Question Regarding Super Saiyan and Fusion

[GohanSatan]

Hello everyone, I just have a question about something that I've been wondering for awhile and was wondering if anyone can shed some light on this.

Does Gotenk's (or any other fusion for that matter) power depend on the power levels of the two people fusing at the time, or does when he become Gotenks, his power is pretty much set. What I mean by asking is this.

Let's say Goten and Trunks fuse in their base forms resulting in Base Gotenks. Base Gotenks then transforms into Super Saiyan and is at Super Saiyan power.

Now let's say that Goten and Trunks fuse again as Super Saiyans, resulting in Super Saiyan Gotenks right off the bat. Would this Super Saiyan Gotenks be stronger than the first Super Saiyan Gotenks because he's the result of two Super Saiyans fusing, or would he be the same strength?

I guess what I'm asking is does it make a difference if Trunks and Goten fuse as Super Saiyans or if they fuse in their base form and then go Super Saiyan.

[Rocketman]

(300 + 350) x 50 = 650 x 50 = 32,500

(300x50) + (350x50) = 15,000 + 17,500 = 32,500

Same result.

[GohanSatan]

Ok that's what I thought but I guess seeing the "Fusion Mutliplier" topic on this page confused me a bit and made me think that you would multiply their powers together.

[Rocketman]

You could, and you would get the same result. I just went with addition so I wouldn't fill my post with zeroes.

[GohanSatan]

Oh ok that makes sense. Thanks for clearing that up

[Bussani]

Ok that's what I thought but I guess seeing the "Fusion Mutliplier" topic on this page confused me a bit and made me think that you would multiply their powers together.

One of the Super Exciting Guides said that fusion was "more like a multiplication than an addition", but I think that's mostly just another way of saying fusions are stronger than the sum of their parts--which, of course, is the whole point of fusion. But even though it's definitely not a simple addition of two powers, I agree with Rocketman: there's nothing in the manga that suggests Gotenks' power would be any different if Goten and Trunks were Super Saiyans before fusing.

[Fox666]

You could, and you would get the same result. I just went with addition so I wouldn't fill my post with zeroes.

How?

If it really is a multiplication, it would have a huge impact if you are a Super Saiyan or not before the fusion

[1,000 × 1,000] × 50 = 50,000,000

[1,000 × 50] × [1,000 x 50] = 2,500,000,000

And it's very simply. Transforming in Super Saiyan before the power are multiplied will result in a increase of 2,500 (50²) rather than mere 50 times.

And that's another reason why I don't believe that the Potara fusion is the multiplication of powers. The correct equation is "random large plot-induced artistic number" which apply for all kind of fusion (Potara, Metamorian, Piccolo with Nail/Kami). It works much like the saiyan near-death power-up, just a unpredictable value.

[Kroni_Hunter]

(300 + 350) x 50 = 650 x 50 = 32,500

(300x50) + (350x50) = 15,000 + 17,500 = 32,500

Same result.

Actually, the 350 would have to be suppressed to 300, since they have to have equal power levels for dancing fusion.

Also, that math is not quite right.

(300 x 300) = 90,000 is base Gotenks, who would get another x50 when he transforms SSJ, 90,000 x 50 = 4,500,000

(300 x 50) x (300 x 50) = 15,000 x 15,000 = 225,000,000 this would be SSJ Goten and SSJ Trunks doing the fusion. So yes it makes a difference assuming Fusion takes that into account.

Basically, you get another x50 in there for having 2 SSJ transformations instead of just 1.

[TheDevilsCorpse]

(300 + 350) x 50 = 650 x 50 = 32,500
(300x50) + (350x50) = 15,000 + 17,500 = 32,500
Same result.

Actually, the 350 would have to be suppressed to 300, since they have to have equal power levels for dancing fusion.
Also, that math is not quite right.

You sure you paid full attention to his post? Yes, Trunks would have to be suppressed, but you also jumped his math for being wrong when he used addition and you used multiplication..

[Kroni_Hunter]

You sure you paid full attention to his post? Yes, Trunks would have to be suppressed, but you also jumped his math for being wrong when he used addition and you used multiplication..

Yes, I did. The guides state that fusion works more like multiplication than addition. Also it wouldn't really make sense logically for just the added powers of Goten and Trunks to be as powerful as they are portrayed.

Even if you use addition, it doesn't work.

(300 + 300) = 900 x 50 = 45,000
(300 x 50) + (300 x 50) = 30,000
The powers are not equal, no matter what method you use for the same reason I stated above.

[Fox666]

Actually, the 350 would have to be suppressed to 300, since they have to have equal power levels for dancing fusion.

I don't believe this affect the resulting being power. Supression of power is something natural.

[Rocketman]

Even if you use addition, it doesn't work.

(300 + 300) = 900

Hm.

It's the distributive property of multiplication, sirrah.

"Distributive property: The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example 4 * (6 + 3) = 4*6 + 4*3" or in this case, 50 x (300+350) = 50x300 + 50x350.

[Fox666]

It's basic in mathematics. Multiplying the values before and after makes no different.

[1,000 + 1,000] × 50 = 100,000

[1,000 × 50] + [1,000 × 50] = 100,000

However, in multiplication case the result is different, as I noted before

[1,000 × 1,000] × 50 = 50,000,000

[1,000 × 50] × [1,000 x 50] = 2,500,000,000

And the reason is very simply, you are also multiplying 50 by 50. The result will be very different of simply multiplying everything by 50.

[Bussani]

This is why trying to explain fusion with just math is a bad idea.

[Fox666]

Yes, as I said before, the fusion works much like a saiyan near-death power-up. You can't predict how strong they can get

[jackjack]

This is why trying to explain fusion with just math is a bad idea.

It could be as simple as the fusees' power multiplying a fusion boost. I don't think it needs to be more complicated than Kaioken.

Even if you use addition, it doesn't work.

(300 + 300) = 900 x 50 = 45,000
(300 x 50) + (300 x 50) = 30,000

The powers are not equal, no matter what method you use for the same reason I stated above.

Try again?

[ggf31416]

I don't believe that potara fusion can be simply multiplying their power levels.

That would fail dimensional analysis. Since the fusion power level and the power levels of each fused individuals are power levels they have to have the same dimension. Let call it [Ki].
If we have powerFusion = powerA * powerB, we have [Ki] = [Ki] * [Ki] = [Ki]^2, then [Ki] = [Ki] ^ 2, which is false. That means that such formula is not possible.
If we tried to calculate using such formula we would get different results if we use different units, which doesn't make sense, for example:
1 foo (made up unit) = 100 Ki units (scooter)
A = 1000 ki = 10 foo
B = 2000 ki = 20 foo
Fusion = 1000 ki * 2000 ki = 2000000 ki
Fusion = 10 foo * 20 foo = 200 foo = 20000 ki
2,000,000 != 20,000

However that could be solved if the result is divided by a another magnitude of dimension [Ki]. Most likely that would be a constant derived from physical laws.
powerFusion = powerA * powerB / constant => [Ki] = [Ki] * [Ki] / [Ki] = [Ki] ^2 / [Ki] = [Ki], then [Ki] = [Ki].

If we assume that the constant is 10 ki units (scooter) = 0.1 foo we have:
fusion = 1000 ki * 2000 ki / 10 ki = 200000 ki
fusion = 10 foo *20 foo / 0.1 foo = 2000 foo = 200000 ki
200,000 = 200,000

The constant could be 1 ki units (scooter), in which case a direct multiplication would get correct results, but it could be any other number as well.

Still if it was a multiplication divided by a constant we would still have 2 problems:
1) Fusion with relatively weak individual still results in much stronger results as long as the constant is below the weaker individual. For example if Goku's ki = 1 billion and Mr. Satan's ki = 20 and the constant is 1 the fusion would be 1 billion * 20 / 1 = 20 billion, a 20x increase in power. That would make worthwhile to fuse with weak individuals like Dende or Mr. Satan, which Goku ruled out.
2) If one of the individuals is weaker than the constant it would make the fusion weaker than the stronger individual.
If Goku fused with Turtle, assuming constant = 1: fusion power level = 1 billion * 0.001 / 1 = 1 million
1 million is 1000x weaker than 1 billion.

An addition followed by multiplication by a dimensionless constant doesn't fail dimensional analysis ([Ki] = ( [Ki] + [Ki] )* 1 = [Ki] * 1 = [Ki]), solves problem 2 but still has problem 1.

[rereboy]

Hello everyone, I just have a question about something that I've been wondering for awhile and was wondering if anyone can shed some light on this.

Does Gotenk's (or any other fusion for that matter) power depend on the power levels of the two people fusing at the time, or does when he become Gotenks, his power is pretty much set. What I mean by asking is this.

Let's say Goten and Trunks fuse in their base forms resulting in Base Gotenks. Base Gotenks then transforms into Super Saiyan and is at Super Saiyan power.

Now let's say that Goten and Trunks fuse again as Super Saiyans, resulting in Super Saiyan Gotenks right off the bat. Would this Super Saiyan Gotenks be stronger than the first Super Saiyan Gotenks because he's the result of two Super Saiyans fusing, or would he be the same strength?

I guess what I'm asking is does it make a difference if Trunks and Goten fuse as Super Saiyans or if they fuse in their base form and then go Super Saiyan.

To answer your question without any math, we must be aware that the only moment in the series where they talk about the difference in fusing in base form or SSJ is when Rou Kaioshin gives Goku the Potara earings.

Rou Kaioshin say that it would be a bad idea for Goku to fuse as SSJ because then he wouldn't be able to return to base form, which would be eventually stressful for the body since he would be fused forever.

He didn't state that if he was SSJ before the fusion he would be stronger than he would if he fused at base nor did he mention any other difference in power, just his inability to return to base form.

So, I think its safe to assume that, with the potara at least, being SSJ or base before the fusion, doesn't produce a real difference in overall power. It just matters to the transition between forms since the fusion takes the characteristics of the fighters at the time of the fusion.

So, the SSJ Vegetto we saw in the series would have the same power as another SSJ Vegetto formed by Goku and Vegeta fused as SSJs. The second Vegetto just wouldn't be able to return to his base form.

With the fusion dance it might be the same thing, since the only time Goten and Trunks fused as SSJ, Gotenks never returned to base before the time ran out on the fusion.

[Bussani]

If we tried to calculate using such formula we would get different results if we use different units, which doesn't make sense

That's what I've explained in the past. The Super Exciting Guide does make mention of battle powers (aka "scouter units") when talking about it, though. I just choose not to take it all too literally.