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thanks so much in advance

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- #1

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thanks so much in advance

- #2

Simon Bridge

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... it is possible to represent most relationships as a sum of sine waves.

ie. if ##y=f(x)## then we can write: ##f(x) = A_0+\sum_n A_n\sin (n x) + B_n\cos(n x)##

... this works very well for periodic functions. For non-periodic functions it works well for a range of values of x.

Some sums have to be infinite terms to be exact.

Does that answer your question?

Also look up: "Fourier transform".

- #3

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I guess I mean more instead two variables and the relationship between them being represented by a single sine wave. simply because a line is one dimensional and I was looking for something that has more dimensions. is this possible?

and thank you will look up and continue learning

- #4

Simon Bridge

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Such approaches exist: look up, for example, "spherical harmonics".

A simple example would be the vibrations on the surface of a drum - such functions can be represented as a sum of the 2D harmonics of the drum-skin.

- #5

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I don't know a field of study that focuses on the space between objects besides trigonometry, which only measures distance. are there more subjects, preferably mathematic, that study the dimensions between objects?

- #6

Simon Bridge

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Perhaps you mean to quantify morality? In which case you measure the badness of killing rather than why killing is bad in the first place (though why things are bad would be how you'd inform your choice for scale.) If you want to measure why killing is bad then you are measuring the validity of the reasons given for a moral judgement ... so "because mommy said so" may be less of a why than "because it may have consequences for the wellbeing for society as a whole".

My point here is that unless you can clearly state what you are measuring, you won't get anything meaningful.

But you are asking about maths:

A sine wave, itself, is a 1D object: notice how it has no depth or width? It's a curved line.

Though it is used to relate two variables so we think of it as a curve with an extent in 2 or more dimensions.

So ##z=A\cos(kx)## tells you how ##z## varies with ##x##.... same as any ##z=f(x)##.

You can have functions of two variables: i.e. z=f(x,y) ... and example may be ##z=A\cos k \sqrt{x^2+y^2}## which would be a radial sinusoidal surface - a 2D object which we represent in 3D. A sine wave in 3D would look like ##z=A\cos (k_x x + k_yy+k_zz)## which is a regular sine wave but oriented in an arbitrary direction.

The sine wave is continuous ... so there are no spaces between adjacent points on the curve.

Building a continuous curve from a set of discrete points is called "interpolation".

The study that includes the "dimensionality" of mathematical spaces, and how different parts of that space relate to each other, is called "topology".

Al this is probably overkill for your purposes.

It sounds more like what you want is a morality scale that works along a line like a thermometer does - so you can say one thing described by a host of factors is more or less moral than another thing.

It is likely that morality does not work like that ... but that never stops anyone from coming up with such scales.

You will have N dimensions of measures that contribute to the morality value of an act ... like how many kittens are killed by the act, how many starving are fed, homeless housed ... etc. You want to "map" those values onto a single 1D number line ... so you write ##z=f(x_1,x_2,\cdots, x_N)## ... where the details of ##f## are the particular "mapping" that describes how the different factors you measured contribute to the overall morality.

i.e. for the example - we may naively think: ##f(x_1,x_2,x_3)=x_3+x_2-x_1## for the above examples where ##x_1## is the number of kittens killed, and the other two are starving fed and homeless housed respectively. Or you may say ##z = x_3x_2/x_1## ... how you do the function related to how you think morlality works.

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topology, thank you so much, I'm going to school to start into maths again. ive been living on the streets off and on for the past few years trying to get my act together. just came up with some theories and I wanted to know what to study

for morality I wrote a translation chart from making subjective to objective by attaching an objective base, as you did, by saying murder is bad because of the retardation of emotional quotient by chemicals in your head, the loss of productivity tied to that etc etc

I worked out there are 3 dimensions to space separating us with one of them being depth, the other talking about broad vs specific (history vs geography) and the other direction. I'm having trouble trying to quantify the effect of it but I came up with any variable times zero is always going to be zero. so the more money or morality you have the more complex ways there are to get it and relate with it. intelligence works the same way I guess

I should also say I'm using john deweys definition of morality as in its pragmatic

- #8

Simon Bridge

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The line itself is 1D ... treating the paper's edges as axes, then the line has an extent in the resulting 2D space

But the paper could be on a sloping desk ... using "up" as one direction, and the floor as the other two, then the line now has extent in 3D.

You can extend this to any number of dimensions: it's just the orientation of the line.

- #9

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thanks ive got a lot to go

- #10

Simon Bridge

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No worries.

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