Markus Hanke

Those concepts aren’t part of pure mathematics either. The equation defines the elements of a set - in this case a set with two real numbers. Your knowledge of what those elements are is quite distinct from that. Essentially, when it comes to mathematics, knowledge (epistemology) implies a process and thus time, but ontology (the existence of the underlying object) does not. Truth be told, I am struggling to make sense of what you trying to say here In some sense, time is what makes it possible to know things. Information can exist without any reference to time or space, but you need both of these to have an observer who can know information - without time, no observation is possible, so nothing can be known. In that picture, a “mind” is not a thing (so it is neither separate from nor the same as the body), but an information-structuring mechanism, and the primary structure that is imposed is spacetime. This is not an ontological necessity, but an epistemological one. Well, that bit is obvious, isn’t it? But I would go much further and say there is nothing inherent in mathematical structures that require you to impose any notion of dimensionality or coordinates at all. After all, it is perfectly reasonable to have a topological space with just a connection, but without any metric. To obtain something that more closely resembles the world as we experience it, we need to extraneously impose further structures - such as a metric, and a notion of causality. But these are not intrinsic to mathematics, and in no way required per se. The status of (3+1)-dimensionality is very privileged indeed. I believe (personal opinion!) that this is so because it is the only possible spatiotemporal embedding that gives rise to an internally self-consistent model of the world, based on the structure of our mind. Were our mind different in any way, for example if it featured parallel processing or non-linear thinking, then there is no guarantee that we’d see the world in (3+1) dimensions, because we would be presented with a (possibly very different) model thereof. I think what is ‘out there’ (for lack of a better term) is simply information, perhaps reflecting a very complicated network of relationships of some kind. That is all. I think this network is self-referential in some way (since the mind has to be part of that reality) - so when we experience the world, what actually happens is that reality creates a model of itself through some mechanism of self-referencing. I think the spatiotemporal embedding in (3+1) is a feature of that self-referencing; and I also suspect that the laws of physics (and perhaps maths?) we concern ourselves with aren’t really what we typically think they are - rather, they describe the internal structure of the mind-created model of the world, so they are inherently features of the mind. I would wager a bet that, were our minds differently structured, we would be working with an entirely different set of physics laws. But all this is just speculation and personal opinion, and I think we are deviating very far away from the scientific mainstream here

I think you need to be careful not to confuse the cosmological horizon (i.e. the limit to how far out we can observe) with the actual size of the universe. These are not the same things. The physical universe itself does not have any borders. But this is not what physically happens - refer again to relativity of simultaneity. I would recommend a read of the link I gave earlier on the ladder paradox (if you haven’t already), it is conceptually quite similar to this scenario. But whichever way you look at it, there will of course never be a physical paradox, since you can’t construct those within the axioms of special relativity.

Even though Strange chose those words to describe the situation, there isn’t actually any if-then relationship - there is just an equivalence in the set theoretic sense. But even if there was, the answer would still be ‘no’ - there is neither time nor causality implicit in it. What is really interesting to me about this isn’t so much the subject matter itself, but rather the subtle differences in how our minds operate. It would never occur to me to look at a mathematical derivation in terms of causality or time, separate from our process of thinking about it. This is another indication of our reality being a mind-made model. There is no ‘input’ and ‘output’; those terms are not part of the theory of equations in pure mathematics. The equivalence between these statements is an ontological relationship, and does not imply any process. However, proving that the relationship holds is indeed a process (and thus implies time); this belongs to epistemology and computational theory, which is quite a distinct thing.

Indeed! Good point This essentially renders the entire scenario unphysical, because you can never make the total distance =1m, regardless of how close to c you get.

Sorry, I am still not sure if I am getting the point of this. I can only guess that by ‘derivation’ what is meant is the steps involved in formally solving an equation on paper (as per Strange’s comment). However, that’s just an arbitrary human activity, it is in no way, shape or form a structure inherent in the maths themselves - because each and every statement within such a derivation is mathematically precisely equivalent to all other steps. We’re essentially just formulating the same mathematical statement in different ways; of course, the process of doing so takes time, but that isn’t inherent in the maths themselves, it’s down to the linear nature of our mind and the limitations of our body, which is quite separate from the maths at play here. Consider the mathematical statements \[2x+4=0\] and \[x=-2\] There is neither a temporal nor a causal relationship between these; the relationship between these statements is in fact one of mathematical equivalence. Of course, as humans, we can take pen and paper and manipulate these statements in any number of arbitrary steps (according to the usual rules governing such manipulations) to show that they are equivalent - but there is no requirement or necessity to do this, in a mathematical sense; the statements are equivalent whether we choose to write down intermediary steps or not. There is no cause-and-effect to this, it’s essentially just set theory. Also note that a) there is no one preferred way to get from one statement to the other, and b) you could in principle put an arbitrary (even infinite) number of steps between them, and c) you can run any such sequence of steps both backwards and forwards and it will still be correct. So there is no notion of causality or time-ordering implicit in any of this - such notions arise only extraneously from our linear thinking, and the physical limitations of our bodies or computational machine. They are not inherent to the maths itself in any sense.

I’m afraid I don’t understand - what does ‘derivation’ have to do with causality? What type of derivation are you referring to?

There is no inherent concept of time-ordering in pure mathematics. Given a manifold that has one (or 2,3,4,...!) time-like dimension, then, in a pure mathematics sense, there is nothing inherently there that distinguishes between past, future, present, before, and after. You can impose such a structure ad-hoc, by endowing the manifold with a connection and a metric, and then requiring the interval between causally connected points to be time-like; this effectively defines a notion of causality, i.e. time ordering. However, none of these choices are inherently unique - you can endow the manifold with different connections, different metrics, and even the orientation of the time axis (what is past and what is future) is an external convention you impose. And then of course there’s nothing stopping you from giving the manifold a non-trivial topology, e.g. multi-connectivity, which again complicates things, since locality now becomes a blurry concept (at best). So I would say that time-ordering is a physical convention, not a mathematical necessity.

This is not as straightforward as you might think, because the universe does not have a “length” since it doesn’t have any boundaries; it’s also not an inertial frame. At most it can have the topology of a closed manifold, in which case, if one travels long enough in one direction, one would eventually return to one’s starting position. The problem with this is that, if this is the case, then the geometry of that manifold cannot be Minkowskian, so you cannot naively apply Lorentz contraction - you’d have to find a solution to the Einstein equations which combine relativistic motion with FLRW spacetime (which probably exists, though I haven’t seen it). Note that this is necessary because you’d have the manifold curve back onto itself over a total circumference of 1m, so curvature is definitely not negligible here. It is conceivably still possible to make the total distance travelled appear to be 1m, though calculating how the ship needs to move in order to get that effect is quite nontrivial. Even if it is possible, there still wouldn’t be a paradox, because of relativity of simultaneity (which is also non-trivial here due to the background manifold not being Minkowski). This whole thing is conceptually similar (albeit more complicated due to the above considerations) to the well-known ladder paradox.

What do you mean by ‘soul’? Can you provide a specific definition? The problem with this is that different spiritual/religious traditions understand this concept in different ways, and some traditions don’t have any concept of ‘soul’ at all. So you need to first specify exactly what it is that should be scientifically investigated, and then we can see whether it is feasible (i.e. amenable to the scientific method) or not.

I don’t know about tennis players, but this site contains a number of visualisations of what happens when relativistic kinematics become relevant, and also some GR stuff (click on ‘continue’ at the bottom of the page). Perhaps this might be of interest for you. You can use the time-ordering operator: https://en.wikipedia.org/wiki/Path-ordering

Since the gauge-covariant tensor contraction of magnetic self-interacting dipoles is inversely proportional to the third power of geodesic divisiveness, and in any case Maxwell's equations do not actually allow for any prediction of force-induced oscillatory processes, magnetic field lines must be devoid of sources. This being the case, and due to the fact that gravity cannot be reduced to any Poynting invariants of the twice-summed Riemann tensor, as is clearly evident using simple Kac-Moody algebras, EM cannot logically be related to gravity. So you are wrong.

Time is a purely local concept; hence, when you place clocks in different spatial locations and then compare them, you will find that in general they record different readings (unless there are suitable symmetries in that region of spacetime). The ratio between their apparent tick rates is just what is known as gravitational time dilation, i.e. it's a relationship between clocks, not some change that happens to them.

You wouldn't need to escape! Since tachyonic motion is by definition space-like, it will always be possible (given suitable boundary conditions) to find a geodesic that is precisely perpendicular to the local time axis. There then exists at least one observer for whom you are both above and below the event horizon simultaneously. Luckily for us, such a thing as a tachyon in all likelihood does not exist, because this would create all manner of awkward issues and problems.

Good point! So obvious that it is easily overlooked

To mutate / mutation. And how about the concept of to morph? Metamorphosis?

It could be completely different, in the sense that much of what we take to be indispensable properties of the world (space, time, causality,...) might not actually be aspects of external reality at all. It would be like the UI on a computer - we see all those pretty little icons and menus and windows, and manipulate them with a mouse or our finger. But in actual reality, what is in a computer is just bits of information, sequences of '0' and '1'. There is nothing there that even remotely resembles an icon, or a mouse pointer, or a window - that graphical user interface is just a constructed model of what the computer's RAM modules contain. We need such a model in order to make sense of the information within the memory, since a long sequence of binary bits would be meaningless to us. Could it be similar in the case of the mind? It is at least conceivable. I can't answer this...are there any neuroscientists here?

In order to maximise one’s chances of survival and procreation. For example, if you are in the middle of the Savanna, and come across a hungry lion, it is not in the mind’s interest to create an accurate model of all colour variations in the leaves on that bush, or the fragrance of the morning air, or the patterns of the clouds above you. Instead, it will create a model that is almost exclusively focused on the lion, and what you are going to do about it in terms of self-preservation, and the feeling of fear, anxiety, and being threatened. Everything else gets largely filtered out. That isn’t an accurate representation of the world around you at that moment (which consists of much more than the lion, and doesn’t contain anything that corresponds to the emotions felt), but it is one that serves your evolutionary interests in that particular situation. Would the above example work?

Yes, I agree, especially with the part about enhancing one’s own understanding...I’ve experienced that many times myself. So you are right, sometimes it can be skilful to engage. Not in this instance though, the site referenced in the OP is way too far ‘out there’.

Indeed I think we all were, simply because that is what they are conventionally/historically called. Nonetheless, the formal definition of a function is a relationship between sets, so ‘argument of a function’ would probably be a better term.

Note the word ‘approximation’ in this. It’s valid only for the low-velocity, low energy domain.

Well, in the very first place, the sentence you quoted is completely meaningless word salad - it's a bunch of scientific-sounding terms jumbled up into something resembling a sentence, and is devoid of any meaning. So there isn't actually anything there to be responded to. Don't worry about that, because there's nothing there to be understood - the whole thing is completely devoid of any meaning. The one thing you may be able to respond to is the idea that gravity is somehow electromagnetic in nature, which is an old chestnut amongst the crank community, and occasionally resurfaces on various forums. You could suggest the proponent to step into a large enough Faraday cage, which blocks out EM radiation; by their own claims, they should then be weightless. Evidently this is not what happens. Do remember though that ultimately any discussion with adherents of pseudoscience and crackpottery is a waste of time, you aren't going to get anywhere. You simply can't reason someone out of a position that hasn't been arrived at by way of reason in the first place.

Ok, thank you. It would appear to me - and maybe I am wrong and this is just my own ignorance of the subject - that there are a lot of ad-hoc impositions going on that do not necessarily follow from the model/formalism itself. I don't mean boundary conditions, I mean 'doing things to make things fit' kind of prescriptions. This isn't necessarily meant as a criticism of QFT, which evidently works well enough, but rather as an observation that invokes a sense of QFT either not being fundamental, or of us having chosen a mathematical formalism that just doesn't fit the underlying ontology very well, and thus obscures whatever the fundamental physics actually are. Somewhat like Maxwell's equations written with 3-vectors being an unholy mess that obscures the real physics, whereas same become immediately and intuitively obvious when the equations are written in terms of differential forms. I am not even sure what the fundamental ontology of a quantum field is actually supposed to be - it's clearly not the concept of 'particle', but neither is it the field itself, since an operator-valued field is only a mathematical abstraction. So I don't really know what to make of it. I'm afraid not, no. I don't really follow much of what is going in particle physics, since I am more comfortable with GR. Hm...I don't even think that the excitations of quantum fields are ontologically fundamental to the world. After all, both the concepts of 'vacuum ground state' and 'number of particles in a given region of spacetime' are observer-dependent and not invariants; so how could they be fundamental in any real sense? I think there has to be more going on here, which we don't see at the moment. Perhaps it is hidden by an archaic and messy formalism.

The BU concept is kind of related to this, but I am going a step further by saying that information itself requires neither space nor time - these concepts arise only at the point where one attributes context to that information, which requires the imposition of a structure, which generally will be a spatiotemporal embedding. But I say this is an extraneous thing, and not inherent in the information itself. Ok, I haven't actually taken it that far For me, a Hausdorff space simply seems a natural way to think of a complex network such as the brain. Another option would be to think of it as a tensor network that maps inputs (sense data) into outputs (brain states? specific behaviours?). Whether or not spacetime itself can be modelled as some kind of Hausdorff space is another matter, albeit an interesting one. It reminds me of a model called Causal Dynamical Triangulations - one result of this model is that, while spacetime has the usual (3+1) dimensions on large scales, it reduces to just 2D with a fractal geometry on small scales. I don't know too much about this model, but it's an interesting concept. Fair enough, but I'd put it the other way around - 'to vary' inevitably implies a process (and thus time) to me, whereas 'change' does not. But that's just convention Exactly - information vs the embedding of it.

Yes, that's true. But then the question arises of course - if there is no 'external' world, why would the mind need to conjure up any models at all? There seems to be no discernible reason for it, if the mind is already all that exists. In the realist view, at least you can pinpoint a practical reason for the mind's building of a world-model, namely to maximise the individual's chances of survival and procreation. Which is in itself an important point: the mind's model of the world is not designed to reflect actual reality, it is designed to ensure survival and procreation. Thus you have all kinds of distortions, filters and overlays going on that have no analogue in the external world, but do serve a specific evolutionary purpose. Overall I would say that there being an external world is the more likely and philosophically less problematic position - but I would also say that the external reality in itself is almost certainly very different from our mind's model of it.

This is a valid point. But I think the chief problem with a world that is purely invented is the fact that everyone shares a roughly similar ‘invented world’. How is that possible, if it is not based on some external reality? It would mean that either everyone shares the same mind (that’s all there is), and the concept of us being separate individuals is an illusion; or that the ways in which the mind can invent things is somehow intrinsically constrained, so that the end result is always similar.