me)
I rediscovered most of the more widely agreed upon ontological categories (minus one that I still don’t believe to adhere to the definition) before I knew they were called that, at about the age of 17. The idea of researching them came to me after reading a question from some stupid personality quiz they gave us in high school, something like “If you were a color, which color would you be?”—and something about it rubbed me the wrong way, it just felt ontologically wrong, conflating entities with properties like that. (Yes, I did get the intended meaning of the question, I wasn’t that much of an Aspie even back then, but I could also see it in the other, more literal way.)
I remember it was in the same afternoon that I also split up the verb “to be” into its constituent meanings, and named them. It seemed related.
I came up with a basic version of Tegmark’s level 4 multiverse in high school and wrote an essay about it in English class. By that time though I think I’d already read Permutation City which involves similar ideas.
I independently constructed algebra (of the ‘3*x+7=49. Solve for x.’ variety) while being given ‘guess and check’ word problems in second grade. That’s a slightly different variety than most of the other examples here, though.
Under 8: my sister and I were raised atheist, but we constructed what amounted to a theology around our stuffed animals. The moral authority whom I disappointed most often, more than my parents, was my teddy bear. I believed in parts of our pantheon and ethics system so deeply, devoutly, and sincerely that, had I been raised in a real religion, I doubt my temperament would have ever let me escape.
Around 8: My mother rinsed out milk bottles twice, each time using a small amount of water. I asked her why she didn’t rinse it out once using twice as much water. She explained that doubling the water roughly doubled the cleansing power, but rinsing the bottle twice roughly squared the cleaning power. The most water-efficient way to clean a milk bottle, I figured, would involve a constant stream of water in and out of the bottle. I correctly modeled how the cleaning rate (per unit water) depends on the current milk residue concentration, but I couldn’t figure out what to do next or if the idea even made sense.
University: (1) use Kolmogorov complexity to construct a bayesian prior over universes, then reason anthropically. When you do this, you will (2) conclude with high probability that you are a very confused wisp of consciousness.
What sophisticated ideas did you come up with independently before encountering them in a more formal context?
I’m pretty sure that in my youth I independently came up with rudimentary versions of the anthropic principle and the Problem of Evil. Looking over my Livejournal archive, I was clearly not a fearsome philosophical mind in my late teens, (or now, frankly), so it seems safe to say that these ideas aren’t difficult to stumble across.
While discussing this at the most recent London Less Wrong meetup, another attendee claimed to have independently arrived at Pascal’s Wager. I’ve seen a couple of different people speculate that cultural and ideological artefacts are subject to selection and evolutionary pressures without ever themselves having come across memetics as a concept.
I’m still thinking about ideas we come up with that stand to reason. Rather than prime you all with the hazy ideas I have about the sorts of ideas people converge on while armchair-theorising, I’d like to solicit some more examples. What ideas of this sort did you come up with independently, only to discover they were already “a thing”?
When I was a teenager, I imagined that if you had just a tiny infinitesimally small piece of a curve—there would only be one moral way to extend it. Obviously, an extension would have to be connected to it, but also, you would want it to connect without any kinks. And just having straight-lines connected to it wouldn’t be right, it would have to be curved in the same sort of way—and so on, to higher-and-higher orders. Later I realized that this is essentially what a Taylor series is.
I also had this idea when I was learning category theory that objects were points, morphisms were lines, composition was a triangle, and associativity was a tetrahedron. It’s not especially sophisticated, but it turns out this idea is useful for n-categories.
Recently, I have been learning about neural networks. I was working on implementing a fairly basic one, and I had a few ideas for improving neural networks: making them more modular—so neurons in the next layer are only connected to a certain subset of neurons in the previous layer. I read about V1, and together, these led to the idea that you arrange things so they take into account the topology of the inputs—so for image processing, having neurons connected to small, overlapping, circles of inputs. Then I realized you would want multiple neurons with the same inputs that were detecting different features, and that you could reuse training data for neurons with different inputs detecting the same feature—saving computation cycles. So for the whole network, you would build up from local to global features as you applied more layers—which suggested that sheaf theory may be useful for studying these. I was planning to work out details, and try implementing as much of this as I could (and still intend to as an exercise), but the next day I found that this was essentially the idea behind convolutional neural networks. I’m rather pleased with myself since CNNs are apparently state-of-the-art for many image recognition tasks (some fun examples). The sheaf theory stuff seems to be original to me though, and I hope to see if applying Gougen’s sheaf semantics would be useful/interesting.
I really wish I was better at actually implementing/working out the details of my ideas. That part is really hard.
I had to laugh at your conclusion. The implementation is the most enjoyable part. “How can I dumb this amazing idea down to the most basic understandable levels so it can be applied?” Sometimes you come up with a solution only to have a feverish fit of maddening genius weeks later finding a BETTER solution.
In my first foray into robotics I needed to write a radio positioning program/system for the little guys so they would all know where they were not globally but relative to each other and the work site. I was completely unable to find the math simply spelled out online and to admit at this point in my life I was a former marine who was not quite up to college level math. In banging my head against the table for hours I came up with an initial solution that found a position accounting for three dimensions(allowing for the target object to be in any position relative to the stationary receivers). Eventually I came up with an even better solution that also came up with new ideas for the robot’s antenna design and therefore tweaking the solution even more.
That was some of the most fun I have ever had…
I did the Taylor series thing too, though with s/moral/natural/
I came up with the idea of a Basic Income by myself, by chaining together some ideas:
Capitalism is the most efficient economic system for fulfilling the needs of people, provided they have money.
The problem is that if lots of people have no money, and no way to get money (or no way to get it without terrible costs to themselves), then the system does not fulfill their needs.
In the future, automation will both increase economic capacity, while also increase the barrier to having a ‘valuable skill’ allowing you to get money. Society will have improved capacity to fulfill the needs of people with money, yet the barrier to having useful skills and being able to get money will increase. This leads to a scenario where the society could easily produce the items needed by everyone, yet does not because many of those people have no money to pay for them.
If X% of the benefits accrued from ownership of the capital were taken and redistributed evenly among all humans, then the problem is averted. Average people still have some source of money with which they can purchase the fulfillment of their needs, which are pretty easy to supply in this advanced future society.
X=100%, as in a strict socialism, is not correct, as then we get the economic failures we saw in the socialist experiments of the past century.
X = 0%, as in a strict libertarianism, is not correct, as then everyone whose skills are automated starve.
At X = some reasonable number, capitalism still functions correctly (that is, it works today with our current tax rate levels, and hopefully in our economically progressed future society, it provides sufficient money to everyone to supply basic needs).
Eventually I found out that my idea was pretty much a Basic Income system.
Once a Christian friend asked me why I cared so much about what he believed. Without thinking, I came up with, “What you think determines what you choose. If your idea of the world is inaccurate, your choices will fail.”
This was years before I found LW and learned about the connection between epistemic and instrumental rationality.
P.S. My friend deconverted himself some years afterwards.
This is not a direct answer: Every time I come up with an idea in a field I am not very deeply involved in sooner or later I will realise that the phenomenon is either trivial, a misperception or very well studied. Most recently this happened with pecuniary externalities.
Came up with the RNA-world hypothesis on my own when reading about the structure and function of ribosomes in middle school.
Decided long ago that there was a conflict between the age of the universe and the existence of improvements in space travel meaning that things such as we would never be able to reach self-replicating interstellar travel. Never came to the conclusion that it meant extinction at all and am still quite confused by people who assume its interstellar metastasis or bust.
Derivatives. I imagined tangent lines traveling along a function curve and thinking ‘I wonder what it looks like when we measure that?’ And so I would try to visualize the changing slopes of the tangent lines at the same time. I also remembering wondering how to reverse it. Obviously didn’t get farther than that, but I remember being very surprised when I took calculus and realizing that the mind game I had been playing was hugely important and widespread, and could in fact be calculated.
For as long as I can remember, I had the idea of a computer upgrading its own intelligence and getting powerful enough to make the world a utopia.
Oh, another thing: I remember thinking that it didn’t make sense to favour either the many worlds interpretation or the copenhagen interpretation, because no empirical fact we could collect could point towards one or the other, being as we are stuck in just one universe and unable to observe any others. Whichever one was true, it couldn’t possibly impact on one’s life in any way, so the question should be discarded as meaningless, even to the extent that it didn’t really make sense to talk about which one is true.
This seems like a basically positivist or postpositivist take on the topic, with shades of Occam’s Razor. I was perhaps around twelve. (For the record, I haven’t read the quantum mechanics sequence and this remains my default position to this day.)
In 6th or 7th grade I told my class that it was obvious that purchasing expensive sneakers is mostly just a way to show how cool you are or that you can afford something that not everyone else could. Many years latter I would read about signalling http://en.wikipedia.org/wiki/Signalling_(economics)
The following are not ideas as much as questions I had while growing up, and I was surprised/relieved/happy to find out that other people much smarter than me, spent a lot of time thinking about and is “a thing”. For example I really wanted to know if there was a satisfactory way to figure out if Christianity was the one true religion and it bothered me very much that I could not answer that question. Also, I was concerned that the future might not be what I want it to be, and I am not sure that I know what I even want. It turns out that this isn’t a unique problem and there are many people thinking about it. Also, what the heck is consciousness? Is there one correct moral theory? Well, someone is working on it.
At school my explanation for the existence of bullies was that it was (what I would later discover was called) a Nash equilibrium.
I had drawn up some rather detailed ideas for an atomic powered future: The idea was to solve two major problems. The first was the inherent risk of an over pressure causing such a power plant to explode. The second problem to solve was the looming water shortage facing many nations.
The idea was a power plant that used internal sterling technology so as to operate at atmospheric pressures. Reinforcing this idea was basically a design for the reactor to “entomb” itself if it reached temperatures high enough to melt its shell. The top of the sterling engine would have a salt water reservoir that would be boiled off. The water then would be collected and directed in a piping system to a reservoir. The plant would then both produce electricity AND fresh water.
Of course then while researching thorium power technology in school I discovered that the South Korean SMART micro reactor does in fact desalinate water. On one level I was depressed that my idea was not “original” however, overall I’m exited that I came up with an idea that apparently had enough merit for people actually go through and make a finished design based upon it. The fact that my idea had merit at all gives me hope for my future as an engineer.
I’m another independent discoverer of something like utilitarianism, I think when I was in elementary school. My earliest written record of it is from when I was 15, when I wrote: “Long ago (when I was 8?), I said that the purpose of life was to enjoy yourself & to help others enjoy themselves—now & in the future.”
In high school I did a fair amount of thinking (with relatively little direct outside influence) about Goodhart’s law, social dilemmas, and indirect utilitarianism. My journal from then include versions of ideas like the “one thought too many” argument, decision procedures vs. criterion for good, tradeoffs between following an imperfect system and creating exceptions to do better in a particular case, and expected value reasoning about small probabilities of large effects (e.g. voting).
On religion, I thought of the problem of evil (perhaps with outside influence on that one) and the Euthyphro argument against divine command theory.
16-year-old me also came up with various ideas related to rationality / heuristics & biases, like sunk costs (“Once you’re in a place, it doesn’t matter how you got there (except in mind—BIG exception)”), selection effects (“Reason for coincidence, etc. in stories—interesting stories get told, again & again”), and the importance of epistemic rationality (“Greatest human power—to change ones mind”).
I’ve found that ideas that affect me most fall into two major categories: either they will be ideas that hit me completely unprepared or they are ideas that I knew all along but had not formalized. Many-Worlds and and timelessness were the former for me. Utilitarianism and luminosity were the latter.
After learning the very basics of natural selection, I started thinking about goal systems and reward circuits and ethics. I thought that all of our adaptations were intended to allow us to meet our survival needs so we could pass on our genes. But what should people do once survival needs are met? What’s the next right and proper goal to pursue? That line of reasoning’s related Googling led me to Eliezer’s Levels of Intelligence paper, which in turn led me to Less Wrong.
Reading through the sequences, I found so many of the questions that I’d thought about in vague philosophical terms explained and analyzed rigorously, like personal identity vs continuity of subjective experience under things like teleportation. Part of the reason LW appealed to me so much back then is, I suspect, that I had already thought about so many of the same questions but just wasn’t able to frame them correctly.
This made me curious enough to skim through my childhood writing. Convergent and divergent infinite series, quicksort, public choice theory, pulling the rope sideways, normative vs positive statements, curiosity stoppers, the overton window.
My Moloch moment is what led me to seek out Overcomingbias.
Tangent thread: What sophisticated idea are you holding on to that you are sure has been formalized somewhere but haven’t been able to find?
I’ll go first: When called to explain and defend my ethics I explained I believe in “Karma, NO not the that BS mysticism Karma, but plain old actions have consequences in our very connected world kind of Karma.” If you treat people in a manner of honesty and integrity in all things, you will create a community of cooperation. The world is strongly interconnected and strongly adaptable so the benefits will continue outside your normal community, or if you frequently change communities. The lynchpin assumption of these beliefs is that if I create One Unit of Happiness for others, it will self propagate, grow and reflect, returning me more that One Unit of Happiness over the course of my lifetime. The same applies for One Unit of Misery.
I’ve only briefly studied ethics and philosophy, can someone better read point my to the above in formal context.
This seems like a good place to ask about something that I’m intensely curious about but haven’t yet seen discussed formally. I’ve wanted to ask about it before, but I figured it’s probably an obvious and well-discussed subject that I just haven’t gotten to yet. (I only know the very basics of Bayesian thinking, I haven’t read more than about 1⁄5 of the sequences so far, and I don’t yet know calculus or advanced math of any type. So there are an awful lot of well-discussed LW-type subjects that I haven’t gotten to yet.)
I’ve long conceived of Bayesian belief statements in the following (somewhat fuzzily conceived) way: Imagine a graph where the x-axis represents our probability estimate for a given statement being true and the y-axis represents our certainty that our probability estimate is correct. So if, for example, we estimate a probability of .6 for a given statement to be true but we’re only mildly certain of that estimate, then our belief graph would probably look like a shallow bell curve centered on the .6 mark of the x-axis. If we were much more certain of our estimate then the bell curve would be much steeper.
I usually think of the height of the curve at any given point as representing how likely I think it is that I’ll discover evidence that will change my belief. So for a low bell curve centered on .6, I think of that as meaning that I’d currently assign the belief a probability of around .6 but I also consider it likely that I’ll discover evidence (if I look for it) that can change my opinion significantly in any direction.
I’ve found this way of thinking to be quite useful. Is this a well-known concept? What is it called and where can I find out more about it? Or is there something wrong with it?
I don’t understand where the bell curve is coming from. If you have one probability estimate for a given statement with some certainty about it, you would depict it as a single point on your graph.
The bell curves in this context usually represent probability distributions. The width of that probability distribution reflects your uncertainty. If you’re certain, the distribution is narrow and looks like a spike at the estimate value. If you’re uncertain, the distribution is flat(ter). Probability distributions have to sum to 1 under the curve, so the smaller the width of the distribution, the higher the spike is.
How likely you are to discover new evidence is neither here nor there. Even if you are very uncertain of your estimate, this does not convert into the probability of finding new evidence.
I think you’re referring to the type of statement that can have many values. Something like “how long will it take for AGI to be developed?”. My impression (correct me if I’m wrong) is that this is what’s normally graphed with a probability distribution. Each possible value is assigned a probability, and the result is usually more or less a bell curve with the width of the curve representing your certainty.
I’m referring to a very basic T/F statement. On a normal probability distribution graph that would indeed be represented as a single point—the probability you’d assign to it being true. But we’re often not so confident in our assessment of the probability we’ve assigned, and that confidence is what I was trying to represent with the y-axis.
An example might be, “will AGI be developed within 30 years”? There’s no range of values here, so on a normal probability distribution graph you’d simply assign a probability and that’s it. But there’s a very big difference between saying “I really have not the slightest clue, but if I really must assign it a probability than I’d give it maybe 50%” vs. “I’ve researched the subject for years and I’m confident in my assessment that there’s a 50% probability”.
In my scheme, what I’m really discussing is the probability distribution of probability estimates for a given statement. So for the 30-year AGI question, what’s the probability that you’d consider a 10% probability estimate to be reasonable? What about a 90% estimate? The probability that you’d assign to each probability estimate is depicted as a single point on the graph and the result is usually more or less a bell curve.
You’re probably correct about this. But I’ve found the concept of the kind of graph I’ve been describing to be intuitively useful, and saying that it represents the probability of finding new evidence was just my attempt at understanding what such a graph would actually mean.
OK, let’s rephrase it in the terms of Bayesian hierarchical models. You have a model of event X happening in the future which says that the probability of that event is Y%. Y is a parameter of your model. What you are doing is giving a probability distribution for a parameter of your model (in the general case this distribution can be conditional, which makes it a meta-model, so hierarchical). That’s fine, you can do this. In this context the width of the distribution reflects how precise your estimate of the lower-level model parameter is.
The only thing is that for unique events (“will AGI be developed within 30 years”) your hierarchical model is not falsifiable. You will get a single realization (the event will either happen or it will not), but you will never get information on the “true” value of your model parameter Y. You will get a single update of your prior to a posterior and that’s it.
Is that what you have in mind?
I think that is what I had in mind, but it sounds from the way you’re saying it that this hasn’t been discussed as a specific technique for visualizing belief probabilities.
That surprises me since I’ve found it to be very useful, at least for intuitively getting a handle on my confidence in my own beliefs. When dealing with the question of what probability to assign to belief X, I don’t just give it a single probability estimate, and I don’t even give it a probability estimate with the qualifier that my confidence in that probability is low/moderate/high. Rather I visualize a graph with (usually) a bell curve peaking at the probability estimate I’d assign and whose width represents my certainty in that estimate. To me that’s a lot more nuanced than just saying “50% with low confidence”. It has also helped me to communicate to others what my views are for a given belief. I’d also suspect that you can do a lot of interesting things by mathematically manipulating and combining such graphs.
One problem is that it’s turtles all the way down.
What’s your confidence in your confidence probability estimate? You can represent that as another probability distribution (or another model, or a set of models). Rinse and repeat.
Another problem is that it’s hard to get reasonable estimates for all the curves that you want to mathematically manipulate. Of course you can wave hands and say that a particular curve exactly represents your beliefs and no one can say it ain’t so, but fake precision isn’t exactly useful.
Taken literally, the concept of “confidence in a probability” is incoherent. You are probably confusing it with one of several related concepts. Lumifer has described one example of such a concept.
Another concept is how much you think your probability estimate will change as you encounter new evidence. For example, your estimate for whether the outcome of the coin flip for the 2050 Superbowl will be heads is 1⁄2, and you are unlikely to encounter evidence that changes it (until 2050 that is). On the other hand, your estimate for the probability AI being developed by 2050 is likely to change a lot as you encounter more evidence.
I don’t know, I think the existence of the 2050 Superbowl is significantly less than 100% likely.
What’s your line of thought?
It wouldn’t be the first time a sport has gone from vastly popular to mostly forgotten within 40 years. Jai alai was the particular example I had in mind; it was once incredibly popular, but quickly descended to the point where it’s basically entirely forgotten.
Why? I thought the way Lumifer expressed it in terms of Bayesian hierarchical models was pretty coherent. It might be turtles all the way down as he says, and it might be hard to use it in a rigorous mathematical way, but at least it’s coherent. (And useful, in my experience.)
This is pretty much what I meant in my original post by writing:
But expressing it in terms of how likely my beliefs are to change given more evidence is probably better. Or to say it in yet another way: how strong new evidence would need to be for me to change my estimate.
It seems like the scheme I’ve been proposing here is not a common one. So how do people usually express the obvious difference between a probability estimate of 50% for a coin flip (unlikely to change with more evidence) vs. a probability estimate of 50% for AI being developed by 2050 (very likely to change with more evidence)?
I believe you may be confusing the “map of the map” for the “map”.
If I understand correctly, you want to represent your beliefs about a simple yes/no statement. If that is correct, the appropriate distribution for your prior is Bernoulli. For a Bernoulli distribution, the X axis only has two possible values: True or False. The Bernoulli distribution will be your “map”. It is fully described by the parameter “p”
If you want to represent your uncertainty about your uncertainty, you can place a hyperprior on p. This is your “map of the map”. Generally, people will use a beta distribution for this (rather than a bell-shaped normal distribution). With such a hyperprior, p is on the X-axis and ranges from 0 to 1.
I am slightly confused about this part, but it is not clear to me that we gain much from having a “map of the map” in this situation, because no matter how uncertain you are about your beliefs, the hyperprior will imply a single expected value for p
I believe you may be confusing the “map of the map” for the “map”.
If I understand correctly, you want to represent your beliefs about a simple yes/no statement. If that is correct, the appropriate distribution for your prior is Bernoulli. For a Bernoulli distribution, the X axis only has two values: True or False. The Bernoulli distribution will be your “map”. It is fully described by the parameter “p”
If you want to represent your uncertainty about your uncertainty, you can place a hyperprior on p. This is your “map of the map”. Generally, people will use a beta distribution for this (rather than a bell-shaped normal distribution). With such a hyperprior, p is on the X-axis and ranges from 0 to 1.
I am slightly confused about this part, but it is not clear to me that we gain much from having a “map of the map” in this situation, because no matter how uncertain you are about your beliefs, the hyperprior will imply a single expected value for p.
The influence of the British Empire on progressivism.
There was that book that talked about how North Korea got its methods from the Japanese occupation, and as soon as I saw that, I thought, “well, didn’t something similar happen here?” A while after that, I started reading Imagined Communities, got to the part where Anderson talks about Macaulay, looked him up, and went, “aha, I knew it!” But as far as I know, no one’s looked at it.
Also, I think I stole “culture is an engineering problem” from a Front Porch Republic article, but I haven’t been able to find the article, or anyone else writing rigorously about anything closer in ideaspace to that than dynamic geography, except the few people who approach something similar from an HBD or environmental determinism angle.
I believe Rational Self Interest types make similar arguments, though I can’t recall anyone breaking it down to marginal gains in utility.
I figured out utilitarianism aged ~10 or so.
I had some thoughts about the “power” of mathematical proof techniques that I now recognize as pointing towards turing completeness.
Well, this isn’t quite what you were asking for, but, as a young teenager a few days after 9/11, I was struck with a clear thought that went something like: “The American people are being whipped into a blood frenzy, and we are going to massively retaliate against somebody, perpetuating the endless cycle of violence that created the environment which enabled this attack to occur in the first place.”
But I think it’s actually common for young people to be better at realpolitik and we get worse at it as we absorb the mores of our culture.
In middle school I heard a fan theory that Neo had powers over the real world because it was a second layer of the matrix—the idea of simulations inside simulations was enough for me to come to Bostrom’s simulation argument.
Also during the same years I ended up doing an over the top version of comfort zone expansion by being really silly publicly.
In high school I think I basically argued a crude version of compatibilism before learning the term, although my memory of the conversation is a bit vague
This happened when I was 12 years old. I was trying to solve a problem at a mathematical contest which involved proving some identity with the nth powers of 5 and 7. I recall thinking vaguely “if you go to n+1 what is added in the left hand side is also in the right hand side” and so I discovered mathematical induction. In ten minutes I had a rigorous proof. Though, I didn’t find it so convincing, so I ended with an unsure-of-myself comment “Hence, it is also valid for 3, 4, 5, 6 and so on...”
When I was in high school, creationism seemed unsatisfying in the sense of a Deus Ex Machina narrative (I often wonder how theists reconcile the contradiction between the feeling of religious wonder and the feeling of disappointment when facing Deus Ex Machina endings). The evolution “story” fascinated me with its slow and semi-random progression over billions of years. I guess this was my first taste of reductionism. (This is also an example of how optimizing for interestingness instead of truth has led me to the correct answer.)
Cartesian skepticism and egoism, when I was maybe eleven. I eventually managed to argue myself out of both—Cartesian skepticism fell immediately, but egoism took a few years.
(In case it isn’t obvious from that, I did not have a very good childhood.)
I remember coming close to rediscovering pseudoformalism and the American caste system, but I discovered those concepts before I got all the way there.
I independently conceived of determinism and a vague sort of compatibilism when I was twelveish.
I remember being inordinately relieved/happy/satisfied when I first read about determinism around 14 or 15 (in Sophie’s World, fwiw). It was like, thank you, that’s what I’ve been trying to articulate all these years!
(although they casually dismissed it as a philosophy in the book, which annoyed 14-or-15-year-old me)
Good one! I think I also figured out a vague sort of compatibilism about that time.
When I was first learning about neural networks, I came up with the idea of de-convolutional networks: http://www.matthewzeiler.com/
Also, I think this is not totally uncommon. I think this suggests that there is low-hanging fruit in crowd-sourcing ideas from non-experts.
Another related thing that happens is that I’ll be reading a book, and I’ll have a question/thought that gets talked about later in the book.
I rediscovered most of the more widely agreed upon ontological categories (minus one that I still don’t believe to adhere to the definition) before I knew they were called that, at about the age of 17. The idea of researching them came to me after reading a question from some stupid personality quiz they gave us in high school, something like “If you were a color, which color would you be?”—and something about it rubbed me the wrong way, it just felt ontologically wrong, conflating entities with properties like that. (Yes, I did get the intended meaning of the question, I wasn’t that much of an Aspie even back then, but I could also see it in the other, more literal way.)
I remember it was in the same afternoon that I also split up the verb “to be” into its constituent meanings, and named them. It seemed related.
Maybe these aren’t so sophisticated, but I figured out determinism + a form of compatibilism, and the hard problem of consciousness in 10th grade.
In second or third grade, I noticed that (n+1) (n+1) = (n n) + n + (n+1).
I came up with a basic version of Tegmark’s level 4 multiverse in high school and wrote an essay about it in English class. By that time though I think I’d already read Permutation City which involves similar ideas.
I think I was a de facto utilitarian from a very young age; perhaps eight or so.
I independently constructed algebra (of the ‘3*x+7=49. Solve for x.’ variety) while being given ‘guess and check’ word problems in second grade. That’s a slightly different variety than most of the other examples here, though.
Fun question!
Under 8: my sister and I were raised atheist, but we constructed what amounted to a theology around our stuffed animals. The moral authority whom I disappointed most often, more than my parents, was my teddy bear. I believed in parts of our pantheon and ethics system so deeply, devoutly, and sincerely that, had I been raised in a real religion, I doubt my temperament would have ever let me escape.
Around 8: My mother rinsed out milk bottles twice, each time using a small amount of water. I asked her why she didn’t rinse it out once using twice as much water. She explained that doubling the water roughly doubled the cleansing power, but rinsing the bottle twice roughly squared the cleaning power. The most water-efficient way to clean a milk bottle, I figured, would involve a constant stream of water in and out of the bottle. I correctly modeled how the cleaning rate (per unit water) depends on the current milk residue concentration, but I couldn’t figure out what to do next or if the idea even made sense.
Around 14: Composition is like multiplication, and unions (or options, or choices)) are like addition.
University: (1) use Kolmogorov complexity to construct a bayesian prior over universes, then reason anthropically. When you do this, you will (2) conclude with high probability that you are a very confused wisp of consciousness.