Math, or at least this part of it, is all about relationships between values. Let’s ignore numbers for a bit. If you take a long stick and put a big rock under it, then when you move your side of the stick down, the other side will move up. And if you were to measure how much you moved your side versus how much the other side moved, you’d notice that unless you put the rock right in the dead middle, the other side would move a different amount. This isn’t because something is magically making this happen, it just a property of the construction of your system. The other side just does move more or less, and it’s different depending on where the pivot point is.
Similarly, if you have two gear wheels with different numbers of teeth, and you mesh them together, and you turn one and count how many times you’ve turned it, and also count how far the other one has turned, you’ll find a relationship there too! And again, this relationship is just built into the way these objects interact. It’s just the way this system works.
Okay, so, stay with me now, saying y = 2x + 5 is the same. It’s defining a relationship, it’s building a system that’s says the value we’re calling “y”, chosen arbitrarily it could be any name, is always twice as big as “x” (also chosen arbitrarily), and then 5 more than that. It’s a system we’ve built, just like the levers or gears, that produces a relationship we want to express for some reason. And you can put them together in any way, and they’ll always describe some relationship, even if it’s not a useful one.
Now, people have spent hundreds of years, depending on how you want to count, trying to find relationships that also happen to have predictive power. They’ve built systems where the relationship between “d” and “t” is modeled to be the same as the relationship between “the distance that rock flew from me” and “the time since I threw that rock”. And what’s nice about finding these relationships is that now that you know what the relationship is, now that you’ve built the system of levers and pulleys and gears that turn in just the right way, you can start guessing about the rocks before you even throw them, because this relationship you’ve got on the page is similar to the one you’ve seen in real life with the rock and the stopwatch.
Once you’ve got a bunch of these, picking the right one and combining them because more like a puzzle or a maze. I’ve got these things I know, like the weight of the rock, and the size of the Earth, and how stiff the metal in the spring I’m using to launch this thing is. And I’m trying to figure out its top speed. And I’ve got a bag of relationships I know are battle-tested. So all I have to do now is start finding relationships that depend on stuff I know to get me stuff I don’t know. And if I can link them together like a Rube Goldberg machine, I can figure out something I didn’t know using this one relationship, which is handy because this other relationship I’d quite like to use needed that thing I didn’t know before but do now.
And so I can work through a chain of relating things to things until I can get to the point where I have enough to use one of the relationships I do know that predicts speed. And once I’ve got that, I’m done! I trust the relationships I’ve used, presumably I used them properly and didn’t make any dumb mistakes, and so I followed a chain of things I knew, through tools that used those things, to tools that used the things the other tools produced, until I found a path to my goal.
The only thing stopping you from there is the complexity of the relationship, the accuracy of the relationship to the real situation, and how accurately you can measure the things you know.
I haven’t it described as relationships before. I can get behind that thought process. Thank you so much for your comment! I have to read it a agian to get it lodged into the grey matter.
Do you think physics is worth studying if numbers themselves are beyond someone? I get it’s abstraction. Agian, thank you.
Physics is a way to generally describe the relationship between things, mathematics is to predict specifically how would those relationships affect the things involved.
You can learn the general theory but application needs mathematics.
One way to do it would be instead of learning numbers use numbers as names of the objects. And other characteristics as adjectives to describe them.
It’s okay not to understand everything about Math. I used to be a big enthusiast, even went to engineering school and loved the Math parts of it. But there are many, many, many topics I don’t have the time or energy to grasp them, and I’m okay with that.
But yeah, nothing too magic about it. If you have one apple and you know that someone will give you another apple in 30 minutes, how many apples will you have in 45 minutes? That’s right. 2 apples. Of course, predicting orbital trajectories is much more than that. But that’s pretty much about it (lol!)
Yeah i understand the theories and “why” (kind of) it’s mainly the numbers that get me lol and also how do you know what formula to use
I think it’s very cool. I listen to podcasts about mathamatics all the time, special and general relativity, time, lightwaves, etc all that stuff is fascinating
Oh no i never thought that, your comments perfectly fine, imo.
Right? You can figure out where any object will be in the future, it seems. That’s insane, and very cool. I wonder what people like Euclid would think about math and geometry in our time.
It’s not so much math doing that, but physics. Math is just a basic concept of relations. Physics equations are what turns it into a prediction method.
Math is amazing to me. It’s ability to so somehow predict most things is a mystery, I’m math intolerant so I’ll never be able to understand it.
Math, or at least this part of it, is all about relationships between values. Let’s ignore numbers for a bit. If you take a long stick and put a big rock under it, then when you move your side of the stick down, the other side will move up. And if you were to measure how much you moved your side versus how much the other side moved, you’d notice that unless you put the rock right in the dead middle, the other side would move a different amount. This isn’t because something is magically making this happen, it just a property of the construction of your system. The other side just does move more or less, and it’s different depending on where the pivot point is.
Similarly, if you have two gear wheels with different numbers of teeth, and you mesh them together, and you turn one and count how many times you’ve turned it, and also count how far the other one has turned, you’ll find a relationship there too! And again, this relationship is just built into the way these objects interact. It’s just the way this system works.
Okay, so, stay with me now, saying
y = 2x + 5is the same. It’s defining a relationship, it’s building a system that’s says the value we’re calling “y”, chosen arbitrarily it could be any name, is always twice as big as “x” (also chosen arbitrarily), and then 5 more than that. It’s a system we’ve built, just like the levers or gears, that produces a relationship we want to express for some reason. And you can put them together in any way, and they’ll always describe some relationship, even if it’s not a useful one.Now, people have spent hundreds of years, depending on how you want to count, trying to find relationships that also happen to have predictive power. They’ve built systems where the relationship between “d” and “t” is modeled to be the same as the relationship between “the distance that rock flew from me” and “the time since I threw that rock”. And what’s nice about finding these relationships is that now that you know what the relationship is, now that you’ve built the system of levers and pulleys and gears that turn in just the right way, you can start guessing about the rocks before you even throw them, because this relationship you’ve got on the page is similar to the one you’ve seen in real life with the rock and the stopwatch.
Once you’ve got a bunch of these, picking the right one and combining them because more like a puzzle or a maze. I’ve got these things I know, like the weight of the rock, and the size of the Earth, and how stiff the metal in the spring I’m using to launch this thing is. And I’m trying to figure out its top speed. And I’ve got a bag of relationships I know are battle-tested. So all I have to do now is start finding relationships that depend on stuff I know to get me stuff I don’t know. And if I can link them together like a Rube Goldberg machine, I can figure out something I didn’t know using this one relationship, which is handy because this other relationship I’d quite like to use needed that thing I didn’t know before but do now.
And so I can work through a chain of relating things to things until I can get to the point where I have enough to use one of the relationships I do know that predicts speed. And once I’ve got that, I’m done! I trust the relationships I’ve used, presumably I used them properly and didn’t make any dumb mistakes, and so I followed a chain of things I knew, through tools that used those things, to tools that used the things the other tools produced, until I found a path to my goal.
The only thing stopping you from there is the complexity of the relationship, the accuracy of the relationship to the real situation, and how accurately you can measure the things you know.
I haven’t it described as relationships before. I can get behind that thought process. Thank you so much for your comment! I have to read it a agian to get it lodged into the grey matter.
Do you think physics is worth studying if numbers themselves are beyond someone? I get it’s abstraction. Agian, thank you.
Physics is a way to generally describe the relationship between things, mathematics is to predict specifically how would those relationships affect the things involved.
You can learn the general theory but application needs mathematics.
One way to do it would be instead of learning numbers use numbers as names of the objects. And other characteristics as adjectives to describe them.
Nice nice, that makes sense. Thank you
It’s okay not to understand everything about Math. I used to be a big enthusiast, even went to engineering school and loved the Math parts of it. But there are many, many, many topics I don’t have the time or energy to grasp them, and I’m okay with that.
But yeah, nothing too magic about it. If you have one apple and you know that someone will give you another apple in 30 minutes, how many apples will you have in 45 minutes? That’s right. 2 apples. Of course, predicting orbital trajectories is much more than that. But that’s pretty much about it (lol!)
Yeah i understand the theories and “why” (kind of) it’s mainly the numbers that get me lol and also how do you know what formula to use
I think it’s very cool. I listen to podcasts about mathamatics all the time, special and general relativity, time, lightwaves, etc all that stuff is fascinating
Knowing how the formulas work is physics. Math is just the language used by the models.
Yeah, sorry if my tone seemed patronizing.
And I can relate with you. Orbital predictions? “This body will collide with that other body 7 years from now”? Whoa. Magic indeed!!
Oh no i never thought that, your comments perfectly fine, imo.
Right? You can figure out where any object will be in the future, it seems. That’s insane, and very cool. I wonder what people like Euclid would think about math and geometry in our time.
It’s not so much math doing that, but physics. Math is just a basic concept of relations. Physics equations are what turns it into a prediction method.
Math “Infinite and Zero are units like others” Physics “Infinite and Zero are the worst Nightmares”
Theoretical Math < Applied Math
Same. I was very bad at math in school.