Currently, a lot of people made money by investing into Bitcoin and Ethereum. As a result the transaction fees for both are at the moment high enough to make most use-cases of the technology that existed two years ago impossible.

IOTA promizes to be a digital currency without transaction costs.

IOTA promizes to be able to deal without transaction costs by using a complicated concept called the Tangle. I have a hard time myself thinking through their framework. If the total transaction volumne is high enough that the whole transaction log spands multiple terabytes and nobody is incentivized to hold all that data to make transactions, does IOTA still work or will that make the system crash?

Is there anyone in this community who looked more into the concept and has a good idea of whether IOTA can till with terabytes (or even petabytes) worth in total transaction data?

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From what I've understood of the white paper, there's no transaction fee because, instead of rewarding active nodes like in the blockchain, the Tangle punishes inactive nodes. So when a node performes few transactions, other nodes tends to disconnect from it and in the long run an inactive node will be dropped entirely.

On the other hand, a node has only a partial copy of the entire Tangle at each time, so it is possible to keep it small even when the total volume is large.

Economically, I don't know if switching from incentives to partecipate to punishments for leaving makes sense.

Trivially, no. Transaction agreement, propagation, and validation cannot literally be free - someone is expending resources to do it.

Trivally, the promise does seem to be to good to be true. At the same time it might be that IOTA does something clever to hold the promise. If it does that likely means that IOTA will grow 10x or more over a relatively short timeframe.