I know math states that a number line is one dimension but I never understood how it exists outside the math concept.
In: Biology
> I know math states that a number line is one dimension but I never understood how it exists outside the math concept.
Simplest explanation is that no math concept exists. They’re all just something we imagine. It makes no more sense to ask if 3d space exists than to ask if Moby Dick or Voldemort exists. We can reason about these things, we can ask things like, “what color is Moby Dick”, and these questions may have answers, but that doesn’t mean there ever was or will be a Moby Dick.
When applying math to reality, you would try to ensure that the defining math characteristics of math thing are there in reality. Which is partially why math starts out often by just listing the defining features, and then using only those features and nothing else. So if you notice that in reality, something complies with those defining characteristics, well, you know that theorems in math land apply to this thing as well.
Say, if you are able to ignore width of a string, well, there you go, it’s one-dimensional. Time seems to be one-dimensional. Temperature is one-dimensional measure.
Think of one dimension as a position. When you’re in a car and you have GPS navigation system it doesn’t tell you the volume of space that the car is taking up, it gives you a point around which the car exists. One dimension is that point. Two dimensions are the direction that point is travelling and three dimensions are the volume of space that the car that point represents is taking up.
It’s not. The idea is that a perfect line doesn’t actually have any width, but as the width approaches infinity, it approaches only one dimension.
Sorry if that sounds stupid I just don’t know how else to explain it.
There is no such thing as a one dimensional object in “reality”. It is a mathematical abstraction. The simplest analogy of a one dimensional mathematical object is the number line. This is a way to visualize an abstract idea or concept.
In reality, there is nothing in the universe that is one dimensional. We live in a universe that has 3 spatial dimensions and 1 time dimension and, as far as we know, everything exists within this framework. This is physics not mathematics.
Physicists use mathematics to describe reality but that does not work in reverse. It isn’t usually possible to actualize abstract math ideas with “real” physical objects. For example, a perfect circle exists as mathematical idea but a perfect circle cannot be realized in the universe.
> but I never understood how it exists outside the math concept.
It doesn’t. Nothing in math exist outside math. Just like numbers, there is no “five” in real life. You have have five fingers, or five apple, but you cannot have only “five”. It only exist in math.
It’s not meant to be a representation of an entire thing in real life. Just remember what a spatial dimension is– a measurement of the distance between two points. Yes a ruler is a 3-dimensional object, but you care most about the length.
The concepts you learn in geometry are simplified from reality so you can understand them better. If the teacher were to preface with something like “Well, nothing is actually this perfect, there’s no such thing as a 1-dimensional object, or completely straight infinite lines,” etc. then it would just be a waste of time. What’s important is knowing when to apply such little tidbits to solve real-life problems.
Lots things around us are one dimensional and it doesn’t both us, time, brightness, volume, speed, weight, just because space is 3d does not mean the concept of 1d is hard to understand. Yes the concept of a 1d object is very abstract at it limits, but a line or a string are “close” enough.
Without getting into the deeper existential questions about math as a model of reality, I think the simplest answer is that literally anything you measure with a single number exists in one dimension. For example:
Your age.
The time of day.
The temperature of your stove.
To say these things have one dimension is to say that any change can either increase, decrease, or stay the same. Your age cannot change in some sense that you would use the same number to describe it.
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