The time is gone anyway, and barring industrial accident you still have your entire body to sell again afterwards. That is not true of kidney donation — you can't donate a second time¹ and if your remaining one fails you are up shit creak because if you were in the position of being willing to sell one back then you are unlikely to be in the position to buy one now.
Donation of blood and other replenishables is a bit different of course, but allowing open sale opens some bad avenues in terms of people effectively being forced to (which could carry risks they wouldn't normally want to take).
It is unintuitive to me why the rational numbers are dense in the reals, since rational numbers are countably infinite, as opposed to the reals. I think infinity is hard to grasp.
It’s because for every pair of irrational numbers, there is a first place in their decimal representation where their digits differ, which means you can construct a number with finite decimal representation that fits between the two, which thus is rational.
In other words, it’s because while there are uncountably many irrational numbers, their representation is still only countably infinite each.
Or in yet other words, uncountable infinity is only a teensy bit larger than countable infinity, not that much larger. Consider that every prefix of an irrational number is a rational number. ;)
In decimal form, almost every real number between 0 and 1 is zero-point followed by an infinite sequence of random digits. No computer in the universe has enough hard drive space to store an arbitrary fixed real number between 0 and 1. This is of course not true for rationals: any rational number can be saved on a big enough hard drive. In particular, given unbounded resources, we can build a computer that approximates (0,1) by storing a finite set of rational numbers, and reaches a given real number x with arbitrary nonzero error. But we will never get zero error on a physical computer.
The tough part with analogies like this is there are obviously rationals too large for any computer in the universe as well and anything which fixes that portion goes back to needing to reckon about the different types of infinities involved in the original problem.
I don't think that's the case here unless you are referring to a busy beaver thing I don't understand :)
If you are referring to the observable universe being finite, then that's not relevant for the discussion: I am just putting a few more grounded terms on the theorem that computable reals (including rationals) are a countable set. The point is that "for every integer n you can get n+1" is unphysical, yet "grokkable" symbolically, so it works well within a conceptual mathematical universe (regardless of what the physical universe has to say about it). Within this math universe we build an abstract computer that can hold an arbitrary rational/computable number, but only a countable subset of the real numbers, since almost all real numbers cannot be described by any "physical" program, even if that program is larger than the entire universe.
I wish I understood the busy beaver problem / connections to Ramsey theory / etc. However for this intuitive discussion it seems like a serious digression.
This is what I mean in that it only appears more grounded if you already understand why a countable set has a different type of infinity than an uncountable set in the first place and what type of universe that implies. Otherwise you're left wondering what type of universe is needed and why it is that type of universe can account for some infinities but not others. The latter part is just the answer to the original question of what the difference between a countable and uncountable set is again so if you can answer that you didn't have the question to start with!
I think you are getting away from the actual original question, which is why (intuitively) the rationals are dense in the reals despite being a different form of infinity. The confusion wasn't about different forms of infinity, it was really about the topology of R with respect to Q - why is Q "big enough" yet Z "too small" despite the sets having the same cardinality? And that is intimately related to any fixed real number having a computable/rational approximation up to any accuracy, yet most real numbers not actually being computable.
I think precisely the rationals being dense in the reals means that for any two real numbers x and y where x < y there exists a rational number m/n (m and n being integers) such that x < m/n < y.
Rationals are also dense in the p-adic numbers, which you can think of as the other way to form their completion, if I understand correctly (with a different notion of absolute value.)
I always thought using countable and uncountable was a little confusing and that introducing aleph/beth numbers would have made things clearer when those ideas were introduced.
I am reading this as "it has to be this way, or the model does not hold", but it does not explain why. What causes it? Consistency of a model cannot be the ultimate reason, right?
> I am reading this as "it has to be this way, or the model does not hold", but it does not explain why. What causes it? Consistency of a model cannot be the ultimate reason, right?
Perhaps 'because' if the consistency did not exist then the universe would fail to exist.
There was the Big Bang, but we do not know what caused the Big Bang. But the particular Big Bang that started our particular universe may not have been the only one to occur. There could have been multiple previous Big Bangs where the 'properties' of each of those created universes may not have had the same consistency as we experience, and the inconsistency(s) could have resulted in a 'collapse' or 'destruction' of those universes.
Whereas it was just a coincidence that our Big Bang got things 'right' for the universe to continue to develop.
We could simply be experiencing survivorship bias in/with our universe.
As someone who dabbles in philosophy, and to use its language, our existence is contingent (we, and our universe, do not have to exist):
Which leads to the wonderful question: why are there any contingent things? And: why are the contingent things that there are as complex as they are?
I don't know of any plausible naturalist explanation besides Many-Worlds. And that supposes for the sake of discussion that Many-Worlds is in fact naturalist.
I've heard an amusing conjecture that I'm not sure how much to take seriously unless there's a mind underlying the universe (like in simulation theory).
The void in its infinite time and endless space (the same as neither existing) became bored with itself, and in its attempt to destroy itself, split and created the universe we have now. Full of endless wonders and anomalies and beauty and travesty. All for the amusement of itself as one that remembers the abyssal void.
Many-worlds doesn’t explain the complexity of the standard model at all. It merely gets rid of the arbitrariness and discontinuity implied by wave-function collapse.
I don't think many worlds is strong enough, since it still doesn't say anything about why anything exists to begin with. You need something like the principle of plenitude.
> Perhaps 'because' if the consistency did not exist then the universe would fail to exist.
I think the unsatisfactory feeling I get from these answers is that nobody ever tries to model worlds with different physics or different physical parameters and try to make them work.
It's one thing to know that everything will break down if parameters of this universe change slightly, but I don't think anyone ever actually seriously tried to make alternatives work, and simply assumed that the only model we know that works is the only possibility.
Of course, I understand it's hard, and we might not have the compute to properly run the simulations to see how things actually work out (without quantum computers, apparently the problem is exponentially hard on classical computers). But philosophically it feels lazy and unimaginative.
> nobody ever tries to model worlds with different physics or different physical parameters and try to make them work.
Alternative models are being explored all the time. There is incentive to do so, because coming up with better explanations is likely to win Nobel prizes. What is now called the standard model, however, so far explains the existing observations the best, despite being more complex and having a higher amount of arbitrariness than most physicists would like.
You're talking about better models for our current physical reality.
I'm talking about consistent models that don't match our physical reality, but that can potentially simulated and which can give rise to intelligent life.
I'm curious how the field that allows vibration exists instead of just pure nothing that isn't a field that doesn't allow vibration or bending or virtual particles etc. Heisenberg's principle seems contingent on the void of nothing being a field that can wobble.
> Heisenberg's principle seems contingent on the void of nothing being a field that can wobble.
Sadly (?) the word "nothing" seems to have become overloaded, so now—depending on who you talk to—you can have the word pointing to different concepts. See "seven types/levels of nothing":
A silly thought I had while reading that article: it presupposes that "nothing" is a noun. In doing so, it assumes that in the sentence "the <noun> <verbs>" you can substitute "nothing" and it would mean "<nothing> is an entity that does the <verbing>" instead of "<verbing> simply does not happen", and I feel that is a meaningful distinction.
> Sadly (?) the word "nothing" seems to have become overloaded
"Infinity" is another one of those things that used to be murky, but simple; after Cantor we now have different infinities ℵ0, ℵ1... an un-Ockhamian proliferation of terms, and we have to worry about the spaces between them. Science ruins everything!
I recently came into the concept of the great attractor; the mysterious force that our galaxy is hurtling towards. It is thought to be some supermass of star material and other things.
What if that supermass is another(the next?) big bang forming; energy just slides around some universe space banging off here and there, forever?
But it does feel like you might have a point here. If everything is moving away from each other, things must have a center some where, and thats where this new big bang is forming?
> If everything is moving away from each other, things must have a center some where
This is not correct: every object is getting further from every other object it's not gravitationally bound to, at a rate approximately proportional to the distance between them.
Not a physisist, but "consistency with the model" doesn't mean "because that's how some arbitrary model says it should be".
It's more like: "Because we have arrived at a model that describes well most other aspect of those particles and their behavior, and has verified predictive power, and given the constrains and calculations based on that model, that's what its charge would be".
Exactly this. Or to put it another way we don't actually know how the rules of the universe work. So we can't follow a process of deductive reasoning that "why" follows from this or that implication.
Take quantum mechanics. This came out of observations that particles exhibited wave-like behaviour. Mathematics predicts certain things when you start to apply the wave equation. These are then experimentally verified and the model is shown to be pretty good, although it has some deficiencies like not fully linking up with relativity. There are some doubts in some areas of what it predicts as well from what I understand from talking to researchers.
As the article says the original model was that protons were fundamental particles: nothing smaller. This model held up for quite some time but then observational data demonstrated it was insufficient. Same with the three quark model. Knowing the various deficiencies we might go so far as to say "the model that a proton is a +1 charge is good enough" and use that because that works for many situations and that's as much as we need. Although of course, there are always scientists looking to complete the picture.
Science is the incremental acquisition of knowledge through observation and experimentation - and there's an awful lot we haven't figured out.
I just would like to point out that "why" is not a scientific question.
Feynman mentions this quite a lot. The question "why" doesn't have answers in science. A question of "How" has a better chance of being answered in science.
I think that was a fairly idiosyncratic point of view of Feynman's. In actual scientific practice you can find hundreds of examples of published scientific papers that address 'why' questions. Here are a couple of completely random examples:
They answer the why's with the same way @hansbo complained about not answering the why, e.g:
" We show that the symmetries of this non-commutative space unify the standard model of particle physics with (2)
chiral gravity. The algebra of the octonionic space yields spinor states which can be identified with three generations of quarks and leptons. The geometry of the space implies quantisation of electric charge, and leads to a theoretical derivation of the mysterious mass ratios of quarks and the charged leptons. Quantum gravity is quantisation not only of the gravitational field, but also of the point structure of space-time."
It's not uncommon for a scientific paper to raise a question without fully answering it (science is hard). The point is that actual scientific practice does not appear to care about any distinction that can usefully be described as a distinction between 'how' and 'why' questions. You can keep asking 'but why?' ad infinitum and never arrive at a fully satisfying explanation. However, the same is also try of 'but how?' We will find no ultimate answers, but the questions that stimulate scientific research certainly seem to include 'why' questions.
"Why" is more of a philosophy question, pre-scientific or a-scientific if you like. Science question would be "How". Maybe not this particular Q, but having in mind that on every A-answer, one can again ask Q-question "Why". That's more philosophy not so much science, imo.
i.e. it's the only combination that works. A proton is a bunch of other particles that, when combined together, balance out an electron. The 'why' is 'because that's a stable configuration' in the same way that water at 25c is liquid not gas because the 'rules' of the local environment dictate that.
I mean, why do those particles exist at all? That's really what you're asking. Why do electrons exist, why do protons 'form' from subatomic particles to balance them out? Existential kinda question.
There are causal links, but we always have axioms for which either there is no reasons, they are just how they are, or we don't know the reasons, we have just experimental evidence for them. At the end, the answer to "why" is always, because they are just how they are.
Whenever you're asking for an explanation this deep in the ontology stack, you need to think about what kind of explanation would be satisfying to you, and whether you can reasonably expect intuitive answers in domains that lie far outside of your everyday experience. Human brains aren't built to grasp this stuff intuitively.
At a certain point, the reason we like some particular wacky physical model is always going to be "it has the best combination of explanatory power and simplicity"
A thing can be explained with its constituent parts or explained by a parallel analogy. If you don't understand the constituent parts or the analogy or there are neither of these. You won't understand it.
“The model does not hold” === “existence wouldn’t be possible”. We found atomic particles, then did some more experiments and found quarks within the atomic particles. The quarks appear to be complex but predictable subsets of the particles. So “why do those subsets add to 1” invites a tautology, because the whole reason we found them in the first place is that they add up to exactly one, and therefor can be part of atoms.
It’s like asking why the left engine of an aircraft happens to emit the same amount of thrust as the right engine; if that wasn’t the case, there wouldn’t be a plane to talk about in the first place, just an art piece or a flaming crash.
Isn't the primary experimental argument beta decay from that link? A nucleus can emit a positron, and observably loses nuclear charge equal to one positive electron.
So by a pretty simple inferrence you could conclude the proton has a positive in it, hence the charge (it of course isn't literally like this for other reasons though).
And since we also observe antiprotons, the opposite can clearly apply.
So a proton can emit a positron. Does that mean that the positron is somehow "part" of the proton? Does it mean that their wave functions interact in some specific way? Is there another reason?
Quantum physics has always bothered me, personally, since I find it difficult to understand reasons. Not philosophical reasons, I am fine with axioms and foundations to models, but rather intuitive reasons why it works a certain way. I know it is an extremely strong theory which makes unexpected, later confirmed, predictions, but there is a frustration that the only explanation to things is "math".
Sort of? But it's less "there is a particle doing things" and more "there's a probability field which can describe a particle doing something" (alongside a bunch of other probabilities it interacts with).
One of the ways you can calculate the probability of nuclear decay for example is to assume that the particle you expect to see is literally existent and trapped inside a potential well defined by the atomic nucleus and then calculate the probability it tunnels out of that to free space.
The thing is "why" does get pretty anthropic: protons match electrons because we observe them to, and then on top of that we observe nuclear decay causing the conversion of a proton to a neutron + a positron (within the limits of our instruments) - so our model predicts that these are in fact the same value, and we keep measuring to check that they converge in that direction (it would be a big deal, for example, if we discovered this wasn't the case - every physicist would love to find out that proton charge and electron charge are actually slightly different).
> Does that mean that the positron is somehow "part" of the proton?
No, and the standard intuition that there are discrete things made out of smaller parts breaks down when you look closely enough. The proton is a bound state of the quark and gluon fields, but it only "contains" individual quarks and gluons in a loose heuristic sense, and positrons are a different thing entirely.
> Does it mean that their wave functions interact in some specific way?
Yes, or more precisely it means that the quark fields interact with the electron field (free electrons and positrons are different states of the same underlying bispinor field) and the W boson field in some specific way.
> Quantum physics has always bothered me, personally, since I find it difficult to understand reasons.
Ultimately, the sort of mechanistic explanations you're looking for do not exist: the universe runs on differential equations and linear algebra, not billiard balls and clockwork.
I would posit that self-consistency is the only possible ultimate reason. Whatever other reason there is, you can always continue asking “why”, like children like to do, and will never come to an end. The only final explanatory is the absence of reduction ad absurdum. Another way to state this is to say that everything logically consistent probably exists, because there cannot be any other ultimate reason why it wouldn’t.
This is probably politically incorrect, but there was always a path to end crime, just like there was and is a path to end slavery and collective punishment. That path is kindness: get a job, don't feel the urge to commit a crime, avoid prison to be sure you live a good life, and abstain from crime if you are poor. Crime continue to exist because selfish people put selfish needs ahead of sociology and human rights. People refuse to change their behavior, and, because (not "so long as") they refuse, there will be no end to crime of any sort. Sure, there are edge cases of accidental theft or something else non-criminal, but the vast bulk of cases are from irresponsible criminal behavior.
Actually, this doesn't work. Many people who are homeless--and thus, constantly committing small 'crimes' like loitering--actually have jobs. According to recent statistics, 53% of people in shelters and 40% of people living on the street are 'working homeless'.[1] It's simply not practical to live off of a single job in parts of the country where it's easy to get a single job--which makes it harder to make an honest living. And if you can't make an honest living anymore...
> Avoid prison to be sure you have a good life...
This is another problem with "Get a job". Most places will not hire someone once they have a criminal record of any kind, which means that going to jail once permanently ruins your life--there are some places that hire people with a record, but those are few, far between, and take full advantage of how desperate the people who work there are. Of course, this is only exacerbated by flaws in the criminal justice system, which include things like "evidence presented as rock-hard proof may actually be complete bunk"[2].
> Crime continue to exist because selfish people put selfish needs ahead of sociology and human rights...
I mean, I'd agree with you if you were talking about tax evasion or wage theft. In fact, wage theft makes up a larger percentage of overall theft than any of the things people think of when you say the word 'theft'. However, you explicitly stated that you're talking about people who are poor or who have a risk of going to prison, which excludes a lot of white-collar crime.
> That path is kindness: get a job, don't feel the urge to commit a crime, avoid prison to be sure you live a good life, and abstain from crime if you are poor. Crime continue to exist because selfish people put selfish needs ahead of sociology and human rights. People refuse to change their behavior, and, because (not "so long as") they refuse, there will be no end to crime of any sort. Sure, there are edge cases of accidental theft or something else non-criminal, but the vast bulk of cases are from irresponsible criminal behavior.
I'd wager the guess that a lot of crime committed by poor people is committed because they are poor. Think of a single mother stealing food for her and her children. They are putting their "selfish needs ahead of sociology and human rights", but I don't think people would call them unethical. You're proposing too simplistic a framework.
The reply about how to end crime was sarcastically mocking the original comment, similarly to the way "A Modest Proposal" mocked other helpful suggestions of its time.
That (the IPA designations) could, and probably is, helpful for breaking down sounds on paper but taking that /t/ from what is a manual of sorts and dropping it into a foreign transliteration is the opposite of helpful.
Everybody expect the French won't have any problem reading out without stumbling Chkalov or Chmil. Supplying the /t/ is a copout to please the French and, as a bonus, to piss of the Russians (especially the Chekalovs ones).
It's cheaper to raise kids since you would already have paid the cost in taxes if you didn't get kids. The important metric is the difference in cost of having kids vs not having kids, and since daycare is heavily subsidized, the difference is small.
Same things go for schools, food in schools, universities, et.c., they are all "free", as in paid for by everyone in proportion to their wealth, instead of individually by the parent.
If we start with the assumption that the cost of childcare is costly enough that it would lead to an unacceptable drop in living standards for the average couple, and then force them to pay that cost anyway (regardless of whether they actually have children) it is unlikely that the follow up is going to be the couple having kids. They'll probably be busy desperately working to get their living standard up to a state that is bearable.
It isn't cheaper to raise kids. They're actually losing more under the socialised system because they still have to give up enough resources to raise the kids and now also to cover inefficiencies in the government program. On average everyone would be worse off. Or you're going to be taxing grandma so instead of her providing helpful childcare services she has to go and work at McDonalds to make up the difference or something. Society is geared towards supporting children already - routing the resources through the state or through the family can't make it easier. Men work to support families, women work to support families, grandparents have nothing better to do than support families. The resources were already tagged to support families. The government can't magic more resources into existence if raising kids is expensive. They'd be taxing families so instead of using the resources to support their families, the resources are being ... handed out to support families. There are no gains, so it isn't going to help.
State spending can reallocate; I can see some potential success in using childcare to free up high performing parents. But if the problem is median experience, reallocation can't do much.
Postscript The taxes in these countries are no joke. Young families are losing a lot more to the tax system than the "free" childcare makes up for. If you traded the free childcare for paid childcare and low taxes, they'd likely be in a much better position to have kids. [Taxes] approx. = [Cost of Services] + [Admin Costs] + [Cost of Rorts]. That isn't making it easier to fund a family.
Main problem with your logic is that it assumes a situation where most people are having kids. Given the situation in Scandinavia is that many people aren’t having children, you end up in a situation where everyone is being taxed to fund childcare, while most people aren’t actually taking advantage of that taxation, so those who are can actually gain more resources than they put in.
The average woman in a Scandinavian country has 1.6 kids. That suggests it is quite common. Going by averages, literally every woman has a child, and half the men.
In actual practice there will be particularly fertile women that have more children and their childcare needs will be draining resources from others, making it harder for them to form families.
I should stress that I don't think childcare costs are the big driver of low fertility. But to say that resource reallocation is going to help is a bit ... I mean, where are these resources going to come from? Everyone was already putting their resources towards their families, diverting money away from those families is the engine that powers the state. That is where the soldiers come from, the welfare comes from, all the labour, where the goods get produced, etc. We'd be asking them to stop caring for their families and instead spend all day caring for their families but according to how the government wants instead of what they actually think they need. You can't take from them, give it back to them and expect them to have more. They aren't even going to have the same.
