The universe might be infinitely large. As Jacob Barandes and I have argued (Ch 7 of The Weirdness of the World; free draft version here), infinitude seems the most straightforward extension of current mainstream physics and cosmology. A finite universe would presumably require either an edge, which produces complexities for which there is no evidence, or the right kind of curvature, contra evidence that the universe is approximately flat at large scales.
If the universe is infinitely large, then it is at least conceivable that there are conscious entities compared to whom we are arbitrarily small. Here's how I express the idea in the conclusion of Weirdness:
I stroll through my suburban neighborhood in heavy rain. Gushing runoff strikes a fallen branch, and droplets leap a foot in the air. I imagine, inside one of those droplets, creatures so tiny that the universe they see through their telescopes is a trillionth of the radius of a proton, while a nanosecond encompasses 10^30 lifetimes. What could they know of us, from deep inside that arcing droplet? If the cosmos is infinite, we might know as little as they do about the unimaginably vast structures that embed us.
At sufficiently small scales, the effects of gravity are virtually undetectable. Compared to the strong nuclear force, the "weak" nuclear force, and electromagnetism, gravity is about 10^29 to 10^38 (approximately a trillion trillion trillion) times weaker. It has virtually no influence over what happens at subatomic scales. However, it accumulates over long distances, making its influence detectable at larger scales.
If there were entities as small as the ones I imagined in my droplet, it's plausible that they would be too small to detect the influence of gravity, even if they had technological tools as good as our own, scaled to their size. Correspondingly, if there are entities vastly larger than us, we might imagine them knowing of a force vastly weaker than gravity but which accumulates detectably over distances much larger than the mere tiny, minuscule, virtually negligible 93 billion light years that we can observe.
Of course we have no direct evidence that such a force exists. But neither do we have evidence against the possibility. Whether it's reasonable to guess that such a force exists depends on what we should assume as the null hypothesis or default presupposition.
In one way of thinking, the default presupposition should be that there is no such force. According to Occam's Razor, we should not multiply entities beyond necessity. If forces are "entities" in the relevant sense, this suggests that without positive evidence of an extremely weak, extremely long distance force, we should assume there is no such force.
On the other hand, Copernican or anti-specialness principles hold that we should default toward assuming that we aren't in a special position in the universe (such as its exact center), pending contrary evidence. Considered in a certain way, we would be oddly special if we were just the right size to observe all the forces of nature. If there are entities vastly vastly bigger, they presumably would not be able to observe the strong nuclear force with equipment of the caliber we have (scaled to their size). If there are entities vastly vastly smaller, they presumably couldn't observe gravity. Why should we be so special as to see every force there is? Better to assume that we are not so special, and thus that there are forces that operate on scales we cannot (as a practical matter) observe.
Consider a scale of force-strength ranging from arbitrarily close to zero to positive infinitude, scaled so that gravity counts as force-strength = 1, the weak nuclear force as 10^29, electromagnetism as 10^36, and the strong nuclear force as 10^38. Even just on a finite scale from 10^-1000000000000000 to 10^1000000000000000, this would be a remarkable clustering near the middle. If the force-strengths we could potentially detect with our equipment are in the range from, say, 10^-15 to 10^60, then that is the space of possible force-strengths that we have sampled in. If we find forces scattered at values 1, 29, 36, and 38 in the range -15 to +60, then it's not an unreasonable guess that these four values constitute a random distribution within our detection capacities and that if we could sample from a wider range we would find other forces that we cannot currently detect.
(I don't have a good sense of realistically what force-strengths we could potentially detect. The larger the scale -- say from 10^-1000 to 10^1000 -- the less that 1, 29, 36, and 38 look like a random sample, and the more reason we would have to think that something ensures that force-strengths stay within a magnitude not far from 1. If it seems odd that there would be forces too strong for us to detect, consider that on our scale and speed, an entity held together by a very strong, fast-acting force that diminishes very sharply with distance might look to us like an unbreakable fundamental particle.)
The case for entities vastly larger than us seems stronger than the case for entities vastly smaller than us. If the universe is infinite, then there will be structures arbitrarily vastly larger than us, and unless something ensures that those structures are flat and bland, some of those structures will be complex and possibly even support the evolution of intelligence through natural selection.
But now we can again apply the Copernican Principle. If we accept -- look, I know I'm already far out on a limb here, but humor me -- that there are infinitely many complex structures vastly larger than us in an unending upward scaling (the first set of vastly larger entities being vastly smaller than the next set of vastly larger entities and so on), it would be strangely un-Copernican if we just happened to be the smallest scale intelligent entities.
ETA 09:32, Aug 21:
The following concern has arisen several times in discussion, so I'll add it here:
Concern: Isn't the speed of light a constraint that would make extremely large entities incoherent, since it would take so long for a signal to go from one end of the entity to the other?
Response: Assuming the speed of light as a constraint, vast entities would have to be extremely slow-paced (from our perspective). But since we have literal infinitude to play with, that shouldn't matter. They might seem static to us, if we could detect them, just as we might seem static to the entities in my water droplet who experience 10^30 lifetimes in a nanosecond.
22 comments:
A contrary perspective it might be worth engaging with is that of David Deutsch, who (as far as I understand) thinks that anything explicable in principle is explicable by humans.
Here's David Albert summarizing the Deutsch perspective in an old book review:
"There is a famous collection of arguments from the pioneering days of computer science to the effect that any device able to carry out every one of the entries on a certain relatively short list of elementary logical operations could, in some finite number of steps, calculate the value of any mathematical function that is calculable at all. Devices like that are called “universal computers.” And what interests Deutsch about these arguments is that they imply that there is a certain definite point, a certain definite moment, in the course of acquiring the capacity to perform more and more of the operations on that list, when such a machine will abruptly become as good a calculator as anything, in principle, can be.
Deutsch thinks that such “jumps to universality” must occur not only in the capacity to calculate things, but also in the capacity to understand things, and in the closely related capacity to make things happen. And he thinks that it was precisely such a threshold that was crossed with the invention of the scientific method. There were plenty of things we humans could do, of course, prior to the invention of that method: agriculture, or the domestication of animals, or the design of sundials, or the construction of pyramids. But all of a sudden, with the introduction of that particular habit of concocting and evaluating new hypotheses, there was a sense in which we could do anything."
If that's right, then it doesn't violate any Copernican principle to assume we're the "right size" to detect all the forces, because we shouldn't expect creatures much smaller or much larger than us--but still using the same set of scientific methods--to be able to detect different stuff.
It's like...give and take in positions' processing...
...the processings' of being...here there and inbetween...
Excellent post Eric!
Somewhere recently (maybe on a podcast) I heard a physicist point out that the real significance of the Planck scale is not that it's guaranteed to be fundamental, but just that it's the smallest scales that we can say anything meaningful about. In that sense, there could be entire universes within our Planck length. And to your point, we might be inside the Planck-like values of some broader reality.
It seems like these scales would apply to time as well as space. So entire universes might begin and undergo their version of heat death within one of our Planck times. If there is a reality larger than us, and we could get any information about the structures there, they might look static and unchanging from our perspective.
All of which is to say, we can only work with scales that we can have some causal interaction with. Any reality outside of it can only be known by its effects on things we can interact with. Although we shouldn't give up finding ways to explore that way. It's taken us much farther than anyone could have imagined in 1543.
Thanks for the comments, folks!
Anonymous: I'm inclined to think that Deutsch's argument, if it works, would be constrained by access to empirical evidence. No matter how great a calculator you are, if you don't have evidence about domain X, you won't be able to reach the right empirical conclusions about X. So I think he would or should still be open to the possibility that we aren't of the right scale to collect the right kind of knowledge.
SelfAware: That all sounds right to me. Given the relationship of time and space, the most natural way to develop the thought is that much larger scale entities will seem static to us and much smaller scale entities will undergo lifetimes' worth of changes in a tiny fraction of a second.
Whoops, didn't mean to be anonymous up there.
I agree the argument for optimism shouldn't go through if our size limits what evidence we can get, but I guess I'm more optimistic about what sort of evidence we can (in principle) get. With electron microscopes we can see really small stuff, and space telescopes let us see incredibly large stuff. We can already see galaxies, and could probably create machine learning programs that could detect structures on much larger scales (if there are any to be found) by analyzing the vast amounts of data produced by something like the HST. Even if we were as big as planets, I'm not sure why different sorts of evidence would be available in principle.
Thanks for following up, Daniel! We are as big as planets, I mean plus or minus a several orders of magnitude (10^8 meters vs our one meter, if we're measuring diameter). Since we're playing with literal infinitude, then I'm imagining entities who are vastly vastly larger than that -- entities for whom the whole observable universe (10^27 m) is relatively the size of a Planck length (10^-35 m) -- a difference of *at least* 62 orders of magnitude, though we can go arbitrarily higher if we need to to establish the point. The idea is that if they are *that* large, their observational powers will be very different from ours. Now maybe there couldn't be entities that large; but that would require a different argument.
I arrived late here, because of technical difficulty. Insofar as I am neither mathematician nor physicist, please forgive (or pity) my relative ignorance. At least I am not running for president. So, here is my other problem. Inasmuch as the quantities being considered are smaller still than cells or viruses, I think(?), how does one ascertain measurability and/or formulation of physical laws with which to measure or predict their behavior? Haeckel once said something about ontogeny and phylology. His remark was predictive and appears to hold with much(?) of what we now know. OK, yeah, quantum mechanics and physicists know far more than I. I accept this. But when someone(s) start speaking of physics in a similar tone as they might use in discussing philosophy, a tone of doubt and uncertainty, I just sort of wonder. I am not a devil---only an advocate.
Got it. Yeah I wonder if considerations relating to the speed of light might rule out certain kinds of complexity on that scale. We couldn't function as organisms if it took millenia for our brain to send signals to our limbs. If you think the speed of light is a hard cap on signals of any kind, that's some reason to think certain kinds of extremely large scale structure couldn't exist. Or at least, that's where I'd be inclined to look to defend the idea that what we can see is what there is.
(PS. I accidentally left this comment on the other thread about demographics of authors cited in the SEP. Feel free to delete it there.)
Thanks for the continuing comments, folks!
Paul: Right, the idea would be that we cannot formulate the laws or make predictions, due to our limitations.
Daniel: If we accept the speed of light as a cap, then very large creatures would also have to be very slow. But since we have literal infinitude to work with, that arguably isn't a problem.
Thanks, Eric! If I may, may I remark on your reply to Daniel? This addresses *infinitude*, or, infinity, something I have mused over. I wrote several years ago:
Infinity is neither destination nor objective. You can't get there from here. There is no *there*, there. This is sorta, (as Dennettt often put it) analogous with other philosophical conundrums we face, in the face of doubt and uncertainty..
Over an expanse of maybe fifteen rears, my brother and I have discussed Julian Jaynes' book on the origins of consciousness. You may or may not know of Jaynes, but he still has a substantial following. I will leave you with that much. For now.
Warmest Wishes.
That philosophy is questioning uncertainty in the acceptance of the certainty of observation,...
...subjects of finding ourselves, in-between-here-there, for one's own purpose and value...
Thanks, Paul and Arnold!
Arnold: Yes, I agree that questioning and uncertainty are (or should be) central to philosophy.
Paul: Yes, I've read a bit of Jaynes (and find the view pretty difficult to accept). On infinitude -- exactly the point, one never arrives.
Storytelling by me and Gemini A I...towards the necessity of Certainty in living in-between and understanding the concept of In-Between...
When we talk about living in-between, we're often referring to a state of transition, ambiguity, or uncertainty. It might be the space between two opposing ideas, two cultures, or two life stages.
Here are some potential conceptual models for Certainty that can help navigate learning and living in-between spaces:
...Dialectical Thinking: This approach recognizes that truths' Certainty often lies in the synthesis of opposing ideas. By exploring the tensions and contradictions between different perspectives, we can find creative solutions and deeper understandings.
...Attention and Meditation: These practices can help us cultivate the certainty of awareness and acceptance of our current state, regardless of its uncertainty by focusing on the present moment...
...Storytelling and Narrative: Sharing our experiences and learning from the stories of others can help us understand and contextualize our own "in-between" moments and provide a sense of guidance...
...Systems Thinking: This approach helps us see the interconnectedness of different elements in our lives. By understanding how various factors influence our experiences, we can develop more certain nuanced and holistic perspectives.
...Experimentation and Flexibility: Being open to new experiences and willing to adapt to changing circumstances is crucial for navigating in-between spaces. By trying different approaches, we can discover new possibilities and opportunities.
Am striving to keep an open mind on the role of AI in the modern world. I think it fair to say I am primitive and suspicious of this *tool*. The controversy over what is a tool is double edged, seems to me: Is AI a legitimate aid to education or, is it a *legitimate* justification for cheating? Experts say it is is pretty easy to know when a product has been generated via AI. This lends an air of transparency to the matter. All good, I suppose. And, I suppose my suspicions are shared by others---more transparency. Yet, there are concerns around ethics and morality. Hmmmm. This is not the only arena where such concerns are emerging. That must tell us something about permissibility?
Paul, my interactons with AI help clarify things I am writing and questions I have. It has limitations: it analyzes and collates, however it is incapable of doing philosophy for instance, and there are a lot of sources unavailable, such as cartoons in the New Yorker or articles in the Stuyvesant High School Spectator (I've asked) plus they are mostly politcally correct and if pressed with counterarguments often resort to repetitiveness. I have specific questions and uses for it; I am not a student so I don't cheat with AI, I use it as a tool to help me learn and have self undertsanding with fiction I write. All those students cheating with AI would pretty much write the same thing, or so it seems to me.
Good points, Howard. I think you are on point with your final remark also. If that is right, it would add a bit of insurance, so to speak--- make some think more clearly about their own work and what that means.
Deutsch, and you, have sussed this well.. All good. Whether goldfish want vacations, matters not. Think I am being facetious? No, I am being pragmatic.
Do you have any thoughts on the suggestion that the universe might in fact have a finite scale at which things cannot be smaller? It's almost like an atomism of space and gravity. It's the theory of loop quantum gravity I believe which Carlo Rovelli suggests.
Do not know of Rovelli. Will think on it, and see what I can learn of Rovelli. Thanks!
Anon Aug 25: Yes, it's certainly possible. It would be odd from a Copernican perspective if we were the smallest observers in a large hierarchy of sizes, but Copernican/Anthropic reasoning is tricky and uncertain; and one might flip the direction of inference: To the extent we have good reason to think there couldn't be vastly smaller observers, maybe Copernican reasoning gives good reason to think that there also could be (too many levels of) vastly larger observers.
So, preliminary assessment: Rovelli runs with a good pack!Whenever I see the names Penrose and Smolin mentioned in a summary, I have to pay attention. Eric's post talks about things large and small, and, at some point largeness and smallness are immeasurable. Unless I am sadly mistaken, the *loopness* is there, somewhere. Sorta like Hofstadter's * strange loop* idea years ago when he and Dennett worked together and apart on projects, including *...Mind's Eye...*. Yes, I remember stuff. It is a curse. Maybe.
Physicists, Philosophers and Theologians believe we can know anything we want to know. Mathematicians are more realistic. Rovelli is is a Physicist.
Bertrand Russell was, first, a mathematician---taught Wittgenstein well.
I just don't happen to have much regard for Wittgenstein. The account from Rovelli around LSD?---all familiar. My experience sprang from black, opiated African hashish. And yes time and motion. stood still...
No, not sorry.
Will think on this more. thank you.
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