You Can Use Decibels For Anything

What?

A decibel is “a unit of ratio”. In fact, it’s ‘unitless’, insofar as it’s a ratio of two values with units.

The ratio of a 60-pound dog’s weight to a 6-pound dog’s weight is the unitless value “10”, as in “that dog is 10 times the weight of this dog”. It’s like that.

Specifically, the decibel is really good at representing “pretty big” or “pretty small” ratios.

Separate post for background: what’s a decibel, anyway?

Anything can use decibels!

It’s just ratios!

Case study: Botania

Botania, the mod by Vazkii, famously doesn’t do numerics. A lot of progression involves ramping up production by orders of magnitude. To decibelify it, all we have to do is pick a reference point; the base unit of storage is a “mana pool”, which conveniently is rather large, so we’ll pick it to be our value.

And that’s it!

  • In the code, a mana pool holds one million “mana points”; thus the smallest representable is 1:1000000 relative to the mana pool, or -60dB.
  • Infusing a “manasteel ingot” costs 1600 “mana points”, or -28dB.
  • There’s a “diluted” mana pool, which holds 1/100 of the mana pool’s capacity; it has a capacity of -20dB.
  • Crafting a “terrasteel” costs half a mana pool, or -3dB of mana.
  • The “Terra Shatterer” can absorb up to 1000 mana pools’ worth of mana; it can store 30dB.

And so on and so forth. This is so sensible and normal.

You can do this for anything, actually!

  • Got an 80/100 on a test? That’s fine, pal— it’s a -1dB grade, and a passing grade is a -1.55dB!

  • Instead of a “3.5% APR”, you can take the 103.5:100 ratio at face value and say you get a 0.1494 dB annual rate on interest.

  • The Milky Way is about 49.4dB across in diameter (pegged to the light-year for reference).

  • Playing Wii Golf? Made par 2 on a par 5 course? That’s a -4dB albatross, baby!

  • The Switch 2 costs $450, which is about 17dB on the BPI (Burger Price Index) (about $9 in 2024) (god prices are dire)

  • Musically? In the frequency domain, going up an octave is 3dB, going up a perfect fifth is 1.75dB, going up a half-step is 0.25dB, …

  • Lost half your net worth on crypto? No problem— it’s only a -3dB change!

Anywhere there’s a ratio, or you can imagine a ratio, you can use decibels! The possibilities are endless.

And now for something completely different(worse).

Decibels to bits??

In terms of information theory, bits (like octaves) mean “doubling”: adding a “bit” to a pool of information means there are 2 times the possibilities. 2x multiplier is about 3dB; meaning you can convert bits to decibels directly by saying 1 bit = 3.01 dB.

Anything can use… bits?

Now that we have a unit conversion, we can apply it willy-nilly. This may be getting a bit out of hand.

Case study: Botania again??

Let’s move our reference point to the lowest bit, the single mana point, just because I don’t want to fuck around with negative bits(!!)1.

  • A mana pool holds just under 20 bits of mana.
  • Infusing a “manasteel ingot” costs about 10.6 bits.
  • There’s a “diluted” mana pool, which holds about 13.3 bits.
  • Crafting a “terrasteel” costs half a mana pool: 19 bits. Woah.
  • The “Terra Shatterer” can hold 30 bits of mana.

This is really really sensible and normal.

  1. If you are willing to deal with negative bits, and you want to play Frankenstein, subtract 20 bits from all quantities quoted. God rest your soul.↩︎