That doesn't mean the design didn't introduce valuable new concepts and techniques, but it failed to reach the goal it set out to. You can either consider it a prototype (the designers knew, didn't expect it to get this big) or a failure (they were idiots and didn't foresee this)
There are N people in the network. As N grows, each individual person also has more potential people to transact with - transactions would be O(N²). Since each person has a copy of all transaction history, the network requires O(N³) storage overall.
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Ah, so N isn't the size of the block or the storage needed because the block is bigger. It's the scaling factor of transaction counts as networks in general get bigger. So every network scales by O(n3)?
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No, the problem here is requiring everyone to have the entire transaction history stored locally. I'm oversimplifying of course, but I'm saying overall throughput scales with O(n²) (and thus individual bandwidth with O(n).
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I am making the assumption here that individual transactions scale linearly with the network popularity (with some small constant factor of course, since a single person doesn't transact with everyone else); early-adopter effects may reduce this, so perhaps O(nᵏ) for 2 < k < 3
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Number of transactions is number of people squared? Nah. That implies that the newborn will transact with every person on the planet. Let N be number of transactions. Number of full nodes is constant. Therefore O(n) storage.
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O(n²) does not mean n². Yes, there is a (small) constant factor because not everyone transacts with everyone. If you prefer, make the exponent somewhere between 1 and 2 if you expect sub-linear growth with user base. How is the number of full nodes constant?
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N should be the number of transactions, not the number of participants. A is some number of nodes. Storage required = O(A*N) = O(N) Even I known that. What do I win?
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