I don’t think we can answer this question until we understand what calculus is used for.
I’m not sure that most people really understand what calculus is and how it is applied in the real world. I suspect that the vast majority of people who take the class are never called upon to use it for anything, even in other classes. I think my university (Carnegie Mellon) was unusual in that they made the business majors use calculus in their business classes. I had to use calculus to design production schedules, for instance.
This is not to say that I have any deep understanding of calculus. I don’t. But I do have a deep appreciation for it.
And my edumacated guess to answer the OP: Without calculus, we would not be able to manage complex systems with as much efficiency. Increased efficiency and the economies of scale inherent in larger operations are major drivers of economic growth and technological innovation.
Yeah, I think I remember my dad talking about how it’s impossible (or really, really difficult) to plot shell and rocket trajectories without calculus.
I was thinking also that a lot of engineering would use calculus. Can you calculate lift and air flow without it? Do architechts use calculus? High rises might no exist otherwise.
dwalin, in what way is calculus used in computers? In designing chips, or in the actual functioning of the hardware, or what? Not saying you’re wrong, just can’t think off the top of my head how they’re related.
Without calculus there would be essentially no high technology. Physics needs calculus at an absolutely fundamental level - without calculus almost no real understanding of force, etc. is possible. This limits you to extremely basic engineering, absolutely no theory of eletricity, etc. We could probably build a steam engine of some sorts, although I’m not convinced one could power a train, but an internal combustion engine? I really doubt it.
We’d probably have some sort of electricity, but certainly no electronics or higher understanding of what it really is. We would have no good theory of statistics, so all the rest of science is shot to hell as well. There’d probably be some hit and miss versions of biology and chemistry, but they wouldn’t even approach the level of sophistication we have today (among other things because, with the lack of decent physics, it’s no guarantee we’d even have an atomic theory. There certainly wouldn’t be a quantum theory).
Seriously, Bad Things. Doom and damnation will come to thee without calculus.
Can you tell that I’m a mathematician?
loopydude, infinitesimals are daft things used by people who are being lazy or don’t understand calculus. (Included among the second category are two idiots called Newton and Leibniz). Calculus is about limits. Infinitesimals are silly fluff that gets in the way.
There wouldn’t be a senior year calculus class so I wouldn’t need to take Precalc next year so I wouldn’t be taking Algebra/Trig this year so I wouldn’t have three pages of Algebra/Trig homework to have to do sometime today :mad:
Yes, it’s my own damn fault for not making up the homework earlier. I’m just saying that without calculus, I’d be in European History and just having to make up a worksheet or something
For openers, voltage and electron flow tend to act as first derivatives of one another. In AC circuits they lead and or follow one another by 90 degrees; the voltage across an inductor is dependent on a change in current through th inductor and the current in and out of a capacitor is dependent on a change in voltage across the capacitor. IANA circuit designer, but I’m pretty sure that these rates of change are used to model how quickly each circuit can operate.
You might be able to make shift with successive approximations or one-off “infinite division” methods. For instance, some greek calculated the volume of a sphere, IIRC, by dividing it into pieces and taking a limit, which was calculus, but didn’t use the general theory. But we might assume even that’s cheating.
If so, imagine that. You can’t find the volume of a shape. Given a formula, you can’t find the maximum.
No maths. No physics. No epidemiology. No orbital mechanics. Probably no transformers. No weather prediction. I doubt you’d manage much radio so no mobiles, TV, etc.
I believe Newton established that the planets’ orbits were governed by gravity without calculus, but he used a similar method. If you rule that out, you mightn’t even be certain about the earth going round the sun.
OK, I was exagarating rather in that post. Sorry. But if every time you design a petrol tank you have to go dip it in water every five minutes that’s not easy.
The orbit of planets? OK, yes, you’d find the orbit by plotting the observations and finding an equation that fit. But you’d be SOL for asteroids or anything that had two non-negligible masses acting on them.
I don’t really agree with that. It’s pretty hard to put myself in the mindset of not knowing things you do know, But most of those things seem like they could be created without any math at all.
Internal combution engine for example. You can see an explosion, you can feel that the explosion pushes things. You know that pushing things is a very useful ability. With an observed knowlegde of gearing, I don’t think it would be impossible to eventually come around to something like the piston-crankshaft model. Again I can’t say how easy that end result would come to somebody who had to invent it, But I think humanity would have eventually come around to it.
And electricity. Some guy playing around with a few different materials, perhaps magnetic, in different ways notices something happens when they are connected on different sides. Experimentation, observation, eventually heat is observed. more experiments and light appears.
I just don’t see how an understanding of Calculus is required to reach a 1930s level of technology. You don’t have to know it to find out that it works, you just expeiriment until somebody somewhere finds that it does work. Electronics, usuable atomic nuclear therory, and the most recent stuff I can agreee with, But I can see eventually developing 1930s era tech, including early flight, without understanding of Calculus.
Just about ALL primitive technology is not cost effective compared to the efficiencies we can achieve today. So what? In their day they only had to be more cost effective than horse and buggy or oxcart to be the hottest things going.