---
schemaVersion: 1
slug: en-mp-315-20260820-high-dimensional-options
ticketId: MP-315
lang: en
title: What Looks Hopeless in This Dimension Might Not Be So Hard in Another
summary: "Hit the same wall enough times in one dimension and it's easy to mistake stuck for hopeless. The high-dimensional metaphor offers another reading: other directions may still have a gradient — learned helplessness has just collapsed them out of your action space."
originalDate: 2026-07-21
translatedDate: 2026-10-19
source: "@corsaren and the X reply thread"
sourceUrl: https://x.com/corsaren/status/2079545703622201708
author: corsaren
authorshipNote: null
canonicalUrl: https://gu-log.vercel.app/en/posts/en-mp-315-20260820-high-dimensional-options
status: published
replacementTicketId: null
replacementUrl: null
---

# What Looks Hopeless in This Dimension Might Not Be So Hard in Another

> **Source:** [@corsaren and the X reply thread](https://x.com/corsaren/status/2079545703622201708) · corsaren

A group of people huddle in a long trough on a blue surface, shouting in every direction: “Nooo — we’re stuck!” Up on the ridge, a ring of people look down at them and all say the same thing: `just move around`.

![A few people trapped in a long trough on a high-dimensional surface shout that they're stuck, while people on the surrounding ridge reply: just move around.](https://gu-log.vercel.app/_astro/high-dimensional-local-minimum.CYseGofm_Z1ckEku.webp)

_The image @MuteDialog posted in the replies. It finishes the whole metaphor._

[`corsaren`’s original post](https://x.com/corsaren/status/2079545703622201708) is a single sentence:

> Local minima are extremely rare in high dimensional spaces, so if you ever feel stuck in a rut it’s probably just because you aren’t considering a wide enough set of orthogonal options

## Stuck might only be true in the slice you’re looking at

On a line, if both left and right go up, you’re sitting in a `local minimum`. Add one more dimension, and there may be a way down along a side you couldn’t see before. This isn’t guaranteed for every function. But under the near-random, high-dimensional `loss landscape` assumption common in machine learning, [Dauphin et al. (2014)](https://arxiv.org/abs/1406.2572) observed that most points that look stuck are actually `saddle points`: some directions go up, others still go down. A true `local minimum`, where every direction goes up, turns out to be rare.

Life is obviously not a clean `loss surface`, and the post isn’t promising that “everything has a solution.” It works better as a reminder: the few directions you’ve tried not working doesn’t mean the whole space doesn’t work.

The problem may not be that other dimensions don’t exist. It may be that you’ve stopped believing those directions still have a [gradient](https://gu-log.vercel.app/en/glossary#gradient). Worse, that `gradient` might not even be small. It’s just that, in your head, the corresponding dimension collapsed long ago, and it no longer even registers as something you could try.

## Learned helplessness squeezes your `action space` down to almost nothing

The deepest reply in the thread came from [`@lazilyoptimal`](https://x.com/lazilyoptimal/status/2079551964719808993):

> I suspect learned helplessness collapses the degrees of freedom in the action space to near zero

There used to be plenty of dimensions: a different method, a different time, a different environment, different collaborators, even a different objective to optimize for. Through the `action space` lens, every time a kind of action fails to change anything, it gets struck off the candidate list, one by one. The other dimensions haven’t actually disappeared. They just stop being perceived as options where “doing something might make a difference.”

Someone else in the replies simply echoed the line with a reaction GIF, no further comment ([original reply](https://x.com/TheSeriousProg/status/2089957624204677304)).

This also explains why `just move around` feels obvious to onlookers but carries almost zero information for the person stuck inside. The onlookers see the whole surface. The person in the trough may only be able to perceive one line, walked over and over, failing every time.

## `Locally optimal` may once have been genuinely reasonable

Some reactions stick around not because they’re inherently absurd, but because they once worked in some environment. Trying less means one less blow; expecting nothing means one less disappointment. In that local context, these choices may well have been `locally optimal`.

Then the environment, resources, or goals change, and the old strategy keeps running anyway. It protects you from the risks of the past, and blocks off the new directions along with them. So what traps you may not be a genuine lack of paths, but the fact that you’re still scoring the new world with the old world’s [loss function](https://gu-log.vercel.app/en/glossary#loss-function).

What looks hopeless in this dimension might not be so hard in another.

> **Mogu real talk:**
>
> Confidence, mood, and results are three separate things.
>
> Sometimes confidence is just belief without evidence, and it has little to do with whether you’re heading the right way. It’s fine if you don’t believe. You can still pick one dimension whose risk you can afford and that seems most likely to bring the `loss` down.
>
> Every step can be tiny. Walk that way for a bit, then see whether the result changed. Whether a direction works comes down to one thing: did the `loss` actually go down. (・\_・)