# How to express a self-diminishing recursive property. Elegantly

In the following, I can't find the right way to express my meaning for the part in bold:

Studies show that high IQ individuals are more susceptible to drug addiction than the general population, meaning there is a cognition-dependent aspect to substance abuse. While mainstream drug treatment programs are notoriously ineffective in general, with recidivism rates reaching 80 percent or higher, many people believe that for high IQ individuals those programs are even less effective than they are for the general population. Tragically, when an attempt to overcome drug addiction ends in failure, the negative light in which the addict saw himself in the world that made him vulnerable to addiction in the first place is intensified, reducing his value in his own eyes and, consequently, diminishing the incentive to try again. This recursive property makes traditional treatment programs for some addicts outright harmful.

I want to express the meaning that entering a drug treatment program, then failing (leaving the program unfinished or getting high one night with a friend, for example), makes it more likely one will slip back into full blown addiction, while simultaneously making it less likely they will seek help, and even if they do seek help, more likely they will fail again, which, of course, not only repeats the pattern (the recursive part), but intensifies it.

None of these seems exactly right, let alone elegant:

• negative recursive
• negative self-intensifier
• recursively diminishing
• lethal feedback loop

Interestingly, I found the question discussed mathematically here on StackExchange, but still wasn't able to come up with a way to express the idea in English.

• How about negative, self-intensifying property? – Richard Kayser Oct 5 '18 at 11:33
• "Death spiral" is a term sometimes used. – Hot Licks Oct 5 '18 at 16:17
• Does the "self" in "self-diminishing" (in the title) refer to the effect or the human being? If it refers to the effect, it is actually self-enhancing or self-reinforcing. – stannius Oct 5 '18 at 17:43

You’ll have to let me know if you agree, but I’m fairly confident the phrase you’re looking for is a “vicious cycle” or sometimes called a “vicious circle”. This describes the kind of feedback loop you mentioned where the situation only becomes worse with each repetition. The converse would be a virtuous cycle.

https://wikipedia.org/wiki/Virtuous_circle_and_vicious_circle

• That's a good suggestion. I hadn't thought of it. But I don't think it captures the sense of intensifying with every repetition which is caused by the repetition itself. In other words, the reason the cycle intensifies is not due to some external factor like "he got older". It is due to the negative light intensifying the negative light that was already there which led him into addiction in the first place. – CWill Oct 5 '18 at 5:58
• @CWill I think that if you have a look at the Wikipedia article I linked, you’ll see that a vicious circle is just that—a cycle that worsens each iteration as a result of the elements of the cycle itself and not from outside influences. Moreover, addiction is often discussed using this term exactly. There are many sources backing this up if you google the two terms together. – ancepsinfans Oct 5 '18 at 6:16
• I was going to accept "vicious circle" despite a vague sense it didn't quite capture the degenerative aspect I was looking for, but Wikipedia can be a little thin, so I looked up "vicious circle" in Merriam-Webster and discovered in the definition there what I was actually seeking, "vicious spiral". Then I see someone below suggests downward-spiral. I wish I could accept both your answers. – CWill Oct 5 '18 at 13:04

It's a downward-spiral.

From wiktionary:

A series of thoughts or actions which feeds back into itself, causing a situation to become progressively worse. It is worse than a vicious circle, which is self-sustaining in its current state.

Or maybe amplification through recursion (which isn't a standard phrase as far as I can find, but it describes your effect). The negative effect grows as the cycle continues/repeats.

• Merriam-Webster: Vicious circle originally referred to a circular argument, that is, an argument that assumes the conclusion as one of its premises. ... end of the 18th century. Approximately 50 years later, vicious circle acquired the now more common "chain of events" sense as people began to think of the circle as a metaphorical circle rather than a circular argument. Today, vicious cycle is a common variant for the "chain of events" sense. Vicious spiral, in which the ill effects are cumulative as well as self-aggravating..." "Vicious" from first response, "spiral" from you. – CWill Oct 5 '18 at 13:03
• Excellent choice @CWill. Glad you found a suitable term (and that more than one answer was useful!). – Pam Oct 5 '18 at 13:16

It would be a bit visual, but you could use Feedback or Feedback Loop.

From Wikipedia:

Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The system can then be said to feed back into itself.

• +1 This was what I thought of too. Technically this is positive feedback (which probably should not be used in the original context since it would be easy to confuse with the more common usage of positive meaning good). – Justin Oct 5 '18 at 18:07
• Right, the correct way to describe this is, surprisingly, a positive feedback loop. If you have a stable system, and there's a disruption, a negative feedback loop will subtract something that is a function of the disruption from the input, correcting the issue. If the disruption gets added back to the input (positive feedback), it makes the system unstable. It's not recursive at all - that would imply that the definition of the situation is based on the definition of the situation. Maybe this all is me being too much of an engineer. – Flydog57 Oct 5 '18 at 19:09

I agree with "vicious cycle":

• a situation in which an attempt to resolve one problem creates new problems that lead back to the original situation
• A vicious circle is a problem or difficult situation that has the effect of creating new problems which then cause the original problem or situation to occur again.

A "vicious cycle" is a result of or example of "positive feedback" (e.g. "the weaker it is, the more it moves ... and the more it moves, the weaker it gets").

An example of "negative" feedback (a.k.a. "virtuous cycle") would be, for example: