So, I did warn you that I'd write about misc. ramblings - here is one of those.
The last few nights I've been plagued by a recurring dream of a concept I want to first code and then make. A wave calculator. What is a wave calculator (this will come full circle)?
I had this theory that if the fundamental building blocks of the Universe were based on particles, something we describe as wave functions, then all math - ALL OF IT (not just the addition/subtraction/multiplication/division described below but ALL MATH) - should be able to be described as waves interacting with each other. I first had this idea when finding the pattern of prime numbers and the limitations of modern computers (I'll get into that later).
So I set out to initially make a proof of concept.
Addition and Subtraction:
When describing the interactions of two waves in the same space - specifically when multiplied (multiplier/mixer), I noticed that the frequencies are always additive and subtractive - meaning the 2 new frequencies will be frequency A+B and frequency A-B (or B-A). This wave interaction happens simultaneously with no math needed - they just are there.
Multiplication and Division:
When we examine the amplitude of these two new frequencies, the amplitude is always exactly half of both amplitude multiplied by each other: amp (A * B)/2. So, the multiplication is always right there - just double one of the amplitudes. Further, the ratio between the two new waves leaving the amplifier/mixer preserves division. The new wave A will always cycle exactly A/B times before they phase at their peak amplitude.
Example:
What does this mean - it means that amplifying/mixing two physical waves together provides us addition/subtraction/multiplication/division all at the same time. In my proof of concept, if I get a number from the user - lets say 10, this creates my first wave with an amplitude and frequency of 10. Then I get the operator from the user. Then I get the second number from the user - lets say 2and this creates the second wave with amplitude and frequency of 2. I pass these two waves through an amplifier/mixer and I get two new waves. Both new waves have the amplitude of 10 and the frequencies of the waves are 8 and 12. It takes exactly 5 cycles for the faster wave to cycle until both waves reach their first maximum amplitude that, when this happens, makes the amplitude peak to 20. So 10+2=12, 10-2=8, 10*2=20 and 10/2=5. All done simultaneously.
Conclusion:
Why on earth am I excited about this and why does it matter. First, I realized in a waking dream that musicians have been doing this since the beginning of human time. A piano is a wave calculator using air as the mixer. Second, one of the limitations of modern computers, even upcoming "quantum" computers is that they stop to calculate - another is communication between parts and memory (this is where Aaron's prime pattern he discovered had issues and what lead me down this path - I'll save that for another post another day).
Imagine a "computer" that didn't even need a CPU - the math was just done by mixing waves and this could be done via the communication between different devices/areas - ironically similar to how our brains work. Someone would yell "BALL!" and a part would recall what a ball looks like, another would recall what it smells like, another would recall what it feels like to get hit in the head with it because another part recalled the tone of the panicked voice and when all these waves met up the new wave pattern told me to duck. No CPU was required any ANY of those enormously complicated decisions/memories by modern computer standards - they just simply were there - baked into the wave.
The Darker Hypothesis
I also have a darker hypothesis that plays into things like the double slit theory and other quantum mechanics. This comes about when trying to describe ZERO. I realized that waves travel. We, the observers, are time forward facing - meaning we only can see and experience time in one direction. Waves don't necessarily have to do that. A wave function traveling at the speed of light has zero time - time doesn't even make sense to it (which is why a particle can "appear to us" to be in multiple spots at the same time - it's a function of time not 'spooky' superposition). When a wave function travels at zero speed (supercooled), it has ALL the time at once - again, time doesn't even make sense to it.
For a wave function to describe zero, it would take a wave with the same amplitude (inverted), the same frequency but traveling backwards in time. This would be impossible for us to see because we don't experience time like that - what we'd see is two waves just the past tense of one and the present of the other. This doesn't mean we need to "invent" spooky math to describe this or for that matter the double slit experiment - we just need to understand how relativity works, how time dilation isn't screwing up the test - it's screwing up the observer.
As a simply thought experiment - imagine traveling as fast as the speed of a photon next to your friend - a photon. When you look over (ignoring the obvious how do you see things while traveling that fast) - what would you see? Would you see a particle in multiple positions at the same time? Obviously not - you'd see your friend - the photon. There, right next to you behaving normally would be a single particle - no superposition. This is because you and your friend are in the same time reference.