If you're arguing with someone, it's presumably because you're trying to alter how they are thinking: Whether you want to call it convincing, persuading, or converting, is largely a question of semantics, for our purposes here.
Religion depends on both reason and logic (a tool in the use of reason.) The church does have beliefs that feed into logical systems that they hold. They do not hide them; They have an entire encyclopedia online that you can peruse through. Choices of hiding reasons and explanations have always existed for strategic purposes, this is universe to almost all big positions, at some time or another. Buddhists have almost certainly concealed their beliefs, rationals, and logical chains for strategic purposes at one time or another.
The fundies will think you're a fool for both declaring that they are anti-logical, because they know that they exercise logic (which is true, otherwise there could be no sequiters in their reasoning -- "God demands worship from all men, you are a man, ergo God demands worship from you." -- An utterly logical line of thinking, if you accept the premises.), and they'll think you are a fool for not on your knees and prostrating yourself, or following what they believe to be true, and common sense.
Religion, actually, is obviously and entirely reasonable. Self-consistent logic still requires faith, because logic always has base premises. 5-axiom geometry only comes to life if we find reason to accept those base axioms.
Reason involves the use of logic, but logic is not the main tool of reason. Imagination, perception, comparison, desire, remembrance, simulation, and several other tools are crucial in the practice of reason. Reason is, in no way, shape, or form, a forward chaining or reverse chaining reasoner,..!
It would be nice if we could just wave a wand and say, "Be reasonable, enemies of reason!" But the problem is that they are reasoning, and they're reasoning within a harmful complete system of thought that, like all systems of thought that survive, have developed a tough armor that answers questions and deflects questions behind a veil of knowingness.
Similar to how you are doing, right now, avoiding the idea that there is no one logical way of reasoning! That is, you are using a cartoon model, in which there is "logical" reasoning, and there is "illogical thinking," which isn't reason. But if you study this for a while, you find that reason is vastly more complicated than the cartoon model. But because the cartoon model provides answers to your questions, you are uncomfortable stepping out of it. It might awaken questions that you don't know how to answer, such as, "Well, if they are being reasonable, how can I condemn their thinking?" You can, it's just going to take time to work out your thoughts.
The first thing to do, though, is get a proper picture of logic: Logic is just like a network of pipes. If you accept that the water goes in a certain way, and if your fasteners between the pipes are tight, than you accept the way the water goes out. All logic is, is a network of pipes. Mathematics "works" because it doesn't have any faiths, except that others have correctly laid out and tested their pipe networks. (In case the link dies: When you're reading the second half of a proof, having checked the first half, you trust that your check was "good," and that your memory is true.) Mathematics is just a gigantic network of pipes. It makes no claims, whether the axioms are true or not. But for anything connected to the material world, there are all sorts of trick things: "Are the inputs correct?" Usually the inputs are described in words, which are tricky little beasties, even in themselves. Do we understand the idea worlds where pipes meet,
In the example you cited, most people already thought something, and they just needed to be able to establish internal communications.
However, there are situations where most people don't think something, but it's possible, given the proper arguments, that they could be convinced.
The question is then: "Can they hear the arguments?"
If the people who believe in the idea are destroyed before they can ever put their arguments together and present them, then no change in perspective can occur.
The progress of society decays.
My argument is not that the future will turn out one way or another; My argument is there merely to point out something that could go wrong.
Well, there are those situations where society is wrong, and needs to be called on it.
Will society be responsive? That's the question.
If society is not responsive when society is wrong, then this is horrific and terrible and should be opposed.
If society is responsive, then we should welcome our new neighborly overlords.
Example: "Women shouldn't be allowed to vote." Suppose we had this high technology, and it's early 1900's. You and your subversive friend are having a discussion, and whisper that you think women should be able to vote. Obviously, you are trying to create a subversive cell movement; And unfortunately for you, someone with a microphone and a camera caught it, and posted it online. You are visibly and painfully ostracized from society. Anyone who thought at least some bit of sympathy for your way of thinking either changes their mind (against you,) or decides to stay quiet. Because a critical mass of people are able to express their opinion, society is incapable of changing, and the passages of perspective are blocked.
Will society be responsive in our future environment? We do not know. It seems reasonable to believe that the future may resemble a panopticon, but that piece of evidence alone doesn't tell us enough; We don't know what balancing forces may exist.
But, anyways: There's an example of how the system you described might be flawed.
Religion doesn't teach logic, it teaches anti-logic, and these well-indoctrinated fools are thus unable to follow the above arguments.
It's unfortunate that the situation is complex.
Reason is not logic, and religion does not teach anti-logic, because it so often depends on logic.
That you disagree with the inputs (and therefor outputs) of their logical constructions is your problem with it.
The indoctrinated have not had conversations, or have shied away from conversations, that contradict their primary theses. Your challenge is to figure out how to convert them, and their challenge is to figure out how to convert you; That's the way the passages of perspective work.
Telling them that they're not logical is going to do absolutely nothing, because from their vantage point, you've just proven yourself for a fool.
So find your rational bases and your compelling points, and argue from those.
I don't doubt for a second that religious parents will use their vouchers to send their children to a religious school.
What I doubt is that forcing their kids to learn something that their parents, pastors, and friends tell them is nonsense, is going to sway minds, and improve national dialog. I think people will believe what they want to believe, and that parents will continue to indoctrinate their children.
Consider people as embodied ideas, and the attempt to control the thoughts of children (however unsuccessful) can only be viewed as theft of children.
Statements to the effect that "The law ought to require schoolkids to be vaccinated against it" are directly comparable to the belief that the United States should be a Theocracy. The battle that could come of such thinking could only be an armed civil war. I do not believe that the movement of the Enlightenment could stomach such a battle.
The struggle between religious horseshit, and an evolutionary naturalistic spirituality, will have to be won with direct dialog, or it, quite simply, won't be won at all.
You are right to identify that most people believe in evolution by way of authority, rather than knowledge.
That said, the authority that people are entrusting has done a lot to earn that trust by following and explaining processes that work to build a good understanding of the world. Those scientists are sincere, meticulous, and well organized. There's every reason to trust them and believe them. Further, that their processes work is repeatedly vindicated: Every year, they see further, discover new things, and invent new machines, that become part of our daily world. So, their clout does not seem to be entirely artificial, and it is clear that they are engaged in honest rational processes.
This is far better than the multitude of competition, in most circumstances.
Your first paragraph's argument I find interesting.
I disagree that violence is the only result when you fervently believe in something: Many times, children are the result (parents believing in one another's love,) sacrifice can be a result (the followers of Ghandi,) some times a company or a new product are a result (belief that the company can make it,) or the discovery of a new country ("there's something over there.")
You are concerned that evangelizing science, thoughtful skepticism, appreciation for the Universe, the common humanity of all people, and the Enlightenment will lead to violence, but that indoctrinating religious people's children will not. I remain unconvinced.
As for a baseline literacy and knowledge; I'm not so sure that it really works. Perhaps we're stealing away the minds of some fundamentalist Christians children, and perhaps it's the school system that does it, but I remain unconvinced. I think that, when children picked up science in schools, it's because their parents were open to it already, and encouraging their children: "Study this. Learn what we have not." And how did that happen? I think that people looked around, at the scientific discoveries, and talked with scientists they knew, or read a book, or read an argument in a newspaper, and talked about it with people, and made up their own mind. I don't think it was the school. I think the school battle is near irrelevant, really. You can teach kids things, but if their parents oppose it, especially in an organized way, I'm not convinced you get traction; I think you just annoy people.
As for just the concept of schooling, as necessary to teach the basics and so on; This is the most radical thing you'll hear me say here (and feel free to dismiss it,) but I don't believe in it at all. I say that because I visited a Sudbury school, after reading an article on Boing Boing that Cory Doctorow wrote. I interviewed several of the kids there, and checked out what they were reading, and what they were doing. I was impressed: Kids actually do teach themselves how to read, and more than that, I was impressed with how articulate, thoughtful, confident, good natured, responsible, and adult they were. They were still kids, and they weren't geniuses, but there was an unmistakable clarity, thoughtfulness, and deliberateness there, and it was there with all of them (teenagers mostly) that I talked with. If you bring an argument to them, and say, "What do you think about this?"...they'll give you a thoughtful reply, from many angles.
What I'm saying is: I'm not convinced that "schooling" is one tenth as necessary as our society believes that it is. Yes, many of these kids (I don't know the figures)
I've put my money where my mouth is, incidentally; I've enrolled my almost-6-years-old daughter in the school, and I'm, personally, very impressed.
I doubt I've convinced you of anything particular, but, please carry this with you, and if you ever get a chance, perhaps look into this a little.
Unfortunately, the West does not recognize it and chalks this up as perversion of the "Religion of Peace".
Actually, a lot of us do realize the situation, and we're focusing on the lot of Muslims are nominal Muslims whose humanity trumps the call of oppression.
By appealing to what is noble in their religion, rather than what is not, (which our enemies are doing,) we hope to give those Muslims a way out of the choices they are being presented with by our opposition.
That is, they can say, "Are we not the religion of Peace?"...and transform (or recover) their religion.
That's the plan.
Christianity liberalized and modernized, so can Islam. The alternatives are very nasty.
Easy: give the vouchers for care of children, not any particular schooling.
Everyone needs children taken care of, and it's in societies best interest to make sure that children are cared for.
The matter of curriculum, testing, and so on, is left totally up to parents and who they contract to.
"What if they're teaching abiogenesis?" Well, what if? What do you suppose we should do instead: Have teachers tell their students that their parents are stupid?
That may be the present strategy, but I think it's the wrong one. I don't believe in any of that nonsense either (straight up evolution & scientific determinism, for me.) But I don't believe in stealing children from their parents, either.
It's been standard practice for a long time now, but I think it's about time we stop.
I think we should start understanding and evangelizing our own perspective. Most who have a trust in scientists can't really tell you what standard candles are, what kinds of radioactive dating there are and why we use different ones, what evolved from what, what the major epochs of our 13.7 billion year history are, and so on. But the bible kids and the Mormons understand the fundamentals of their religion. They know King David, they know Paul, they know Peter. They know what Jesus said, and when, and why. They know their Judges. They hold contests amongst themselves to prove they can memorize so many versus.
I strongly believe it's time that we understand, and teach, and preach, what it is that we believe, and why we believe it. Understand the world like the Bible people understand scripture, and then get evangelical.
Go door to door: "Hi! We were wondering if you would be interested in having a very brief conversation about the Good News!" What good news? "The Good News, of our (at least) 13.7 billion year history, and the evolution of our planet." (Evangelical hands over some photographs of Deep Space hubble imagery, novas,...) "All of this..." "Is this something that interests you? Would you have a conversation with us? Our planet is in peril, but we have an opportunity to make something really beautiful here..."
"all logically sound lines of reasoning contain exactly 0 logical gaps."
Yes, but all lines of reasoning, about anything that matters, beyond mathematics, have logical gaps. I'll make a prototype-based definition, and put into "anything that matters:" politics, economics, business, religion, the nature of the world,...
There are no flawless bases of axioms, followed by lines of logic without gaps, in any of those discussions. They are based entirely on defeasible reasoning.
This being TRUE, it is sufficient for someone to demonstrate a single logical gap to utterly discredit a line of reasoning.
And that's totally and utterly false. The vast majority of reasoning is done on the basis of appealing undercuts, not on the basis of logic. Logic as a tool, yes. Logic as a basis, absolutely not. Indeed, it would be impossible to justify most anything, on the basis of logic alone. Political parties persist, regardless of holes being found on a continuing basis. Holes are found in scientific discoveries, too, and it's just shrugged off, or people say, "Well, let's perform another test." Persistent flaws may hold some sway, but that's different.
This is how reason works, my friend in the study of reason.
Perhaps you should read the web pages you cite as support for your position.
Perhaps you should read it, but more carefully so: The page says, "If you have a single gap in the chain, logic no longer asserts anything beyond the chain."
Ah-hah! And here's the thing: Logic no longer asserts anything beyond the chain.
But does reason assert anything beyond the chain? Regularly, daily, continuously.
Because your inability to respond when someone points out holes in your reasoning does NOT make your own argument more persuasive.
Non-sequiter, (just because I don't respond, it doesn't follow that I can't respond,) and a dash of ad-hominim.
Interpretation, persuasion, reason, contemplation, estimation, heuristic,... These are the things that reason is made of. We use Logic as a tool, and can apply it to segments of our reasoning process. But the presence of logic doesn't make an argument good, and breaking off parts of logic in someone's argument doesn't make it bad. In worlds constructed purely of logic, reasoning purely in logic goes a long way. But our understandings of the happenings in the material world don't operate that way.
If I sell shoes and have sufficient processing power to sell my shoes and no additional cpu power would affect my sales. Then preventing me from having any more cpu power is NOT MATERIAL to the business of selling shoes. It is a limit of no consequence.
I suspect not anybody, except for people in very poor places, will be selling shoes in 25 years. If you're still selling shoes in 25 years, I don't think your outlook is so good. The vast majority of work involve & require computation, and it will be "intelligent."
The END goal of a cpu is NOT merely to have processing power. It is to achieve some USEFUL COMPUTATION fast enough to facilitate some kind of DECISION. Any processing power beyond that end is utterly immaterial to the goal. And prohibiting it is hardly any great inconvenience.
Ah... And, so, you know just how much processing power should be enough for anybody, and beyond that, no useful computation that is not harmful to society could happen?
What you are talking about, and what you should concede, is the idea that governments should limit the intelligence of their peoples. The hard limit is a processor count, as you are describing. A type of processing, I can understand, since we already do it: You cannot draw up blueprints, (as far as I understand,) to stage an assasination. (Good luck to enforcers, though...) But you are going beyond this, saying, (
What should I do: dress up in Black and Red, Viva La Anarquia, and stick an Anarchist symbol on my bag?
When people get tired of the Starbucks brand, someone will start a new business for a different taste. The business world will make as many tastes as people like.
You want something different? Make a new taste, and sell it: Make the world a more diverse place. New brand of clothing, new brand of whatever.
Actually, I just find your arguments totally unpersuasive, and your projections about what my arguments are, what they mean, and what my motivations are, unwarranted and unreasonable.
So I'm not sure how you get the conclusion that this is a "material limit" on intelligence.
Well, look here:
Put a hard legal limit on the processing power any person is allowed to possess. Measured in gigaflops or some other metric.
Those are your words, and there is your material limit.
I don't think I'll be conversing with you much longer; I think if your method of argument continues like it is here, there's not much benefit, for either of us. You seem to be trying to point out gaps in logic, in your opponents position, implying that your own thinking does not hold similar gaps. (If you did recognize the ubiquity of gaps, you wouldn't be criticizing on the basis of their existence.) I do not find your undercuts persuasive; I hear them, but I think you have still missed more important things. Sadly, your battery of trivial undercuts are so numerous, I feel no motivation to respond to them: You will find only other little unimportant things to undercut, which are always present, in all thinking, always, and make up more ridiculous extrapolations about what I mean, and so on.
So, farewell, for now. Maybe again, some other time.
Put the numbers -1.0 through 1.0 onto the edge of a half circle, and mount it on the ceiling, hanging down. (0.0 is the lowest point, -1.0 and +1.0 touch the ceiling.) Set your infinite real number line down on the floor, with it's origin (0) directly beneath the 0.0 lowest point hanging down. Now it runs infinitely in one direction, and infinitely in another. Cast a ray from the center of the half circle, out to the real number line. For every point on the real number line, there is a unique point on the half circle's edge, and vice versa.:)
There are theories that the universe has shape, and is finite. There are theories that the universe has shape, and is infinite. There are theories that the universe goes on and on, forever and ever. There are theories that the universe goes on and on, and that we'll never know for how far. There are theories that the universe goes on and on, and that we'll one day know "how far," because we'll (in theory) know the shape. There are many theories. Presently, there are many tests, and it's very likely that we will huck a number of these theories within 10 years, and focus more on the remaining theories.
I just looked up GRbs, and found this page, which seems to say that they're distributed equally. Also that they are from the beginning of the universe. But I don't know much about this, and may well be wrong.
I wasn't about to go all Max Tegmark... Interesting ideas, though.
Imagine that the distance between the walls of your bedroom, and all the objects in your bedroom, are expanding. Next year, everything is twice as big, and twice as far apart. But the objects themselves stay the same size. (Due to various gravitational, electromagnetic, whatever effects.) This is basically what it's like in the universe. The "big bang" is that a bunch of space appeared between things, very quickly. But we don't know that the universe doesn't go on forever. There is stuff out beyond your apartment, you have neighbors and so on, entire cities.
New space has been appearing, and we are seeing light from "far away." It is plausible (likely?) that the entire observable universe that we see right now, occupied a space, at the time of the big bang, filled a space smaller than a centimeter, perhaps even just a plank length (smallest meaningful distance.) It doesn't mean that that was the size of the entire universe.
We'd be seeing this light from the other end of the centimeter only now, because a lot of new space appeared, and continues to appear, between one end of that centimeter, and the other end of the centimeter. (Don't take this "centimeter" figure too literally, though; I'm just pulling that out of the air. I just mean "a very small distance.")
We do not and cannot observe the big bang from our own position in space. We just assume that people N billion light years away (50-something?) see the light that was at our particular spot, 13.7 billion light years ago. "Wait, how can someone 50+ billion light years away see light that came from here 13.7 billion years ago? Did it travel faster than light?" No; The difference is because new space has appeared before and behind the light, as it was traveling. Sort of like if I drove what for me was 100 miles by the car's count, but then we found that the road had grown to 200 miles by the time I arrived at my destination.
Does this help explain?
The main thing is that the big bang wasn't just a point; It happened everywhere. When we see the big bang in the Cosmic Background Microwave Radiation, we are seeing the light of the big bang as it happened in other places. Granted, we were all scooched together a bit more at the beginning, than we are right now. But the fact remains, the light traveled from somewhere else, and it was somewhere else, back then, too.
Oh; No, we- we actually see the Big Bang, today. We see not only the big bang, but the times between the big bang, and the present. It's sort of like looking at inverted tree rings-- the center tree rings are the present, and the outer tree rings are the past. We even see "bands" of history; For example, radio galaxies only appear within a certain radius. There are "growth stages" to the matter in the universe. You only see such-and-such at ye distance, and such-and-such things at ye further distance, and so on, all the way back to the very "beginning," the Cosmic Microwave Background Radiation. With Mitaka, you can see also the formation of the large scale structure of the universe, very clearly. The futher away you go, the more jumbled the matter is. As you get closer and closer and closer, you see more segregation, and then the nodal points and the filament and so on.
In a sense, the answer to your question is a "Yes!" We do see "space become very bright all around." That is, we see the Cosmic Microwave Background Radiation. That is what it is. It is the initial light from the Big Bang. Or rather, it is the surface of last scattering. The CMBR was predicted by the Big Bang model, (more or less by the reasoning you just gave,) and then observed, after the prediction.
We are conditioned to think that the big bang was "bright" in the sense of shining visible white light, but my understanding is that our eyes simply observe the wrong frequency range, to be able to see it. If you look with microwave vision, you do indeed see it.
Incidentally, there's some truth to what you are saying about "if the universe continues to expand..." We already see the initial light from the Big Bang, like I just explained, but, as time passes, there's less and less of the big bang that we can truely see. The end-game scenario of the expansion of the universe would be the big rip, where we can't even see beyond the end of our own galaxy, our own solar system, our own planet, 3 feet in front of us, our own body, our brain, individual molecules, atoms, subatomics,...
So, we can see the Big Bang, we just see less and less of it as time goes by. Basically on the lines you were arguing.
Oh, one thing that may help to explain this, is that the big bang didn't happen at "a point." Rather, it happened everywhere. Or, rather, the entire observable universe fit into roughly the space of a point, (though the big bang may well have happened in infinite space, we have no idea,) and our observable universe is the only thing observable to us. We don't think the entire universe is shrinking; Only our field of vision. But it seems unlikely that the galaxies beyond our field of vision are actually disappearing. Just because I turn my head, doesn't mean my girlfriend goes away from the universe.
We know that the observable universe almost certainly came out of a volume roughly the size of a point, but we have no reason to believe (as far as I understand) that the entire universe came out of a single point, that a single point is all there was, and so on. It could be that there are "adjacent points," and next to them, more adjacent points, and so on, and that the points are a continuum, not discrete points.
If a scientist says, "The universe was a point," you don't know (without further conversation) whether they mean the entire universe or just the observable universe. We're pretty clear that the observable universe was pretty much point-like. Think like, Planck length, or perhaps whole centimeters, but definitely not light years. But scientists rarely conjecture beyond the observable universe. "We don't know" is the usual response.
This is, to me, really amazing. I only learned these things recently, after playing around with Mitaka, and then combining that with studies over Wikipedia and the Internet, and then asking some scientist friends, "Do you guys really believe that?!" It's all very different than the understanding I was given in the early 1990's, studying in school. I just was taught, learned, and assumed that the universe was closed, looped back around on itself, and was a few billion light years across, all exploding out from a point.
I now understand that that's an outdated view of things.
What I understand now, and what I see in Mitaka, makes it fairly clear to me that the universe is unknowably large. It's still possible that the universe "loops back," and there are groups of scientists researching that, looking for evidence, to see if it's true. But the sense I have, and the sense I have of what most astrophysicists have, is that it's much much larger than what we can observe, and very plausibly infinitely so.
We have good reason to believe that all of the galaxies in the visible universe were extremely close to one another- think, "a point," or something extremely small, perhaps even planck length small.
Looking backwards, what is now the visible universe occupies less and less space.
But, we think the universe is likely much larger than the visible universe. There may have been "neighboring points," no? In fact, the space that the big bang occurred in may well have gone infinitely, in all directions, with the big bang occurring everywhere; a universe of infinite plasma in infinite space. It may be that if you travel along, today, forever, you just see more and more galaxies, without limit.
When scientists talk about "all the mass in the universe," they're almost always talking about all the mass that we can see. And we think it's very likely that there's a lot (perhaps infinitely more) of mass that we don't see. I'm not talking about "dark matter," I'm talking about entire galaxies and so on.
Most scientists think that the universe doesn't have an "edge." It either wraps around in on itself, or it just keeps on going, going, going, for infinity. Is there some point where you get to "no more matter, beyond this point?" Almost certainly not. Everywhere we look, we see the same large scale structure of the universe. We have no reason to believe that, just because light hasn't had time to reach us from "further afield," that there are no galaxies over there.
First is WMAP Cosmology 101: Big Bang Concepts. I think this page is reputable, because the domain is map.gsfc.nasa.gov. There are a few things about this link- First, it makes no real commitments to shape. It says it's possible that the universe has a more complex shape than "closed sphere, flat, or open," but it's unwilling to commit to anything. That said, it suggests flat, by pointing out that "If the density just equals the critical density, the universe is flat, but still presumably infinite.... While the answer is not yet known for certain, [the average density of matter] appears to be tantalizingly close to the critical density."
Another important thing to note there, is that they use the terms "universe" and "visible universe" almost interchangably. (See, for example, the first paragraph under "The Origin of the Cosmic Microwave Background.") This jives with what Wikipedia says about "Observable universe:""Both popular and professional research articles in cosmology often use the term "universe" to mean "observable universe"." I try not to use Wikipedia, but if it points out something that seems to agree with other websites, I conditionally take it. So: When they talk about the "size" of the universe, they almost always mean the size of the observable universe. (see also...)
Yet another thing to note here, is that it says that the universe doesn't necessarily start at a point. The Big Bang may have occurred everywhere. The "bang" is about the space that is appearing between all galaxies, not that the universe was first bound into a nutshell, and then exploded outwards. A picture I have made in my head, (which may reflect astrophysicists understand, which may not reflect astrophysicists understanding,) is that, plausibly, first there was stuff everywhere, infinitely, in all direction, but, that as time passed, "additional blank space" was put between all the things that exist. The entire observable universe came from just one small tiny dot of the stuff that is everywhere. The space that we see is mostly stuff that was added, since time began. So it's not so much that the universe started out small, and then grew large, as it is that the universe started out infinite, and that infinite universe is scaling outward, like scaling the real numbers out by some multiplier, over and over and over again. (Supporting link: "In this picture the Big Bang occurred everywhere."
Here's another website, on curious.astro.cornell.edu. Cornell "astro".edu sounds reliable enough, to me. Sadly, this site is dated January, 1999.
Here's a 2006 educational publication, chapter 4 says that the universe is very nearly flat. This is typical of what I've seen on most sites. Note that in 5.1, he notes that the universe may be infinite; This, too, is fairly typical, in sites I see.
There are a number of newspaper articles, that have news of astronomers finding "hints" at one shape, or another shape, but there's nothing conclusive. In my experience, these articles are usually (A) confusing, and very likely (B) confused, and seem to be okay with that: "What will these wacky scientists come up with, next?" A funnel, a soccer ball, a pill,...
Slashdot Mirror
If you're arguing with someone, it's presumably because you're trying to alter how they are thinking: Whether you want to call it convincing, persuading, or converting, is largely a question of semantics, for our purposes here.
..!
Religion depends on both reason and logic (a tool in the use of reason.) The church does have beliefs that feed into logical systems that they hold. They do not hide them; They have an entire encyclopedia online that you can peruse through. Choices of hiding reasons and explanations have always existed for strategic purposes, this is universe to almost all big positions, at some time or another. Buddhists have almost certainly concealed their beliefs, rationals, and logical chains for strategic purposes at one time or another.
The fundies will think you're a fool for both declaring that they are anti-logical, because they know that they exercise logic (which is true, otherwise there could be no sequiters in their reasoning -- "God demands worship from all men, you are a man, ergo God demands worship from you." -- An utterly logical line of thinking, if you accept the premises.), and they'll think you are a fool for not on your knees and prostrating yourself, or following what they believe to be true, and common sense.
Religion, actually, is obviously and entirely reasonable. Self-consistent logic still requires faith, because logic always has base premises. 5-axiom geometry only comes to life if we find reason to accept those base axioms.
Reason involves the use of logic, but logic is not the main tool of reason. Imagination, perception, comparison, desire, remembrance, simulation, and several other tools are crucial in the practice of reason. Reason is, in no way, shape, or form, a forward chaining or reverse chaining reasoner,
It would be nice if we could just wave a wand and say, "Be reasonable, enemies of reason!" But the problem is that they are reasoning, and they're reasoning within a harmful complete system of thought that, like all systems of thought that survive, have developed a tough armor that answers questions and deflects questions behind a veil of knowingness.
Similar to how you are doing, right now, avoiding the idea that there is no one logical way of reasoning! That is, you are using a cartoon model, in which there is "logical" reasoning, and there is "illogical thinking," which isn't reason. But if you study this for a while, you find that reason is vastly more complicated than the cartoon model. But because the cartoon model provides answers to your questions, you are uncomfortable stepping out of it. It might awaken questions that you don't know how to answer, such as, "Well, if they are being reasonable, how can I condemn their thinking?" You can, it's just going to take time to work out your thoughts.
The first thing to do, though, is get a proper picture of logic: Logic is just like a network of pipes. If you accept that the water goes in a certain way, and if your fasteners between the pipes are tight, than you accept the way the water goes out. All logic is, is a network of pipes. Mathematics "works" because it doesn't have any faiths, except that others have correctly laid out and tested their pipe networks. (In case the link dies: When you're reading the second half of a proof, having checked the first half, you trust that your check was "good," and that your memory is true.) Mathematics is just a gigantic network of pipes. It makes no claims, whether the axioms are true or not. But for anything connected to the material world, there are all sorts of trick things: "Are the inputs correct?" Usually the inputs are described in words, which are tricky little beasties, even in themselves. Do we understand the idea worlds where pipes meet,
In the example you cited, most people already thought something, and they just needed to be able to establish internal communications.
However, there are situations where most people don't think something, but it's possible, given the proper arguments, that they could be convinced.
The question is then: "Can they hear the arguments?"
If the people who believe in the idea are destroyed before they can ever put their arguments together and present them, then no change in perspective can occur.
The progress of society decays.
My argument is not that the future will turn out one way or another; My argument is there merely to point out something that could go wrong.
Well, there are those situations where society is wrong, and needs to be called on it.
Will society be responsive? That's the question.
If society is not responsive when society is wrong, then this is horrific and terrible and should be opposed.
If society is responsive, then we should welcome our new neighborly overlords.
Example: "Women shouldn't be allowed to vote." Suppose we had this high technology, and it's early 1900's. You and your subversive friend are having a discussion, and whisper that you think women should be able to vote. Obviously, you are trying to create a subversive cell movement; And unfortunately for you, someone with a microphone and a camera caught it, and posted it online. You are visibly and painfully ostracized from society. Anyone who thought at least some bit of sympathy for your way of thinking either changes their mind (against you,) or decides to stay quiet. Because a critical mass of people are able to express their opinion, society is incapable of changing, and the passages of perspective are blocked.
Will society be responsive in our future environment? We do not know. It seems reasonable to believe that the future may resemble a panopticon, but that piece of evidence alone doesn't tell us enough; We don't know what balancing forces may exist.
But, anyways: There's an example of how the system you described might be flawed.
Religion doesn't teach logic, it teaches anti-logic, and these well-indoctrinated fools are thus unable to follow the above arguments.
It's unfortunate that the situation is complex.
Reason is not logic, and religion does not teach anti-logic, because it so often depends on logic.
That you disagree with the inputs (and therefor outputs) of their logical constructions is your problem with it.
The indoctrinated have not had conversations, or have shied away from conversations, that contradict their primary theses. Your challenge is to figure out how to convert them, and their challenge is to figure out how to convert you; That's the way the passages of perspective work.
Telling them that they're not logical is going to do absolutely nothing, because from their vantage point, you've just proven yourself for a fool.
So find your rational bases and your compelling points, and argue from those.
I don't doubt for a second that religious parents will use their vouchers to send their children to a religious school.
What I doubt is that forcing their kids to learn something that their parents, pastors, and friends tell them is nonsense, is going to sway minds, and improve national dialog. I think people will believe what they want to believe, and that parents will continue to indoctrinate their children.
Consider people as embodied ideas, and the attempt to control the thoughts of children (however unsuccessful) can only be viewed as theft of children.
Statements to the effect that "The law ought to require schoolkids to be vaccinated against it" are directly comparable to the belief that the United States should be a Theocracy. The battle that could come of such thinking could only be an armed civil war. I do not believe that the movement of the Enlightenment could stomach such a battle.
The struggle between religious horseshit, and an evolutionary naturalistic spirituality, will have to be won with direct dialog, or it, quite simply, won't be won at all.
You are right to identify that most people believe in evolution by way of authority, rather than knowledge.
That said, the authority that people are entrusting has done a lot to earn that trust by following and explaining processes that work to build a good understanding of the world. Those scientists are sincere, meticulous, and well organized. There's every reason to trust them and believe them. Further, that their processes work is repeatedly vindicated: Every year, they see further, discover new things, and invent new machines, that become part of our daily world. So, their clout does not seem to be entirely artificial, and it is clear that they are engaged in honest rational processes.
This is far better than the multitude of competition, in most circumstances.
Your first paragraph's argument I find interesting.
...they'll give you a thoughtful reply, from many angles.
I disagree that violence is the only result when you fervently believe in something: Many times, children are the result (parents believing in one another's love,) sacrifice can be a result (the followers of Ghandi,) some times a company or a new product are a result (belief that the company can make it,) or the discovery of a new country ("there's something over there.")
You are concerned that evangelizing science, thoughtful skepticism, appreciation for the Universe, the common humanity of all people, and the Enlightenment will lead to violence, but that indoctrinating religious people's children will not. I remain unconvinced.
As for a baseline literacy and knowledge; I'm not so sure that it really works. Perhaps we're stealing away the minds of some fundamentalist Christians children, and perhaps it's the school system that does it, but I remain unconvinced. I think that, when children picked up science in schools, it's because their parents were open to it already, and encouraging their children: "Study this. Learn what we have not." And how did that happen? I think that people looked around, at the scientific discoveries, and talked with scientists they knew, or read a book, or read an argument in a newspaper, and talked about it with people, and made up their own mind. I don't think it was the school. I think the school battle is near irrelevant, really. You can teach kids things, but if their parents oppose it, especially in an organized way, I'm not convinced you get traction; I think you just annoy people.
As for just the concept of schooling, as necessary to teach the basics and so on; This is the most radical thing you'll hear me say here (and feel free to dismiss it,) but I don't believe in it at all. I say that because I visited a Sudbury school, after reading an article on Boing Boing that Cory Doctorow wrote. I interviewed several of the kids there, and checked out what they were reading, and what they were doing. I was impressed: Kids actually do teach themselves how to read, and more than that, I was impressed with how articulate, thoughtful, confident, good natured, responsible, and adult they were. They were still kids, and they weren't geniuses, but there was an unmistakable clarity, thoughtfulness, and deliberateness there, and it was there with all of them (teenagers mostly) that I talked with. If you bring an argument to them, and say, "What do you think about this?"
What I'm saying is: I'm not convinced that "schooling" is one tenth as necessary as our society believes that it is. Yes, many of these kids (I don't know the figures)
I've put my money where my mouth is, incidentally; I've enrolled my almost-6-years-old daughter in the school, and I'm, personally, very impressed.
I doubt I've convinced you of anything particular, but, please carry this with you, and if you ever get a chance, perhaps look into this a little.
Unfortunately, the West does not recognize it and chalks this up as perversion of the "Religion of Peace".
...and transform (or recover) their religion.
Actually, a lot of us do realize the situation, and we're focusing on the lot of Muslims are nominal Muslims whose humanity trumps the call of oppression.
By appealing to what is noble in their religion, rather than what is not, (which our enemies are doing,) we hope to give those Muslims a way out of the choices they are being presented with by our opposition.
That is, they can say, "Are we not the religion of Peace?"
That's the plan.
Christianity liberalized and modernized, so can Islam. The alternatives are very nasty.
Easy: give the vouchers for care of children, not any particular schooling.
...) "All of this..." "Is this something that interests you? Would you have a conversation with us? Our planet is in peril, but we have an opportunity to make something really beautiful here..."
Everyone needs children taken care of, and it's in societies best interest to make sure that children are cared for.
The matter of curriculum, testing, and so on, is left totally up to parents and who they contract to.
"What if they're teaching abiogenesis?" Well, what if? What do you suppose we should do instead: Have teachers tell their students that their parents are stupid?
That may be the present strategy, but I think it's the wrong one. I don't believe in any of that nonsense either (straight up evolution & scientific determinism, for me.) But I don't believe in stealing children from their parents, either.
It's been standard practice for a long time now, but I think it's about time we stop.
I think we should start understanding and evangelizing our own perspective. Most who have a trust in scientists can't really tell you what standard candles are, what kinds of radioactive dating there are and why we use different ones, what evolved from what, what the major epochs of our 13.7 billion year history are, and so on. But the bible kids and the Mormons understand the fundamentals of their religion. They know King David, they know Paul, they know Peter. They know what Jesus said, and when, and why. They know their Judges. They hold contests amongst themselves to prove they can memorize so many versus.
I strongly believe it's time that we understand, and teach, and preach, what it is that we believe, and why we believe it. Understand the world like the Bible people understand scripture, and then get evangelical.
Go door to door: "Hi! We were wondering if you would be interested in having a very brief conversation about the Good News!" What good news? "The Good News, of our (at least) 13.7 billion year history, and the evolution of our planet." (Evangelical hands over some photographs of Deep Space hubble imagery, novas,
Oh come now; We've all seen Star Wars.
We all know how this one ends: "Now witness the firepower of this fully ARMED and OPERATIONAL battle station!"
Try out the demo for Urwid.
You can use both desktop text user interface, and web based text user interface.
AND, It's open source!
Now how much would you pay?!
"all logically sound lines of reasoning contain exactly 0 logical gaps."
...
... These are the things that reason is made of. We use Logic as a tool, and can apply it to segments of our reasoning process. But the presence of logic doesn't make an argument good, and breaking off parts of logic in someone's argument doesn't make it bad. In worlds constructed purely of logic, reasoning purely in logic goes a long way. But our understandings of the happenings in the material world don't operate that way.
Yes, but all lines of reasoning, about anything that matters, beyond mathematics, have logical gaps. I'll make a prototype-based definition, and put into "anything that matters:" politics, economics, business, religion, the nature of the world,
There are no flawless bases of axioms, followed by lines of logic without gaps, in any of those discussions. They are based entirely on defeasible reasoning.
This being TRUE, it is sufficient for someone to demonstrate a single logical gap to utterly discredit a line of reasoning.
And that's totally and utterly false. The vast majority of reasoning is done on the basis of appealing undercuts, not on the basis of logic. Logic as a tool, yes. Logic as a basis, absolutely not. Indeed, it would be impossible to justify most anything, on the basis of logic alone. Political parties persist, regardless of holes being found on a continuing basis. Holes are found in scientific discoveries, too, and it's just shrugged off, or people say, "Well, let's perform another test." Persistent flaws may hold some sway, but that's different.
This is how reason works, my friend in the study of reason.
Perhaps you should read the web pages you cite as support for your position.
Perhaps you should read it, but more carefully so: The page says, "If you have a single gap in the chain, logic no longer asserts anything beyond the chain."
Ah-hah! And here's the thing: Logic no longer asserts anything beyond the chain.
But does reason assert anything beyond the chain? Regularly, daily, continuously.
Because your inability to respond when someone points out holes in your reasoning does NOT make your own argument more persuasive.
Non-sequiter, (just because I don't respond, it doesn't follow that I can't respond,) and a dash of ad-hominim.
Interpretation, persuasion, reason, contemplation, estimation, heuristic,
If I sell shoes and have sufficient processing power to sell my shoes and no additional cpu power would affect my sales. Then preventing me from having any more cpu power is NOT MATERIAL to the business of selling shoes. It is a limit of no consequence.
I suspect not anybody, except for people in very poor places, will be selling shoes in 25 years. If you're still selling shoes in 25 years, I don't think your outlook is so good. The vast majority of work involve & require computation, and it will be "intelligent."
The END goal of a cpu is NOT merely to have processing power. It is to achieve some USEFUL COMPUTATION fast enough to facilitate some kind of DECISION. Any processing power beyond that end is utterly immaterial to the goal. And prohibiting it is hardly any great inconvenience.
Ah... And, so, you know just how much processing power should be enough for anybody, and beyond that, no useful computation that is not harmful to society could happen?
What you are talking about, and what you should concede, is the idea that governments should limit the intelligence of their peoples. The hard limit is a processor count, as you are describing. A type of processing, I can understand, since we already do it: You cannot draw up blueprints, (as far as I understand,) to stage an assasination. (Good luck to enforcers, though...) But you are going beyond this, saying, (
Every group embraces conformity.
What should I do: dress up in Black and Red, Viva La Anarquia, and stick an Anarchist symbol on my bag?
When people get tired of the Starbucks brand, someone will start a new business for a different taste. The business world will make as many tastes as people like.
You want something different? Make a new taste, and sell it: Make the world a more diverse place. New brand of clothing, new brand of whatever.
Read Rebel Sell for your intro. Then read Howard Bloom for the depths on diversity and cohesion, and follow it with a chaser of Happy Feet.
Actually, I just find your arguments totally unpersuasive, and your projections about what my arguments are, what they mean, and what my motivations are, unwarranted and unreasonable.
So I'm not sure how you get the conclusion that this is a "material limit" on intelligence.
Well, look here:
Put a hard legal limit on the processing power any person is allowed to possess. Measured in gigaflops or some other metric.
Those are your words, and there is your material limit.
I don't think I'll be conversing with you much longer; I think if your method of argument continues like it is here, there's not much benefit, for either of us. You seem to be trying to point out gaps in logic, in your opponents position, implying that your own thinking does not hold similar gaps. (If you did recognize the ubiquity of gaps, you wouldn't be criticizing on the basis of their existence.) I do not find your undercuts persuasive; I hear them, but I think you have still missed more important things. Sadly, your battery of trivial undercuts are so numerous, I feel no motivation to respond to them: You will find only other little unimportant things to undercut, which are always present, in all thinking, always, and make up more ridiculous extrapolations about what I mean, and so on.
So, farewell, for now. Maybe again, some other time.
Put the numbers -1.0 through 1.0 onto the edge of a half circle, and mount it on the ceiling, hanging down. (0.0 is the lowest point, -1.0 and +1.0 touch the ceiling.) Set your infinite real number line down on the floor, with it's origin (0) directly beneath the 0.0 lowest point hanging down. Now it runs infinitely in one direction, and infinitely in another. Cast a ray from the center of the half circle, out to the real number line. For every point on the real number line, there is a unique point on the half circle's edge, and vice versa. :)
The Secure Hardware Environment. ;)
Inevitable, in my book.
Oh; I'm just wearing a full body burqah, and sleeping in a random house each night.
There are theories that the universe has shape, and is finite. There are theories that the universe has shape, and is infinite. There are theories that the universe goes on and on, forever and ever. There are theories that the universe goes on and on, and that we'll never know for how far. There are theories that the universe goes on and on, and that we'll one day know "how far," because we'll (in theory) know the shape. There are many theories. Presently, there are many tests, and it's very likely that we will huck a number of these theories within 10 years, and focus more on the remaining theories.
You are right; It is possible that we have reached the end of physics, as we know it.
I just looked up GRbs, and found this page, which seems to say that they're distributed equally. Also that they are from the beginning of the universe. But I don't know much about this, and may well be wrong.
I wasn't about to go all Max Tegmark... Interesting ideas, though.
Ah!
Yes; I understand what you're saying.
The thing is, we didn't "explode out" from a point. Rather, the big bang happened "everywhere." (support)
The raisin bread analogy of expansion works better, for understanding this.
Imagine that the distance between the walls of your bedroom, and all the objects in your bedroom, are expanding. Next year, everything is twice as big, and twice as far apart. But the objects themselves stay the same size. (Due to various gravitational, electromagnetic, whatever effects.) This is basically what it's like in the universe. The "big bang" is that a bunch of space appeared between things, very quickly. But we don't know that the universe doesn't go on forever. There is stuff out beyond your apartment, you have neighbors and so on, entire cities.
New space has been appearing, and we are seeing light from "far away." It is plausible (likely?) that the entire observable universe that we see right now, occupied a space, at the time of the big bang, filled a space smaller than a centimeter, perhaps even just a plank length (smallest meaningful distance.) It doesn't mean that that was the size of the entire universe.
We'd be seeing this light from the other end of the centimeter only now, because a lot of new space appeared, and continues to appear, between one end of that centimeter, and the other end of the centimeter. (Don't take this "centimeter" figure too literally, though; I'm just pulling that out of the air. I just mean "a very small distance.")
We do not and cannot observe the big bang from our own position in space. We just assume that people N billion light years away (50-something?) see the light that was at our particular spot, 13.7 billion light years ago. "Wait, how can someone 50+ billion light years away see light that came from here 13.7 billion years ago? Did it travel faster than light?" No; The difference is because new space has appeared before and behind the light, as it was traveling. Sort of like if I drove what for me was 100 miles by the car's count, but then we found that the road had grown to 200 miles by the time I arrived at my destination.
Does this help explain?
The main thing is that the big bang wasn't just a point; It happened everywhere. When we see the big bang in the Cosmic Background Microwave Radiation, we are seeing the light of the big bang as it happened in other places. Granted, we were all scooched together a bit more at the beginning, than we are right now. But the fact remains, the light traveled from somewhere else, and it was somewhere else, back then, too.
Oh; No, we- we actually see the Big Bang, today. We see not only the big bang, but the times between the big bang, and the present. It's sort of like looking at inverted tree rings-- the center tree rings are the present, and the outer tree rings are the past. We even see "bands" of history; For example, radio galaxies only appear within a certain radius. There are "growth stages" to the matter in the universe. You only see such-and-such at ye distance, and such-and-such things at ye further distance, and so on, all the way back to the very "beginning," the Cosmic Microwave Background Radiation. With Mitaka, you can see also the formation of the large scale structure of the universe, very clearly. The futher away you go, the more jumbled the matter is. As you get closer and closer and closer, you see more segregation, and then the nodal points and the filament and so on.
...
In a sense, the answer to your question is a "Yes!" We do see "space become very bright all around." That is, we see the Cosmic Microwave Background Radiation. That is what it is. It is the initial light from the Big Bang. Or rather, it is the surface of last scattering. The CMBR was predicted by the Big Bang model, (more or less by the reasoning you just gave,) and then observed, after the prediction.
We are conditioned to think that the big bang was "bright" in the sense of shining visible white light, but my understanding is that our eyes simply observe the wrong frequency range, to be able to see it. If you look with microwave vision, you do indeed see it.
Incidentally, there's some truth to what you are saying about "if the universe continues to expand..." We already see the initial light from the Big Bang, like I just explained, but, as time passes, there's less and less of the big bang that we can truely see. The end-game scenario of the expansion of the universe would be the big rip, where we can't even see beyond the end of our own galaxy, our own solar system, our own planet, 3 feet in front of us, our own body, our brain, individual molecules, atoms, subatomics,
So, we can see the Big Bang, we just see less and less of it as time goes by. Basically on the lines you were arguing.
Oh, one thing that may help to explain this, is that the big bang didn't happen at "a point." Rather, it happened everywhere. Or, rather, the entire observable universe fit into roughly the space of a point, (though the big bang may well have happened in infinite space, we have no idea,) and our observable universe is the only thing observable to us. We don't think the entire universe is shrinking; Only our field of vision. But it seems unlikely that the galaxies beyond our field of vision are actually disappearing. Just because I turn my head, doesn't mean my girlfriend goes away from the universe.
(shakes head)
No, here; Check this out, and check this out.
We know that the observable universe almost certainly came out of a volume roughly the size of a point, but we have no reason to believe (as far as I understand) that the entire universe came out of a single point, that a single point is all there was, and so on. It could be that there are "adjacent points," and next to them, more adjacent points, and so on, and that the points are a continuum, not discrete points.
It does not help that when astrophysicists say "universe," they almost always mean "observable universe."
If a scientist says, "The universe was a point," you don't know (without further conversation) whether they mean the entire universe or just the observable universe. We're pretty clear that the observable universe was pretty much point-like. Think like, Planck length, or perhaps whole centimeters, but definitely not light years. But scientists rarely conjecture beyond the observable universe. "We don't know" is the usual response.
This is, to me, really amazing. I only learned these things recently, after playing around with Mitaka, and then combining that with studies over Wikipedia and the Internet, and then asking some scientist friends, "Do you guys really believe that?!" It's all very different than the understanding I was given in the early 1990's, studying in school. I just was taught, learned, and assumed that the universe was closed, looped back around on itself, and was a few billion light years across, all exploding out from a point.
I now understand that that's an outdated view of things.
What I understand now, and what I see in Mitaka, makes it fairly clear to me that the universe is unknowably large. It's still possible that the universe "loops back," and there are groups of scientists researching that, looking for evidence, to see if it's true. But the sense I have, and the sense I have of what most astrophysicists have, is that it's much much larger than what we can observe, and very plausibly infinitely so.
I'm not so sure... (link)
We have good reason to believe that all of the galaxies in the visible universe were extremely close to one another- think, "a point," or something extremely small, perhaps even planck length small.
Looking backwards, what is now the visible universe occupies less and less space.
But, we think the universe is likely much larger than the visible universe. There may have been "neighboring points," no? In fact, the space that the big bang occurred in may well have gone infinitely, in all directions, with the big bang occurring everywhere; a universe of infinite plasma in infinite space. It may be that if you travel along, today, forever, you just see more and more galaxies, without limit.
When scientists talk about "all the mass in the universe," they're almost always talking about all the mass that we can see. And we think it's very likely that there's a lot (perhaps infinitely more) of mass that we don't see. I'm not talking about "dark matter," I'm talking about entire galaxies and so on.
Things aren't "exploding out" from this point; That whole explanation is problematic.
Most scientists think that the universe doesn't have an "edge." It either wraps around in on itself, or it just keeps on going, going, going, for infinity. Is there some point where you get to "no more matter, beyond this point?" Almost certainly not. Everywhere we look, we see the same large scale structure of the universe. We have no reason to believe that, just because light hasn't had time to reach us from "further afield," that there are no galaxies over there.
OK!
... While the answer is not yet known for certain, [the average density of matter] appears to be tantalizingly close to the critical density."
.edu sounds reliable enough, to me. Sadly, this site is dated January, 1999.
...
First is WMAP Cosmology 101: Big Bang Concepts. I think this page is reputable, because the domain is map.gsfc.nasa.gov. There are a few things about this link- First, it makes no real commitments to shape. It says it's possible that the universe has a more complex shape than "closed sphere, flat, or open," but it's unwilling to commit to anything. That said, it suggests flat, by pointing out that "If the density just equals the critical density, the universe is flat, but still presumably infinite.
Another important thing to note there, is that they use the terms "universe" and "visible universe" almost interchangably. (See, for example, the first paragraph under "The Origin of the Cosmic Microwave Background.") This jives with what Wikipedia says about "Observable universe:" "Both popular and professional research articles in cosmology often use the term "universe" to mean "observable universe"." I try not to use Wikipedia, but if it points out something that seems to agree with other websites, I conditionally take it. So: When they talk about the "size" of the universe, they almost always mean the size of the observable universe. (see also...)
Yet another thing to note here, is that it says that the universe doesn't necessarily start at a point. The Big Bang may have occurred everywhere. The "bang" is about the space that is appearing between all galaxies, not that the universe was first bound into a nutshell, and then exploded outwards. A picture I have made in my head, (which may reflect astrophysicists understand, which may not reflect astrophysicists understanding,) is that, plausibly, first there was stuff everywhere, infinitely, in all direction, but, that as time passed, "additional blank space" was put between all the things that exist. The entire observable universe came from just one small tiny dot of the stuff that is everywhere. The space that we see is mostly stuff that was added, since time began. So it's not so much that the universe started out small, and then grew large, as it is that the universe started out infinite, and that infinite universe is scaling outward, like scaling the real numbers out by some multiplier, over and over and over again. (Supporting link: "In this picture the Big Bang occurred everywhere."
Here's another website, on curious.astro.cornell.edu. Cornell "astro"
Here's a 2006 educational publication, chapter 4 says that the universe is very nearly flat. This is typical of what I've seen on most sites. Note that in 5.1, he notes that the universe may be infinite; This, too, is fairly typical, in sites I see.
There are a number of newspaper articles, that have news of astronomers finding "hints" at one shape, or another shape, but there's nothing conclusive. In my experience, these articles are usually (A) confusing, and very likely (B) confused, and seem to be okay with that: "What will these wacky scientists come up with, next?" A funnel, a soccer ball, a pill,
When