Skip to main content

Continuous versus discrete

I was watching that video and it led me to a realisation that my friend Chatty put nicely for me

The mystery of 0.577 - https://youtu.be/4k1jegU4Wb4

All real physical measurements are fundamentally discrete—we only sample the world in finite steps, with finite precision—while continuous mathematics is an idealized limit we use because it is simpler, more powerful, and often extraordinarily accurate. Every smooth concept in math—derivatives, integrals, π, e, γ—arises as the limit of increasingly fine discrete approximations: polygons approach a circle to produce π, discrete compounding approaches e, and the mismatch between discrete harmonic sums and continuous logarithms produces γ. These constants are the “fingerprints” left behind when the discrete world is modeled by continuous mathematics.

Which led me to this question. Is the world and reality, discrete or continuous?

My friend Chatty tells me that modern physics does not give a final answer, but evidence increasingly suggests that reality is fundamentally discrete at extremely small scales: matter and energy are quantized, spacetime may come in tiny units near the Planck length, and the universe appears to contain only finite information. Continuous mathematics remains incredibly useful because these discrete building blocks are so small that the world looks smooth at human scales.

In my mind it boils down to if there is a smallest particle. If there is a smallest particle, then the world is discrete. If there is no smallest particle then reality cannot exist because you cannot build anything.

My friend Chatty tells me that my intuition is powerful: true discreteness implies smallest building blocks. But even if reality were continuous with no smallest particle, it could still exist — the problem is not existence but the mathematical infinities that come with infinitely divisible physics.

Now I am thinking. Does it make sense to say that you can create finite from the infinite but you cannot create the infinite from finite. Infinity is the source. Infinity is what God is. God is everything.

My last thought for this blog post is that, can we say that just like something cannot exist without nothing (think light without darkness), the finite cannot exist without the infinite. On the other hand, we can say that darkness does not exist, it is just the absence of light and only light exists. Humans only exist because God exists.

I like how my exploration after watching that video brought some clarity to my thoughts on the infinite while at the same time opening up a whole new world of questions and thoughts.

*I like how 5+7+7 = 19 ( 1 is smallest digit and 9 is largest digit )

Comments

Popular posts from this blog

God opens doors

It is 1203am and I have decided to write. Saturday I spent the night coding. I was trying to get a FastAPI app up and running, all from my budget Android phone. The test cases were written to use Puppeteer. I ended up using Replit for that. Coding is more challenging when using a mobile phone. Not impossible but more challenging. I hardly blog about technology and coding anymore but the love is still there. I still have a dream of creating my own coding and youtube studio with a nice desk setup. That is nice but what should I make this blog post about? What do I want to write about? What should I write about? I love creating presentations. That is something I could do to revive my youtube channel. I love Maths too. I have this feeling that I could solve one of those longstanding Maths problems that seems impossible. Sometimes, like right now, I feel like abandoning my blog post. It is going nowhere. Maybe I should get up and go wash the wares. I wish God could tell me what to write abo...

What we do not know

It is 1245am and I have decided to write. I had this weird alienish dream and it ended with me winning by simply stating "the truth is that we do not know". In the dream everyone was having an opinion of what was happening as if they knew. On to something random. I had this question. What is the most unrandom thing? Then what is the most random thing? What if everything is equally random. My friend Chatty thinks that randomness is not an absolute property—it is a relation between you and the system you observe. Randomness is not absolute—it depends on perspective. Something perfectly ordered can seem random if you do not know its pattern. So in a sense, everything can be "equally random" relative to the observer's knowledge, making randomness more about perception than an intrinsic property. The more we know the less random things become. Let me make a detour. Suppose we do not predict things but things predict us. For example, when I flip a coin, did I predict ...

We are explorers

It is 215pm and I have decided to write. I had this question. What does God really want from us? Then I remember that God does not need us, we need God. What I am really wanting to ask is why create us, why life, why test us, why the mystery? Why not? It is human nature to ask questions. No matter how much we know, we will ask questions. We are always looking for reasons. We are always looking. We are always seeking. We are explorers. We could have been anything but God chose for us to be explorers. There is joy in exploring. There is joy in discovery. There is joy in not knowing. What I have arrived at is a reminder. Appreciate the now. Appreciate what is. Appreciate that one day things will make sense but for now we get to live. To live, to learn and to laugh. I like this quote by Frank Borman that I found, "Exploration is really the essence of the human spirit." If there was nothing to explore we would be static. There would be no movement. There would be no existence. Exi...