joigus

Sorry. You're right. You do make a point. I was under the influence of the last couple of comments I've had to answer to, which were quite pointless. Thank you. +1 You do make a good point here.

Told you. Thinking is hard, and you have opted for a simplified version of it. You've thrown away tens of thousands of years of human knowledge right there. Hardly the point.

Empty means vacuum Einstein equations (T=0). That's what it means. There are solutions to the Einstein field equations that are non-trivial. The matter term is zero. Gravity gravitates, did you know? So gravity itself (curvature) can perturb space time and deviate from the globally constant metric (flat spacetime). You must know these things if you don't want to be involved in a non-ending conversation about words that have a very precise technical meaning. The vacuum Einstein field equations \[R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=0\] Do not imply, repeat, not imply that: \[g_{\mu\nu}=\left(\begin{array}{cccc} -1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 \end{array}\right)\] globally. That's where you're wrong. Edit: As MigL has said too, sorry I didn't notice. +1 Edit 2: This is because the theory is non-linear. This is getting ridiculous, really. Words have a special meaning. I suppose you're trying to tackle it from philosophy or common language. That's not how it works. Then there's another non-sensical conversation going on about quantization of time I won't address for obvious reasons. There's a reason why Pauli introduced the words "not even wrong". Exactly. +1

Nor to me.

Very droll. Is it something I said? Don't go there. Now seriously. You need something to move through space-time to even start talking about gravity. Even if you just have imaginary points trying to follow the closest-to-a-straight-line trajectories you can find, you do have gravity. But Gravity can be defined even if there are no sources (energy-momentum tensor). Those are empty space-times. They can be defined theoretically. Out of this context, I don't know what you're talking about.

Maths is the language of physics. Common language and diagrams are useful complementary tools. That's just how it is. Physics cannot be formulated in just words (however philosophically sophisticated) or pictures. It just can't. I'm afraid I must insist on @Strange's question: What else is required?

Of course it's more than that. I don't see the "only" bit in my statement about how observers cannot get rid of time in their view of the universe. Volume is also. All observers have volume. That doesn't imply that "volume" is an only-observer kind of concept. You can formulate gravity in different dimensions. Not only 4. 4 is special as concerns topology, not Einstein's equations. Although going down to fewer dimensions than 4 makes gravity more tractable, or trivial, if you will. In 3 dimensions the Ricci tensor codifies all possible degrees of freedom to deal with gravity. In 2 dimensions the Ricci scalar is enough. And in 1 dim there is no gravity because there can be no intrinsic curvature. But I'm not quite sure what you mean by, Can you elaborate? Just like observers. I would distinguish pure speculations as rigid frames of thinking that ignore the basis of generally agreed-upon physics from open-ended lines of reasoning that strive to incorporate what's known and try to grope a bit further. That's what I was trying to do here. I wouldn't be surprised that some of the more adroit users here find some kind of overlapping with what I've said. Although I think disagreement among equally adroit users would be just as likely.

Was thinking about this some 24 hours ago and wondering what had become of you and your problem. I'll keep an eye on it. It's interesting.

I agree. I wasn't trying to put the blame on anybody. I was just interested in the definitions. Different countries seem to have different thresholds for what is justifiable. But you can never gladly ignore the social cauldron in which those concepts are formed.

Interesting. I thought the criterion for "justifiable" would be self-defence. But no: That's a bit loose. If you point your gun at a guy who's holding up a shop, tell him to raise his hands, and he does, and you shoot him in cold blood. Would that be considered as the killing of a felon during the commission of a felony, thus justifiable? Another example: http://www.bjreview.com.cn/forum/txt/2009-04/28/content_193066.htm I tend to agree with this kind of thinking, for this and other similar problems. +1

Are you contemplating the possibility of being both shallow and insane? Or sane but shallow? It's certainly possible. +1

That's probably because you're an architect. I suppose that when you're thinking about buildings, you must be careful that they don't flip in any sense. That would be a liability for a building. The longer a building lasts unchanged, the better. We're all constrained by the theoretical framework of our guild. Physical systems* do flip. An Ising magnet for example, is a physical system that must make a choice (take a decision). Spontaneous symmetry breaking is the paradigmatic example. Some time in the remote past, the Higgs multiplet took what I've called "a decision", thus breaking a symmetry, filling the world with massive gauge bosons and fermions by pointing towards an abstract direction in the configuration space. Edit: So I suppose my point is: Could the direction of time that we perceive be the result of some kind of accidental orientation-taking that we now know to be at the basis of much symmetry breaking in Nature? Could conscience be some version of this kind of symmetry breaking? When you are exposed to the concept of spontaneous symmetry breaking, it just blows your mind. Edit 2: Natural-born physical systems, not programmed, like a building.

I am to you too, and to all of you. @Ghideon caught me a couple of days ago on an important example about tiling the plane with regular polygons I had omitted. Thank you for being sensitive to that. +1 I would agree, had you said: Time is sooo fundamental that it underlies almost everything we do, say, understand, or think.

I'm trying to grope towards a setting in which a mind is not a thing, but a particular condition in the universe that accretes locally. I'm also struggling to make myself clearer. I'm also trying to read everybody and I'm aware of the conversation that's going on involving @michel123456, @Strange, @studiot and yourself about directionality in mathematics. Let's go back to geometry and minds. Let us suppose the geometrical structure of the universe is more symmetrical with respect to the sign in the metric. The simplest model I can think of is: \[ds^{2}=\left(dt_{1}\right)^{2}+\left(dt_{2}\right)^{2}+\left(dt_{3}\right)^{2}-\left(dx_{1}\right)^{2}-\left(dx_{2}\right)^{2}-\left(dx_{3}\right)^{2}\] The forming of a "mind" (robot, human, squirrel...) implies some set of some series of "decision-taking". Please, let me be a bit vague or I won't be able to get it out. Now a "decision" is taken about what is the inside and what is the outside in the particular part of the universe where this "mind" forms. We're all thinking about that inside/outside decision. Look: But what is inside? You can't see your brain, I can't see mine. Nobody can. Own brains are completely out of the picture biologically. They're just not there in the representational parameter space of the world. It's the interior of the box that we can intuit but we cannot see. I think this connects with an observation that @michel123456 has been trying to make for years, that I will re-phrase here at the risk of adulterating it, as follows: You can't see your past worldline, because that is you, and you are not a signal for yourself. Maybe Michel has been a bit naive in not distinguishing carefully enough that this is not a general setting in physics. In particular, elementary particles can "see" themselves by emitting a virtual boson and re-capturing it. In a cartoonish way of speaking they'd go like "look, that's myself a nanosecond ago". We could discuss whether a virtual particle is really a signal, but... Drifting off-topic. The point is brains are extended objects that need to sacrifice most of their internal dynamical states in order to represent what's outside. So they lose focus of what they are, on what's inside (thoughts and some chirps and clicks aside). They need to. Let's go back to our completely signature-symmetric metric. Now something in the physics of your brain has decided what "inside" and "outside" mean. This seems to automatically suggest a decision about what is after and before. In a non-invariant language (why should it have to be? we're trying to represent perceptions of the observer)* we would have two distinguished parameters: \[dr=+\sqrt{\left(dx_{1}\right)^{2}+\left(dx_{2}\right)^{2}+\left(dx_{3}\right)^{2}}\] \[dt=+\sqrt{\left(dt_{1}\right)^{2}+\left(dt_{2}\right)^{2}+\left(dt_{3}\right)^{2}}\] But time now presents itself as some kind of radius in this 6-dimensional geometry. This leaves us with 6 polar coordinates, two to represent orientation outside; and two to represent orientation inside: \[t,r,\theta_{\textrm{int}},\phi_{\textrm{int}},\theta_{\textrm{ext}},\phi_{\textrm{ext}}\] This would leave the t-angular coordinates free to represent the external world by means of constraints: \[\theta_{\textrm{int}}\left(\theta_{\textrm{ext}},\phi_{\textrm{ext}}\right)=0\] \[\phi_{\textrm{int}}\left(\theta_{\textrm{ext}},\phi_{\textrm{ext}}\right)=0\] And now the (t1,t2,t3) coordinates do point to an origin in time the very same way that spherical coordinates point to an origin in space (call it the "self"). This in some crude way would represent that being conscious implies an origin in time. Of course, as @studiot pointed out, angular coordinates have no meaning at any of the loci r=0 or t=0, foreshadowing at the same time, admittedly in a crude mathematical way, why you cannot represent your own position or your mind's birth consistently. You see nothing there. Now, irrespective of how accurate this simple-minded model may be (it's probably not), it shows that, in a universe geometrically richer than we perceive it to be, constraints defining what a conscious system is could account for the familiar (1,3) structure that we perceive on the basis of what a conscious system needs to do to represent the world, rather than what the world is in its intrinsic structure. I may have misinterpreted you completely, Markus, but something like that is what I thought you were referring to. I'm also trying to answer to what @vexspits was asking me about. * It's about charting the universe locally at this point; not about mapping it out globally.

Deal.

Today's best "gotcha"!!! +1 Yes. Where is the line between one and the other?

I'm going to focus on this. I'm interested in its logical structure. Religious belief is based on wishful thinking and misguided intuitions. Less wishful thinking would imply less religious thinking. (What you propose is a little bit like saying "an improved lie is one that lowers the percentage of false information in it". It doesn't sit well with the intuitive idea of what a good lie is. An improved lie would be one that more efficiently conceals the "mis" bit in "misinformation".) Following your premise: The best religion (the most improved) is that that lowers the % of wishful thinking to naught, while actual knowledge takes its place and substitutes the hierarchy of its tenets to completion (tenets gone). Therefore the best religion is no religion. Which clinches the proof.

Oh, but there is: https://en.wikipedia.org/wiki/Donaldson's_theorem https://mathoverflow.net/questions/47569/what-makes-four-dimensions-special#:~:text=A comment is that 4,live in 4-dimensional cohomology. 4-dimensional manifolds codify important topological properties of any n-dimensional manifold. The latter is my clumsy attempt at re-phrasing what I see. There are more special things about dimension 4. I'm no expert. Most technicalities go over my head. My intuition is that 1+3 codifies something very specific about how anything that merits being called an observer (whatever the definition is) needs to "do" to represent the universe around in itself. That's how I understood Markus and that's why his comments drew my attention so strongly. But I'm stepping on very slippery ground. I may be neither making much sense, nor understanding other people's comments here.

So, are we getting closer to an answer to the question? What is time? Some level-the-playing-field work seems to be necessary here. Maybe a less ontologically-loaded question would be: Where does time come from? Let me rephrase: What geometrical context in which some principles to characterize observers can be formulated would allow anybody to guess possible mechanisms from which these observers would see a single parameter emerge as necessary to map observations of the world around them? Something like that. Sorry if I don't make much sense. It's 35 ºC (95 F) here. My brain is about to reach boiling point.

I suppose it's about here: Phillip K. Dick Now, religions have invented a mechanism for fueling themselves on while not bothering too much with facts. Language can accommodate anything. That's why you cannot rely on language alone.

Some of that.

Curiously enough, the picture started to change at about the same time that we realised that we Europeans may have up to a 5% of their genome. We never learn.

Sorry, my mistake. N=6 is the last one. +1

That's your department. Tell me the rules and I'll play.

One important reason why 5-fold approximate symmetry is interesting is that you cannot tile the plane with regular pentagons for a very special reason. It's some kind of peculiar geometrical frustration. If N is the number of sides of a regular polygon. You have, Triangles (N=3) --> You can tile the plane Squares (N=4) --> You can tile the plane N-gones, N>5 --> You cannot tile the plane because angle is too big N=5 is special because you still have angle left, there's no angular "deficit", but there is a mismatch. Penrose re-discovered this tiling, which appears in some mosques and other religious buildings. The idea is that it creates the illusion of symmetry, but the pattern does not really repeat itself. Here's an interesting lecture by John Baez on number 5, and why it is an amazing number: https://www.youtube.com/watch?v=2oPGmxDua2U He mentions Penrose tilings, but it's about number 5 in general. I'm not aware of any practical use, but approximate 5-fold symmetry does appear in Nature. Baez mentions diffraction patterns in some crystals as another example.