So, Naps, here’s a true story. I had a cool green copper wind chime with five or six tubes of different lengths when I was a teenager. One afternoon I was lying in my bed and spacing out listening to the wind chime ring its different and random clusters of notes here and there. For about five minutes I got into a zone where could anticipate what the next cluster of sounds would be. I heard them in my Inner ear before they happened. They were each different. I got so freaked out, I jumped up and took the wind chime down from outside my window and buried it in the back yard. In hindsight, sad, one should not give in to fear.
I believe it is possible to have contact with the numinous, infinite, & divine. You know it when it’s happening. Just a drop of the infinite in a system goes a long way; can change everything.
Hm. Assuming the visible universe (~10^27 meters in diameter) consisted of planck-length (~10^-34 meters) voxels and assuming they could be in one of two states (on/off, if you will), also assuming the universe was cubic with side length ~10^27 meters… (because otherwise it’s spherical and calculating 4/3 x pi x r^3 is probably not worth the hassle)
10^81 cubic meters, with each cubic meter subdivided into 10^102 voxels, that’s a total of 10^183 voxels and a grand total of 2^(10^183) possible states of the universe, or about 10^(10^182) A decimal number with 10^182 digits. Quite big, but still finite. xD
Sometimes I feel that considering my mortality is a way to get a taste of the infinite. It is quite likely that there’s nothing after death, and that I will never exist again forever; not existing, no time or experience, but still never coming back again forever. Very strange
The universe isn’t cubic though, it’s flat
Unless there are infinite big bangs and infinite earths
right, not steady state, but possibly cycling forever; with no beginning
It’s turtles all the way down!
Round like a circle in a spiral, like a wheel within a wheel
Never ending or beginning, on an ever-spinning reel
Jack ruby -Apathy
turn like a wheel inside a wheel…
talking heads - slippery people
Thank you for such a thorough, thoughtful post! Really enjoying this discussion.
Rather than mathematics, my background is that of a writer / story-teller. I am also very interested in philosophy, psychology, and evolutionary biology, so a lot of my opinions and frameworks come from those backgrounds. However, it’s interesting that the same problems and questions come up - i.e. “are we finding truth or inventing it?” or “are we seeing reality as it really is or are we fundamentally limited to seeing what we are expecting to see?”
If one studies comparative philosophy long enough, something quite unsettling becomes clear: while any philosophical viewpoint allows one to gain insight into the universe in some particular way, it will necessarily blind the viewer in another way. As in your example above - things that make perfect explanatory sense from the Platonist point of view become nonsensical from the formalist view.
There is also the problem that - regardless of our philosophical background - our conceptual frameworks are innately, inescapably human. They are based on human experience and try as we might, we cannot avoid painting our reality with the colors and metaphors gained from that experience. And so our religious mythologies become filled with stern fathers, loving mothers - we make arguments for or against abstract concepts based on what our experience has trained us to expect (i.e “it can’t be turtles all the way down” or “God doesn’t play dice with the universe” etc.)
The philosophical framework of Zen gives us some interesting clues and tools in this regard, in that it asks us to explicitly focus on how our mental structures draw limits on what we are ready to accept, and urges us to actively break through those limits. However, just like any philosophical framework, Zen also has boundaries - in that - if you’re not using those tools to approach a particular goal (i.e. detachment / going beyond ego) then you’re “doing it wrong”
So, given that we are hobbled by our human perspective in all these different ways, is the whole process of making sense of the universe doomed? I don’t think it is - and again - I use a framework from evolutionary biology. At any one point there is a dialectic between our approaches and the reality outside of us. If our approach doesn’t fit - if it fails to explain the reality outside of us, we have to discard it, adapt, and evolve something else.
The point isn’t to get to some final answer at the back of the book, the point is to continuously evolve our frameworks, approaches, and answers to the reality before us because Reality is That Which Does Not Go Away When We Stop Believing In It - which is pretty darn close to the Scientific Method. I like this approach because - at any given point - we acknowledge our limitations. We aren’t seeing Reality as it really is - we acknowledge that it might be beyond our current ability to measure with the instruments we have at hand, or might even be more complex and strange than we can wrap our human minds around - but at least we are constantly building and discarding frameworks rather than being stuck in any one particular framework.
I think about these kinds of things a lot. How do you take something so huge and abstract and make it concrete? We look out at the darkness between stars and we can tell ourselves “That goes on forever”* - but again, we are limited by our human experience. Since nothing in our living experience is infinite, we are reduced to abstractions.
(*and yes, I know that our universe may not in fact be “infinite”: https://phys.org/news/2015-03-universe-finite-infinite.html)
For me, it helps to think about much smaller infinities like repeating decimal fractions. I know that 1/3 = 0.333333333… is in some ways just an artifact of base10 math, but there is something there about those 3’s going off into infinity that helps me make the abstract more concrete. The same thing goes for Pi - on one hand, I know that this irrational number goes on forever, on the other hand I know that they all fit in to that little tiny chunk of red between 3 and Pi.
It’s the same with fractals. Using a good computer program and diving deep into the Julia set, one gets that awe-inspiring feeling that it is bottomless. Now, some part of me knows that this is an illusion - that the software I’m using is only rendering so many iterations of the equation, and that my monitor is only able to display only so much granularity of that image, because of the limits of the pixel sizes. However, the thing that works for me isn’t the actuality of infinite depth but the POTENTIAL for infinite depth - that given these particular conditions - one could perform the calculations and they would theoretically go on forever.
So maybe that is the most useful way for me to think about infinity - something that has the potential for being an infinite process because there is no natural limit to keep it finite.
So, so back up and bring this around full circle - the idea I started with was that once the capacity for embodied awareness evolved, it began adding additional layers of complexity to the universe in ways that
- accelerated the universe’s natural process of adding those layers
- made novel resources and products available for complexity to use and
- created a situation where the process of adding additional layers of complexity had the potential to become an infinite process.
So from this point of view - if you think about the state space of the universe as not only the positions of the atoms in the universe, but also the motion of those atoms, and the procedural/interactive information that is made possible by all the processes and forces acting on those atoms - then you approach a framework where new ideas really do expand the state space of the universe.
What do I mean? Well for one - the presence of living beings has reshaped the chemistry of our planet many times, the most famous being the Oxygen Holocaust:
Once that great chemical change occurred, and a more energetic element was available as an energy source (i.e. oxygen metabolism) that then led to all these other evolutionary and metabolic pathways evolving, increasing the overall complexity of the system.
Or, let’s look at something like the hormone Oxytocin:
At one point in biological evolution, you had sexual reproduction, but no pair bonding, no parents taking care of offspring, etc. Along comes this new hormone (note: from an evolutionary perspective, this first evolved in sea birds, see this book for more: https://www.goodreads.com/book/show/262728.The_Naked_Neuron)
and suddenly you have these internal reward pathways that lead animals to develop new behaviors to nurture their young, form pair bonds, form larger societies of animals that are capable of more complex group behaviors than any individual. This increase in behavioral complexity then circles back and becomes the evolutionary pressure which leads to development in language complexity, group dynamics, and eventually the beginnings of theory-of-mind, etc.
Fast forward to modern times and we have scientists filling in the Table of Elements by creating new elements that were once only theoretical. We can even misuse those things, and create huge nuclear disasters (Chernobyl / Fukushima) that create long-term physical changes in our world. We are sending our machines and information about ourselves out into space. And now, we are working towards technology that is taking our embodied/physical awareness and transferring those processes into machines. Will we ever get a strong/general AI? I don’t know! But I do see it as something likely, and if we ever do succeed, it will create new configurations of matter, energy, and information - it will open up entire new situations where complexity can take root and grow - it will create its own new by-products and secondary/tertiary effects that we cannot predict.
So - yes - I do see our ideas as increasing the available state spaces which are possible in the universe in a very real / physical sense. I also see this entire process as something that has the potential to be infinite - even though I cannot hold the actuality of that infinity in my hand. Of course there are many factors that might limit it - our potential to destroy ourselves - the finite lifespan of our local star - even the potential heat death of the universe. But again, I can stipulate that this might be an infinite process because it has the property of constantly jumping beyond its limitations - creating new configurations of matter, energy, and information - making new forces, new materials, and new ideas available.
Hi - so I was a little confused by your over-use of the pronoun THEY/THEM. Are you doing this because you’re trying to use gender-neutral pronouns? Or are you so beyond self/other that there is no distinction between your thoughts and your co-worker’s thoughts? Either way, it made it a bit difficult to understand who thought what and who said what…
I was also confused by the SWIM thing - I just looked it up and I’m guessing you meant Someone Who Isn’t Me… right?
Anyway, I guess I just wanted to point out that humans have this amazing capacity for non-verbal communication and theory of mind. We have entire centers of our brain cooperating to feed us theories of what might be going on inside other people’s brains.
Some people are naturally better at this than others, and I’ve certainly read a lot of anecdotal evidence, and had my own share of psychedelic experiences which let me know that our capacity to do this particular trick can increase in those situations.
So yeah, while it might be possible that some sort of telepathy was taking place, it’s probably a lot more possible that this was just one person’s mind being really good at making sense of the world. In other words
- the person not feeling well was giving off all these non-verbal signals that this is what was going on in their head
- another person absorbed those signals and - without even trying - created a complex mental model that predicted what was going to happen next, and then
- the thing they predicted actually happened
I’m not saying that this is somehow 100% proof that telepathy doesn’t exist, but it is the much simpler explanation…
I like to fall back on that ‘ol rock & roller William Blake who tells us “If the doors of perception were cleansed, every thing would appear to man as it is: infinite.”
To see a World in a Grain of Sand
And a Heaven in a Wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour
The rubaiyat of Omar Khayyam -
“the flower once blown, forever dies”
The way that can be told is not the eternal way.
Swim is clearly me lol and yeah he didnt see me, he was walking past talking to someone else and my half cubical blocked me from his vision. It was the timing too it wasn’t like 5 mins past it was like i thought it he said it level creepy.
Stage 1 cleared. Now repeat “We would like to offer you a position at our company” and wait for the phone call.
So it’s funny you say wait for the phone call lolz
Guess I didn’t follow the white rabbit to clear stage 2.
This is more a taste of what empty means than what infinite means. Quite the opposite.
perhaps. You’re right
No I have watched infinite totem poles scroll in front of my vision. Even simulated infinity is pretty intense.
This is more of an awkwardness in our representation system. We cannot fully write down 1/3 or pi in our decimal system, so in a certain way our decimal system is lacking in expressive power. The actual value of those numbers is found by their definition (1/3 as the ratio of the whole equal to the ratio of 1 to 3, and pi being the ratio of the circumference and the diameter of a circle). Their decimal expansion is a way to approximate their value, and in that way yet another infinite process, comparable to “keep counting”. This is indeed the potential infinite, and not the actual infinite.
The same story holds for fractals, although I think fractals are an excellent example of how something extremely basic can create an extraordinary amount of complexity. It’s a good argument for something as mysterious and complex as conscious being part of something “simple and understandable” as nerves.
It’s quite difficult to get an appreciation for what the actual infinite might look like without involving infinite processes. It is possible though. For example, the following is a characterisation of infinity: a collection of things is infinite, if we can remove some elements from the collection without changing the size of the collection. If we remove less elements than the size of the collection (for example any finite number of elements), then we won’t change the size, and there are indeed even ways to remove the same number of elements as the size of the collection and still not change the size of the result (for example as I did with the even numbers).
Not in how I understand the universe. I don’t see how life / humans changed the motion of elementary particles or the information made possible by the forces acting on elementary particles. You could see the great oxidation event as not much more than a chemical reaction being sped up by a catalyst. Somehow (in my view by chance) some chemical structures in the form of molecular biological life started catalysing a chemical reaction that produced O2. As far as the atoms are concerned, not much changed, really.
It seems the point you want to drive home, is that the universe grew in complexity, in the sense that in order to describe the state of the universe, we would need more words to do so: A dead planet made completely out of iron atoms is easier to describe than a dead planet with our composition of chemicals, which is easier to describe than a living planet.
However, this is describing the complexity of describing the state space of the universe, but it is not a measure of the size of the state space of the universe.
Compare it with a (hard) erased hard drive containing only zeroes in all its memory cells to the same one after it had been used to store the entire content of Wikipedia. The former has very low complexity, since it’s easy to describe completely (I just did), whereas the latter will be comparatively difficult to describe (I estimate it could be compressed a bit, but still will be barely less than the actual size in memory of the Wikipedia, in orders of magnitude). We could make it even more complex by filling the hard drive with pure random noise, in which no patterns emerge, and hence it will take describing every bit of information individually to describe the state of the hard drive (as there will be almost no recurring patterns).
In the meantime, the state space did not change, since the hard drive still has the same number of bits of information in each of those cases.
Note that it is a law of physics that the entropy (and thus the informational complexity) of the universe can only increase, so it is not even the human element that makes the universe more complex: it’s expected to happen regardless of what we do or have done.