[a9h74j]

It does have negative external effects, as you observe, in the sense of a viscious circle. But even a viscious circle, mathematically, has positive feedback, resulting initially in a positive exponent growing against time, not a negative exponent damping out in time.

[robotresearcher]

Doesn’t positive feedback require a positive loop gain? Right now, not enough chips are available to make new chips. So the loop gain is less than zero, damping the output recursively.

[randomswede]

I have always understod "positive feedback" as "feedback that prompts the existing change to continue in the same direction, with equal or larger speed".

So positive feedback on a falling signal would tend to make it drop more. And positive feedback on a rising signal would cause it to rise more.

So, basically, for any signal S at time t, we would expect something like S(t+1) = S(t) + S'(t) * k, for some k > 0. And blatantly abusing derivatives for "should probably be a delta between S(t) and S(t-1)".

But, then, I am not a control theory specialist, I don't even play one on TV.

[zsmi]

The problem is, if the feedback signal is too slow in getting back to the thing which measure error (i.e. too much phase lag), then negative feedback can turn into positive feedback and this leads to an instability.

One of the most complex pieces of the semiconductor fab is the building itself. Even with plans and permits in hand, it takes years to make one that can output at reason throughput and yield.

This report is from 1999 and it hasn't gotten easier.

https://www.imia.com/wp-content/uploads/2013/05/Construction...

"Typically the product life of a semiconductor chip (nine to 12 months) is less than the time required to construct the facility and install the equipment for manufacturing (24 to 36 months). As such, the construction/commissioning process is a rapid, constantly overlapping and complex set of events. In addition, construction of semiconductor facilities is very complex and costly (about USD 1.2 to 1.5 billion) due to the extraordinarily sophisticated processes and equipment required to manufacture semiconductor chips."

[CamperBob2]

"Typically the product life of a semiconductor chip (nine to 12 months) is less than the time required to construct the facility and install the equipment for manufacturing (24 to 36 months).

That's an absurd underestimate of market lifetime. I'd bet that fully 80% of the chips available in 1999 when that report was written are still in production today (or would be, if not for the crunch.)

[a9h74j]

Yes, and same situation in every mining-related commodity market. Multiple time delays of order several years. Large up-front investments. Large uncertainties in payoff. Look at the multi-year price behaviors in those markets and see too if there is much stability.

[throwawaygh]

I'm also confused by the confusion here... probably naive pattern matching? Reminds me of TAing undergrad courses where you could get more than half the class to confuse "positive feedback" and "negative feedback" on a midterm by just giving examples where stability = bad :)

[robotresearcher]

Grandparent gives the choices of ‘positive exponent growing against time’ or ‘negative exponent damping out against time’. Here we have a positive exponent damping (reducing) the output over time, because it’s value is less than one, resulting in a negative loop gain. The Wikipedia article linked up thread defines positive feedback as having positive loop gain, and negative feedback negative loop gain.

[a9h74j]

IIRC, generally a positive loop gain greater than one will lead to diverging behavior aka instability, whereas even a positive-sign to feedback, if loop gain is "less than one" will not. I might be brain-farting here, but I cannot be precise anyway, which IIRC gets into plotting poles in a complex plane. (Cue joke my applied math professor would tell, about why all the Polish people were asked to sit in the right-hand aisle of an aircraft.)

[a9h74j]

Self-reply: Not a derogatory reference. Just: "Poles in the left half-plane cause instability."

[robotresearcher]

Self-reply, too late to edit. Looks like I remembered the definition of loop gain incorrectly. This should say a loop gain less than 1, not negative