bitcoin's value is not important in the long run because the block reward (number of bitcoins created every 10 minutes) drops every 4 years and eventually go to zero by 2140. More people using bitcoin will definitely attract more energy in the short run, but the energy alocated to mine bitcoin is not going to consume the whole world as some people say. The increase of energy consumption by bitcoin miners will probably look like a sigmoid function in the far future.

No. The block reward will be replaced by increasing transaction fees. If at any point the net income of miners is negative, miners will stop mining, and bitcoin becomes impossible to spend, driving transaction fees up. If the total amount of electricity wasted is ever small relative to its market cap, there will be a financial incentive to launch a 51% attack on the blockchain. Bitcoin does not scale. Bitcoin's design relies on not scaling.

Bitcoin will either be wasteful in proportion to its market cap, or it will be vulnerable to attack. There are no other options.

> there will be a financial incentive to launch a 51% attack on the blockchain

Anyone with that computing power will use it to earn transaction fees, not to attack Bitcoin by sniping funds through double-spends. If Bitcoin were ever attacked such that transactions were not immutable once confirmed, people would stop using it and the value of Bitcoin would drop. A 51% attack only destroys Bitcoin. There is no financial incentive (at least not in terms of Bitcoin).

(This is in the original white paper.)

That is assuming a 51% attack is only about double-spends. There are other attacks which can be done without trying to double spend.

Still it this exact belief in math that will become a self fulfilling prophecy and keep bitcoin afloat way past someone executing 51% attack.

Right, my reply simplified the issue.

But generally, it's a fair generalization that if step #1 in taking down Bitcoin is acquiring >50% of mining power, most rational actors will go off-mission and decide that step #2 is mine Bitcoin, not screw with it.

Nobody mines any more, there are too many people doing it.