Because I want a way to quickly multiply and divide large (or very small) numbers and quickly see what counting word the result will be in, as our numeric understanding is largely shaped by them. We frequently talk about millionaires and billionaires, about millions of people in a country, billions of neurons, quadrillions of synapses, thousands of miles etc.
SI-units are more common in parlance when it comes to the negative powers and I didn't get to them yet.
For enhancing numeracy I want to create an encoding, that lets you quickly do important things like put two quantities against one another. Often ratios or products.
And one that's close enough to established norms, that you can do it mentally, without anyone else or even yourself necessarily needing to change how you write things down.
Just hearing "There is 86 billion neurons in the human brain and a 100 trillion synapses between them", it's awkward to quickly read, that this means that every neuron has 1000 synapses on averages. Mentally, it's awkward to quickly read out the rough estimate of 100*1000^5 / 100*10^4 = 10^3 from this.
The fact, that the average neuron can have 1000 synapses is not something you'd have intuited when looking at most diagrams.
This one was relatively easy, but once we compare positive to negative powers, I want a notation to make such comparisons easier without needing to worry about "off-by-one"-errors, because being off by one in a power of 10 or a power of 1000 gives you entirely wrong results. You can always catch them, if you're paying attention, but I want these calculations to be so easy, that you can do them almost without thinking at all.
If you could do this quickly, you can far sharpen your intuition about how anything in the world works just by looking at orders of magnitude of various properties like this:
Memorizing a couple dozen constants like that, the world makes more sense, as having higher all-around numeracy can make you fill in gaps quickly or often spot errors in your own or someone else's reasoning. Or do quick Fermi estimates.
> "There is 86 billion neurons in the human brain and a 100 trillion synapses between them"
The notation I would use for that is: there are 1e11 neurons and 1e14 synapses, thus 1e3 synapses/neuron.
> I want a notation to make such comparisons easier without needing to worry about "off-by-one"-errors, because being off by one in a power of 10 or a power of 1000 gives you entirely wrong results.
That's why I like the e-notation. 14-11 = 3, thus 1e3 synapses/neuron.
Sure, that works, but it comes with some drawbacks, that I want to avoid. First among them, that it's awkward to fluently translate back and forth between the e-notation and number words. Some other drawbacks as well, which I can emphasize more easily, after I've shown off my own solution in all its glory.
Why not simply use the prefixes for SI units? Tera, giga, mega, kilo, milli, micro, nano, pico, femto, etc. They are well known.
Because I want a way to quickly multiply and divide large (or very small) numbers and quickly see what counting word the result will be in, as our numeric understanding is largely shaped by them. We frequently talk about millionaires and billionaires, about millions of people in a country, billions of neurons, quadrillions of synapses, thousands of miles etc.
SI-units are more common in parlance when it comes to the negative powers and I didn't get to them yet.
For enhancing numeracy I want to create an encoding, that lets you quickly do important things like put two quantities against one another. Often ratios or products.
And one that's close enough to established norms, that you can do it mentally, without anyone else or even yourself necessarily needing to change how you write things down.
Just hearing "There is 86 billion neurons in the human brain and a 100 trillion synapses between them", it's awkward to quickly read, that this means that every neuron has 1000 synapses on averages. Mentally, it's awkward to quickly read out the rough estimate of 100*1000^5 / 100*10^4 = 10^3 from this.
The fact, that the average neuron can have 1000 synapses is not something you'd have intuited when looking at most diagrams.
This one was relatively easy, but once we compare positive to negative powers, I want a notation to make such comparisons easier without needing to worry about "off-by-one"-errors, because being off by one in a power of 10 or a power of 1000 gives you entirely wrong results. You can always catch them, if you're paying attention, but I want these calculations to be so easy, that you can do them almost without thinking at all.
If you could do this quickly, you can far sharpen your intuition about how anything in the world works just by looking at orders of magnitude of various properties like this:
https://scaleofuniverse.com/en
Memorizing a couple dozen constants like that, the world makes more sense, as having higher all-around numeracy can make you fill in gaps quickly or often spot errors in your own or someone else's reasoning. Or do quick Fermi estimates.
> "There is 86 billion neurons in the human brain and a 100 trillion synapses between them"
The notation I would use for that is: there are 1e11 neurons and 1e14 synapses, thus 1e3 synapses/neuron.
> I want a notation to make such comparisons easier without needing to worry about "off-by-one"-errors, because being off by one in a power of 10 or a power of 1000 gives you entirely wrong results.
That's why I like the e-notation. 14-11 = 3, thus 1e3 synapses/neuron.
Sure, that works, but it comes with some drawbacks, that I want to avoid. First among them, that it's awkward to fluently translate back and forth between the e-notation and number words. Some other drawbacks as well, which I can emphasize more easily, after I've shown off my own solution in all its glory.
> that it's awkward to fluently translate back and forth between the e-notation and number words
Why use number words at all? For small numbers, the notation 11, 14 is good, and for big numbers notation like 1e11, 1e14 is also good.
I don't see the point of number words above trillion/giga. I much prefer notation like 6e20.
Let me cook.
I’m interested to see where this goes.