"Dimension regulated the general scale of the work, so that the parts may all tell and be effective." -Vitruvius
In a four-dimensional Universe (3 space and 1 time), it’s easy to get lost. If you take a random walk, the chances of you coming back to your original starting point in a finite number of steps gets lower and lower the more dimensions you have. If all you could do was walk along a sheet of paper -- or even better, along the surface of a pipe -- you’d have a much greater chance of return than if you had all three spatial dimensions to deal with.
Isotropic random walk on the euclidean lattice Z^3. This picture shows three different walks after 10 000 unit steps, all three starting from the origin. Image credit: Zweistein, under c.c.a.-s.a.-3.0.
There’s an interesting property of mathematics that if you treat all four dimensions as “space” rather than spacetime and you add in the laws of quantum mechanics, then at very short distance scales, the probability of a random walker returning to their original position behaves like they’re in a two dimensional Universe, rather than four.
A 3-D object like a pipe will have a Hausdorff dimension of 1, as the lines only have one dimension to spread out as long as they’d like, which is also seen in the reduction to a line as you zoom out. Image credit: Alex Dunkel (Maky) of Wikipedia, based on Brian Greene’s The Elegant Universe, under a c.c.a.-s.a.-4.0 license.
Could this be a way of reducing the quantum gravity problem from a difficult (perhaps unsolvable) 4D case to an easier (and solvable) 2D one? Sabine Hossenfelder investigates!
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Would this mean it is possible to collapse 4 dimensions down to 2, or that the 4 dimensions that we perceive all around us are in fact 2 dimensions when viewed on the QM scale?
The article seems to read as the latter (if the math actually translated to something physical), but our universe seems more like the former with the example being space inside versus outside a black hole.
As I understand it, the space on the inside of a black hole is 2 dimensional. One dimension is Time. The other dimension is the Distance to the Singularity, and even that dimension is time-like. The X, Y, Z, and T have collapsed to X and T.
Are the 4 dimensions we perceive in regular space an illusion that breaks down at an event horizon? Or are the dimensions inside and outside a black hole different with QM only being solvable on one side while Relativity is only solvable on the other?
Can we cease talking about the universe in 4 dimensions?
Shouldn't we consider the quantum realm as well when we consider dimension?
Say for example 4X dimensions?
Just asking.
Thanks
I'm at present even more unable to view Forbes than usual; is the subject being raised again because of Carlip's arxiv.org/1605.05694?
@2: you should read the article before posting; it specifically talks about quantum interactions lowering the dimensionality
“And, of course, this idea has no observational evidence speaking for it. Maybe never will.”
And, of course, that doesn’t stop you guys/gals from writhing and writing about it.
Publish or perish, as they say.
Even if it's puke.
If you think it's puke, why do you come here?
@Narad #3
The scope seems beyond just Carlip's work although it is included as both your linked paper and arXiv:1304.7247v2. Also cited is Ambjorn's et al's work on causal triangulated geometries (arXiv:hep-th/0505113v2), Modesto's LQG work ( arXiv:0812.2214v1), and Horava-Lifshitz gravity (arXiv:0902.3657v2).
Thanks.
Jesus Christ, that blast of irony was nearly at the St. Lucy level.
After nearly two weeks of S.N. radio silence, I had my hopes up that the L-rd had granted him a fortune-cookie-like dermoid cyst holding an arrangement of the typically whimsical contents that actually spelled things out for him.
The comparison (to puke) is entirely predictable. An infatuation with purity and analogizing things they don't like to filth has been an obsession of political conservativism since long before the character of Jack D. Ripper created possibly the first Poe moment.
To eric #10:
Whatever.
But surely, you’re not disappointed with, or disapproving of, me or my comments.
After all, you’re an evolutionist, right?
So, don’t even think of blaming me.
Blame evolution!
I just mutated this way.
Sorry, S.N., it's the same either way: G-d gave you the choice whether to be a pathetically resentful, stupid asshοle, as well as a whole world of observers to provide feedback, in your version, and you not only chose wrong, but you cower in the face of owning up to the reekingly frustrated, misogynistic, racist pile of crap that you have happily fashioned for others in your own image and presenting it for competent pastoral evaluation.
Oh, wait, silly me. S.N. is also using his absence (grabber? pancreatitis? DUI? erection lasting for more than four hours?) to distract from this disaster.
Yoo hoo, Brave Sir Robin.
SN, are you making the "nontheists can't have morals" fallacious insult or the "if you believe in evolution you should be a social Darwinist too" fallacious insult? From your comment it's not clear which of those two idiotic lines of reasoning you're using.
Of course I disapprove; I think your comment about puke is inappropriate to the topic, insulting to the host, and doesn't do anything to contribute to the overall conversation. You might as well just attach an audio file of you farting - it would have the same intellectual content and argumentative force.
@ #4 I did read it and my question is opposite what sabine suggest.
@ #11 See Hebrews 11:3
That verse sums up this article to a point. It really is a powerful quantum physics Bible verse.
'It really is a powerful quantum physics Bible verse."
You really brought the stupid with that one.
To eric #11:
Me: “But surely, you’re not disappointed with, or disapproving of, me or my comments. After all, you’re an evolutionist, right? So, don’t even think of blaming me.
Blame evolution! I just mutated this way.”
You: “SN, are you making the “nontheists can’t have morals” fallacious insult or the “if you believe in evolution you should be a social Darwinist too” fallacious insult?”
Neither.
On the latter, if you believe in evolution, there is no “should”. So no “should” either way on Social Darwinism.
On the former, I have never claimed or implied that “nontheists can’t have morals”. I have said only that whatever “morals” they do hold have no basis other than that of a *matter of taste*.
And that is true.
“Of course I disapprove;”
As you may disapprove of receiving butter pecan ice cream, instead of vanilla.
Bon appétit.
Um, 'there is no should' is exactly the "nontheists can't have morals" fallacy. Expanded; you think nontheists can have no moral basis except taste. Evidently it doesn't occur to you that people can use logic and reason under conditions of uncertainty.
Well, except for that "there is no should" thing So, we can have morals but if we believe in evolution there is no should. I don't really know why you disagreed with my first option, other than to be obtuse. As far as I can tell it captures what you're saying correctly.
SN,
I'm sure you'll just retreat to a blind faith in your beliefs, but the notion that a theistic religion provides a firm basis for morality is highly problematic to say the least. The real question dates all the way back to Plato (at least) with the Euthyphro dilemma: are moral actions moral because God commands them or does God command them because they are moral?
The former leads to a theological position known as divine command theory, which basically states that any action commanded by God is by definition a moral one. This certainly leads to problems and is not really a rational, objective basis for morality any more than saying that whatever Barack Obama commands is by definition moral (or use whatever other name you want). It is merely substituting divine taste for human taste, and is just as arbitrary. For instance, according to the Bible, God allowed polygamy among the ancient Hebrews, but not among modern societies. Is polygamy objectively moral or not? From divine command theory, the answer is that it depends on when you ask the question. 6000 years ago, it was. Now it isn't. Not much different than the malleability of ethics you no doubt decry among non-theists.
Given that divine command theory doesn't really provide a solid basis for morality, we must consider the opposite, namely that God commands certain actions because they are moral. That then begs the question. Why are those actions moral? God is no longer the basis for morality; He's merely the messenger who tells us what is moral and what is not. Why then, if there's some basis other than God for morality can't a non-theist utilize this basis for morality?
Obviously, I can't expect you to clear this dilemma up. Theologians and philosophers have pondered this issue for millennia without any real success. What it does show, though, is that religion is not really the firm basis for morality that you seem to believe that it is.
Sean - another problem is that the "objectivity" of biblical morality seems quite subjectively interpreted by different Christians. A host of objectivists each claiming to have access to the one true objective morality, but yet all disagreeing on what it is, is pretty functionally equivalent to a host of subjectivists disagreeing about morality.
"Um, ‘there is no should’ is exactly the “nontheists can’t have morals” fallacy. Expanded; you think nontheists can have no moral basis except taste. Evidently it doesn’t occur to you that people can use logic and reason under conditions of uncertainty."
Moreover, since See Nowt CHOSE their religion AND which bits of that religious texts to take as "gospel truth", THEIR "Divinely Inspired" morality is ALSO based on taste.
Just like nontheists.
To eric:
I read your comment #18 twice,
and it didn’t make sense either time.
What remains true, however, is that the “morals” an atheistic evolutionist holds have no basis other than that of a matter of taste.
For example, much of morality centers on valuing human life - human life, a rare and very recent anomaly in the evolutionist's alleged 13 billion year history of the universe.
In your view, there is no inherent goodness or badness about the “accident” that is human life. Your life has no inherent value, other than that you’d probably *like* to keep it.
Just as you might *like* vanilla.
And as the Romans said, de gustibus non disputandum est.
To Sean T #19:
“For instance, according to the Bible, God *allowed* polygamy among the ancient Hebrews, but not among modern societies. Is polygamy objectively moral or not?”
God *allows* the existence of many evil, or at least less-than-ideal, things. Then and now. That doesn’t mean those things are moral or good or ideal.
Perhaps it’s a bit like babies – they poop their pants.
But they don’t after they grow and learn and mature over time.
Perhaps God allows human beings/families/societies time to grow and learn and mature, too.
And now is no longer the time for “pooping” polygamy.
Mirrors are your friends, S.N.
To eric #20:
“Sean – another problem is that the “objectivity” of biblical morality seems quite subjectively interpreted by different Christians. A host of objectivists each claiming to have access to the one true objective morality, but yet all disagreeing on what it is, is pretty functionally equivalent to a host of subjectivists disagreeing about morality.”
Quite true.
But apparently, you believe all opinions are created equal. You may even believe the $10 Rolex you bought on the sidewalk in Times Square is worth as much as one coming from the factory.
“Evidently it doesn’t occur to you that people can use logic and reason under conditions of uncertainty.”
Oh, but it does. And doing so can lead you to the “real deal.”
So, you can't think of any reason for valuing something rare unless God tells you you should? Nothing springs to mind?
Nope, that's you putting words in my mouth. Where did I ever say that?
Or that? Good gracious man, you can look around and see that the millions of nonbelievers in the US aren't naively believing $10 knockoffs are as market-valuable as a real Rolex. What's your explanation for the fact that your claims of how nonbelievers behave is directly contradicted by their actual behavior?
I'm running out of quantifiers for degrees of irony.
Let's get back to 3D space; I'm starting to 'ribbonize' in 2D.
:)
Get some sleep, eric.
@ dean #16 "You really brought the stupid with that one."
Neanderthal, Did you even read the verse?
I know you can't comprehend it because you're spiritually dead but at least you can see how from my perspective it ties into quantum physics.
Ragtag, the verse By faith we understand that the universe was formed at God's command, so that what is seen was not made out of what was visible. in no way implies quantum mechanics as a theory. It could just as easily support the ether theory, or invisible angels pushing planets around - both ideas supported by Christians in the past, Christians who read and accepted Hebrews 11:3 just as much as you do.
The verse is vague enough that it could be claimed by different people to support a near limitless number of contradictory ideas. Like many believers and many such biblical verses, you appear to be interpreting it in a way that mirrors your preconceived beliefs. But there is no deep, denotational connection of this text to quantum mechanics, you're simply reading your own personal connotation into it. And if, years from now, physics refines its ideas and discovers some deeper structure to the universe, you and folks like you won't miss a beat; you'll claim Hebrews 11:3 supports that deeper understanding instead, without giving a single thought to how you used the same verse to support inconsistent scientific concepts as science changed over time - changing the verse's connotation as needed, in order to protect your religious belief that the verse is meaningful.
Yes rt, I did read your little reference. It is simply a statement that some (unsupported by evidence) god created everything, written by people who hadn't yet developed any method for working to understand the world around them. That latter part must be why it appeals to you.
SN,
Shocking, but you missed the whole point again. The point was not whether the example I gave was really changing morality or not. The point is whether moral actions are moral because they are divine or whether God acts the way he does because He's moral.
Consider a hypothetical. During the Cuban Missile Crisis, the US was desparate to have the Soviets withdraw missiles from Cuba. Suppose we sent in paratroopers to Moscow and they went door to door and killed the oldest child in every house in Moscow in order to convince Kruschev to remove the missiles. Is this a moral action?
If actions that are performed by God are necessarily moral by virtue of having been done by God, then we must conclude that this action is indeed moral. After all, God killed all the first born children in Egypt in order to convince the Pharoah to let the Israelites go. If an action is moral by virtue of having been done by God, then the action of killing a bunch of children to influence a political leader is a moral one.
If you conclude that the action of killing a bunch of children to influence a political leader is immoral, then God was guilty of performing an immoral action. If so, how do we know that it was indeed immoral if God is the basis of morality? In this case, there must be some other basis for morality that doesn't involve God.
I fully expect you to again dodge the issue. Somehow you'll conclude that God's action is moral whereas the hypothetical similar American action is not. I am just trying to point out the problems inherent in divine command theory here. Without divine command theory, though, your whole notion that morality is based on God goes up in smoke.
Well, eric and dean, thanks for at least looking. I find it interesting. I just think it more interesting that such learned scholars such as yourselves eliminate any and everything biblical.
I realize the Bible is not a science book but it does have some very interesting things that any open minded person of rational thought would consider.
Take a few commandments for example don't steal, don't lie, don't murder.. Those seem like some decent concepts that Science may regard as beneficial to a decent and productive society.
But that's just me.
Anyhow, thanks for at least looking.
Kind Regards
rg, first: thanks for one of your more considerate responses at 34. It's a rare bit of sunshine (especially today, when it is storming here like a son of a gun on a day when I'm supposed to do a bit of outdoor photography for our nature conservancy.)
"I realize the Bible is not a science book but it does have some very interesting things that any open minded person of rational thought would consider. ... don't steal, don't lie, don't murder."
Those are concepts that rational people back, but they are not uniquely expressed in the Bible, nor is that the first time they were expressed in or out of religious settings.
Again - thanks for the calm post @34. Keep it up.
To Sean T:
#33: “SN, Shocking, but you missed the whole point again. The point was not whether the example I gave was really changing morality or not [about polygamy]. The point is whether moral actions are moral because they are divine or whether God acts the way he does because He’s moral.”
#19: “… are moral actions moral because God commands them or does God command them because they are moral?”
Probably *both*.
A good rule of thumb is that if God, or His Church, tells you to do something, do it.
Too hard to understand completely? Don’t be surprised.
For it is written:
“For my thoughts are not your thoughts,
neither are your ways my ways, says the LORD.
For as the heavens are higher than the earth,
so are my ways higher than your ways
and my thoughts than your thoughts.”
[Isaiah 55: 8-9]
"A good rule of thumb is that if God, or His Church, tells you to do something, do it."
That would explain the child molesting and worse by priests the catholic church has been ignoring for a few hundred years.
I'm actually dismayed that S.N. trotted this one out here. His normal response to observations of centuries' worth of evil carried out by the RCC is to start blabbering about how Christ's Vicar on Earth is only infallible in spiritual terms, not (the arbitrarily divided) secular ones.
I would suggest that one not lose sight of the trajectory:
1. S.N. pops by to describe this post as "puke."
2. S.N. further asserts that things like that from his keyboard cannot be criticized by "evolutionists."
3. He weirdly asserts the provable epistemological supremacy of the Roman Catholic Church ("all opinions are created equal," etc.).
4. He contradicts his previous assertion and tries to shift over to the "let's trade Bible verses" game.
I'm not above wondering whether simply feeding him old-fashioned, fanfold-paper, ASCII pinup pictures would be enough to drive him into a frankly deranged cork-popping.
RM:
@ eric #39
"Very selective citation there, RM. Yup, the 10 commandments got 3.5 right. Shall we discuss the ones you chose not to mention?"
Sure if you like, I just posed those because they are a very direct and immediate example that humanist can relate to.
But I can go down the list if you like.
"#1 – our first amendment is directly opposed to such a concept in law. We aren’t just ‘meh’ about this – we actively think its a bad idea that we proudly rejected when we created our country."
Before the constitution was the Declaration of Independence. To which I am sure you are familiar with this part:
"We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, "
It is VERY important that MAN is removed from mankind's natural rights as the granter.
Otherwise MAN can take them away.
Notice Obamacare is the first law of the land now that individuals by law HAVE to purchase a product?
God commands you to but your free to not. Obama/Govt Now commands you to Otherwise you are fined and penalized if you choose not.
#2) You shall not make idols.
Reason? Because Man can control the idol and thus those who worship it.
#3) You shall not take the name of the LORD your God in vain.
Reason, brings about a unified respect for said liberties. Kinda like don't desecrate the Flag.because it represents all our will to protect and defend our compact.
#4 Remember the Sabbath day, to keep it holy..
A day of rest? That should be pretty simple eric. Don't you appreciate a day off?
5) Honor your father and your mother.
Seriously eric, do I need to explain that one? Were you molested by your parent? If so then of course the Lord does not expect that. But some respect should be due to parents who busted their asses off to raise their kids to be decent people no?
Shall I go on?
Man CAN take them away, under our constitution. Its called the amendment process. And given that the process has increased the rights of blacks, women, and the ability of the public to elect their senators (among many other things), I'm very very glad we allow a process for humans to modify the basic law. The idea that humans can change it isn't a bug, its a feature.
But I'm very interested in the more substantive question of, when it comes to 1-5, you think its better if we legally require people to follow these commandments, or whether you think we should legally allow people to disobey them. IOW, if you think they're that good, do you support these being the law of the land?
Yes, that makes a nice right-wing talking point, but I've been involuntarily purchasing other people's education, other people's health care, government tanks, roads, and so on for decades. The reason ACA is more direct out of pocket and not funded through taxes is because the GOP objected to it being funded through taxes. So this is a case of conservatives demanding a compromise funding strategy, getting the compromise they asked for, and then complaining about how unconstitutional that compromise is once they're given it. I'd suggest that you be very careful what you wish for at this point. If SCOTUS were to find that the method of paying for ACA was unconstitutional (like you probably want), the response of a split Congress and Democratic executive (the most likely outcome) would be to create a single-payer revision. IOW, by complaining about the compromise you aren't going to turn back the clock, you're going to push our government into adopting exactly that system you don't want.
"“A good rule of thumb is that if God, or His Church, tells you to do something, do it.”
That would explain the child molesting and worse by priests the catholic church has been ignoring for a few hundred years."
It also explains ISIS: OBVIOUSLY god is telling them to kill christians and the wrong type of muslims and create a new caliphate.
That bastard, god, told them.
"What’s your explanation for the fact that your claims of how nonbelievers behave is directly contradicted by their actual behavior?"
What's his explanation for the same morality appearing in, not merely the higher apes, but Vampire Bats?
If god makes what's good, why are there so many gods? If god makes what's good, why do so many people read the intent *of apparently the same god* differently?
Obscene incompetence????
As a layperson in physics it strikes me that a conundrum with all physical models of nature, including the Standard Model, is the assumption that objects with zero dimensions (points), one dimension (strings), and two dimensions (sheets), are taken to actually exist in the natural world. But does nature actually oblige us in this regard? That is, does nature admit to the existence of objects that by definition do not exist in the sense of not occupying 3D space, having at least one less dimension?
True, the Standard Model, based on zero dimensional points, has been phenomenally successful. But this required a mathematical procedure called renormalization, to banish the infinite energy that arises due to the assumption that particles are zero dimensional points. Theorists, early on, could not accommodate particles as spatially extended objects, since the surfaces of such particles would move faster than light. So the next best thing was to postulate particles as zero dimensional, and subtract one infinity from another (renormalization) to make things work out.
Perhaps nature is constructed from objects with some minimum volume - a Planck Volume - which somehow circumvents the velocity of light issue that plagues models that postulate particles as being extended object.
"the assumption that objects with zero dimensions (points), one dimension (strings), and two dimensions (sheets), are taken to actually exist in the natural world."
No such assumption is made, David, and your complaint is nonexistent, having been created either by your unthinking or deliberate misunderstanding of science and the models.
"God commands you to but your free to not. Obama/Govt Now commands you to Otherwise you are fined and penalized if you choose not."
So we're still free to choose not.
Just like your myths claim that if we choose not to do as gawd commands, we will be tortured for eternity. Or is that not penalized for you, teabagger?
"#4 Remember the Sabbath day, to keep it holy..
A day of rest? That should be pretty simple eric. Don’t you appreciate a day off?"
It's supposed to be Saturday.
And you have to observe holy rites, abstain from, for example, collecting fuel to keep you warm, since this is "work" and therefore you're not "keeping it holy".
For someone who claims it's a day off, there's a hell of a lot of restrictions you can place on life on your "day off".
"#2) You shall not make idols.
Reason? Because Man can control the idol and thus those who worship it."
See that statue at the back there of the dude on the dod o wood? That's an idol.
See those graven images in the window of the saints? Idols.
Got a St Christopher or cross? Idol.
Should all religious statuary and paintings be made illegal by law to obey commandment #2?
"Kinda like don’t desecrate the Flag.because it represents all our will to protect and defend our compact."
Kinda like "Don't make cartoons of Mohammed", innit.
If before the marriage ot Time and Space was two and two, making two, making one, that is only observational to a very few that do not exactly go against the Gravity of the thing itself.
Only educated humans do not know this. That is unfortunate.