# Derivatives provide Direction > **Derivatives** provide a way for us to determine which **direction to move** in a high dimensional space. ### More details... The real power of [Neural Networks MOC](Neural%20Networks%20MOC.md) comes from [Differentiability](Differentiability). In a Neural Net, the output changes *smoothly* if you tweak the parameters (weight matrices). Then you are able to use many powerful methods that we have for *optimization* in science. You are able to tweak the input parameters slightly and see if your output was improved or worsened, and then (and this is crucial!) update your parameters in a direction that should *improve* your output next time. Consider the alternative: you have a program written in some language (say python) and your tweak letters of the program, hoping to improve the output. Maybe you change `print` to `srint`. Was that for the better or worse? First off, most changes will be clearly for the worst since the programs won't even run. But, in general, even legal changes will be very hard to tell if they lead to an improvement. It is very hard to determine the correct direction to move in. The changing of letters is not differentiable. Meanwhile, in neural nets, every setting of the parameters is a differentiable program and you can tell if it is better or worse. --- Date: 20211104 Links to: [Mathematics MOC](Mathematics%20MOC.md) [Calculus MOC](Calculus%20MOC) [Big Ideas MOC](Big%20Ideas%20MOC.md) Tags: References: * [Max tegmark on lex fridman, transcript](https://www.happyscribe.com/public/lex-fridman-podcast-artificial-intelligence-ai/155-max-tegmark-ai-and-physics) * [Max tegmark on lex fridman, youtube](https://youtu.be/RL4j4KPwNGM?t=743)