I don't understand the seed management on Electrum

[Cricktor]

Dear OP, it's just difficult to grasp the magnitude of such big numbers, be it 2¹²⁸ or worse 2²⁵⁶.

Have a look here: https://www.youtube.com/watch?v=S9JGmA5_unY

[I corrected my previous wording as I tricked myself with exponent arithmetic, sorry, didn't really spend a thought on it.]
To reach required computations for 2¹²⁸ tries which might roughly be what's needed to "break" a 12-word mnemonic seed phrase should convince you that you simply can't brute-force a 12-word mnemonic seed phrase at all. There's likely not enough energy on earth or maybe the whole solar system to accomplish such a task, given you'd be able to harvest all of it in an efficient way for solely your cracking attempt.

As others already said, there's a huge huge difference to brute-force 2048*2048*2048 (equals 2048³ or three mnemonic words) and 2048¹² (equals 12 mnemonic words). It's math and lack of computational power and energy!

[Pmalek]

The list of 2048 words that Electrum uses in its recovery phrases is publicly known. Feel free to find any Bitcoin address with enough coins in it to make it worth your time, which is also something that is publicly available information, and start bruteforcing. Let us know how that works out for you. Since the network has gone live, no one has done it yet. People do have fears that quantum computers might one day be strong enough to find a private key from a public key, but even that is unimaginable right now. Bitcoin wouldn't be where it is today it its security was this fragile. 

[o_e_l_e_o]

Even to reach half of the shown required computations shown in that video which might roughly be what's needed to "break" a 12-word mnemonic seed phrase should convince you that you simply can't brute-force a 12-word mnemonic seed phrase at all.

2¹²⁸ is not half of 2²⁵⁶.

Half of 2²⁵⁶ is 2²⁵⁵. 2¹²⁸ is 2¹²⁸ times smaller than 2²⁵⁶. This is obviously exponentially smaller than just halving, but still orders of magnitude beyond what will ever be realistically possible to crack.

[Cricktor]

Haha, oh dear, got me, I knew something was fishy in my head. You're right...

Well, isn't that proof enough, that those big numbers are just beyond comprehension? (How can I get out of this situation??)

[TrAsHeR]

I loved you're video Cricktor

Thanks for all replies.