The Power of Exponential Sharing.
AI prompt 1:
spreading information — how fast everyone knows in world if every receiver of a message forwards it in average to another two people in a day since receiving the message. please give me two versions: an idealistic one where message is forwarded to only those who still don’t have it, and a realistic one where some people receive the message from different people. please respond with bullet points only, with no tables and no formulas — those cannot be copied to my notes or blog.
AI response 1:
– Idealistic version (no repeated receivers):
– Each person who receives the message forwards it to 2 new people who have not received it yet.
– The number of people who know the message doubles daily (two new people per receiver).
– Spreading is exponential and very fast; the entire world population can be reached in just a few days.
– For example, starting from 1 person, in day 1 → 2 new people; day 2 → 4 more; day 3 → 8 more, and so on.
– This means the total informed grows roughly as powers of 2: 1, 3, 7, 15, 31, 63… quickly covering billions of people in under 30 days.
– Realistic version (message forwarded to some who already have it):
– Message spreading is slower due to overlap — some people receive it multiple times from different senders.
– Forwarding to “new” only is not guaranteed; many get repeated sends and do not increase total reached.
– This leads to diminishing returns over time, the growth is slower than ideal exponential.
– Clustering and social network structure means some groups saturate early, reducing new receivers.
– Studies show such spread resembles epidemic or cascade models with partial overlaps and varying response times.
– Real data and simulations indicate it might take weeks or even months for message saturation globally, depending on network connectivity and forwarding behavior.
Overall, while in an ideal world the message doubles reach every day making global coverage very fast, realistically the overlaps and repeated forwards slow it down significantly though it still can reach most people in weeks to a couple of months at most.
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AI prompt 2 (follow-up):
if the message was sent ten years ago, how many times in average each person in world has got the message, realistically.
AI response 2:
Realistically, if a message was originally sent 10 years ago, the average number of times each person in the world has received that message is estimated to be several times over. This is because:
– People receive messages multiple times due to overlaps in social networks; repeated forwards to the same person are common.
– Empirical studies of social media show that messages tend to be forwarded multiple times, with users often exposed 2-3 times on average before forwarding.
– The forwarding behavior depends heavily on network structure, user engagement, and the nature of the message, causing some users to get the message repeatedly.
– Over a 10-year span, given continuous re-sharing, transformations, and new audiences, messages can circulate widely, cumulatively resulting in an average of a few times per individual.
– Exact averages vary by platform and content type, but multiple exposures per user are consistent with observed social media propagation patterns.
Thus, realistically, each person who has access to the message would have received it on average at least 2 to 3 times, if not more, over such a long timeframe given typical forwarding and re-sharing dynamics.
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