Hacker News Comments on
The other way to visualize derivatives | Chapter 12, Essence of calculus
3Blue1Brown
·
Youtube
·
46
HN points
·
1
HN comments
- This course is unranked · view top recommended courses
Hacker News Stories and Comments
All the comments and stories posted to Hacker News that reference this video.> I still have some doubts that people actually do visualize thingsI can't imagine not visualizing things. My undergrad was in mechanical engg, so it was kinda central to our field.
Imagining a 2d machine drawing as a 3d figure, imagining the interactions between various moving parts or system of joints and levers is expected of you.
The way I think reflects the visualization itself. Usually, it takes quite long to 'load' a complex system in your head and visualize it. But after it is done, I can describe intricate details of it. I also get irrationally irritated when someone interrupts me in the 'loading' phase, cuz I have to start all over again.
For a similar reason, I have a very natural affinity to graphs = undirected-trees and flow charts as they serve as a visual representation of what is a symbolic relationship. I am also completely unable to recall language or isolated-facts perfectly, but can do the same for visual systems.
I am famously 'the whiteboard guy' at what is now an ML job, so I can believe that not everyone thinks of these systems visually. But, visual intuition in some form is and has always been core to how to how I understand stuff.
> Are they really visualizing these goofy versions of the machines?
In my case, the key points of interaction are visualized clearly. (eg: point of contact for gears, or a joint, or multi head attention on a single node). The rest is invisible in an out of focus sort of way, like things in our peripheral vision are out of focus and practically invisible, but you're still seeing them.
> I tend to think that I have a better understanding,
I maintain that vision is a crutch. It helps develop an easy to grok intuition, that works within the realm of visible way you'd think of interacting with the system. True intuition of things requires moving away from the visual intuition, and one that is grounded purely in the key axioms of that idea itself.
An example would be us thinking of differentiation as slope of a curve. The visual grounding is helpful but a more axiomatic understanding would allow you to grok concepts like [1], where the slop method falls short.
⬐ doliveiraI'm pretty sure I have aphantasia, but I didn't struggle at all in my Engineering or Physics undergrads.I guess can visualize the abstract aspects of it, if it makes any sense? Kinda like I'd imagine having a Daredevil-like radar sense would feel, or Toph's sense in Avatar. I can kind of have a feeling for shapes, movement, position without the sight itself.
⬐ NoneNone