He does make the rather blithe assumption that mathematics is somehow real, and not an idiopathic artefact of our cognition, as much as the apparently respectively static and dynamic nature of space and time that he notes most posess. Perhaps mathematics is also a stubbornly persistent illusion.
Me, I see the universe as information, and everything else flows from that. We are needles scratching out the tune from a hyperdimensional record. Our mathematical laws may well be encoded within that information, or are representative of symmetry within it, which is also reflected on the structures and strictures of our minds, but I see mathematics as effect rather than cause - not that there's really such a thing as causality, either, if you stop thinking of "the arrow of time" as being a thing other than how we experience spacetime. Causality is as human an invention as sunrise.
Then again, I'm assuming that information can exist.
Perhaps it's turtles^W simulations all the way down.
You can argue that Time is an illusion. You can argue that our intelligence allowed us to break free from the harsh laws of nature and evolution too soon, so we never acquired the necessary sensors and abilities. Maybe if we had to compete against multiple equally intelligent species, we would have acquired them. However, I think that using a "vision of Time as it really is" sensor correctly would require a far more complex and energy-hungry brain, so it's probably not "worth it" from an evolutionary perspective. Or maybe it's out of reach of carbon-based organisms.
However Mathematics are different. It's not a perception. It even allowed us to discover things we could not perceive, and explore things we cannot perceive. It is independent from us and the universe. And if you still want to throw away Mathematics, you'll also have to throw away logic, which is kind of an issue. The only thing one could seriously argue, is that something better than Mathematics exists, like General Relatively is "better" than Newtonian mechanics. But maybe that is out of our reach, too.
Meanwhile, repeat after me: I believe in modus ponens, set theory and monads.
>However Mathematics are different. It's not a perception. It even allowed us to discover things we could not perceive, and explore things we cannot perceive. It is independent from us and the universe.
You only say that as someone inside a universe with mathematics entangled with it. I don't think we can say anything about mathematics being "independent of the universe" just because we conceive them with our minds.
One could imagine another "universe" where even standard logic (A=A for starters) doesn't hold.
When you say "information" what do you mean exactly? I can see information as a set of constraints that arises in the system due to how it evolves, and that those constraints enable structure to emerge, and that with the law of conservation of energy no energy can be created or destroyed, it means that all those structures can only do what they can do, any deviation from the constraints will require new energy or removing energy from the system to alter the course.
I like your needles - hyperdimensional record analogy. I would say mathematics encodes for and predicts a certain set of constraints, but we can never be sure we have observed or found the most fundamental constraint, and so to us, an incomplete mathematical 'law' will look like it needs energy added or removed to fit with the real world, but in reality it's just a constraint somewhere that we haven't seen that will readjust the series. All of this is kind of written on a whim, I'm not sure I thought it through enough :
All that can be, is. A mathematical proof is a statement about what can be in a particular system. A system can be anything that can be dreamed, by yourself, or indeed by the universe. Therefore mathematics in it's widest definition is the study of what can be in the universe.
Its like this: If something is to exist, would it not be absolutely absurd that only this exists? This universe in this particular configuration, out of all the possible configurations? It cannot be. Either there is nothing or there is everything. If there is everything then all possible configurations of thing are. Some of those things have patterns within them that 'percieve' the world to be time like. When really the whole thing is timeless, it is like all configurations of thing saved onto one giant hardrive, your life in bits on a 2 dimensional substrate. From the outside its timeless. From the context of you at x,y,z it is timefull.
Is this not totally obvious? How can this not be obviously true to everyone?
> Me, I see the universe as information, and everything else flows from that.
I admire the Integrated Information Theory of consciousness (by Giulio Tononi) a lot. It provides an impressive intuition pump towards the nature of consciousness and the necessary conditions for it to arise. It also goes much deeper than "consciousness is a complex pattern in space-time", by detailing "what does it mean to be complex?", what kind of complexity leads to consciousness and how can we compare various systems to see their degree of consciousness/complexity.
The IIT surely does not give a definitive answer on consciousness, it is not even able to compute an approximate complexity score for the human brain, and doesn't explain why complexity is linked to consciousness in the first place, but it helps us see in many directions where we could only stumble in darkness before.
The idea of "spacetime" makes a fun narrative, fun thought experiments, and interesting ways to graph and visualize events.
But many physicists wish that popularizing this concept would stop and go away, because it is misleading. There is both evidence and theoretical work demonstrating that time, unlike the spatial dimensions, is not a choice when it comes to direction of travel, and never will be.
The definition of time as a numerical order of change in space is replacing the 106-year-old concept of time as a physical dimension in which change runs,” Sorli said. “We consider time being only a mathematical quantity of change that we measure with clocks. This is in accord with a Gödel view of time. By 1949, Gödel had produced a remarkable proof: 'In any universe described by the theory of relativity, time cannot exist.' Our research confirms Gödel's vision: time is not a physical dimension of space through which one could travel into the past or future.”
Sounds like some think this phys.org article is BS. I don't know, I am not a physicist. But I have been wondering for many years whether it makes sense to treat time as a dimension. I assumed it made sense in relativity study, and has been mistranslated in popular science culture as a thing that somehow opens up the option of time travel.
Time can be a dimension and still be treated differently.
In fact, in special relativity, it is. When calculating the spacetime "distance" between two events, we use something that looks like the Pythagorean theorem, but we must always make sure to put a different sign in front of time than we do space. (If we sum the squares of space, we must subtract the square of time) (see: minkowski metric, really any metric)
Another point of interest would be the matrix representation of the Lorentz transformation (the way to go from one reference frame to another). The matrix "mixes" the values of the time coordinate with the space coordinates, and the space coordinates with each other, but time is mixed differently. (This is a nice one to bring up because its clear if you just look at the matrix.)
This is very significant for people wondering about time's status as a dimension. It is emphatically not the same kind of dimension as space, even if we choose to represent it as a component of the position vector.
Not a physicist -> My assumption is that this is because x,y,z are just constructs to model physical space. They don't exist and we could just as well describe space with cartisian coordinates or some other system where the dimensions would not be isometric. Meanwhile, as you point out, t as a vector is also itself a convenient model for something, not an actual dimension.
Hmm... if t is also then not a Cartesian dimension, it makes me wonder if the whole Cartesian model isn't a bad model of fundamental reality. Maybe it's just a mathematical shortcut.
It helps me think of it as the iteration number in simulations. The state of the world at every iteration i+1 is a function of the state at i. Therefore it's impossible for a phenomenon in the simulation to alter the previous states.
My take on it is that special relativity provides no evidence that time is an extra dimension (like the spatial dimensions) in anything but a mathematical sense.
General relativity however has quite a lot of effects that mingle together space and time in various ways, so I'm still thinking about that one.
I really like the presentation in one of Lev Landau's books. He calls it a fictitious 4-dimensional space. That's the correct way to look at it, spacetime is just a mental model, a tool for describing physical laws. So depending on the mental model or framework we decide to use, time can be a dimension or something completely different.
dahart: >> has been mistranslated in popular science culture as a thing that somehow opens up the option of time travel.
Ah, time travel isn't science fiction. Clearly we have concrete experiments that show this is common place, easy and done all the time.
The faster you go in the space dimension, the slow you move in the time dimension. Now certainly being able to go back in time is something of speculation, and more the realm of science fiction. but that you can jump into other people's future is fact.
You're right, and that's my understanding too. But I would say that relativistic perception of time does not classify as "time travel", unless mere existence classifies as time travel. Yes, time slows down or speeds up depending on velocity, but not in a way that you have any control over. Time is not a choice, its not an axis upon which you can choose your direction of travel, it is only something you are subjected to and can observe.
Now, I guess this is a very subjective discussion, but saying you can "jump into other people's future" feels like a way to make it sound sexy while glossing over the boring detail that you have to sit through all the intervening time along the way, the "jump" isn't instantaneous, and once you "jump", there's no going back. In this sense, we're always jumping into the future each and every second, and it would be equally correct to state as fact that we can wait into other people's future.
I love the idea that the atoms of our bodies are replaced over the years - that no part of me today was a part of me in my twenties - and this concept, the braid in spacetime, puts it more eloquently and more bravely than I could think.
It's great to be able to take words written by some guy on another part of the world and have them rearrange my brain and my thoughts - this is beautiful.
Thinking of lifelines in space-time got me through some dark times years ago.
Have a look at Primo Levi's The Periodic Table - the book is a collection of biographical essays each themed with a chemical element. The last essay, Carbon, tells the story of a single carbon atom over the years. Another perspective.
Actually there are parts of you that were parts of you in your twenties. Some of the brain cells, some of your heart cells, and if you are a woman, your eggs.
Unless you are talking about how matter pops in and out of a apparent reality, in which case we're going too far down for me.
If you are left only with some of your brain cells and some of your heart cells and if your are a woman your egs, are you still an aware human being?
You and other people are missing the point of the perspective and on top of that you are even admitting that even what you claim is constant isn't really when it comes down to it (matter popping in an out).
The insight is of course that things are always in flux and that they are much less "solid" than they might look.
You are obviously free to dismiss this as interesting but I find it hard to swallow this kind of "the hole in the cheese" comments. It's everything thats wrong with critical thinking.
Speaking as a physicist, I in general like this article, however there is a nasty technical point to make, which is that if you actually use distance units to measure time, we look like the "inanimate object, simple pattern", not the "living object, complex pattern." Moreover the "death, disintegration" slide is not going to be what you look like unless you happened to be in the vicinity of a bomb at your death.
Still the question of how we reconcile our sense of ourselves as speech-act-performing free-will-having conscious-feeling observers embedded in a changing world, with a relativistic perspective which says "there probably isn't one constantly-updating 'present' because a 'present' can be any hyperplane between two light cones, and therefore we can never have any physical basis to choose one as the correct one," is one of many really important philosophical questions that I think are important, though not really my domain.
As a trained, but non-practicing, physicist, I would like you to elaborate about your first paragraph. I am used to using units where c=1, I think that is what you are referencing: a "meter" of time is the time it takes light to go a meter (which is to say, a very small amount of time) and so a second is 3x10^8 m. I don't see how this changes the pattern we would make in spacetime. If we assume no one ever moves (a nice physics-y approximation), but the particles that make them up do, so I don't see why we wouldn't look like the middle pattern while alive. Then after death, the disintegration is exaggerated, but again, it seems more-or-less right to me. What am I missing?
Because the timescales that you're "moving" on are very long from a relativistic perspective. If we localize you in spacetime you're maybe a meter long in one direction, two meters in another, half a meter in a third, and... 30,000 km in the fourth. If we look at you on the nanosecond timescale that you need to see time as "meters" we find that except for, say, electrons' worldlines about the nuclei, your worldlines are very much all parallel to each other.
I'm studying topological quantum computation, and in this field one considers particles confined to 2 dimensions called anyons. As a collection of anyons move around, the paths they take in spacetime "tangle together" and have the structure of an element of the braid group (https://en.wikipedia.org/wiki/Braid_group). Two anyons cannot exist at the same place and time, and thus their world lines cannot pass through each other. This is useful, since any sort of physical error in the system will preserve its braid structure, saving the need for quantum error correction.
This article is mostly fluff (except for the two diagrams, whose captions contain more content than the article), but I'm sure it makes an interesting read for those wishing for light philosophical thought rather than deep and novel technical concepts.
Interesting that everyone automatically defaults to Greg Egan when thinking of hard mind-bending sci-fi that explores concepts like these. I don't even remember how I got into Greg Egan, but do you have any other favorite authors who play with concepts like these?
In my head, Greg Egan is filed under the "Math-Fi" directory, as that's what I generally associate him with but he's very well versed in pretty much everything (Biology, Physics, etc).
Of course, this begs the question of "How does this empower me to create a more glorious life?"
Perhaps the takeaway is that I am not a brain in a body moving through the world to do things. Instead, I am a mind and these patterns swirl around me and come and go and my awareness drives decision-making as to how to interact with these swirling, complex braids. Then, being the architect of the future is more like knowing where to put your finger.
I'll buy that your spacetime braids disintegrate at death altho i'd think they be more like the parallel braids of a stone, not like those shown helicoptering out as in the picture.
But as for birth, clearly your start branches off of the braids of your mother. and so start immensely tangled to begin with.
A wonderful picture of space and time. My religion fits very well with the concepts of fate and destiny suggested by this picture. Our benevolent creator has for us woven a fantastically complex braid and I am humbled by the chance to take it in. Busy busy busy
Physics is a description, maths is the best method of describing things in physics, but when things head to infinity it's a sign that the descriptive system is breaking down.
Me, I see the universe as information, and everything else flows from that. We are needles scratching out the tune from a hyperdimensional record. Our mathematical laws may well be encoded within that information, or are representative of symmetry within it, which is also reflected on the structures and strictures of our minds, but I see mathematics as effect rather than cause - not that there's really such a thing as causality, either, if you stop thinking of "the arrow of time" as being a thing other than how we experience spacetime. Causality is as human an invention as sunrise.
Then again, I'm assuming that information can exist.
Perhaps it's turtles^W simulations all the way down.