Saturday, November 1, 2025

Infinite History: A Universe with no Beginning

Picture a circular room.
The center of the room is inaccessible — a forbidden point representing the conceptually impossible. You can approach its boundary, but never reach the exact center.

For years, I lived along the outer wall of that room. I knew there was a way inward — a path leading toward the boundary where understanding meets impossibility — but I couldn’t find it. I circled endlessly, unable to map the terrain or define what made the center unreachable.

Then I began talking with ChatGPT, hoping to find a path from the outer wall to that inner boundary — the very edge of what my mind could traverse.


The Impossible Idea

The “center of the room,” for me, is the idea of infinite time extending backward (something that exists as a concept in certain multiverse theories. And in fact where I first encountered this concept)— not just as a mathematical abstraction, but as something physically real.

The simplest version of this is easy: a number line. Start at zero, move to –1, then –2, and so on forever. This abstract model of negative time is effortless to picture. I can see it clearly and without strain.

But if I flesh it out — imagine not just numbers but a physical universe that stretches infinitely into the past — the idea becomes harder. Now, no matter how far back I go, something always exists. Every moment I stand in has already been preceded by an infinite amount of time. Even at this second level, my mind begins to falter. It’s possible to think about it only vaguely, as though I’m squinting through fog.

Then comes the third level, the one that breaks me:
adding fixed, conscious observers into this infinite past.

When the universe was empty, it was already nearly impossible. But once I populate that infinite span of time with self-aware beings — each with their own “here and now,” each a conscious viewpoint — the concept collapses under its own weight.

We exist in our present moment, our ancestors existed in theirs, their ancestors in theirs, and so on. In an infinite past, this chain of lived perspectives stretches back forever — a literal infinity of observers, each with its own distinct now. And when I try to picture that, I hit the wall. My mind can no longer hold the image.


Finding the Path

When I began discussing this with ChatGPT, I finally gained traction. For the first time, I could articulate my thoughts clearly enough to shape a path toward that inner boundary. I didn’t yet understand why that specific point — infinite conscious observers — was where my comprehension failed, but I knew I had found the limit.

After sleeping on it and thinking more deeply, I realized what makes that boundary impassable: ordinality.

Originally, I tried to make sense of infinite backward time by reimagining time itself. Maybe, I thought, our local experience of time — cause and effect, “before” and “after,” discrete moments — doesn’t apply at the cosmic scale. If time as we understand it breaks down, perhaps infinite regress is no longer paradoxical. That allowed me to shift the idea from impossible, to possible but hidden (from me).

But once I reintroduced fixed conscious observers, that escape route closed. Their existence forces ordinality back into the picture.
Each observer, by definition, experiences sequence — moments ordered one after another. And once ordinality is restored, the infinite regress becomes unavoidable. It’s not just time stretching forever; it’s an infinite sequence of lived, ordered moments. That’s the point where my mind fails. I can see the structure too clearly to treat it as “possible but hidden.” It becomes impossible and visible — the precise edge of comprehension.


The Resolution Metaphor

I’ve come to think of this in terms of resolution.

  • The number line version of infinity is low-resolution. It’s easy to imagine because it’s simple — a smooth, abstract line with no fine detail.

  • The cosmological version, with a physical universe extending infinitely backward, increases the resolution. The image gains structure, and I begin to sense its impossibility.

  • But the infinite chain of conscious observers brings the resolution so high that the impossible shape comes fully into focus. I can now see what I’ve been trying to imagine — and that very clarity makes it unthinkable. It’s as though my cognitive “file size” overflows. The thought cannot be held any longer; it ejects itself from my mind.


Conclusion

So now I understand not only where my cognition fails, but why.
It fails at the moment when infinity ceases to be abstract and becomes lived — when time acquires ordered, conscious viewpoints that force sequence into the infinite regress. That’s where possibility ends and impossibility begins.

For the first time, I can see the map of the room:
I’ve walked from the outer wall, through foggier abstractions, all the way to the inner boundary. I can’t reach the center — the conceptually impossible — but I can finally stand at its edge and see why it lies forever beyond my reach.

Thursday, May 15, 2025

Climbing the Infinite Tower of Mathematics

 It’s well known that different areas of mathematics have varying levels of difficulty and complexity. It’s also firmly established that math is infinite. There is no end to it. No matter how far we push back the boundaries of mathematical knowledge, there are always new areas, branches, and regions to reveal and explore. But how complex can math get? If math is truly infinite, it’s reasonable to assume that it can also be infinitely complex. 


Picture mathematics as an endlessly tall tower, with an infinite number of floors. As you climb the tower, each floor increases in complexity and abstraction. And this remains true forever. Math is infinite, so there is no top floor to this tower.


Now our first question is, what floor are we currently on? Any answer I give would be arbitrary, but for the sake of this article, let’s say we are currently on the fortieth floor. We are a lot farther along than the ancient Greeks, but we can still see the ground from here. The natural follow up question is, how high can we climb?


There are two ways to look at this. If you recall, each subsequent floor is more mathematically complex than the last. Let’s assume that one always ascends to the next floor via a 20 step staircase. Despite the growing mathematical complexity of each successive floor, moving between any two floors requires only these same 20 steps, eliminating the need for any significant cognitive leaps, no matter which floor you might find yourself on.


Alternatively, you can say that as each level increases in complexity, you reach a point where human cognitive ability hits a ceiling. Let’s say that occurs at floor 100. At that point, despite only being 20 steps away, floor 101 is forever out of reach because the mathematics on that floor requires a level of intelligence beyond what biological humans are capable of. We CANNOT get beyond floor 100 because our brains just aren’t up to the task. On these higher floors are problems whose very nature might require a level of abstract thought, pattern recognition, or information processing that our current biological intelligence cannot achieve.


The underlying mathematical structures or the complexity of the relationships involved might be so far removed from our intuitive understanding that we lack the cognitive architecture to truly comprehend them, let alone solve them.


These problems might involve concepts that are as alien to us as, perhaps, advanced quantum field theory is to a caterpillar.


But this is where computers and AI come in. As technology improves, as AI improves, it will reach a point where it is more capable than us. As such, it will be able to reach floors beyond 100. Then, via biotech, we can merge with our machines and thereby augment our own intelligence to the point that we can reach those higher floors ourselves.


So in this future, where our cognitive functions are artificially enhanced, how high can we climb? Let’s say floor 500. Much better than floor 100, right? But still nothing compared to the infinite height of this mathematical tower. So then, how do we climb higher? Let me ask a slightly different question. How high can ANY intelligence in our universe climb?


What do I mean by this?


Whether it's the biological architecture of a brain or the silicon and wiring of a computer chip, intelligence is a physical phenomenon. It arises from the organization and interaction of matter and energy according to the laws of physics.


Because intelligence is physical, it must be subject to the constraints and limitations imposed by physical reality. There are upper bounds on factors like information processing speed, memory capacity, energy efficiency, and the complexity of interconnectedness that can be achieved within the framework of our universe's laws.


Therefore, it logically follows that even the most advanced intelligence allowed by the laws of physics would eventually reach a ceiling in its ability to comprehend and solve increasingly complex mathematical problems. The sheer vastness of the mathematical landscape will inevitably extend beyond the cognitive reach of any physically realizable intelligence.


This suggests that there are mathematical truths and solvable problems that will forever remain beyond the grasp of any intelligence that can exist within our universe, simply because the level of cognitive power required to understand them exceeds the physical limits of what's possible.


So now let’s say an intelligence, upon reaching this limit, would find itself able to access the 1,000th floor of our mathematical tower. What about floor 1,001 or higher? These floors would forever remain out of the reach of any intelligence in our universe. 

But surely there MUST be a way to surpass this limit. All that unexplored math on those higher floors are just begging to be explored. The answer… maybe. But to explore this idea, we must now enter the realm of the highly speculative.


Solution 1: Wormholes to parallel universes where the fundamental constants are different


Ignoring the difficulty of getting to another universe (if such alternate universes even exist), it's conceivable that in another universe, the fundamental constants governing the interactions of particles and the structure of spacetime could be different. These differences might theoretically allow for a higher maximum density of stable matter or different ways of encoding information at a fundamental level, potentially leading to a higher information density limit. This in turn could allow for intelligence levels beyond what is possible in our universe. In such a universe, perhaps an intelligence could access floors higher than 1,000.


Granted, such a parallel universe, having its own laws, would also have an upper limit to intelligence. By definition, a universe is a physical system governed by some set of laws and composed of matter and energy (or their equivalents). All physical systems we understand are subject to limitations. And whether it's a brain or a machine, intelligence needs a physical medium to exist and operate. The capabilities of this medium will be bound by the physical laws of the universe it inhabits. 


Given that any universe would have physical limitations, and intelligence is a physical phenomenon requiring physical resources, it logically follows that the level of intelligence achievable within any conceivable universe must also be finite. There would ALWAYS be an upper bound, even if that bound is vastly higher in some universes than in others.


So this chips away at the higher floors in our Math tower, but what are a few more floors in the face of infinitely more floors? This would get us closer to the “top floor” of the tower. But it would ultimately fall short.

What next? How do we get to the top? Time to jump into an even more speculative area of thought.


Solution 2: Decouple Reality from Physicality


The latest obstacle we have encountered is that intelligence is an emergent property from physical reality, and by its very nature, there are always fundamental limits to any physical reality one can conceive of. Ergo, there are limits to intelligence. Which has us falling far short of climbing this infinite tower of mathematics.

So what about a non-physical reality? Is such a thing even conceptually possible or is the very idea nothing but hogwash?

From a purely scientific standpoint, envisioning a reality entirely decoupled from the physical is exceptionally difficult because our very understanding of "reality" is built upon our sensory experiences and the laws we've observed governing the physical world. Our tools for understanding – our brains and our scientific instruments – are themselves physical.

However, some physicists and philosophers propose that information, rather than matter or energy, is the fundamental building block of reality. In this view, the physical world we perceive might be an emergent phenomenon from an underlying realm of information. While this doesn't necessarily mean a non-physical reality, it shifts the emphasis away from tangible matter.

Now if we entertain the idea that information is the fundamental substrate of reality, and our physical universe is just one emergent property of its organization and dynamics, then it's certainly conceivable that other emergent properties could exist, potentially leading to entirely different types of realities or domains.

Here's how we might envision this:

The way information is structured, interacts, and flows could be different in other emergent phenomena. Just as specific patterns of information give rise to particles, forces, and spacetime in our universe, other patterns might give rise to entirely different fundamental entities and laws.

Some of these emergent properties might not manifest as what we would traditionally consider "physical" in our sense of the word. They could be realms of pure information, mathematical structures that become self-sustaining, or even the substrates for consciousness in ways we don't currently understand.

If other emergent properties of information exist, some of them might provide substrates or environments that are far more conducive to the development of intelligence than our, or any, physical universe. They might allow for higher information processing capabilities, or perhaps different forms of consciousness or awareness. Or even the ability to explore concepts and solve problems in ways that are fundamentally limited by the physics of a physical universe.

It's also possible that these emergent properties could themselves give rise to further levels of emergence, creating a vast and complex hierarchy of realities or domains, each with its own characteristics and laws.

In that same vein, what’s to say that our own universe is not the physical substrate to even higher and more complex levels of emergence?

A common characteristic of emergent systems is that the emergent properties at a higher level can often exhibit greater apparent complexity than the fundamental components at the lower level. And as we mentioned previously, greater complexity could mean greater upper limits for intelligence levels.

And in the "upward" direction, towards more complex emergent properties, there doesn't seem to be an inherent reason why there must be a limit to the number of layers. Each emergent level could, in principle, become the foundation for even more complex structures and behaviors at the next level. This aligns with the idea of infinite mathematical complexity – you can always build more intricate structures upon existing ones.

So how do we keep up with mathematics that reach infinite complexity?

By continually "ascending" through this infinite hierarchy of increasingly complex realities, intelligence could theoretically evolve or adapt to match and comprehend ever-greater levels of mathematical complexity.

In such a scenario, there would be no absolute limit to the complexity of mathematics that could be understood, as there would always be a "higher" reality with the potential to support the necessary level of intelligence. The limitation would then become the ability to traverse these realities and for intelligence to evolve or adapt within them.

If such an infinite hierarchy of increasingly complex emergent realities exists and if we could somehow navigate it and adapt our intelligence, then the potential for mathematical understanding could indeed be limitless.

The tower of mathematics is infinitely tall, so we would never truly reach the “top floor,” but in this scenario, we would also never stop climbing.

No matter how far we delved into the mysteries of mathematics, no matter how many truths we uncovered, no matter how much beauty we revealed, there would always be more to discover. 


Wednesday, May 18, 2016

Real time spoken language translation is here!

Watch the video and be blown away! Soon, not sharing a common language with another person will not be an obstacle to speaking with them in real time. This is straight out of the future!


http://www.popsci.com/watch-how-this-earpiece-will-prevent-you-from-ever-being-lost-in-translation-again-0

Wednesday, January 7, 2015

Who will be Remembered in a Million Years?

Here’s a little thought. Which famous figures from human history (including people from the modern era) that are universally known today will still be remembered one million years from now?

Everyone remembers their beginnings. We know of George Washington and Benjamin Franklin because they were at the founding of this country; at its beginning. They have significance to us. But what about a million years from now? The United States will be just another long forgotten land in 5 millenia, let alone a thousand millennia. And if the whole country is forgotten, then certainly the founders of that country won’t be remembered. They would have no significance to the people of the distant future.

And there’s that word again. Significance. People remember those who are significant to them. They remember those people who’ve had an impact on their lives. And the impact of historical figures diminishes with time. To do something that has a lasting impact just ten years later is impressive. A hundred years even more so. What about a thousand? How many people can you name who lived more than a thousand years ago? Have you ever heard of Edgar the Peaceful? You haven’t? Why not?!? After all, he was King of England for 16 years until his death in the year 975. What about people from more recent times? Auguste and Louis Lumière. Louis died in 1948 and Auguste died in 1954. Hardly ancient history. Yet are they household names? Certainly not. But they should be. After all, they were the inventors of cinema. The moving picture. Movies. Even so, by much of the world, they have already been forgotten.

The point I’m trying to make is that even the most important people with the most brilliant discoveries and the most amazing contributions tend to be forgotten over time. It just seems to be the nature of things. If a person is not immediately relevant to your life, then knowing about them holds no value, except perhaps as an academic curiosity.

So let me ask again: Who will still be remembered a million years hence? What about the Bard? The most brilliant and wonderful Shakespeare? Hardly.True, he’s universally known today, nearly 400 years after his death, which is quite impressive. But his fame stems primarily from his plays, which are too closely connected to the written word to have true staying power. As language continues to evolve over time, his plays will eventually become as indecipherable as ancient Greek. Sure, you can translate, but with each subsequent translation, you lose more and more of the brilliance that made Shakespeare Shakespeare. Take that away, and his plays would fade from the mind as quickly as a bad movie. In fact, it’s highly doubtful that any works of literature (or their authors) (with the exception of those religious works that belong to religions that are still being practiced) will survive the test of time. Given enough time, they lose their relevance. It’s inevitable.
The same holds true for figures in the entertainment industry. Frank Sinatra? Amazing. Michael Jackson? Absolutely brilliant. Laurence Olivier? Considered by many to be the best actor of all time. But these people won’t be remembered in even five hundred years, let alone a thousand years or a million.
So who then, of the great figures of history won’t lose their relevance even after a million years?

-The Greeks and the Romans (and Assyrians and Persians etc.)-

I mentioned earlier that people remember their beginnings. The Greeks and Romans et al are the beginnings of western civilization. However far human civilization advances, however many years into the future one travels, if people look for civilization’s origins, it will take them back to the Greeks and Romans.

-Religious figures-

For religious Christians, the stories and figures of the Christian bible will always have relevance, as will the more famous commentators such as Thomas Aquinas and St. Augustine of Hippo. Religious Jews will know the figures from the Torah and the Talmud as well as the more famous commentators such as Rashi and the Rambam. The same goes for the figures of all religions. Of course, this assumes that all these religions remain into that very distant future, but for arguments sake, let’s say that at least to some degree they do.

-Isaac Newton And Albert Einstein-

The modern world (and the future world) runs on technology. All our technology exists due to the discoveries and inventions of scientists. The two greatest scientists were Newton and Einstein. Newton is credited (along with the lesser known Gottfried Wilhelm Leibniz) with inventing calculus, that area of mathematics essential to modern mechanics. And without mechanics, we have no modern technology
Likewise, Einstein and his theories of Special and General Relativity (as well as the Photoelectric Effect (for which he won the nobel prize in 1921) and many other discoveries and theories) has firmly established himself in the pantheon of the Science Gods. If you removed the contributions of either of these two brilliant scientists, the modern world would crumble.

And that’s it.

It’s a very short list, but a million years is a very long time. And the above mentioned people will stand the test of time. Their contributions to humanity are eternal. Whether for who they were or for what they did, their names will be remembered forever. Or at least for a significant portion of forever. Because who’s to say if anyone or anything will be remembered given enough time? If the descendants of humanity end up dispersing across the universe then it’s conceivable the Earth itself may one day be forgotten as the birthplace of mankind. But such concerns might be a bit premature at this point, wouldn't you say? We can always think about that later.

Sunday, June 22, 2014