Rene Descartes and Nyquist
I have also been thinking about natural world and perceived world. Rene Descartes approach to this was along the lines of “How do we know we are not in a dream”. We can’t know and therefore he came up with “I think therefore I am” as a base truth. However I’d like to give an engineering spin on it. Based on discrete vs continuous.
x is defined for all real, meaning x exists for 1.01, 1.0000101, any number that you can think of it exists, another way of looking at it is that it has infinite divisions. Going from 1 to 2, you can go from 1 to 2 by jumping by 0.5 (1.0 → 1.5 → 2.0) or you can jump with 0.1 (1.1 → 1.2 → 1.3 … → 2.0) or you can jump infinitely smaller and take an infinite amount of jumps to get there, that’s what it means by continuous. Numbers so when
That’s how math works but the real world application is Discrete . Let’s say we do population growth for humans given by
Here,
because it has to be a whole positive numbers since we can’t have half people.
because population can’t be half or quarter humans it has to be a full human.
Now talking this further. We see the world as a discrete machine, even though it seems like your phone is always there, it might not be there in between the little jumps that your eye is taking. The eye is around 60 frames per second. Each second your eye is taking 60 pictures, that string together to seem continuous. My argument is that you can’t know what’s happening in between each frame, what if something is happening 600 frames per second, like someone shooting a gun, things might be happening so fast that we can’t see it.
There are two assumptions that you can take:
The world is continuous.
The world isn’t continuous. - I’m not doing this analysis right now
The world is continuous
If the world is continuous and we are a discrete system, there’s no 100% way of knowing what the continuous reality of the world is because we are at a set frame rate of sensory input.
Then we have to check Nyquist’s theory of aliasing. Nyquist says that if our sampling rate is two times the rate at which the universe is existing, then our sensory input is accurate. In this case our analyzing frequency would a number let’s say 60 Hz, and the universe is infinity.
So through Nyquist we’ve proven that we can’t accurately see a continuous world.
I’m assuming that we live in continuous world, just because we can’t see something it doesn’t stop existing. The phone you are reading on exists even when you blink or look away. My statement is that “the continuous existence of materials is an assumption”. The reason comes back to continuous vs discrete. Although we assume to live in a continuous world we are discrete animals. We can only sample the world as our nerves let us. A better analogy would be the way we see. Your eyes can only perceive an non-infinite numbers of frames. We have no idea if the world exists in between those frames. let’s say you were watching a 10 second video but you could only see one frame per second it would be clunky and you would fill in the gaps in your head. Now imagine you got 2 fps, 3 fps, all the way to max fps you would know what happened. Think about a magician that could choose your fps, the awkward cuts, would be the perfect time to put a bunny in his hat or put the coin in your pocket. So we can’t know what’s happening in between our limited perception. Maybe this is what the Hindus meant by Maya.
Now we can come to the same conclusion that Rene Descartes came to, with more mathematical rigour which is Cogito ergo sum. I think therefore I am. Honestly I like his way of getting to the I think therefore I am argument, his way is by saying we might be living in a dream, because have you ever had a dream and you wake up, and it’s like damn I really thought I was flying for second there.
