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Silverblade5

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7 hours ago, Silverblade5 said:

@Chaos, @Glamdring804, I think you two might enjoy this.

It always bothered me that when looking at a table of trig identities, there wasn't a sum to product identity for sin(a) + cos(b). It's actually a really simple one, but the derivation involves the culmination of almost all the other ones, so it's really elegant in that regard. Below is the identity, and below that will be the derivation.

sin(a) + cos(b) = ((1 + sin(a+b))(1 + sin(a-b)))^.5

Derivation: 

  Hide contents

sin(a) + cos(b)

sin(a) + cos((a+b) - a)

sin(a) + cos(a)cos(a+b) + sin(a)sin(a+b)

cos(a)cos(a+b) + sin(a)(1 + sin(a+b))

let u = cos(a+b) and let v = 1 + sin(a+b)

ucos(a) + vsin(a) = rcos(c-a)

ucos(a) + vsin(a) = rcos(c)cos(a) + rsin(c)sin(a)

Solve for c and r in terms of u and v

u = rcos(c)     v = rsin(c)

r = u/cos(c)

v = usin(c)/cos(c)

v = utan(c)

c = arctan(v/u)

r = u/cos(arctan(v/u))

cos(arctan(v/u)) = u/(u^2 + v^2)^.5

r = (u^2 + v^2)^.5 

With back-substituting, we get

r = (cos^2(a+b) + (1 + sin(a+b))^2)^.5

r = (cos^2(a+b) + sin^2(a+b) + 2sin(a+b) + 1)^.5

r = (2 + 2sin(a+b))^.5

r = (2(1 + sin(a+b)))^.5

Now lets define c.

c = arctan(v/u)

c = arctan((1 + sin(a+b) ) / (0 + cos(a+b)))

c = arctan((sin(pi/2) + sin(a+b)) / (cos(pi/2) + cos(a+b)))

c = arctan((2sin((pi/2 + a + b)/2)cos((pi/2 - a - b)/2)) / (2cos((pi/2 - a - b)/2)cos((pi/2 + a + b)/2)))

Factor out 2cos((pi/2 - a - b)/2), and you get

c = arctan(sin((pi/2 + a + b)/2) / cos((pi/2 + a + b)/2))

c = arctan(tan((pi/2 + a + b)/2))

c = (pi/2 + a + b)/2

If we plug all this into the formula ucos(a) + vsin(a) = rcos(c-a), we get

cos(a)cos(a+b) + sin(a)(1 + sin(a+b)) = (2(1 + sin(a+b)))^.5 * cos((pi/2 + a + b)/2 - a)

Now lets simplify the bit that came from cos(c-a).

cos((pi/2 + a + b)/2 - a)

= cos((pi/2 - a + b)/2)

= ((1 + cos(pi/2 - a + b))/2)^.5

= ((1 + cos(pi/2 - a)cos(b) - sin(pi/2 - a)sin(b))/2)^.5

= ((1 + sin(a)cos(b) - cos(a)sin(b))/2)^.5

= ((1 + sin(a-b))/2)^.5

(2(1 + sin(a+b)))^.5 * ((1 + sin(a-b))/2)^.5

= ((1 + sin(a+b))(1 + sin(a-b)))^.5

Therefore, 

sin(a) + cos(b) = ((1 + sin(a+b))(1 + sin(a-b)))^.5

 

Wow. This is really cool. I had no idea it was that simple. Then again, I'm a physics major, and that's what I think of most trig identities.

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35 minutes ago, Glamdring804 said:

Wow. This is really cool. I had no idea it was that simple. Then again, I'm a physics major, and that's what I think of most trig identities.

To be fair, I don't believe this one was as simple as most :P Replacing 0 with  cos(pi/2) was not a very obvious move initially.

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So... I've got a question.

See, I have a character with electric powers. He can use sparksight to 'see' electricity - electric current glows to him, so he can see the wiring in the walls et cetera. But would he be able to see living organisms? I mean, I know nerves pass electric impulses but the thing is I don't know how much voltage is there (because the less the weaker the glow is). I also remember something about heart being regulated with electricity.

Also - is it possible to stop heart with electricity? Or (if not) to induce strokes? (EDIT: I meant heart attacks - my vocabulary sometimes misleads me) Because I have this scene in mind where he incapacitates opponents by stopping their hearts one by one and then, after dealing with the rest of the enemies, he restarts their hearts before they died.

Edited by Oversleep
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On 2/8/2017 at 4:03 PM, Silverblade5 said:

So, I did some math recently, and came up with the following information:

cos(2 * x) = 2cos^2(x) - 1

cos(2^2 * x) =  2(2cos^2(x) - 1)^2 - 1

cos(2^3 * x) = 2(2(2cos^2(x) - 1)^2 - 1)^2 - 1

cos(2^4 * x) = 2(2(2(2cos^2(x) - 1)^2 - 1)^2 - 1)^2 - 1

Anyway I might be able to condense this into a series representation for cos(2^a * x)?

@Chaos@Glamdring804 Since you're my go to people for calc advice

This certainly can be expanded into a huge polynomial in cos(x), however there is a better way.

One can express cosine in terms of the exponential function.  This has many upsides (including making it easier to derive identities).  The one downside is it involves the imaginary number i.

The formula is: cos(x) = (e^(ix) + e^(-ix))/2.  The formula for sine is: sin(x) = (e^(ix) - e^(-ix))/(2i).

Thus, the quantity you are looking at is simply:

cos(2^a * x) = (e^(2^a i x) + e^(-2^a i x))/2.

This has only two terms; you don't want to expand it as above, because it is already quite simple.  Just two exponentials.

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1 hour ago, Oversleep said:

So... I've got a question.

See, I have a character with electric powers. He can use sparksight to 'see' electricity - electric current glows to him, so he can see the wiring in the walls et cetera. But would he be able to see living organisms? I mean, I know nerves pass electric impulses but the thing is I don't know how much voltage is there (because the less the weaker the glow is). I also remember something about heart being regulated with electricity.

Also - is it possible to stop heart with electricity? Or (if not) to induce strokes? Because I have this scene in mind where he incapacitates opponents by stopping their hearts one by one and then, after dealing with the rest of the enemies, he restarts their hearts before they died.

So basically, they can detect the movement of electric charges, yes? Then yes, they would in theory be able to see impulses in human nervous systems, but it would be very very VERY dim.

If electric current is visible to them, then their sight would only tangentially be related to voltage. A rough analogy is to think of water flowing down hill. The voltage is the slope of the hill, but your character only sees the water flowing. Voltage is in fact a bit more complicated than that, since voltage in a circuit is only really used up in resistors, and not in wires. Which means, if they are able to see current moving in a wire, then they will be able to see electricity without knowing anything about the voltage. Of course, you could decide to let them see both voltage and current, which would be pretty damnation useful.

So what does this mean for his vision abilities? Well, human nerves have a voltage across their inner and outer surfaces of about 0.07 volts. That's small, but not too tiny. It's something you might be able to come across in everyday life. Now, for the actual current of a nerve cell. I did some Googling around, and found that the average movement of charge across a neuron sell membrane is 10e-12 amps. That is tiny. incredibly tiny. Like, a millionth of a millionth of a standard amp. So, of the two, your character would be better able to see nerve impulses using voltage. However, if you limit yourself to just being able to see voltage, your character wouldn't be able to see actual electricity, just places where electricity is being used. I.e they'll be able to see the light bulb, but not the wires. I would recommend letting them see both, as that would give them a pretty wide spectrum of electrical phenomena they could detect.

As for the heart, yes, it is regulated by electrical impulses, but they are very week. You could easily disrupt the flow of charges across a cellular membrane, prevent the neurons from firing, and lock up the muscles. Strokes are a completely different beast. They occur when the brain is deprived of oxygen carrying blood, usually via a blood clot getting stuck in an artery, or internal bleeding in the brain. Neither is really caused by a problem with electrical infrastructure in the body.

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1 hour ago, Glamdring804 said:

If electric current is visible to them, then their sight would only tangentially be related to voltage. A rough analogy is to think of water flowing down hill. The voltage is the slope of the hill, but your character only sees the water flowing. Voltage is in fact a bit more complicated than that, since voltage in a circuit is only really used up in resistors, and not in wires. Which means, if they are able to see current moving in a wire, then they will be able to see electricity without knowing anything about the voltage. Of course, you could decide to let them see both voltage and current, which would be pretty damnation useful.

I know that much. I knew that some electric sources would glow brighter (power lines) and I thought it would scale with voltage. But you're right, it's the current. That makes more sense, I knew something was wrong with my thinking.

But that presents the problem you described here:

1 hour ago, Glamdring804 said:

So what does this mean for his vision abilities? Well, human nerves have a voltage across their inner and outer surfaces of about 0.07 volts. That's small, but not too tiny. It's something you might be able to come across in everyday life. Now, for the actual current of a nerve cell. I did some Googling around, and found that the average movement of charge across a neuron sell membrane is 10e-12 amps. That is tiny. incredibly tiny. Like, a millionth of a millionth of a standard amp. So, of the two, your character would be better able to see nerve impulses using voltage. However, if you limit yourself to just being able to see voltage, your character wouldn't be able to see actual electricity, just places where electricity is being used. I.e they'll be able to see the light bulb, but not the wires. I would recommend letting them see both, as that would give them a pretty wide spectrum of electrical phenomena they could detect.

I could handwave it away with the character having really good at the sparksight... but I'd resort to those kinds of handwaves only if absolutely necessary.

There is a scene where he uses his power to flashbang everyone and tosses in a smoke grenade to make sure everyone is properly blinded. Then he dives inside and takes down enemies, relying on sparksight to locate them.

2 hours ago, Glamdring804 said:

Strokes are a completely different beast. They occur when the brain is deprived of oxygen carrying blood, usually via a blood clot getting stuck in an artery, or internal bleeding in the brain. Neither is really caused by a problem with electrical infrastructure in the body.

I meant heart attack. My biology-related vocabulary is rusty.

2 hours ago, Glamdring804 said:

As for the heart, yes, it is regulated by electrical impulses, but they are very week. You could easily disrupt the flow of charges across a cellular membrane, prevent the neurons from firing, and lock up the muscles.

From what I've gathered, he could stop hearts. That's good. The thing is, I need it to be non-lethal: he stops the hearts and later starts them. Is that believeable? How much time would he have to resuscitate them before their bodies started to die? Three minutes? Two?

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2 hours ago, Oversleep said:

I know that much. I knew that some electric sources would glow brighter (power lines) and I thought it would scale with voltage. But you're right, it's the current. That makes more sense, I knew something was wrong with my thinking.

But that presents the problem you described here:

I could handwave it away with the character having really good at the sparksight... but I'd resort to those kinds of handwaves only if absolutely necessary.

Is it possible to have your main character be a tag-team duo? One could be good at seeing voltage, the other good at seeing current. I don't know. It's your story, so I can't tell you how to solve the problem. Just a suggestion.

2 hours ago, Oversleep said:

From what I've gathered, he could stop hearts. That's good. The thing is, I need it to be non-lethal: he stops the hearts and later starts them. Is that believeable? How much time would he have to resuscitate them before their bodies started to die? Three minutes? Two?

So, heart muscles are unique, in that they will naturally contract without stimulation through the nerves. So, if you left a heart alone, it will continue to contract unless it's damaged. I would suggest that you throw body into fibrillation, where the heard is beating erratically and not pumping blood, and then have your character heal them by using a shock to restore normal rhythm. Give this reddit thread a glance, see if it helps.

 

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14 hours ago, Silverblade5 said:

@Glamdring804@Oversleep

Maybe make the character able to see the power or individual charges instead of just the flow of them(which is current)?

Current is the flow of individual electric charges. I'm not sure just being able to see the charges themselves would give the same effect. Even though countless electrons might be flowing through any part of a circuit, the circuit as a whole will remain electrically neutral. A battery doesn't provide electric charges to a circuit, it creates an electric field that pushes the existing charges in the wires. Same thing with neurons. Each cell has a slight positive charge on the outside and a slit negative charge on the inside. In order to "see" electric charges, you would have to be able to somehow detect individual subatomic particles, as detecting a net charge would only be usable in a few situations. 

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On 5/5/2017 at 4:06 PM, Silverblade5 said:

@Chaos, @Glamdring804, I think you two might enjoy this.

It always bothered me that when looking at a table of trig identities, there wasn't a sum to product identity for sin(a) + cos(b). It's actually a really simple one, but the derivation involves the culmination of almost all the other ones, so it's really elegant in that regard. Below is the identity, and below that will be the derivation.

sin(a) + cos(b) = ((1 + sin(a+b))(1 + sin(a-b)))^.5

Derivation: 

  Reveal hidden contents

sin(a) + cos(b)

sin(a) + cos((a+b) - a)

sin(a) + cos(a)cos(a+b) + sin(a)sin(a+b)

cos(a)cos(a+b) + sin(a)(1 + sin(a+b))

let u = cos(a+b) and let v = 1 + sin(a+b)

ucos(a) + vsin(a) = rcos(c-a)

ucos(a) + vsin(a) = rcos(c)cos(a) + rsin(c)sin(a)

Solve for c and r in terms of u and v

u = rcos(c)     v = rsin(c)

r = u/cos(c)

v = usin(c)/cos(c)

v = utan(c)

c = arctan(v/u)

r = u/cos(arctan(v/u))

cos(arctan(v/u)) = u/(u^2 + v^2)^.5

r = (u^2 + v^2)^.5 

With back-substituting, we get

r = (cos^2(a+b) + (1 + sin(a+b))^2)^.5

r = (cos^2(a+b) + sin^2(a+b) + 2sin(a+b) + 1)^.5

r = (2 + 2sin(a+b))^.5

r = (2(1 + sin(a+b)))^.5

Now lets define c.

c = arctan(v/u)

c = arctan((1 + sin(a+b) ) / (0 + cos(a+b)))

c = arctan((sin(pi/2) + sin(a+b)) / (cos(pi/2) + cos(a+b)))

c = arctan((2sin((pi/2 + a + b)/2)cos((pi/2 - a - b)/2)) / (2cos((pi/2 - a - b)/2)cos((pi/2 + a + b)/2)))

Factor out 2cos((pi/2 - a - b)/2), and you get

c = arctan(sin((pi/2 + a + b)/2) / cos((pi/2 + a + b)/2))

c = arctan(tan((pi/2 + a + b)/2))

c = (pi/2 + a + b)/2

If we plug all this into the formula ucos(a) + vsin(a) = rcos(c-a), we get

cos(a)cos(a+b) + sin(a)(1 + sin(a+b)) = (2(1 + sin(a+b)))^.5 * cos((pi/2 + a + b)/2 - a)

Now lets simplify the bit that came from cos(c-a).

cos((pi/2 + a + b)/2 - a)

= cos((pi/2 - a + b)/2)

= ((1 + cos(pi/2 - a + b))/2)^.5

= ((1 + cos(pi/2 - a)cos(b) - sin(pi/2 - a)sin(b))/2)^.5

= ((1 + sin(a)cos(b) - cos(a)sin(b))/2)^.5

= ((1 + sin(a-b))/2)^.5

(2(1 + sin(a+b)))^.5 * ((1 + sin(a-b))/2)^.5

= ((1 + sin(a+b))(1 + sin(a-b)))^.5

Therefore, 

sin(a) + cos(b) = ((1 + sin(a+b))(1 + sin(a-b)))^.5

 

After playing around with it for a bit, I was also able to derive a difference formula.

cos(a) - sin(b) = ((1 - sin(b-a))(1 - sin(b+a))^.5

Therefore, cos(a) +- sin(b) = ((1 +- sin(b+a))(1 +- sin(b-a)))^.5

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So, a problem I've been facing with a magic system im making based around controlling the elements is that I want these elemental powers to only be able to control their elements, not create them. The main problem about that is that I can't seem to figure out how Fire would work if it cannot create fire, simply manipulate it. Any help guys?

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4 minutes ago, StrikerEZ said:

So, a problem I've been facing with a magic system im making based around controlling the elements is that I want these elemental powers to only be able to control their elements, not create them. The main problem about that is that I can't seem to figure out how Fire would work if it cannot create fire, simply manipulate it. Any help guys?

Fire is merely a visible form of heat, and heat is nothing but thermal energy. By the conservation of energy, which states that energy can't be created or destroyed, only changed, heat can't be created or destroyed. You can't create heat, but you can control how much is present in an area. If you're trying to avoid handwaving the magic, one thing you could do is redefine it as the manipulation of heat, instead of the manipulation of fire. This would open the door for many more interesting and unexpected applications of the magic, such as freezing someone by withdrawing all the heat from a person's body and dispersing it around the area.

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1 minute ago, Silverblade5 said:

Fire is merely a visible form of heat, and heat is nothing but thermal energy. By the conservation of energy, which states that energy can't be created or destroyed, only changed, heat can't be created or destroyed. You can't create heat, but you can control how much is present in an area. If you're trying to avoid handwaving the magic, one thing you could do is redefine it as the manipulation of heat, instead of the manipulation of fire. This would open the door for many more interesting and unexpected applications of the magic, such as freezing someone by withdrawing all the heat from a person's body and dispersing it around the area.

That would work...but I really do love the idea of someone creating a fireball in their hands and throwing it at someone. :ph34r:

I don't wanna be too handwavy with the magic, but the ability to use fire, not heat, has some important plot aspects. And while I like where you're going with drawing the heat away from someone to freeze them, that's not how the magic works. If I went with heat manipulation, you'd be able to draw heat into a location, but you couldn't draw it away. Another example of this is with the three Water powers-Water, Ice, and Vapor. Water can control water in its liquid state, and can turn ice or vapor into liquid water, but not the other way around. Ice can control water in its solid state, and can only turn water into ice, not vapor into ice. Vapor can only control water in its gaseous state, and can turn water into vapor, but not ice into vapor.

What I'm thinking is what Fire does is causes the air itself to burn, which would create the fireball. Not too handwavy, I don't think, but probably not perfectly scientifically possible. 

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4 minutes ago, StrikerEZ said:

That would work...but I really do love the idea of someone creating a fireball in their hands and throwing it at someone. :ph34r:

I don't wanna be too handwavy with the magic, but the ability to use fire, not heat, has some important plot aspects. And while I like where you're going with drawing the heat away from someone to freeze them, that's not how the magic works. If I went with heat manipulation, you'd be able to draw heat into a location, but you couldn't draw it away. Another example of this is with the three Water powers-Water, Ice, and Vapor. Water can control water in its liquid state, and can turn ice or vapor into liquid water, but not the other way around. Ice can control water in its solid state, and can only turn water into ice, not vapor into ice. Vapor can only control water in its gaseous state, and can turn water into vapor, but not ice into vapor.

What I'm thinking is what Fire does is causes the air itself to burn, which would create the fireball. Not too handwavy, I don't think, but probably not perfectly scientifically possible. 

Hmm... I'm more of a math person than a physics person.... @Glamdring804, how much do you know about thermodynamics? 

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22 minutes ago, StrikerEZ said:

That would work...but I really do love the idea of someone creating a fireball in their hands and throwing it at someone. :ph34r:

I don't wanna be too handwavy with the magic, but the ability to use fire, not heat, has some important plot aspects. And while I like where you're going with drawing the heat away from someone to freeze them, that's not how the magic works. If I went with heat manipulation, you'd be able to draw heat into a location, but you couldn't draw it away. Another example of this is with the three Water powers-Water, Ice, and Vapor. Water can control water in its liquid state, and can turn ice or vapor into liquid water, but not the other way around. Ice can control water in its solid state, and can only turn water into ice, not vapor into ice. Vapor can only control water in its gaseous state, and can turn water into vapor, but not ice into vapor.

What I'm thinking is what Fire does is causes the air itself to burn, which would create the fireball. Not too handwavy, I don't think, but probably not perfectly scientifically possible. 

Not an official physicsy person (Yet. Ish. I do plan to major in bioengineering, which will involve some physics, but not exactly focus on it. :P), or the person mentioned but this seems more like like a pretty basic chem problem. 

So air doesn't burn, really. Air (or rather, the oxygen in air) allows other things to burn. :P (And if you somehow had legit air burn, (Despite the main component, nitrogen, being chemically nonreactive in diatomic form, the way it is in the atmosphere.) you'd have to deal with the fact that you'd have decidedly nasty toxic nitrogen oxides as a byproduct. (Which, really could be very cool in and of itself, a magic system that allowed you to change the reactivity/volatility of elements would be very scary and cool.) Either that, or handwave it as causing a spontaneous ionization of the air... which is really coming back to heat (well, more so electricity, in this case) manipulation and the problems you were originally trying to avoid. Although an interesting note if you did go this way, is that the flame would be a bright green-yellow, rather than the traditional orange.) 

Something I saw in a book series I read once that might work for you though were fire mages who controlled flammable gasses, not fire itself. So they can throw fireballs, cause explosions, be human flamethrowers, etc, but aren't just creating fire out of nothing. (With the caveat that they need a ignition source. Depending on the tech level, could be a flint and steel type thing (thinking something attached to ends of fingers, snap fingers to generate sparks) or a battery and some wires. Or you could just combine it with minor heat/reactivity manipulation, and justify it as being akin to changing the state of water in your example.)

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1 hour ago, Aonar Faileas said:

Not an official physicsy person (Yet. Ish. I do plan to major in bioengineering, which will involve some physics, but not exactly focus on it. :P), or the person mentioned but this seems more like like a pretty basic chem problem. 

So air doesn't burn, really. Air (or rather, the oxygen in air) allows other things to burn. :P (And if you somehow had legit air burn, (Despite the main component, nitrogen, being chemically nonreactive in diatomic form, the way it is in the atmosphere.) you'd have to deal with the fact that you'd have decidedly nasty toxic nitrogen oxides as a byproduct. (Which, really could be very cool in and of itself, a magic system that allowed you to change the reactivity/volatility of elements would be very scary and cool.) Either that, or handwave it as causing a spontaneous ionization of the air... which is really coming back to heat (well, more so electricity, in this case) manipulation and the problems you were originally trying to avoid. Although an interesting note if you did go this way, is that the flame would be a bright green-yellow, rather than the traditional orange.) 

Something I saw in a book series I read once that might work for you though were fire mages who controlled flammable gasses, not fire itself. So they can throw fireballs, cause explosions, be human flamethrowers, etc, but aren't just creating fire out of nothing. (With the caveat that they need a ignition source. Depending on the tech level, could be a flint and steel type thing (thinking something attached to ends of fingers, snap fingers to generate sparks) or a battery and some wires. Or you could just combine it with minor heat/reactivity manipulation, and justify it as being akin to changing the state of water in your example.)

I think what I'm gonna do is a combination of a little of everything. They can only control fires that already exist, but they can light things on fire, as long as they're already flammable. The less flammable something is, the harder it is to set it on fire. And when they want to create fire in thin air, they use some sort of flint and steel thing, like you said.

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I think @Aonar Faileas covered what you were looking fore. "Fire" is the combustion of carbon based molecules with oxygen to produce carbon dioxide and other byproducts. Flames are actually just superheated gas, so you don't strictly need combustion to create them. You can make pseudo flames by heating the ambient air until it glows. Of course, as Aonar so astutely pointed out, glowing air wouldn't look like fire flames because of the emission spectrums of nitrogen and oxygen. I solved this problem in my magic system by giving fire mages both the ability to add energy to systems (heat stuff up) and mentally control hot objects and substances. They can create a fireball between their hands, and then launch that fireball forward, etc. 

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11 hours ago, Aonar Faileas said:

(With the caveat that they need a ignition source. Depending on the tech level, could be a flint and steel type thing (thinking something attached to ends of fingers, snap fingers to generate sparks)

Electrostatic gloves:

https://s-media-cache-ak0.pinimg.com/originals/5b/24/ed/5b24ed5e2a826f2a73c58b45a580f45b.gif

http://38.media.tumblr.com/ede360a302339447f434464f07c224d9/tumblr_mu9zotpesD1rnvb0co6_r1_500.gif

Edited by Oversleep
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On 5/6/2017 at 9:59 AM, Oversleep said:

So... I've got a question.

See, I have a character with electric powers. He can use sparksight to 'see' electricity - electric current glows to him, so he can see the wiring in the walls et cetera. But would he be able to see living organisms? I mean, I know nerves pass electric impulses but the thing is I don't know how much voltage is there (because the less the weaker the glow is). I also remember something about heart being regulated with electricity.

Also - is it possible to stop heart with electricity? Or (if not) to induce strokes? (EDIT: I meant heart attacks - my vocabulary sometimes misleads me) Because I have this scene in mind where he incapacitates opponents by stopping their hearts one by one and then, after dealing with the rest of the enemies, he restarts their hearts before they died.

Have you thought about what it is specifically that he can see?

Does he see electrical charge? Electrical current? Voltage? I think to narrow down what he can and cannot see, you'd have to start there. Seeing charge would enable him to see static electricity while current wouldn't. If he can see current, is the visibility a function of the magnitude of that current, or of something else like voltage?

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3 hours ago, jofwu said:

Have you thought about what it is specifically that he can see?

Does he see electrical charge? Electrical current? Voltage? I think to narrow down what he can and cannot see, you'd have to start there. Seeing charge would enable him to see static electricity while current wouldn't. If he can see current, is the visibility a function of the magnitude of that current, or of something else like voltage?

I'm actually working backwards - I thought he can see electricity and so he can see power lines, wiring in the walls and human organisms. Now I have to specify what it is what he sees.

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Okay, how possible would it be for four Earth-sized planets to share a common center of gravity, rotate around a Sun-sized star and still end up with one of them ending up facing the sun most of the time?

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8 hours ago, StrikerEZ said:

Okay, how possible would it be for four Earth-sized planets to share a common center of gravity, rotate around a Sun-sized star and still end up with one of them ending up facing the sun most of the time?

Very possible. As star = sun, there are infinitely many combinations ;) 

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