Not Linear counting, 3D counting billions of billionths

[Peter Gleeson]

Many of the numbers that define us and our world are beyond the scope of linear counting. If you count a billion seconds, it is more than 32 years, but if you can visualize them as a cube, it has sides of 16 minutes and 40 seconds. A billion millimetre cubes in a line span 1000km, but if you put them into a cube, they are a cubic metre. A billion billion cubic millimetres is a cubic km, or it is a line 3 times the distance to the sun. Developing the ability to recognize the true nature of uncountable numbers by visualizing them as 3D cubes gives us access to the dimensions of the universe, the nature of particle physics, the complexity of multicellular life, the number of synapses each second that cause awareness, the way we are related to distant ancestors, the rest of humanity, and how distant future generations will be related to us.
We see an object as being one thing, but it is also a billion billionths, and it is a billionth of a billion. It is a billion billion billionths of billionths and it is a billionth billionth of a billion billion. This is obviously true, but are we able to know truly what these numbers mean? I think such understandings require practice to incorporate them into our 'common sense'. The reward for doing this is a different kind of awareness. One that understands the nature of photons, the retina and the processes that create sight.
If we look back 30 generation we find a billion ancestral links to that population. That is just 750 years. If we go back 1500 year, we find a billion billion ancestral links. Only some of the people in that time possessed the exact genes that caused us to be. But there were individuals alive then who were our ancestors thousands of billions of times over. This is the way people in 1500 years will be related to us.
Every time you multiply or divide by a billion the reality of what you are investigating changes. This doesn't mean you give up and deal with it in purely symbolic ways. There is a way to recognize the limitations of our awareness and the context in which reality exists.
Is this a new idea? I learned it 23 years ago after listening to a documentary on human calculators who saw numbers as landscape. I decided that I could develop something along those same lines. It probably takes practice. It isn't something to rote learn. It has to be known. It has to be recognized without the need for applying a formula. It seems to be an intellectual tool with many applications, all of them good, all of them contributing to our ability to understand awareness, consciousness, intelligence, life, reality, time, universe and cosmos.
But is it a new and original idea? I spoke to a retired professor of particle physics and he was shocked by its implications.

 

[Stephen Tashi]

Visualizing numbers by volumes isn't new. I suggest you search the web for "visualize a trillion dollars" to see various examples.

 

[HallsofIvy]

But the fact that real numbers, of any size, can be placed in a one-dimensional order is crucial to their use. That has nothing to do with "visualizing" large numbers.

 

[Nugatory]

But the fact that real numbers, of any size, can be placed in a one-dimensional order is crucial to their use. That has nothing to do with "visualizing" large numbers.

That's a good point. One of the reasons that logarithms are so useful (statmech, stellar and earthquake magnitudes, pH measurements, ...) is that they preserve this property even as the reduce enormous ranges to a more tractable scale.