What career/major is best for an intuitive thinker?

[CyberShot]

Okay, so hear me out.

I originally came to college as a physics major. I've always grown up loving everything about it, especially the concept of time travel. However, now that I'm now a junior in college I have noticed patterns among professors, who seem to follow mathematics so blindly (dangerously so, imo) that they fail to see the quick, intuitive shortcuts that I see. It's as if he doesn't "see" things with intuition, but rather relies on the crutch of mathematics, which does all the work for him. When, I ask him the answer to a certain problem, it's as if he says: "Hmm, well let's see what math says it should be.., because I don't have my own brain. Let me just take this variable called y, do something funny to it, and wallah, out comes the answer. I didn't figure that out for myself, mind you, I let math do the trick"

The way I've tried to approach every physics problem up until this point is to use the most fundamental logic. For example, I don't like how so many funny looking symbols that really stand for something else are , i.e the integral. Let's say we have a function f(x) = x. There's nothing intuitive about being able to conveniently raise it to one higher power, and divide by that power to get the area function. I mean, sure it's fast and easy, but why are things that convenient for us? The modern world relies on calculus, which means that our survival comes down to simple "gifts" of being able to calculate fluxes, probabilities, volumes, etc with simple, neat tricks. That makes me sick, for some reason, that we allow math to control us in such a way.

I do understand that, on the one hand, we can't really give up on all the learned formulas because the work of scientists, whose formulas we use today, would have been all for nothing if we discarded them and searched for something truly elementary. Things that are irreducible, and only stand for themselves (like counting numbers) instead of using tricks.

I've thus obviously dealt with a lot of frustration, and even depression now. I've just "given up" on physics, and switched to computer science because I feel that all I'll be doing in grad school is applying "complicated" formulas, which really stand for something elementary, without truly understanding them at a deep, intuitive level.

Idk. Maybe I'm better off as a philosophy major, with the way I tend to approach problems? I took one class, and found that my very deep "need for complete intuition" way of approaching things worked way better there than in physics.

I guess what I'm really trying to get at is: what kind of careers/majors is better suited to someone who approaches things with the most deep-rooted intuition, and without regard for things that stand for other things.

Or maybe, I'm just crazy..? anyways, I need your help!

Thanks for reading.

 

[Kevin_Axion]

You don't like mathematics to answer problems? It's the same thing as using intuition and logic except on a piece of paper with symbols. Mathematics is like a 6th sense to understand the world around you.

 

[ParticleGrl]

You seem to be saying that you don't like abstraction. This is a problem for most fields, and you'll have to develop some comfort with it. Every field uses abstraction to make problems manageable.

Honestly, you can develop intuition for calculus. It just takes some practice, and a willingness to play with the concepts. Yes, integration does stand for finding the area under a curve (or the limit of a Riemann sum)- but you can learn to think intuitively about areas and how to manipulate them. Just because you are using a shorthand, doesn't mean you have to lose track of the ideas. As I used to tell my students- you should always try to have some idea of what the answer should look like before you begin a calculation.

The key to physics is to use physical reality to develop an intuition for mathematics, so that when you no longer have good intuition (quantum mechanics, for instance), you can rely on the intuitive understanding of mathematics you have developed.

 

[Pengwuino]

The problem, in my opinion, is that physics is simply hard. You'll find human intuition is no match for what reality has decided to compose itself of. If you take, for example, any non-trivial electrodynamics problem that you see as an advanced undergraduate or grad student, do the work, and plot the solutions and you'll see there is no way in hell anyone could have an "intuition" for what the answers should be. Now, you can eventually develop a form of "intuition", but it's really simply something built off many complex calculations - it's never something you just naturally have.

I doubt you'll find any majors that you can simply have "intuition" for. Considering the millions of people who have come before you, I find it hard to believe any worthwhile major can be done intuitively. Life isn't simple, unfortunately.

 

[Klockan3]

I do understand that, on the one hand, we can't really give up on all the learned formulas because the work of scientists, whose formulas we use today, would have been all for nothing if we discarded them and searched for something truly elementary. Things that are irreducible, and only stand for themselves (like counting numbers) instead of using tricks.

To me seeing that the area under the curve y=x is x squared divided by two is as intuitive as counting numbers, I did even solve that problem long before I had ever seen calculus. Maths is nothing but a logical extension of your intuition, if that is not the case for you then you didn't understand the maths well enough and you should go back to review it to gain more insight. Or you could like you are doing now just dodge it all while stating that it doesn't feel right. But don't come here stating that this doesn't make any sense when it is you who have no clue about it.

I doubt you'll find any majors that you can simply have "intuition" for. Considering the millions of people who have come before you, I find it hard to believe any worthwhile major can be done intuitively. Life isn't simple, unfortunately.

Depends on how you mean, in maths for example you never take any steps which goes against your intuition unless you rush through to the formulas without doing it properly. Sadly most including the OP takes the rushing route which makes them think that maths isn't intuitive.

 

[labinojha]

To me seeing that the area under the curve y=x is x squared divided by two is as intuitive as counting numbers, I did even solve that problem long before I had ever seen calculus. Maths is nothing but a logical extension of your intuition, if that is not the case for you then you didn't understand the maths well enough and you should go back to review it to gain more insight. Or you could like you are doing now just dodge it all while stating that it doesn't feel right. But don't come here stating that this doesn't make any sense when it is you who have no clue about it.

Depends on how you mean, in maths for example you never take any steps which goes against your intuition unless you rush through to the formulas without doing it properly. Sadly most including the OP takes the rushing route which makes them think that maths isn't intuitive.

I had similar poblems as cybershot but i found your explanation helpful. Thanks

 

[CyberShot]

I doubt you'll find any majors that you can simply have "intuition" for. Considering the millions of people who have come before you, I find it hard to believe any worthwhile major can be done intuitively. Life isn't simple, unfortunately.

How about philosophy? When I was in a philosophy class, I felt like I could answer any question
just by thinking intuitively, which is why it appealed so much to me.

To me seeing that the area under the curve y=x is x squared divided by two is as intuitive as counting numbers, I did even solve that problem long before I had ever seen calculus. Maths is nothing but a logical extension of your intuition, if that is not the case for you then you didn't understand the maths well enough and you should go back to review it to gain more insight. Or you could like you are doing now just dodge it all while stating that it doesn't feel right. But don't come here stating that this doesn't make any sense when it is you who have no clue about it.

Depends on how you mean, in maths for example you never take any steps which goes against your intuition unless you rush through to the formulas without doing it properly. Sadly most including the OP takes the rushing route which makes them think that maths isn't intuitive.

It's not that I don't understand the formulas, it's just that I think ridiculously abstractly. I just have this deep-down gut feeling that any and everything in the world can be reduced to +,-,*,/ operations. I also feel like if we can reduce them to this basic, "proper" form, then we have truly conquered and understood the idea. Notations, integrals, matrices are just ways of us "coping" with difficult calculations by using manipulative trickeries.

This, I feel, is the great danger.

I also feel like my thought process is a better match with mathematical philosophy?

 

[CyberShot]

I guess I can make a computing analogy here.

It's as if calculus, or any other invented math is like a language, which gets converted into binary (the mathematical equivalent of + - * /) so that it can be implemented to spit out an answer.

In this way, we should be able to figure out any problem we want by just adding, subtracting, multiplying, or dividing quantities. These 4 concepts are built into the universe (the rest are man-made) and that's the level at which I want to understand physics.

Or maybe it's just too much work to understand things that way, in which case we have to "invent" things that stand for other things to organize and make things easier.

Any ideas on this?

 

[Chairman Lmao]

It's not that I don't understand the formulas, it's just that I think ridiculously abstractly. I just have this deep-down gut feeling that any and everything in the world can be reduced to +,-,*,/ operations.

I think its time for you to confront your guts

I mean you should start asking why everything in the world should be reduced to +-*/(which isn't true btw). Could it be that you feel so because you have become so familiar with them, and their is nothing more to it than that?

Just because you are using a shorthand, doesn't mean you have to lose track of the ideas

This.

 

[ZapperZ]

Okay, so hear me out.

I originally came to college as a physics major. I've always grown up loving everything about it, especially the concept of time travel.

Maybe what you actually love is NOT physics, but rather the romanticized view of it.

Physics just doesn't say "what goes up, must come down". Physics must also say when and where it comes down. This means that there are two important component to it : qualitative (what goes up, must come down) and quantitative (when and where it comes down). This makes it falsifiable whereby one can make empirical tests to verify the validity of something.

The mathematics that you so hate isn't a separate part of physics. It IS physics, because it is the tool and the language. Physicists look at the mathematics of physics the same way musicians look at musical notes - we don't look at just the symbols, but rather what the mathematical expression represents.

I will also point out that what you call "intuition" is nothing more than a series of knowledge that you've acquired till now. I can show you many situations where your intuition will fail, simply because you haven't been exposed to that particular knowledge. And when you have, then you find that to be intuitively obvious. So relying on your intuition is not reliable, especially when you're still learning and when you don't know a lot.

Zz.

 

[micromass]

I understand what you mean, I have the same feeling when it comes to physics. All physics wants to do is make predictions, but I never wanted that. I wanted to understand what exactly happens. I wanted to know why something works, and I never found that physics gave me a satsifactory answer. And somethimes using mathematics in physics is a little bit cheating. I am a pure mathematician, but I don't feel comfortable with the mathematics in physics. For the simple reason that it doesn't answer the question "why?".

I think philosphy will be something for you. They are the ones who are looking for meaning and intuition. They don't want to quantify things, but they look after the deeper reasons of reality. Judging from your post, I'm sure you will like it...

 

[ZapperZ]

I understand what you mean, I have the same feeling when it comes to physics. All physics wants to do is make predictions, but I never wanted that. I wanted to understand what exactly happens. I wanted to know why something works, and I never found that physics gave me a satsifactory answer. And somethimes using mathematics in physics is a little bit cheating. I am a pure mathematician, but I don't feel comfortable with the mathematics in physics. For the simple reason that it doesn't answer the question "why?".

I think philosphy will be something for you. They are the ones who are looking for meaning and intuition. They don't want to quantify things, but they look after the deeper reasons of reality. Judging from your post, I'm sure you will like it...

The major problem with that is that since they make unfalsifiable "meaning", you have no way of knowing if such meanings are valid. This isn't science, and as long as you are aware of that, that's fine. But don't make any delusion that what you are doing is what it actually is, because you have no way of knowing. It also means that what you call as a "meaning" or explanation may not be unique, because since it is untestable, it means that others came up with other explanations.

To me, that is more frustrating than learning mathematics. And considering that philosophy doesn't play a role at all in the advancement of physics, but rather having to play catch-up with the new things in physics, you have to be consider if what you do makes any difference.

Zz.

 

[micromass]

The major problem with that is that since they make unfalsifiable "meaning", you have no way of knowing if such meanings are valid. This isn't science, and as long as you are aware of that, that's fine. But don't make any delusion that what you are doing is what it actually is, because you have no way of knowing. It also means that what you call as a "meaning" or explanation may not be unique, because since it is untestable, it means that others came up with other explanations.

To me, that is more frustrating than learning mathematics. And considering that philosophy doesn't play a role at all in the advancement of physics, but rather having to play catch-up with the new things in physics, you have to be consider if what you do makes any difference.

Zz.

Yes, I agree. I don't really like philosophy to for that very reason. But I simply think that the OP might be more philosophy minded. And I think that the OP should do what he loves best, and in this case I don't think physics is really his thing.

I mean, if you're loving the concept of time travel, then I think philosphy is the field where you can talk about that concept freely. It's not science at all, but I simply think that the OP might like philosophy more then the hard, cold sciences...

 

[Angry Citizen]

It's not that I don't understand the formulas, it's just that I think ridiculously abstractly. I just have this deep-down gut feeling that any and everything in the world can be reduced to +,-,*,/ operations. I also feel like if we can reduce them to this basic, "proper" form, then we have truly conquered and understood the idea. Notations, integrals, matrices are just ways of us "coping" with difficult calculations by using manipulative trickeries.

All mathematics that I've taken so far is based on addition, subtraction, multiplication and division. As my physics prof says, integration is just a fancy way to add stuff. And it's true. What is integration, oh mighty intuition guy? It's an infinite amount of multiplied sums. It's geometry taken to the extreme. What is differentiation? Just a fancy way of dividing a tiny area of a function such that you can determine how fast it's increasing or decreasing at that particular spot. Again, geometry taken to the extreme.

It sounds to me like you'd be better off as a math major, or possibly a math and physics major. You want to develop the intuition behind physics? Learn higher math. You understand exactly where the power rule comes from (and prove it) in any analysis class.

Finally, I'll say that mathematics isn't a 'trick' or a 'tool'. It is literally the language of the universe. No offense, but your paltry 'intuition' says nothing about what's really going on in any basic physics question, much less the harder parts. Take Faraday. He was a brilliant guy, but there's only so much you can do with intuition-based geometric interpretation of electricity before you need good ol' Maxwell to come to your rescue.

 

[ZapperZ]

Yes, I agree. I don't really like philosophy to for that very reason. But I simply think that the OP might be more philosophy minded. And I think that the OP should do what he loves best, and in this case I don't think physics is really his thing.

I mean, if you're loving the concept of time travel, then I think philosphy is the field where you can talk about that concept freely. It's not science at all, but I simply think that the OP might like philosophy more then the hard, cold sciences...

My point isn't to say that the OP shouldn't do philosophy. I was trying to stress that if he thinks that the intuitive approach, as often done in philosophy, gets him closer to "understanding" nature, then he is sadly mistaken. New ideas and concept about nature isn't led by philosophy. It is lead by the sciences, especially physics. And the validity of such ideas are tested and investigated in science, not in philosophy.

Zz.

 

[JDStupi]

I think we should just tell him not to conflate his lack of understanding of the usage of Maths with an entire field. Are there many who simply resort to "formulas" to calculate answers, without any recourse to a deep understanding? Sure. That certainly doesn't imply that this is what the field of Physics is, successfull scientists use intuition and creativity many times, but it is a logically refined and mathematically manifested intuition. Some psychologists believe that the development of human thought and conceptualization is intimatley related to the usage of "psychological tools", given this information, what would make you qualify mathematics as "cheating"? When it is in fact a highly interesting psychological tool (like language) used to develop and express thoughts. Your problem isn't with the tool, but with the motivation for the use of the tool, which is an individual problem and as such, you can only try harder and reproach yourself for your lack of holding up to your own ideal.
Oh yea, and let's not be so sure about philosophy being the easy-breezy place where we can freely speculate on anything we wish. Maybe you should take a philo course, and maybe you'd end up right back where you started. A good Philo course wouldn't stand up for

"These 4 concepts are built into the universe (the rest are man-made) and that's the level at which I want to understand physics"

What is your justification for this statement? Where did you get this idea from? How do you proceed from a personal familiarity to an ontological statement? Assuming you could logically prove that all mathematical operations were reducible to elementary arithmetic operations, how would you proceed from a statement of mathematics/logic to a statement of ontology/metaphysics? ...

Philo uses intuition, but a logically refined intuition

and I agree with Angry Citizen, don't confuse how maths was taught (a simple manipulative algorithm) with how it was devised. I know this is hard because many schools treat Mathematics as a dead collection of facts with no justification, but always say to yourself "At one time, this knowledge was not known, in the past, how did somebody proceed from the lack of this knowledge to attaining this knowledge" Now, you may not want to know exactly the historical method used by the originator (it may be excessively cumbersome) but the logic of its derivation.

 

[Fizex]

Let's say we have a function f(x) = x. There's nothing intuitive about being able to conveniently raise it to one higher power, and divide by that power to get the area function. I mean, sure it's fast and easy, but why are things that convenient for us? The modern world relies on calculus, which means that our survival comes down to simple "gifts" of being able to calculate fluxes, probabilities, volumes, etc with simple, neat tricks. That makes me sick, for some reason, that we allow math to control us in such a way.

Think about it for a second. Integration is the opposite of differentiation; the fundamental theorem of calculus tells us so. Therefore to take the integral of a polynomial you do the opposite of differentiation and hence you raise the power and divide by that. Now if you want to know why differentiation works this way you start getting into limit proofs and you can look those up.

 

[Fizex]

I just have this deep-down gut feeling that any and everything in the world can be reduced to +,-,*,/ operations.

I'd like to see how you can put 5^pi in terms of those operations without infinitely approximating.

Notations, integrals, matrices are just ways of us "coping" with difficult calculations by using manipulative trickeries.

Of course, but that doesn't make us forget all of a sudden that they are constructions of simpler math operations.

How about philosophy? When I was in a philosophy class, I felt like I could answer any question just by thinking intuitively, which is why it appealed so much to me.

Have you taken quantum mechanics yet? No human intuition is going to let you derive the solutions to it's problems.

It's as if calculus, or any other invented math is like a language, which gets converted into binary (the mathematical equivalent of + - * /) so that it can be implemented to spit out an answer.

In this way, we should be able to figure out any problem we want by just adding, subtracting, multiplying, or dividing quantities. These 4 concepts are built into the universe (the rest are man-made) and that's the level at which I want to understand physics.

No, software like mathematica will use subtraction of the power and multiplication just like how you would differentiate polynomials normally. They don't do approximations unless it's an impossible integral and it will use a formula for that.

The rest were not man-made, they were built onto the universe just like those operations and are constructions of simpler operations; you are just not seeing them. Like other members have said, you just don't understand how the math is working behind the scenes; that doesn't mean it's not there!

 

[Ryker]

Idk. Maybe I'm better off as a philosophy major, with the way I tend to approach problems? I took one class, and found that my very deep "need for complete intuition" way of approaching things worked way better there than in physics.

I wouldn't make that conclusion at all. To me it seems you've just convinced yourself what "everything in the world can be reduced to", without having a firm basis for that conviction. And now that Physics doesn't match it, you've got a feeling you've grown apart from it. I think that's fine, but you have to realize it's just you making up standards that aren't given by nature, and if something doesn't conform to them, you don't have to like it, but just don't delude yourself into thinking that's because you're a philosopher, "pure" or whatever.

 

[Studiot]

The world has moved on since the time of Aristotle.

The Ancient Greeks thought that they could explain and interpret the world they saw by thinking how things ought to be and blaming reality as 'imperfect' if it didn't match.


The great leap forward came when we started doing things the other way round ie theory follows observation.

The problem with intuitive thinking is that is is more like the former - it is not impartial.
And science has to be impartial to progress.

As a matter of interest there is a fundamental problem with even +,-,*,/
It is called division by zero.

 

[CyberShot]

Maybe what you actually love is NOT physics, but rather the romanticized view of it.

I will also point out that what you call "intuition" is nothing more than a series of knowledge that you've acquired till now. I can show you many situations where your intuition will fail, simply because you haven't been exposed to that particular knowledge. And when you have, then you find that to be intuitively obvious. So relying on your intuition is not reliable, especially when you're still learning and when you don't know a lot.

Zz.

I actually believe that intuition is not learned, but rather pre-programmed into our brains before birth. I'm sure you're familiar with Molyneaux's problem.

To me, that is more frustrating than learning mathematics. And considering that philosophy doesn't play a role at all in the advancement of physics, but rather having to play catch-up with the new things in physics, you have to be consider if what you do makes any difference.

A bit of a harsh, (no disrespect) miscalculated response, don't you think? Philosophy makes statements about why physics and math are the way they are, or why they're even allowed to work in the first place. It's sort of like the pre-heat part of the instructions in making the universe. Sure, some philosophical statements can probably never be proven, but that's why we're granted some intuition to see if such statements are plausible.

Yes, I agree. I don't really like philosophy to for that very reason. But I simply think that the OP might be more philosophy minded. And I think that the OP should do what he loves best, and in this case I don't think physics is really his thing.

I mean, if you're loving the concept of time travel, then I think philosphy is the field where you can talk about that concept freely. It's not science at all, but I simply think that the OP might like philosophy more then the hard, cold sciences...

Yes, but I have this debilitating fear that studying philosophy ultimately circles back to intuition and is very unfruitful because you don't really learn anything you already didn't have inside you, you just see things in a better light. Whereas if I pursue physics I can have a real grasp of the way the universe physically presents itself.

Oh yea, and let's not be so sure about philosophy being the easy-breezy place where we can freely speculate on anything we wish. Maybe you should take a philo course, and maybe you'd end up right back where you started. A good Philo course wouldn't stand up for

"These 4 concepts are built into the universe (the rest are man-made) and that's the level at which I want to understand physics"

What is your justification for this statement? Where did you get this idea from? How do you proceed from a personal familiarity to an ontological statement? Assuming you could logically prove that all mathematical operations were reducible to elementary arithmetic operations, how would you proceed from a statement of mathematics/logic to a statement of ontology/metaphysics? ...

Simple argument, see if you can break it.

1. If every physics problem can possibly be done by adding, subtracting, multiplying, or dividing a bunch of numbers, then these 4 concepts underpin reality in some way.

2. Every physics problem can possibly be done by adding, subtracting, multiplying, or diving a bunch of numbers. *
---
3. Thus, these 4 concepts underpin reality in some way.

Argument 1 presupposes a connection between mathematical truths and metaphysical ones, a not so improbable one if you deeply think about it.

It might be hard to see 2 right away. To convince yourself, try to think of a counter-example. Granted, to do calculations using the 4 basic operators might take an infinite amount of time to do so, and it may also be infinitely tedious, but it's definitely possible. Things requiring an infinite amount of time does not place them outside the realm of "possibility." Neither does tediousness.

I'd like to see how you can put 5^pi in terms of those operations without infinitely approximating.

Sure you can, and the answer is remarkably obvious and simple. Just add up a bunch of real numbers and decimals and stop when you reach 5^pi. It might take you more time than exists, but who cares? That has nothing to do with the argument. Infinitely approximating is not approximating if we're talking about infinite; it is exacting. Just because integrations and other calculus "tricks" take care of infinitely long processes by conveniently "predicting" what the answer is going to look like if you were to do things the infinite way, doesn't mean that calculations can't be done the very long, tedious way of calculating things.

Have you taken quantum mechanics yet? No human intuition is going to let you derive the solutions to it's problems.

Exactly why it's probably a stubbornly wrong model of reality, not that I'm qualified (as in a physics degree) to make such statements about ludicrous theories that include two particles deciding on their own accord to "communicate" with each other without actually communicating. :-)

 

[Chairman Lmao]

3. Thus, these 4 concepts underpin reality in some way.

Good Lord no they don't. This only shows your own ignorance and inexperience- nothing wrong with that. But jumping to conclusions about the nature of reality (whatever that means) with no knowledge is foolish. I'll say it again- if you insist that the real world should conform to your "gut feelings" then you are not doing Physics.

 

[CyberShot]

Good Lord no they don't. This only shows your own ignorance and inexperience- nothing wrong with that. But jumping to conclusions about the nature of reality (whatever that means) with no knowledge is foolish. I'll say it again- if you insist that the real world should conform to your "gut feelings" then you are not doing Physics.

If A, then B.

A.

Therefore, B.

What part of this logic is physics exempt from?

 

[CyberShot]

I must admit that I just came home a couple of hours ago after listening to a public lecture by Nima-Arkani Hamed, so maybe that's why I'm all fired up at the moment. :-)

 

[ZapperZ]

I actually believe that intuition is not learned, but rather pre-programmed into our brains before birth. I'm sure you're familiar with Molyneaux's problem.

I have a helium-filled balloon in a vehicle, say, a train. All the windows are closed, so that there's noticeable wind in the vehicle. The train then accelerates forward. What happens to the balloon?

Now don't cheat. Solve that using ONLY your present-day intuition.

A bit of a harsh, (no disrespect) miscalculated response, don't you think? Philosophy makes statements about why physics and math are the way they are, or why they're even allowed to work in the first place. It's sort of like the pre-heat part of the instructions in making the universe. Sure, some philosophical statements can probably never be proven, but that's why we're granted some intuition to see if such statements are plausible.

No less of a person like Richard Feynman has said "“Philosophy of science is about as useful to scientists as ornithology is to birds".

What you've done here is simply to make a GUESS. It means nothing. I can say something else, and there's nothing you can do to prove me wrong if I choose to take on the same type of superficial analysis. What you can do is show me an actual study to show that what I just said about philosophy is wrong, NOT some anecdotal made-up scenario.

Again, I think you have a very romanticized view of what science is. When I wrote my "So You Want To Be A Physicist" essay, I tried to present a more realistic view of not only the educational process, but also the reality of what it means to be a physicist. In the end, it is YOUR decision if you are more inclined to actually do science, do a profession that discusses ABOUT science.

Zz.

 

[Vanadium 50]

"Thus, these 4 concepts underpin reality in some way" is a largely content-free sentence. Do you mean that no other concepts "underpin reality" (whatever that means)? If so, you have certainly not proved it. If not, all you mean is addition (and its brethren) are useful in describing reality, which nobody was doubting.

I'm really surprised if they let you get away with this level of discourse in a philosophy class. When I took philosophy, it was pounded into me that I had to be very clear about what I was saying.

 

[thegreenlaser]

Just out of curiosity, who was it who told you that you weren't allowed to break things down into simplistic (+ - * /)? . My point is, nobody's stopping you from doing these things yourself. If you have such a drive to understand material at that level of simplicity, then why not put a little work in and do it yourself? I really doubt gunmen are going to come kick your door down and shoot you for fear that you might find the fundamental secrets of the universe.

I'm not really saying that sarcastically. If you seriously want to learn this stuff at such a level, no-one's stopping you. I'd definitely work on your definition of "base level simplicity" first (You may as well just argue that addition is the only fundamental property. Multiplication can be represented as a series of additions and subtraction/division are just 'inverses' of addition/multiplication), but who knows, maybe you'd notice some things that nobody's noticed before.

However, if you're not willing to put the effort in, then I suspect as someone said before that you're kind of intimidated by advanced math and you want to stick to what you're comfortable with.

 

[G01]

Okay, so hear me out.

I originally came to college as a physics major. I've always grown up loving everything about it, especially the concept of time travel. However, now that I'm now a junior in college I have noticed patterns among professors, who seem to follow mathematics so blindly (dangerously so, imo) that they fail to see the quick, intuitive shortcuts that I see. It's as if he doesn't "see" things with intuition, but rather relies on the crutch of mathematics, which does all the work for him. When, I ask him the answer to a certain problem, it's as if he says: "Hmm, well let's see what math says it should be.., because I don't have my own brain. Let me just take this variable called y, do something funny to it, and wallah, out comes the answer. I didn't figure that out for myself, mind you, I let math do the trick"

Hmm, just wondering, why are you in school if you can solve all the problems quicker and more efficiently and more intuitively than your professors?

For example, I don't like how so many funny looking symbols that really stand for something else are , i.e the integral. Let's say we have a function f(x) = x. There's nothing intuitive about being able to conveniently raise it to one higher power, and divide by that power to get the area function. I mean, sure it's fast and easy, but why are things that convenient for us? The modern world relies on calculus, which means that our survival comes down to simple "gifts" of being able to calculate fluxes, probabilities, volumes, etc with simple, neat tricks. That makes me sick, for some reason, that we allow math to control us in such a way.

Have you considered that you math background may not be as great as you thought? The integral formula you describe above is founded in intuitive geometrical reasoning and logic, expressed using math as a language. We use the formula as a shortcut, but always should remember where it comes from. Just because you may not understand where something comes from, does not mean it isn't founded in solid logic.

I do understand that, on the one hand, we can't really give up on all the learned formulas because the work of scientists, whose formulas we use today, would have been all for nothing if we discarded them and searched for something truly elementary. Things that are irreducible, and only stand for themselves (like counting numbers) instead of using tricks.

If you think that physics is a collection of formulas and tricks and is not based on logic then you have not been taught physics correctly. Again, math is the language used to express that logic.

I guess what I'm really trying to get at is: what kind of careers/majors is better suited to someone who approaches things with the most deep-rooted intuition, and without regard for things that stand for other things.

I don't mean to be too harsh here, but you are essentially asking if there are careers for someone who thinks they already know everything they need to know (i.e. intuition). You need to get a little perspective I think.

And I 'd like to see you find any type of work at all where you don't need to deal with symbols that stand for other things. What do you think letters and words are? Pictures? Symbols are a part of language. All human beings use symbols to express themselves and discuss the world around them. You're doing it on this forum. No way out of it.

 

[Fizex]

Sure you can, and the answer is remarkably obvious and simple. Just add up a bunch of real numbers and decimals and stop when you reach 5^pi. It might take you more time than exists, but who cares? That has nothing to do with the argument. Infinitely approximating is not approximating if we're talking about infinite; it is exacting. Just because integrations and other calculus "tricks" take care of infinitely long processes by conveniently "predicting" what the answer is going to look like if you were to do things the infinite way, doesn't mean that calculations can't be done the very long, tedious way of calculating things.

I made you answer your argument of "Why should we use mathematical constructions instead of addition?". The other 3 operations / * - come from addition and so does all of the rest of math. Q.E.D.

Exactly why it's probably a stubbornly wrong model of reality, not that I'm qualified (as in a physics degree) to make such statements about ludicrous theories that include two particles deciding on their own accord to "communicate" with each other without actually communicating.

You have to prove that it is a wrong model and yes, you don't have the credentials to do so. You can't bend nature to your vision of how the world should work; it does what it wants and ignores you. Therefore it is silly to guess or use 'intuition' to explain the observable. The observable explains itself and you gather it's properties to form conclusions. Not the other way around. Silly. Quantum mechanics came to us in this way and everyone tried to apply their intuition to it and have failed. Nature couldn't care less.

And besides what part of math isn't intuitive (in the way that it makes perfect sense i.e. logical)?

I don't mean to be too harsh here, but you are essentially asking if there are careers for someone who thinks they already know everything they need to know (i.e. intuition). You need to get a little perspective I think.

 

[micromass]

Yes, but I have this debilitating fear that studying philosophy ultimately circles back to intuition and is very unfruitful because you don't really learn anything you already didn't have inside you, you just see things in a better light. Whereas if I pursue physics I can have a real grasp of the way the universe physically presents itself.

Yes, it is only with physics that one can really understand the way the universe works. But physics is inherently connected to mathematics. You cannot do physics without doing the math. Simply using your intuition is not good enough in physics and in math. Of course, having intuition is not a bad thing, but intuition is often misleading. Only mathematics can give you real answers...

If you want to discuss the intuition behind physics and other stuff without doing the math, then philosophy is a nice thing. But if you want a real grasp, then you'll need math...

 

[Caramon]

CyberShot,
I'm working on writing a book that I think you will like. I go over mathematics from it's beginnings and work with intuitive use of complex calculations, etc. Mathematics and even Physics really is intuitive to the core all the way through until graduate school, (while the later may not be try about particle physics, etc.). You just need to stick with it and really look for that conceptual basis, not the OH I WANT THE ANSWER way that far too many students fall into.

I uploaded an excerpt on this website, you guys can all take a look if you want... tell me what you think or if anything I wrote was incorrect.
http://www.freefilehosting.net/historicalandphilosophicalfoundationsformathematicsexcerpt"

 

[micromass]

CyberShot,
I'm working on writing a book that I think you will like. I go over mathematics from it's beginnings and work with intuitive use of complex calculations, etc. Mathematics and even Physics really is intuitive to the core all the way through until graduate school, (while the later may not be try about particle physics, etc.). You just need to stick with it and really look for that conceptual basis, not the OH I WANT THE ANSWER way that far too many students fall into.

I uploaded an excerpt on this website, you guys can all take a look if you want... tell me what you think or if anything I wrote was incorrect.
http://www.freefilehosting.net/historicalandphilosophicalfoundationsformathematicsexcerpt"

Wow, that's a nice piece of work! I wish I could read more of it

 

[Caramon]

Thank you, I didn't mean to hi-jack the topic or anything. Just wanted to point out that there are ways of intuitively understanding even the most complex problems when you have certain mathematical definitions and constructs to work with. Currently working on Section 2: Elementary Mathematics that goes all the way up to and knocks on the door of calculus.

 

[Jack21222]

Exactly why it's probably a stubbornly wrong model of reality, not that I'm qualified (as in a physics degree) to make such statements about ludicrous theories that include two particles deciding on their own accord to "communicate" with each other without actually communicating. :-)

Quantum mechanics is one of the most successful models of predicting reality ever constructed. If that's being "wrong," I don't ever want to be right.

The universe doesn't give a damn how you think it should work. The universe owes you nothing.

 

[axiomatic7777]

The universe doesn't give a damn how you think it should work. The universe owes you nothing.

That should go on a T-shirt.