Trigonometry - sine waves between objects

In summary, the conversation discussed the possibility of using a trigonometric wave to represent the relationship between two different objects, similar to how a line or parabola can describe a relation between two variables. The concept of representing relationships as a sum of sine waves was also mentioned, as well as the use of Fourier transforms for non-periodic functions. The conversation then shifted to the idea of measuring morality and the dimensions between objects, with the suggestion of using topology and creating a morality scale based on multiple factors. Ultimately, the conversation touched on the complexities of quantifying morality and the potential limitations of using a one-dimensional scale to measure it.
  • #1
shawnr
20
0
Can you use any trigonometric wave to describe a phenomenon between two different objects? In the sense like a line or parabola would talk about a relation between two variable

thanks so much in advance
 
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  • #2
It is not clear what you mean.

... 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
thank you so much

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
I suppose you could define a mapping from how ever many dimensions you had onto the number line and then take the Fourier transform of the resulting function... however, you are probably better off with a multi-dimensional analog of the "sum of sines".
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
thank you, I'm trying to measure morals in an objective scale. so to literally measure why killing is bad and people aren't a one or two dimensional object so I was looking for things that had more dimensions and from self study I thought a sine wave would be a good substitute.

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
No such thing as an objective scale for morals... but that is a different discussion.
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.
 
  • #7
is there anyway that the sine wave could stay at a first dimension object and still have an extent into three dimensions?

topology, thank you so much, I'm going to school to start into maths again. I've 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
Note: a ruler draws a straight line on a 2D surface - like a flat bit of paper.
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.
 
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  • #9
thanks I've got a lot to go
 
  • #10
No worries.
 
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1. What is a sine wave in trigonometry?

A sine wave in trigonometry is a graph of a mathematical function that describes the relationship between two objects moving in a circular motion. It is a smooth, repeating curve that oscillates between positive and negative values.

2. How do sine waves help us understand the relationship between objects?

Sine waves help us understand the relationship between objects by showing us the pattern of their motion. The peaks and valleys of the sine wave correspond to the positions of the objects at different points in time, and the amplitude of the wave represents the distance between the objects.

3. What is the role of amplitude in sine waves?

Amplitude is the distance from the center of a sine wave to its peak or valley. In trigonometry, amplitude represents the maximum distance between two objects as they move in a circular motion. It is an important factor in understanding the relationship between the objects.

4. How do you calculate the period of a sine wave?

The period of a sine wave is the amount of time it takes for the wave to complete one full cycle. It can be calculated by dividing 2π (the circumference of a circle) by the frequency of the wave. The frequency is the number of cycles per unit of time.

5. What real-world applications use sine waves and trigonometry?

Sine waves and trigonometry have many real-world applications, including in music, sound waves, and electronics. They are also used in navigation and GPS systems to calculate the distance between objects and in engineering and physics to analyze and predict the motion of objects.

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