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Qumeric t1_je0a9y4 wrote

Reply to comment by [deleted] in Chat-GPT 4 is here, one theory of the Singularity is things will accelerate exponentially, are there any signs of this yet and what should we be watching? by Arowx

No, this is wrong too. Exponential just means growing in %. So if we have a 1% improvement every year then it is exponential.

The thing is that 1% after 1000 years will be incomparably larger than what we started with.

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iNstein t1_je0df7e wrote

It is about impact. For the first 95 years, it seems kinda slow. Then it appears to be sped up because the impact is so great. The graphic of a pond filling up is a great example. 1 drop, 2 drops, 4 drops not gonna interest anyone. When pond is 1/4 full and then doubles to half full and then doubles again to full, it suddenly looks fast as hell. It is the same with the singularity.

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[deleted] t1_je0f6v9 wrote

[deleted]

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Qumeric t1_je0gp4p wrote

No, 1% per year is not linear growth. X% growth per amount of time is a more-or-less definition of exponential growth.

Ask ChatGPT :)

I think what you described is formally also exponential growth for somewhat complicated mathematical reasons but only coincidentally.

Informally, you described the exponential growth of the rate of growth.

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Ahaigh9877 t1_je0lqna wrote

Linear growth is going up by the same amount per unit time; exponential is going up by a proportion of the previous total per unit time. Right?

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kiyotaka-6 t1_je0mxb5 wrote

Linear is Xn+1 = Xn + b

Exponential is Xn+1 = Xn (1+b)

Yes

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