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Mathematics based on science?


noonespecial

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If you plug your battery charger into the mains and it charges your battery, by drawing electrical power from the mains that is positive power.

 

If, on the other hand the result is that the charger drains your battery into the mains that is negative power.

 

In any ac cycle in any real world circuit both of these events happen to some extent; the engineering trick is to make the positive exceed the negative..

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Studiot, so how does absolute zero power occur? Does absolute zero power mean that there is no power or does it mean that the alternating currents are exactly equal (positive and negative at equal strength causing no flow?)

 

Also, don't be discouraged if this first example does not do the trick. Science is about trial and error and very demanding in the proof department. Even if this example agrees with the conjecture and can be considered as evidence it would not suffice to show total proof. No single example can show total proof. A large number of examples that can supply evidence can only be seen as support of the conjecture. And all it will take to ultimately defeat the conjecture is one example of failure. I am open to as many examples as you care to give.

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I am not discouraged, just weighing up if this discussion is worth the effort.

 

I also said that power was the result of multiplication of two (usually sine) waves ie their product.

 

Instantaneous Power = Instantaneous voltage times Instantaneous current.

 

This cannot be achieved by addition.

 

Since we have moved on to addition, here are some thoughts.

 

Conventionally we discuss addition in terms of numbers.

This leads to one of the conceptual difficulties to be avoided in mathematical philosophy.

 

To avoid the circular argument of defining numbers in terms of addition and addition in terms of numbers.

 

You have avoided this but fallen into another bear trap set this time by nature and physics.

 

 

When an object is moved from one location to another two areas are presented for mathematics to be observed; the location where the object originally was and the location where the object ended up. The experiment shows that addition and subtraction are linked and one cannot be performed without also performing the other. In order to add an object to a location that object must be subtracted from another location. In order for an object to be subtracted from a location that object must be added to another location.

 

You are not likely to have come across this but it is possible to add something in one place without subtracting it somewhere else.

In solid state physics we discuss conduction by electrons and 'holes'.

The particles display some interesting properties, not the least being that they sometimes behave as if they possesed negative mass (this is part of what we call the Hall effect)

 

https://www.google.co.uk/search?hl=en-GB&source=hp&biw=&bih=&q=negative+mass+in+the+hall+effect&gbv=2&oq=negative+mass+in+the+hall+effect&gs_l=heirloom-hp.3...1267.19966.0.21414.32.22.0.10.2.0.180.2293.7j15.22.0....0...1ac.1.34.heirloom-hp..9.23.2275.DJnhu7xVxSk

 

To add a hole to a solid we subtract an electron (not a hole)

 

To add an electron we subtract a hole.

 

Edit

 

 

Studiot, so how does absolute zero power occur? Does absolute zero power mean that there is no power or does it mean that the alternating currents are exactly equal (positive and negative at equal strength causing no flow?)

 

I will draw some diagrams and try to explain qualitatively.

 

We often do this, use a qualitative model to attain understanding and then move on to a quantitave model (and mathematics) to obtain numbers, since we need numbers in the real (engineering) world.

Edited by studiot
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Studios, I have read many articles stating that negative mass has never been found. Some of the comments were posted just this year. Can you (or anybody else) post a link to information confirming that negative mass exists? The only thing I could find was that researchers from the Max Born Institute in Berlin had demonstrated that negative mass exists but the information was written in 2010. There are many people who still disagree as recent as February of this year. Please don't take this as an attack but I need to know if this is real or purely theoretical. If I happen to find a page that has information that confirms that negative mass has been observed I will post a link if nobody has beat me to it.

 

Electron holes are also said to be purely theoretical. I will still address this one, purely theoretical or not. Electron holes are said to occur when an electron leaves a valence. The hole is not a physical object. In this case the electron leaves it's position (subtraction) to go elsewhere (addition.) This leaves a hole where the electron was.

 

Scooping a shovel full of dirt out of the ground (subtraction) and dumping the dirt on the ground (addition) leaves a hole in the ground.

 

In order for an object to occupy a given location there must be room for the object to occupy that location. When you subtract an object (which must be added to another location that has room for it to move to) from it's location, it returns the area to it's origin state which is then free for another object to occupy it. The origin of addition and subtraction is zero (or empty if you prefer.) Physical addition and subtraction describes relocation of energy or matter in space. If there is enough space to accommodate an object, it can be added there. When an object is subtracted from a location it leaves a space open where another object can be added if it fits in the space.

 

Multiplication and division works in a similar way. The origin of multiplication and division is one (a single unit or group designated as the unit.) Let's use a picture as our starting point (origin.) We can divide the picture into multiple divisions and make a jigsaw puzzle out of it. The number of pieces (multiplication) our puzzle has is inversely proportionate to the average size (division) of the pieces. So if we divide the picture into 100 (multiplication) pieces, the average size of each piece will be equal to 1/100 (division) of the size of the whole picture. We can then work the puzzle to return the picture to it's state of origin (one picture.) In some cases the origin object will remain fractured, as in our jigsaw puzzle example (100/100 = 1.) Physical multiplication and division involves altering inverse properties of energy or matter.

 

I know this isn't what you expected to read but it really isn't difficult to understand once you accept the fact that this conjecture is not about pure mathematics. The mathematics of the conjecture were determined by observing physical addition, subtraction, multiplication, and division as they occur in nature. Pure mathematics was not. The two systems are different.

 

Do I believe that negative numbers exist? Most certainly. I have seen them. I even use negative numbers to describe physical subtraction. What i haven't seen is negative quantities. I can place an apple on my table (0+1=1.) I can have zero apples on my table (0+0=0.) Pure mathematics says that zero minus one equals negative one. If I have zero apples on my table I cannot remove an apple from the table and leave a negative apple in it's place.

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I know this isn't what you expected to read

 

Once again you seem to know it all despite the evidence to the contrary.

 

Why did you ask for a link to negative mass?

 

I posted a page full of them, did you not read it?

 

 

Do I believe that negative numbers exist?

 

You should always be aware that the mathematical statement 'There exists' means something different from the same statement in the physical world.

 

The mathematical statement means "Is compatible with the given definitions, axioms and derived theorems"

The physical statement has been the subject of philosophical debate for millenia.

Neither are really suitable (as should be the rest of Science) for a belief system.

Edited by studiot
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Studiot, if you have evidence that shows that an object can be added to a given location in space without subtracting that object from another location then you have broken the laws of physics. Matter can't be created or destroyed. If you can show evidence that you can remove an object from a location without leaving empty space where the object was located then you have done something extremely grand indeed. You may even have found a physical example of multiplication as it is presented in pure mathematics if instead of a hole you have another object of the same type.

 

I have read many articles stating that negative mass has never been found. Some of the comments were posted just this year. Can you (or anybody else) post a link to information confirming that negative mass exists? The only thing I could find was that researchers from the Max Born Institute in Berlin had demonstrated that negative mass exists but the information was written in 2010. There are many people who still disagree as recent as February of this year. Please don't take this as an attack but I need to know if this is real or purely theoretical.

Because there are a lot of people who say that negative mass has not yet been proven.

 

You should always be aware that the mathematical statement 'There exists' means something different from the same statement in the physical world.

 

The mathematical statement means "Is compatible with the given definitions, axioms and derived theorems"

The physical statement has been the subject of philosophical debate for millenia.

Neither are really suitable (as should be the rest of Science) for a belief system.

Hence my conjecture and the reason why I have been asking people not to confuse it with pure mathematics. The mathematics presented here (which is not pure mathematics) uses observable occurrences found through experimentation in the real world to formulate a system of mathematics that expresses the observed results.

 

The experiment is to find the fundamental rules to the mathematics that our universe follows. The conjecture based on my findings suggests that it does. The resultant mathematics follow a different rule set than the set of rules that pure mathematics follows.

 

The conjecture assumes that our universe does indeed follow the system of mathematics presented. It needs to be tested to see if it can be of any use. Since the system is based on very real occurrences it must be tested to see if the physical world expresses the rules as well. Please, if you are willing, study what I have written to you as well as the opening post. If you can think of a physical occurrence where these rules are followed or not followed directly, let me know. Concepts that are only theoretical and have not been observed cannot be considered as there is no way to test their validity.

 

Examples that describe the physical world directly are what I am looking for. Finding averages, for example, is not a physical event. There must be an action and a reaction. For every action there is an equal and opposite reaction. This math describes (as a conjecture) the laws of the universe.

Studios, I found a page with some electrical math that sounds like what you were describing.

 

http://www.allaboutcircuits.com/textbook/alternating-current/chpt-3/ac-inductor-circuits/

 

I will write an analysis of my thoughts on it after I study it.

Edited by noonespecial
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Studiot, if you have evidence that shows that an object can be added to a given location in space without subtracting that object from another location then you have broken the laws of physics. Matter can't be created or destroyed. If you can show evidence that you can remove an object from a location without leaving empty space where the object was located then you have done something extremely grand indeed. You may even have found a physical example of multiplication as it is presented in pure mathematics if instead of a hole you have another object of the same type.

 

Once again you are preaching at me, instead of responding to what I actually said.

 

Let us lay this multiplication ogre once and for all.

 

Your explanation / definition of multiplication is a version of replication.

 

This totally fails to include other aspects of multiplication, not accessible from addition, that have physical reality in the real world.

 

The very simplest example is

 

Multiply 6 x 5 and get 30 or 6 + 6 + 6 + 6 + 6

This is certainly true if I had 5 packets of half a dozen apples I would have 30 apples.

This is an example of replication in the real world.

 

But if, instead of apples, I told you that these were the measurements of my front lawn in metres I would not have 30 of the objects I started out with.

 

I would have one new object - 30 square metres, of lawn.

 

Neither the 6 metres nor the 5 metres by themselves refer to lawn as a line (of lawn) with no width is not a physical reality.

 

This business of area has important implications for electrical circuit theory as well.

 

BTW I agree that physics and maths often diverge and I have given many examples myself.

But until we have a two way conversation going, we will be unable to discuss this.

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Studiot, I'm sorry I preached at you. I got frustrated. This is difficult for me. I appreciate you sticking around.

 

It might be best if you explored the system for yourself a while. The system can be used to make predictions and answer hypothetical questions the same way pure mathematics can. Not every problem will have an equal inverse relationship to something else. It's just that the ones that do will have the best chance of supporting the conjecture. I think i got hung up on that. I appologize for that too.

 

And it is possible to use positive and negative numbers as conventions in doing your math. The main rules set only uses them to denote additions and subtractions but after looking into the sine waves as you suggested I can see why they are useful. I don't see them as positive and negative though. I see them as directional. Take some time with the math then get back to me if you are still interested. My guess is that you will find things I didn't.

 

Don't forget that the conjecture offers a second coordinate system. I don't believe these are spatial coordinates. They may have other uses.

 

If you have questions feel free to ask. I will try to be less excitable when answering.

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Again I still have no idea why you have a problem with a negative number compared to a baseline value.

 

If my direction is to the right, a negative direction compared to the original (right). Is mathematically correct.

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I never found anything in this world that would actually represent a negative quantity.

Okay, so you have realised that negative numbers are not cardinal numbers: they can not describe the number of elements in a set. This does not mean that negative numbers are not important in physics. For example, just think of Cartesian coordinate systems in mechanics. Or the notion of deceleration. And so on.

 

 

I also never found a single example of physical multiplication.

I am not sure what you mean by an example, but we multiply quantities in all our descriptions of nature. Just look at simple examples in mechanics.

 

 

To me, if mathematics was indeed one of the physical pillars of the laws of nature then it wouldn't have components that aren't physically observable.

There are lots of things that in our physical models that are not directly observable. So your thoughts are not reflecting reality here. A very simple example could be complex numbers. We need complex numbers in quantum mechanics yet we can never measure something to have a complex value.

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Noonespecial,

 

Please note, I am not saying everything you say is wrong.

Far from it.

But I am saying it is only part of the whole story, as with my example of area or ajb's ones from mechanics.

 

 

 

But you are practising what mathematicians (and other scientists) often do.

Limiting the scope of your domain of discussion to achieve internal self consistency.

 

This is fine so long as you acknowledge these limits and do not try to apply the results outside their scope.

 

Much misunderstanding arises from failure to do this.

 

Now we have (hopefully) agreed that multiplication can lead to new things outside the scope of your definitions, let us revisit addition.

 

What is 10 plus 7?

 

but

 

It is 10 o'clock.

 

What is the time if I add 7 hours?

 

The recipe for a cake reads

"Add two eggs to the dry ingredients."

 

What do I have if I add two spoonsfull of sugar to my cup of tea?

 

What do I have if I add oil to water?

 

Chemical safety instructions read

"Always add acid to water, never water to acid"

 

One of the properties of addition to explore in the above is

 

What happens if I switch the quantities being added

 

That is is (a + b) the same as (b + a)

 

We often want this in mathematics and often phrase our rules to force this.

 

But you can see that in the real world this is not always the case.

 

Now interestingly consider the same question for subtraction

 

 

That is is (a - b) the same as (b - a)

 

If you really want discussion, not a platform, the above are some points of discussion about your material for you to respond to.

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