OT/Four tetrated

[gnomish dwelf]

I was making a character who is all about number 4 in his powers... So I would limit him by 4 tetrated, but in wikipedia the value of 4 tetrated is given in an odd notation and I wanted it in scientific notation, or at least in iterated scientific notation, but it says the following:

https://i.postimg.cc/x1CJxh3V/4-tetrated.jpg (https://postimages.org/)

someone here is enough of a mathematician to know what this number is in scientific notation? pleeease, pretty please.

[Radar]

To be honest, this unusual notation is used here because regular scientific notation will not be able to handle it. This number has 10^153 digits, which means that in scientific notation you would get something like 8.1 * 10^(10^153). It is impossible to expand that stacked exponentiation into something remotely reasonable.

[tyckspoon]

..something sufficiently enormous that it is likely to be utterly irrelevant as a 'limit' unless you are defining the character's abilities in similarly tiny units. Like 'the character can only maintain his power for 4 tetrated yoctoseconds before needing to recharge' levels, and even that probably still works out to being like a solid week of activity.

[Radar]

..something sufficiently enormous that it is likely to be utterly irrelevant as a 'limit' unless you are defining the character's abilities in similarly tiny units. Like 'the character can only maintain his power for 4 tetrated yoctoseconds before needing to recharge' levels, and even that probably still works out to being like a solid week of activity.
You would still end up with time incomparably longer than the estimated heat death of the universe - it's not even close to being reasonable.

[tyckspoon]

You would still end up with time incomparably longer than the estimated heat death of the universe - it's not even close to being reasonable.

Right. So 'Big enough that the number completely destroys a humans sense of scale.' I don't think the -exact- value is likely to be important >.>

[gnomish dwelf]

Well, the character can generate 4 duplicates of anyone he touches, these 4 duplicates are loyal to him and distinguished from one another by representing a different aspect of the being they duplicate, he can make 4 elemental duplicates (fire, water, air, earth), 4 eval duplicates (three progressively younger selves and equally old self), 4 fluidic duplicates (melancholic, sanguine, choleric, phlegmatic), etc. Although he can make only 4 duplicates of any being at the same time he can on averge hold 256 duplicates in his army but, here is the thing, his potential is calculated at four tetrated duplicates under his command... I am assuming an infinite and eternal universe for my fiction. He has a few more powers related to this but that's irrelevant to my question... anyone knows what the "exp3.10-2.18726" means?

EDIT: at his strongest, he can duplicate anyone touched by any of the duplicates he has generated or any of the duplicates they have generated and so forth indefinitely, not just by his own touch.

[Fat Rooster]

Imagine one of these filled up the entire observable universe with clones squashed in. That would use about 80 of your 'digits', and you have 10^153 digits to use up. In other words, that number is so mind bogglingly big that each of those clones could find a new universe, and fill it in the same way, and we could repeat this process every second until the heat death of the universe and still not have made a significant dent in it. We would need to do this branching ~10^151 times. That's not 10^151 universes (you get that on branch 2), that's that many steps of exponentiation.

It's not a practical literary limit, unless you are actually wanting to set a story at the end of his lifetime when he has managed to reach that limit as a bleak study in scarcity and how everything is finite over long enough timescales. The point is that no reader is ever going to have any sort of sense of scale of that.

Scientific notation:

~1x10810000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 000000000

[Radar]

Well, the character can generate 4 duplicates of anyone he touches, these 4 duplicates are loyal to him and distinguished from one another by representing a different aspect of the being they duplicate, he can make 4 elemental duplicates (fire, water, air, earth), 4 eval duplicates (three progressively younger selves and equally old self), 4 fluidic duplicates (melancholic, sanguine, choleric, phlegmatic), etc. Although he can make only 4 duplicates of any being at the same time he can on averge hold 256 duplicates in his army but, here is the thing, his potential is calculated at four tetrated duplicates under his command... I am assuming an infinite and eternal universe for my fiction. He has a few more powers related to this but that's irrelevant to my question... anyone knows what the "exp3.10-2.18726" means?

EDIT: at his strongest, he can duplicate anyone touched by any of the duplicates he has generated or any of the duplicates they have generated and so forth indefinitely, not just by his own touch.
That notation means stacked exponentiation of 10:
exp3.10-2.18726 = 10^(10^(10^2.18726))
For reference, there are about 10^80 elementary particles in the known universe, here you have 10 to the power of more than 10^100.

[gnomish dwelf]

Imagine one of these filled up the entire observable universe with clones squashed in. That would use about 80 of your 'digits', and you have 10^153 digits to use up. In other words, that number is so mind bogglingly big that each of those clones could find a new universe, and fill it in the same way, and we could repeat this process every second until the heat death of the universe and still not have made a significant dent in it. We would need to do this branching ~10^151 times. That's not 10^151 universes (you get that on branch 2), that's that many steps of exponentiation.

It's not a practical literary limit, unless you are actually wanting to set a story at the end of his lifetime when he has managed to reach that limit as a bleak study in scarcity and how everything is finite over long enough timescales. The point is that no reader is ever going to have any sort of sense of scale of that.

Scientific notation:

~1x10810000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 000000000



That notation means stacked exponentiation of 10:
exp3.10-2.18726 = 10^(10^(10^2.18726))
For reference, there are about 10^80 elementary particles in the known universe, here you have 10 to the power of more than 10^100.


Thanks, I guess this is something that has to be told, not shown, because its impossible to show, so at one point an omniscient being woul tell him that four tetrated is the full limit of his power, which means he will never run out of duplicate to make if he tries hard enough.

[Radar]

Thanks, I guess this is something that has to be told, not shown, because its impossible to show, so at one point an omniscient being woul tell him that four tetrated is the full limit of his power, which means he will never run out of duplicate to make if he tries hard enough.
Or you could change the limit to something more reasonable and keeping the theme of fours. Depending on the scale you are going for, he could duplicate four people at a time (so four fours of duplicates available) or 4^4 if you want a lot of them. Or the limit could be softer: each set of duplicates requiring a different 4 aspects (as you mentioned elemental, humoral and so on). Making up enough of such themes and testing which ones actually work would be an interesting challenge.

[gnomish dwelf]

Or you could change the limit to something more reasonable and keeping the theme of fours. Depending on the scale you are going for, he could duplicate four people at a time (so four fours of duplicates available) or 4^4 if you want a lot of them.

That0s how I got to 256


Or the limit could be softer: each set of duplicates requiring a different 4 aspects (as you mentioned elemental, humoral and so on). Making up enough of such themes and testing which ones actually work would be an interesting challenge.

Yeah, that's an elegant solution

[gomipile]

By "four tetrated" do you mean four tetrated by four: 4^^4? Just saying tetrated isn't enough information. It's like saying "four added" or "four multiplied" without specifying what it is added to or multiplied by.

[gnomish dwelf]

By "four tetrated" do you mean four tetrated by four: 4^^4? Just saying tetrated isn't enough information. It's like saying "four added" or "four multiplied" without specifying what it is added to or multiplied by.

Yes, that's what I meant, four tetrated by four. Thanks for the correction.