Mathematics based on science?

[noonespecial]

Mathematics Based on Science?

 

Abstract/intrduction:

 

It has been the practice of science to employ the use of mathematics to support and validate it's findings. Physics in particular uses mathematics to formulate and theorize new ideas. Much of our knowledge base of mathematics has come from the study of physics. Mathematics was the product of human thought and was not designed based on scientific experimentation. I conducted simple experiments to determine whether or not mathematics is truly inherent to our universe. Each experiment produces consistant results for every observer. What I found was that our universe may be following a different set of mathematical rules than we humans are used to.

 

Methods and materials:

 

The first experiment was designed to study physical addition and subtraction. The experiment involves designating two locations and observing what occurs when an object is moved from one location to another. Data was taken from both locations.

 

The second experiment involved physically dividing an object and recording every change that occurred within the properties of that object due to the physical division of that object. I only used divisions involving whole increments since the nature of the experiment was to determine fundamentals involved with the mathematics of physical division. I divided objects into halves, thirds, etc.

 

Results:

 

Addition and Subtraction:

 

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. This seems trivial at first but is essential in determining the rules for multiplication and division which will be discussed later in this paper.

 

A single axis can be used to describe the movement of an object. An axis contains positive numbers that represent additions and negative numbers that represent subtractions. The choice between the positive side of the axis and the negative side is determined by the location being observed. If you are observing the location the object left then the negative side of the axis is used. If you are observing the location the object is added to then the positive side of the axis is used.

 

The following table shows both addition and subtraction problems at the same time using two axes. Since only one operation can govern a mathematical table the operations are combined using addition. Subtraction functions are represented as negative numbers.

 

You will notice that even the numbers on the axes follow the rules for addition and subtraction including the origin. Zero is the origin of addition and subtraction because zero is the only number that can be added to or subtracted from itself and retain it's value. Addition problems can be combined. Subtraction problems can be combined. And addition can be combined with subtraction or vice versa.

 

Addition and Subtraction Table:

 

0....1....2....3....4*...5....6....7....8

-1...0....1....2....3*...4....5....6....7

-2..-1....0....1....2*...3....4....5....6

-3..-2...-1....0....1*...2....3....4....5

-4*.-3*.-2*..-1*..0*..1*...2*..3*..4*

-5..-4...-3...-2...-1*...0....1....2....3

-6..-5...-4...-3...-2*..-1....0....1....2

-7..-6...-5...-4...-3*..-2...-1....0....1

-8..-7...-6...-5...-4*..-3...-2...-1....0

* = number on an axis

 

Multiplication and Division:

 

When an object is divided, two properties of the object change. The number of objects increases and the size of what constitutes a single object decreases. If the object is divided down the middle then the one object becomes two objects each being half the size of the origin object. The increase in number of objects is not due to adding more objects; it is a function only described by multiplication. In the case of dividing an object down the middle we could describe the increase in the number of objects by writing 1 × 2 = 2. To describe the size of the two objects we can use division and write 1 ÷ 2 = 1/2. The results of experimentation for more divisions show the same results. Making two incrementally spaced divisions in an object creates three equal sized pieces. To describe the number of pieces we can write 1 × 3 = 3 (because our one object became three objects.) To describe the size of the three pieces we can write 1 ÷ 3 = 1/3.

 

A single axis can be used to describe the physical division of an object. The axis does not use positive and negative numbers like we are used to. Negative numbers are not used because at no point during experimentation are any negative quantities produced. Zero is also not included in these rules because experimentation involving the division of objects cannot produce a value of zero. The positive side of the axis is represented by incremental multiplication. The negative side of the axis is represented by incremental fractions (divisions.) A single axis can be used to describe the two properties that change when an object is divided. These properties are quantity and size. The quantity is described by the multiplication side of the axis. The size is described by the division side of the axis.

 

The experiment shows that when an object is divided the one object becomes multiple smaller objects. Multiplication and division happen at the same time. In order to multiply (create multiple units of) an object the object must be divided. When you divide an object you create multiple pieces. An apple pie can be divided into multiple slices.

 

The following table uses multiplication to combine the values for performing multiplication or division. As an example, the problem 4 ÷ 2 = 2 can also be written as 4 × 1/2 = 2. You will notice that every number on this table is a correct answer. Even the origin number and the numbers on the axes are correct. One is the origin of multiplication and division because it is the only number that can be multiplied by or divided by itself and retain it's value. There are no imaginary quantities or undefined operations.

 

Multiplication and Division Table:

 

5/5....5/4.....5/3...5/2....5/1*..10/1...15/1..20/1...25/1

4/5....4/4.....4/3...4/2....4/1*...8/1....12/1..16/1...20/1

3/5....3/4.....3/3...3/2....3/1*...6/1.....9/1...12/1...15/1

2/5....2/4.....2/3...2/2....2/1*...4/1.....6/1....8/1...10/1

1/5*..1/4*...1/3*..1/2*...1/1*...2/1*...3/1*..4/1*...5/1*

1/10..1/8....1/6....1/4....1/2*...2/2.....3/2....4/2....5/2

1/15..1/12..1/9....1/6....1/3*...2/3.....3/3....4/3....5/3

1/20..1/16..1/12..1/8....1/4*...2/4.....3/4....4/4....5/4

1/25..1/20..1/15..1/10..1/5*...2/5.....3/5....4/5....5/5

* = number on an axis

 

Discussion:

 

At present we are trying to accomplish science based on mathematics. In my opinion we might be better served using a mathematics based on science rather than mathematics based on human thought. This will require work to be done to understand the mathematical nature of our universe and may open new areas of inquiry for both the mathematician and the scientist. I am not a mathematician or a scientist. If you would like to further study this system to determine if it has any true value I encourage you to do so. It is beyond my ability to prove or disprove.

 

As far as I can tell, this system does not affect how equations operate. What it does is address the lack of negative quantities in our universe and the reason why division by zero cannot be defined. While negative numbers appear on sliding scales such as found on a thermometer, no actual physical negative quantities occur in the real world. Negative numbers on a thermometer are subtractions on a sliding scale where zero is not set at absolute zero. Zero Celsius is not a complete lack of heat.

[Strange]

Mathematics is not dependent on physics or even reality. I can add 1 to something without having to subtract 1 from anything else (unless I am doing double entry bookkeeping).

[EdEarl]

As Strange said, math isn't based on physics or any other part of science.

 

Math is a shorthand that replaces language descriptions of processes and things. I'll do a simple example below.

 

A car travels at 50 miles per hour for 2 hours; thus, it travels 100 miles.

50 m/h * 2 h = 100 m. The equation is valid for cars, motorcycles, ultra-light aircraft, etc.

 

If you can't write or say a problem in a language such as English, you probably can't write math for it either.

[noonespecial]

Hi strange. What you say is true. We use mathematics for many things other than science. My conjecture is that our universe follows mathematical rules (or at least mathematics can be used to describe elements of our universe.) What if the rules that our universe follows (or seems to follow) are different than the rules we follow for pure mathematics?

I'm not saying that a number is a physical construct that you can put in your pocket. What I wonder is if the laws of our universe aren't actually a set of mathematics that is different than the one we teach in school. You can't put "for every action there is an equal and opposite reaction" in your pocket any more than you can put the concept of a number in your pocket. But the universe does seem very mathematical. Also it seems to me that there are no negative quantities in the real world (the physical world, physical objects and forces.) And then there is the problem of division by zero. While you can explore negative numbers on paper, you can't actually show a single example of a physical negative quantity. So this math, if it is useful at all, would only apply to science where physical objects and forces were involved. It is not meant to do what pure mathematics does.

[Strange]

While you can explore negative numbers on paper, you can't actually show a single example of a physical negative quantity.

 

1. So what. Why should it matter.

2. The charge on an electron.

Edited March 28, 2016 by Strange

[Robittybob1]

Is it a type of conservation of objects?

[EdEarl]

There are many ways to misuse mathematics trying to model an observed process. Just because you get a wrong answer doesn't mean anything about the Universe or mathematics. You need to examine your math and whatever it is you are trying to model.

[noonespecial]

Strange, the charge on an electron has nothing to do with mathematics. What the charge indicates is a polarity. We could have just as easily defined polarity as right and left instead of positive and negative. The electron itself can be counted and does not qualify as being less than zero. The electron is physically here and has a positive mass.

 

Robbityrob, I'm not entirely sure. One of the laws of physics states that energy and matter cannot be destroyed. I highly suspect that an object cannot be divided down to nothing (zero.) I was unable to get one to.

[Strange]

Strange, the charge on an electron has nothing to do with mathematics.

 

Neither has anything else you have said.

[noonespecial]

EdEarl, I agree. I wish I had the ability to do that on more than just a fundamental level. That's why I posted it here. So that others could decide for themselves whether or not this system had any use for them.

In experimenting with the mathematics on a fundamental level (applied to physical objects) I have been unable to disprove it. Since I am not a physicist, I can't prove that it is a valid mathematical platform for physics or any other science.

What I do know is that I have never been able to travel at negative velocities. I realize that with pure mathematics you can mentally explore negative velocities. But if it turns out that there is a system of mathematics that forms the rules of our universe I have a difficult time seeing why it would include negative quantities. So I will stress again that this is not meant to be a replacement for our existing mathematics. It is a conjecture about the mathematical nature of our universe. It should be seen as an entirely different entity than pure mathematics and may explain why there is a difference in pure mathematics and applied mathematics. Pure and applied mathematics may need different rules sets. I honestly don't know.

[Mordred]

What's mathematically wrong with a negative value compared to a baseline value?

 

Take pressure for example. You can have negative pressure compared to a different pressure.

 

Same with velocity. If your describing a change in velocity or the resultant velocity you can easily describe the new velocity as negative compared to the original.

[EdEarl]

Mathematics Based on Science? NO

Thus, you need to start over.

[noonespecial]

Mordred, when you set zero at a baseline you are not dealing with absolute zero. Compare an absolute scale to a sliding scale. If you wanted to double the temperature in a given area would you use a sliding scale (such as Celsius) or an absolute scale (kelvin?) For determining the differences on a sliding scale all you are doing is using addition or subtraction to determine the value verses the established point of zero. When trying to double a value sliding scales don't work. If you wanted to double the temperature in a room that was currently at -5 Celsius, your mathematics would tell you that double would be -10 Celsius. If you want to get any use out of this mathematics you need to not treat it as though you were dealing with pure mathematics. Abstract concepts are fun to explore but I think our universe does not deal with abstract concepts. This mathematics needs to be approached from the direction of science, not mathematics.

[Mordred]

Absolute zero is an impossible value.

 

Your argument there is pointless and incorrect. You can set zero at any value you want as the baseline.

Edited March 28, 2016 by Mordred

[noonespecial]

Mordred, absolute zero is an impossible value for multiplication and division. Absolute zero is a starting point for addition and subtraction based scales such as distance or kelvin.

[Mordred]

The baseline in QM is zero point energy. Which isn't zero energy.

Like I said this is mathematics your comparing one value to another. Doesn't matter what scale you set or value you use as the origin.

 

It is value a compared to b

[noonespecial]

Mordred, now you are getting somewhere. I don't know about the baseline of quantum mechanics. So if you don't mind, I have a few questions. First, is the baseline used for addition and subtraction, or is multiplication and division used as well?

If the zero point energy is not absolute zero and multiplication or division is used what happens when the energy is equal to the zero point? If division is used, the results would give us a clear picture of the true answers involving the value of zero when used in division. It is currently unable to be defined as far as I am aware.

If multiplication and division is not used with baseline in quantum mechanics then you would use the rules for addition and subtraction.

[Mordred]

The baseline is essentially where ever choose to set. The multiplication/division doesn't change this.

 

Take for example the Celsius scale. We choose to set zero degrees at the temperature water freezes. Doesn't stop you from adding, subtracting, multiplying or deviding a degree.

[noonespecial]

Mordred, using a sliding scale does indeed make a difference. Let's look again at the example I gave you previously. If you have a sample that is currently -5 degrees Celsius and you wanted to double the temperature of that sample using the Celsius scale, multiplying -5 by 2 (doubling) gives you - 10 degrees Celsius. Not only did you not double the temperature of your sample, you actually reduced it.

 

The rules of addition and subtraction presented above work great with sliding scales like celsius. Setting zero at a point between the ends of your scale allows you add or subtract to determine a value relative to your designated zero. Trying to use multiplication or division on such a scale doesn't produce good science. I imagine this is why the kelvin scale was invented in the first place.

 

Also, you can have a "sliding scale" using the rules for multiplication and division. Instead of setting a value of zero (which does not appear in the rules of multiplication and division I have presented) you change the value of one.

 

Let's use an example everyone should be familiar with. Let's say we are currently using meters as our unit. We can "slide" the scale by changing the value of our unit (our designated value of the number: one) from being a meter to being a centimeter. Anything less than a centimeter on this scale is a division of our unit. Everything greater than our scale is a multiple. In this context, the multiple or division can be a fraction. So long as the fraction is less than one, it counts as a division (much like negative numbers equal subtractions on an addition and subtraction sliding scale.) If the fraction is greater than one, it counts as a multiple (like a positive number equals an addition on an addition and subtraction sliding scale.)

[Mordred]

Yes -5 * 2 is identical to -5 +-5. What of it. When you multiply a number you essentially adding that number by its multiple number of times. Why would you expect the number to increase?

 

Sounds to me like your using the sliding scale wrong.

Take your abacus or sliding scale

 

Count -5 units then count -5 units again. Answer -10 units.

Better yet use a sliding ruler as such

 

....-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10...

 

 

Add -5 slide left. Add +5 slide right. Done. Zero can be wherever you set it.

 

If for example I have a system in one state ie an average temperature, pressure or energy level I set zero to the average. Then shift the slide rule according to the deviation from that average.

 

Same works with coordinates. You have coordinates outside an object.

So you set zero as the center of the coordinates then describe the objects dimensions on either side of its center.

 

-x,x,-y,y-z,z.

 

This works particularly well with a circle. Mathematically you can describe a circle by its radius.

 

Makes having the coordinate 0,0,0 at the center extremely convenient.

 

Ever wonder why relativity is based upon coordinate change in particular Polar coordinates? (Sphere)

 

All interactions are described in a coordinate system. This is why differential geometry is a required field in physics.

Edited March 28, 2016 by Mordred

[noonespecial]

Mordred, the goal of the example I gave you was to double the temperature of the sample. You can't argue that decreasing the temperature is the same as doubling it. That's not scientifically sound. Reducing the heat present in a sample is not even remotely close to doubling the amount of heat in the sample.

 

As far as sliding scales go, it sounds like you have that down. Coordinate systems too. However, every sliding scale you use is based off of positive numbers and negative numbers. That scale exists in the mathematics I have presented here under the rules for addition and subtraction. That scale is still valid here.

 

The rules for the multiplication and division I have presented offer a new avenue for using sliding scales and coordinate systems: sliding scales and coordinates based off of the operations of multiplication and division. Whether these scales and coordinates have any use for physicists remains untested.

 

Pure mathematics defines multiplication as an easy and quick way to add up values that are the same. The rules I presented for this mathematics represent something else. Multiplication in this system is the inverse of physical division. You will notice in the example I gave in the first entry of this post, multiplication has nothing to do with addition since no additional objects were added. The one object became multiple objects when the object was physically divided. Addition doesn't describe that action at all. Multiplication describes it perfectly and so exists in this system as the physical inverse mathematical operation of physical division. Not the same as pure mathematics.

 

Once again I would say that this system of mathematics is not the same system as pure mathematics. Read the experiment again along with everything that has been posted so far.

 

I can't say whether this system ultimately has any merit. What I can say is that science is about testing things and doing experiments. Science is not about personal glory and is certainly not about my personal glory. I have presented here a puzzle. A puzzle needs people to solve it. Experiment for yourselves and if you have success present it here. Anything you do here is your own accomplishment. And whether or not this mathematics turns out successful or not, good science will still have been accomplished. Science is not always about finding some new discovery. Sometimes science is about eliminating possibilities.

 

Everyone is welcome to participate in this discussion if they want to. Even if it turns out that my conjecture is wrong the possibility exists that something useful could be learned. Discarding an idea before even trying to experiment is just not good science. Experiment with the math. Make discoveries if you can. Be proud of the efforts you apply toward science. And for goodness sakes, remember that this is not pure mathematics. The rules are presented here and they are not quite the same as pure mathematics. I can't stress that enough. This is not pure mathematics.

[Mordred]

If your trying to double the temperature why would you use incorrect Mathematics?

[noonespecial]

Mordred, the goal of the example I gave you was to double the temperature of the sample. You can't argue that decreasing the temperature is the same as doubling it. That's not scientifically sound. Reducing the heat present in a sample is not even remotely close to doubling the amount of heat in the sample.

 

As far as sliding scales go, it sounds like you have that down. Coordinate systems too. However, every sliding scale you use is based off of positive numbers and negative numbers. That scale exists in the mathematics I have presented here under the rules for addition and subtraction.

 

The rules for the multiplication and division I have presented offer a new avenue for using sliding scales and coordinate systems: sliding scales and coordinates based off of the operations of multiplication and division. Whether these scales and coordinates have any use for physicists remains untested.

 

Pure mathematics defines multiplication as an easy and quick way to add up values that are the same. The rules I presented for this mathematics represent something else. Multiplication in this system is the inverse of physical division. You will notice in the example I gave in the first entry of this post, multiplication has nothing to do with addition since no additional objects were added. The one object became multiple objects when the object was physically divided. Addition doesn't describe that action. Multiplication describes it perfectly.

 

Once again I would say that this system of mathematics is not the same system as pure mathematics. Read the experiment again along with everything that has been posted so far.

 

I can't say whether this system ultimately has any merit. What I can say is that science is about testing things and doing experiments. Science is not about personal glory and is certainly not about my personal glory. I have presented here a puzzle. A puzzle needs people to solve it. Experiment for yourselves and if you have success present it here. Anything you do here is your own accomplishment. And whether or not this mathematics turns out successful or not, good science will still have been accomplished. Science is not always about finding some new discovery. Sometimes science is about eliminating possibilities.

 

Everyone is welcome to participate in this discussion if they want to. Even if it turns out that my conjecture is wrong the possibility exists that something useful could be learned. Discarding an idea before even trying to experiment is just not good science. Experiment with the math. Make discoveries if you can. Be proud of the efforts you apply toward science. And for goodness sakes, remember that this is not pure mathematics.

[Mordred]

No your doubling the scale to the left hand side of zero. Your not doubling the temperature. Your doubling the units BELOW ZERO.

 

Get your math right.

When you multiply -5 * 2 your stating it is twice as COLD. Not hot.

Edited March 28, 2016 by Mordred

[noonespecial]

Mordred, You are still arguing pure mathematics. This is not pure mathematics. I like relativity although I don't know all that much about it. Not everyone agrees with relativity though. Relativity as far as I know has never been able to stand up as the one unarguably true theory amongst all the theories out there. If you like pure mathematics then use pure mathematics. If you like relativity then work to further relativity. If you can prove my conjecture wrong with physical proof then do so. Write the results of your experiment here but make sure you are using the mathematics I have presented here and not the rules for pure mathematics. This isn't a test to see if pure mathematics works or not. If you want to prove me wrong then show how the rules presented here actually fail in an experiment. Don't just keep arguing pure mathematics because this isn't about pure mathematics. This is about the mathematics presented here.