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Cake day: June 4th, 2023

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  • Orthogonal just means at right angles.

    The way this is defined if you’re a mathematician is two directions are orthogonal to each other if you can move as much as you like in one direction without changing the location with respect to the other direction.

    So it’s like North and East. You can walk east as much as you like without changing how far north you are. But if you have a direction like South East or North West, when you walk that way you will change how far north you are.

    We can make this 3d by adding a new direction that is orthogonal to both North and East. This direction would be up or down. Because you can move up and down without changing how far north or east you are.

    Mathematicians measure orthogonality of directions using an inner product. If you represent the directions as vector then the inner product between them is zero if they are orthogonal.

    Perpendicular means orthogonal, the opposite is parallel.

    Null is more confusing. To define this we need to talk about linear functions. A linear function is something that would e.g. create a map from the 3d world, by throwing away up and down information and shrinking everything down so you have a scaled representation of where things are in terms of North and East.

    The null space is all the information that is destroyed. For linear functions this is a linear subspace(a space that goes through zero and is described by a collection of directions) that is orthogonal to the space of all information which is kept.



  • It’s interesting. There’s a lot of talk about how chatgpt makes people lazy, but honestly I think Google killed the “read the manual” ethos.

    Back in the day when you couldn’t just search for everything, you needed enough understanding of the manual to find anything in the index.

    So a key part of figuring anything out was reading at least the start of the manual.

    Now, fuck it, you just type into Google and try to guess enough context to understand what’s going on.





  • You absolutely can’t use LLMs for anything big unless you learn to code.

    Think of an LLM as a particularly shit builder. You give them a small job and maybe 70% of the time they’ll give you something that works. But it’s often not up to spec, so even if it kinda works you’ll have to tell them to correct it or fix it yourself.

    The bigger the job is and the more complex the more ways they have to fuck it up. This means in order to use them, you have to break the problem down into small sub tasks, and check that the code is good enough for each one.

    Can they be useful? Sometimes yes, it’s quicker to have an AI write code than for you to do it yourself, and if you want something very standard it will probably get it right or almost right.

    But you can’t just say ‘write me an app’ and expect it to be useable.