bgold024

@Strange You are both correct in a non integer solution as b +× b/(b-1) and the only integer solution being 2 and 0, but you can absolutely do this for every number (prime, transcendental, real, imaginary.... Anything.)  There isn't a restriction on the set of numbers you can use, and I suppose you could call this a special case.

Your second solution is a little closer, but there's an equality very similar to a famous equation as the solution.

I guess another way to put it, take a number, x, and split it into two parts such that both parts can sum and produce x.

Pretty sure it's not known, I haven't seen anything like it.  Probably thinking it's kinda useless, but might be a cool design technique for layouts.

4 hours ago, J.C.MacSwell said:

I think it would be helpful if you looked closely at the terms you are using, as they are applied in physics.

Thanks for the reply and the link with some basic definitions, will read that one before bed 😁  could you also maybe point out some of the terminology that I'm using incorrectly?

4 hours ago, Strange said:

Well, "energy" is the generic term for all types of energy. But it is often useful to distinguish different forms of energy: kinetic energy, potential energy, heat energy, etc.

Thanks for the replies, I suppose I am using the word energy a little bit loosely.  Any good reads on the different states of energy or how energy is converted from one form to another?

3 hours ago, studiot said:

There is a form of energy called free energy (in fact there are two types Gibbs free energy and Helmholtz free energy)

Very interesting, thank you.  Will have to read that and more about the work-energy theorem tomorrow.  Seems a little more in depth for a night read lol.

I was just wondering if it is already known which two numbers can both add AND multiply to equal an arbitrary number?

For example, if I choose any number, x, can you tell me what two numbers can both add AND multiply to equal x?

A very easy x would be 4.

2+2=4

2×2=4

In that case, a and b are the same number, 2, but what if I told you that x has to be included.  Can you satisfy the following equality:

4+4=4

AND

4×4=4

Obviously those are not true, but what transform could you do to the left hand sides, without changing the right hand sides.  Simply put, how could you make 4+4 turn into 2+2 and 4×4 turn into 2×2, using the number 4 twice with the same operations, and make them both equal to 4.

(Even harder)

What if x was √2, or π, or i, or anything?  How do you make:

√2+√2=√2 AND √2×√2=√2

Is it already known which two numbers can both sum AND produce any given x?

I found a very cool equality, where using the arbitrary x yeilds both numbers which satisfy the above and was wondering if anyone else found it and if it means anything?

One last way I guess I can say it is, what transformation will make x^2/2x=1?

(keep in mind both x^2 and 2x will become the transform used to make a+b=a×b, where a and b are relatively the same)

The solution is very similar to another famous formula, and also has an interesting, but expected result.  Honestly the solve for this is quite trivial, but it just works out so nicely

2 hours ago, swansont said:

No, for a trivial reason: the transfer of energy doesn't have to be work. There is an entire field of physics (thermodynamics) because of this.

Plus you can often define systems such that no work is being done.

I suppose I meant that energy is basically recycled, or transferred, into other forms of energy.  In another paragraph I was also saying that all the energy we have is what we have always had from the beginning.  No creating energy.

Kinda confused on that though, are you implying energy can be transferred without work?

Also what types of systems could you define where no work is being done without the system being at rest?  (Which wouldn't you need work to put it back into motion?)

2 hours ago, swansont said:

You can't have free energy because it can't be created, whether or not work is being done.

I would definitely say that's trivial lmao 🤦🏼‍♂️  Didn't realize that answers itself, but again it was more about the transfer of energy (which I would have to believe is itself considered work) being a cycle of all the energy we know.  Again can't create nor destroy.

2 hours ago, swansont said:

Yes. As I implied earlier, thermodynamics adds a bunch of different energy items to be accounted for that are not present in mechanics.

If you agree heat energy is transferred into other forms of energy, would you also agree there is really only one energy, that being all the energy we know in all it's forms?

If yes, wouldn't it be easy to say there's not a lack of energy, but merely the lack of knowledge converting it into useable forms?

Also thanks for your reply 😁 any citations or references for reading material is also welcomed... I know I was mostly speculative and theoretical, but would be nice to have a little direction for better understanding.

So I was wondering, and hoping maybe someone smarter than I could help me understand the specifics, the following:

(and please correct me at any point if I'm wrong)

The Law of Conservation of Energy implies that energy can't be created nor destroyed, and the energy taken out of a system can't exceed the work being put in.  Thus, there must be work performed, you can't have a perpetual motion machine.

Wouldn't this also imply that energy can't be created nor destroyed simply by the fact that there is always work being performed  due to the transfer of energy?

I only ask that because wouldn't that mean you can never truly have a "free" energy source?  I guess to avoid philosophical argument of the word "free," I mean in the sense of energy from nothing.  There must be work, right?

Also to add to that, the total energy in a system is the work performed minus the loss of heat, what happens to that heat energy lost?  Does it get transferred into other forms of energy somewhere along the way?

I ask that because to solidify my first argument, energy transfer must be happening all the time and any energy taken from a system (or put in, or lost, I guess you could say) was energy that was already there?  maybe from the Big Bang?

As a side note, I'm curious of these things because it seems to me like there is energy everywhere, everybody and everything was made from work performed in space, and there really should be no issue of energy dependance... The real issue should be energy conversion right?

I know I asked alot but hopefully some knowledgeable minds can help me understand some of the points better.  The main outcome I'd like to see is to discuss if there are methods of physics to harvest energy from work already performed by other things, mainly celestial objects.

One idea I've pondered is to harvest free electrons from ionized particles in the atmosphere.  Not really sure how exactly one could do that, again just the idea of physics, but the basis behind the idea is this:

Ionized particles have extra electrons, which I'm assuming might be relatively easy to break free (that's kinda how they got there in the first place), and with the help of the sun there should be no problem freeing electrons, right?  Isn't that how a solar panel works?  Photons break off free electrons in atoms, although that seems a more brute force method.

Last thought, could this reaction be the cause of lightning storms?  It is believed that lightning comes from friction, but gases try to escape each other... Wouldn't it be more plausible to believe that water vapor (clouds) collect free electrons broke loose by the sun from ionized particles in the atmosphere?

If it were friction, wouldn't lightning happen everytime a cloud rubbed?  lol.  Does it make more sense to believe enough electrons are stored up there that eventually they become so great and discharge?

Plenty of material there, let me know your thoughts on any of them or any thoughts of your own related to the title.  Please try to be kind as I'm only a beginning practitioner in the art of sciences  =p