What is the certain type of phenomenon observable in graphed trend lines
February 13, 2020 3:52 PM   Subscribe

What is the name of the phenomenon when incremental changes over a period of time make little difference to the trend line, but suddenly one change represents "the straw that broke the camel's back" and the trend line changes dramatically and irrevocably? I want to call it an "event horizon" but I know that term is specific to astrophysics. I'm thinking of things like the "hockey stick graph" of climate change.

"The Tipping Point" comes to mind, but that still doesn't feel like the term I'm searching for.
posted by jefficator to Grab Bag (12 answers total)
Inflection point?
posted by basalganglia at 3:56 PM on February 13 [9 favorites]

Criticality or singularity?
posted by JD Sockinger at 4:01 PM on February 13

In its most general form, what you're talking about is a "change point". Hockey stick, tipping point, inflection, etc. are all special cases of this. The problem of figuring out if/when one has occurred is change point detection.
posted by caek at 4:12 PM on February 13 [8 favorites]

It's called the Inflection Point.
posted by humboldt32 at 4:28 PM on February 13 [1 favorite]

posted by mean square error at 5:55 PM on February 13

Change point is the term of art among statisticians and data scientists.
posted by dbx at 8:01 PM on February 13 [1 favorite]

A cusp, in dynamical systems catastrophe theory - also look up hysteresis and bimodality. Examples: a sand pile grows grain by grain and then suddenly has a landslide; irritating a cowed dog makes it more cowed until it suddenly becomes angry, and then reducing the irritation doesn’t return the dog to cowed-ness, just less anger.
posted by clew at 8:21 PM on February 13 [1 favorite]

The Tipping Point by Malcolm Gladwell?
posted by bleep at 9:30 PM on February 13

it’s not an inflection point, that’s when the line goes from curving in one direction to curving in the other direction (inflection/inflexion = where the curve doesn’t flex)
posted by russm at 10:19 PM on February 13 [1 favorite]

Mathematically it's not an inflection point but colloquially that's a common usage.
posted by Lady Li at 6:29 AM on February 14

I'd call it a breakpoint in the context of piecewise regression. See this Wikipedia article.
posted by Ian Scuffling at 12:36 PM on February 14

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