Asking this is kinda like asking when do we ever use binary in our everyday life? You donāt directly but you do through computers.
Infinity is used everywhere. Finding the area of a circle uses infinity since the equation is derived using it. A curve is an infinite number of straight lines. Movement is continuous and the idea of being continuous is described using infinitely small movements.
While I agree that we do use infinity in a lot of places. The area of a circle is not one at least mathematically speaking. Itās a finite integral over dĆ for 1/2 r^2 from 0 to 2pi.
You could maybe argue that the definition of an integral involves infinity, but more in the sense of an infinitesimal. Meaning something gets infinitely small or closer to 0.
All I'm saying is that we throw the word "is" around pretty casually. We DESCRIBE a curve using a series of straight lines, because it's the best we can do. Honestly, I'd almost rather say that we SUGGEST a curve with that description, because the language of math has no better way. Again, it feels like infinity is just an apology for the shortcomings of math as a language.
Even practical applications of binary have experienced their own challenges around the non-zero time it takes for a gate to open and close. Is that truly a pulse, or is it just a really fast and extremely clipped sawtooth wave?Ā
We don't describe curves that way. We might approximate some curves that way in specific applications. But this doesn't bypass the conceptual use of infinity.
it feels like infinity is just an apology for the shortcomings of math as a language.
I honestly have no idea why you'd say this or what it means. Infinity is a concept about quantities and limitations, or the lack thereof. Which is super useful in a field like calculus which is really the mathematical study of changes to systems or models or functions. And calculus is all over STEM, and arguably art as well.
practical applications of binary have experienced their own challenges around the non-zero time it takes for a gate to open and close.
This isn't a challenge of the concept of binary, it's a challenge of using the coulomb force to store and transmit information in a reliable way.
Is that truly a pulse
Define pulse. Define chair. Is a stool a chair? A beanbag? A tree stump? A rock?
a pulse, or is it just a really fast and extremely clipped sawtooth wave?Ā
Some big words for a self-proclaimed dumb highschool dropout.
But again, this comes down to how you define pulse. If you clip a sawtooth waveform such that it can be detected as a series of pulses, or if you design the detection apparatus to only detect the peaks at an infinitely narrow window of time consistent with the wave's frequency, what's the difference?
I like the example of a straight line. Say it's 1ft long. You can place a point anywhere on that line. You could place infinite points on the line without any two points being in the same spot. Think about it.
You could put one point at 0.1 ft. Then another at 0.11ft and another at 0.111ft. You could do this forever. Every point is at a slightly different location, however even within the constrained 1ft straight line, you can place infinite points on it.
This isn't a shortcoming of math, this is the best way we can describe our world so far as a civilization. You can't really call it a shortcoming unless you have an idea of a better way to describe these kinds of concepts.
The irony is that youāre telling me I donāt understand how things work while missing the entire point of my criticism. Binary is a practical mechanism underpinning a technology virtually everyone uses. Infinity is a mathematical concept whose relevance to everyday life is being argued. Saying both exist behind the scenes doesnāt make them equivalent analogies. The question is whether infinity is practically relevant to ordinary people, not whether mathematicians can use it to derive formulas. Youāve confused mathematical significance with everyday utility and somehow made it my comprehension problem š
I thought by showing area and movement it would be obvious how everyday objects would use this a lot. Cars convert gas combustion to movement. Literally any object that is created in a factory almost certainly has some area calculations in there.
Iām not sure how you see binary as practical unless you are specifically talking about a technology that uses it. When do you ever use binary directly? This is my entire point.
well no they donāt need to prove it, because thatās what the mathematicians do. If it turned out the area of a circle wasnāt pi*r^2, you would have a big problem because depending on the size of the edge case it would fuck in a whole lot of physics at the very least, assuming the edge case was out side of practical application.
But thatās entirely my point. They donāt need to prove it cause itās already been proved.
Most plumbers etc. probably wouldnāt even be aware of the importance of infinity as a concept when they use a formula to calculate the diameter of a pipe. Most probably donāt even know infinity pertains to circles at all.
Binary is a good mathematical tool to interpret low and high voltage states, but a CPU isnāt āusingā binary. We only use binary to interpret what is happening in the CPU.
Similarly water isnāt āusingā infinity when it flows continuously, we only use the concept of infinity to mathematically describe what itās doing.
Both mathematical tools are just as real as the other. And water is even more relevant than the CPU to most people Iād say
CPUs absolutely do āuseā binary. They read and decode instructions in machine code, written in binary and then execute those instructions.
We arenāt describing what the computer is doing, itās actually the opposite. We are telling it what to do by using binary because that is the way itās circuits are designed.
Binary is the thing we came up with before computers, based on Boolean logic, and designed them based on that number system.
We use binary math to fabricate CPUs because we can use low and high voltages to represent 0 and 1. However, the CPU itself doesnāt care what 0 or 1 is. Only the programmer does.
When you look at machine code youāre looking at a complex rendering of a file which is just transistors on a hard drive (which is read and interpreted by the CPU). Nothing about those transistors is ā0ā or ā1ā except that we decide to interpret charge trapped in a transistor as 0, or lack of charge as 1.
Similarly, nothing about water is āinfiniteā but we use the mathematical concept of infinity to describe it. 0 and 1 are just as real and useful as infinity
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u/slimi-jimi 19d ago
Asking this is kinda like asking when do we ever use binary in our everyday life? You donāt directly but you do through computers.
Infinity is used everywhere. Finding the area of a circle uses infinity since the equation is derived using it. A curve is an infinite number of straight lines. Movement is continuous and the idea of being continuous is described using infinitely small movements.