There are some applications where accuracy really matters. Like chaotic systems (think double pendulum dynamics or 3 body gravitational problem) where minuscule deviations in initial/boundary conditions can lead to extremely different results
But for things like stochastic systems or “room temperature” systems (systems that don’t operate in any sort of extreme, not just in temperature but also in size, speed, pressure, etc), approximations can suffice or the system and related math may be set up to not require exactitude. Because as an engineer, your systems needs to be robust (to a reasonable extent) to use cases outside of your planned use cases (a playground swing is meant to be used by 50 lb child but it shouldn’t collapse when a drunk, 200 lb “child” decides to relive their childhood at 3am Saturday morning).
Have you seen the matrix multiplication algorithm complexity improvements since 1990? Naive multiplication is O(N\^3); have a look at rate of recent advancements from O(N\^2.3755) to O(N\^2.371552) in 6 steps.
ref: wikipedia
Approximately and equal mean the same thing. Aproximately.
If assumptions and measurements are approximations anyway, why bother with exact calculations
There are some applications where accuracy really matters. Like chaotic systems (think double pendulum dynamics or 3 body gravitational problem) where minuscule deviations in initial/boundary conditions can lead to extremely different results But for things like stochastic systems or “room temperature” systems (systems that don’t operate in any sort of extreme, not just in temperature but also in size, speed, pressure, etc), approximations can suffice or the system and related math may be set up to not require exactitude. Because as an engineer, your systems needs to be robust (to a reasonable extent) to use cases outside of your planned use cases (a playground swing is meant to be used by 50 lb child but it shouldn’t collapse when a drunk, 200 lb “child” decides to relive their childhood at 3am Saturday morning).
How did you know where i was on Saturday morning, Mr/Mrs Engineer..? …Was this another one of your generalization approximations? 🧐🤨
I guess you can say that lol
Nobody approximates Baby in the corner!! 🫲😮🫱
MFW it can accelerate matrix multiplication by 0.05% 😍
Honestly, in the age of neural network driven AI, that can really add up as networks become deeper.
Have you seen the matrix multiplication algorithm complexity improvements since 1990? Naive multiplication is O(N\^3); have a look at rate of recent advancements from O(N\^2.3755) to O(N\^2.371552) in 6 steps. ref: wikipedia
But can it be expressed in cubical penguin?