What career/major is best for an intuitive thinker?

[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.

 

[CyberShot]

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?

Just on a few occasions.

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 think you should clarify and say my "symbology" and "algorithm-following" background is not that great.

Think about it. That's really what's under the hood of calculus and other maths. Following rules to get to the right answer. Consider the power rule, as an example.

My point is that high-level mathematics is incredibly arbitrary, akin to high-level programming languages. It's like somebody decides for you the way these languages are implemented and converted into binary.

The only reason calculus is quick and convenient is because we define things in a way that is convenient for calculus to act upon those things.

For example, consider an arbitrary vector field.

v = 2i + 3j - 4k

Now, why do we need vector calculus to calculate the curl?

Simple answer: we defined a vector field in terms of i's, j's, and k's that are easily manipulated by a bunch of algorithms (such as differentiation) to get the answer

It makes sense to use calculus here because the way we defined a vector just goes hand in hand with the way we defined our calculus to operate on that vector


now, it's perfectly fine to define the same vector field the following way:


v = 3d vector with and x component that of a line with y-int at the origin and a slope of 2

we could def. calculate the curl algebraically using NO calculus and only the notion of slope and 3d perpendicularity.


I'm just saying that things can be done the most basic way, and it's a shame that people don't show much appreciation for calculating things that way. Instead they rely on tricks and handy shortcuts like the power rule, product rule, which of course is the arbitrary "calculus-way" of calculating curl.

Physicists, especially at my university, are so brainwashed into thinking that the complex looking integrals and other funny math symbols are the whole story to the nature of reality that they begin to blindly think through symbols and notations (and get stuck) instead of thinking using their intuition and the fundamental + - way of approaching problems.

 

[Chairman Lmao]

If A, then B.

A.

Therefore, B.

What part of this logic is physics exempt from?

I was referring to your "+ and - underpin reality" thing.

 

[CyberShot]

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.

Am I to assume the balloon hovers in the same y-position above the floor before the train accelerates and does not move after that? If so, then the back of the train will soon meet the balloon, consistent with intuition.

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.Zz.

I wouldn't say philosophers make guesses about reality. Rather, we try to make observations consistent with tautologies.


If I have made statements that can work in the framework of a tautology, i.e making true statements that flow in a logical pattern, then I haven't made a guess about something, I've proved it. Take for example my reductionist argument :

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.

-----
If A, then B

A.

Therefore, B.

-----

The above is a tautology. The one above the above is a bunch of statements I've made to conform to the tautology.

The argument seems to make as much, if not more, sense about the world as physics does.

* I've just thrown in multiplying and dividing for the sake of completeness, but they themselves are really just built on addition and subtraction Why do you require an actual study? Studies are sometimes flawed. All it sometimes takes is just one counter-example that any individual could come up with to invalidate things and shed some light on others.

 

[Vanadium 50]

Physicists, especially at my university, are so brainwashed into thinking that the complex looking integrals and other funny math symbols are the whole story to the nature of reality that they begin to blindly think through symbols and notations (and get stuck) instead of thinking using their intuition and the fundamental + - way of approaching problems.

Ah, so now the truth comes out. The problem is that you're smarter than your professors.

My advice is to drop out. Why pay the college money? It's just a waste if you're smarter than the people trying to teach you.

By the way, the curl of a constant vector is zero. Irrespective of how you notate it.

 

[Fizex]

Mathematics is expressed in the way that it is most convenient for everyone. It is a language that is used to communicate and express ideas to others as well as being a tool to discover the mechanics of nature. You are not going to convince anyone that quantum mechanics is broken with pseudo-logic.

 

[CyberShot]

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.

This is likely the most brilliant response I've received so far! Seriously, I really mean it. Your ideas resonate with my intuition.

I understand that no one's stopping me from doing physics that way; it's just that I feel many physicists just don't show appreciation for doing physics that way. They get so caught up in calculating tricky integrals, that their intuition is fried up and useless.

After all, when it all boils down, every seemingly complicated branch of mathematics is really just built off the foundation of the concept of addition and subtraction. People so easily lose sight of that, that they jump to conclude statements like calculus is discovered, when in reality it is invented (from the theory of pluses and minuses) to cope with complex calculations.

I'll say this once and for all.


Newton/Leibniz did NOT discover calculus. They invented it. It is man made, a piece of fiction. Not woven into the universe in the same way that pluses and minuses are. There was nothing to discover, calculus was never there from the beginning. Adding and subtracting things were, because there's nothing more basic than that. Plain and simple. Calculus is really just a fancy, organized, and highly notational way of representing a bunch of +'s and -'s to do things more efficiently.

 

[denks]

Mind expanding stuff. Where exactly did you prove that everything in the universe can be reduced to basic algebra? This seems to be the point all your arguments stem off yet you have not indicated why this is actually a fact besides that you tell us so. Saying "I have intuition and I say this is a fact" does not a fact make.

 

[romsofia]

I shouldn't really be butting in, but have you learned about ladder operators? If you haven't, I suggest you take the time to learn about them since, I'll go out on a limb, and say you like basic math more than advanced math

EDIT: I'm not saying you don't know how to do advanced math or that it's harder for you, I'm saying that from what I've gotten from your posts was that you like basic math more.

 

[CyberShot]

Ah, so now the truth comes out. The problem is that you're smarter than your professors.

My advice is to drop out. Why pay the college money? It's just a waste if you're smarter than the people trying to teach you.

By the way, the curl of a constant vector is zero. Irrespective of how you notate it.

Perhaps I'm a little guilty of a personal vendetta with my professors, but I'm trying to get people to see where I'm coming from.

By the way, the curl of a constant vector is zero. Irrespective of how you notate it.

Sure. I was rushing through posting trying to think of an example that I carelessly used constants in front of the unit vectors. I'm sure if you found the curl algebraically, you would also find it to be 0.

But the concept is the same, just add a variable before the unit vectors if you want non-zero curl. It doesn't make my argument any less valid.

Mind expanding stuff. Where exactly did you prove that everything in the universe can be reduced to basic algebra? This seems to be the point all your arguments stem off yet you have not indicated why this is actually a fact besides that you tell us so. Saying "I have intuition and I say this is a fact" does not a fact make.

I'm sure haven't proven it 100% rigorously, as I haven't been careful enough in my word-choice.

But if you look at my previous posts and look at the argument in logic form, it's not irrational to say it looks pretty convincing.

 

[denks]

I'm sure haven't proven it 100% rigorously, as I haven't been careful enough in my word-choice.

But if you look at my previous posts and look at the argument in logic form, it's not irrational to say it looks pretty convincing.

You also said everything can be reduced to binary and be solved by basic algebra using a computer. How for example do you represent PI in binary? Yes, PI is a human construct, however I would love to know how you would find the exact circumference of a circle given the radius without using PI (or the means by which it is derived - which still comes to a number which cannot be represented exactly in binary). Simple example but illustrates the point.

 

[denks]

Sure. I was rushing through posting trying to think of an example that I carelessly used constants in front of the unit vectors. I'm sure if you found the curl algebraically, you would also find it to be 0.

But the concept is the same, just add a variable before the unit vectors if you want non-zero curl. It doesn't make my argument any less valid.

Change of co-ordinates, from cartesian to polar as an example, to make a problem easier to solve is hardly something new. You should cover this in first year maths.

 

[CyberShot]

I shouldn't really be butting in, but have you learned about ladder operators? If you haven't, I suggest you take the time to learn about them since, I'll go out on a limb, and say you like basic math more than advanced math

Never heard of ladder operators. Again, I didn't like much matrix mathematics as it seemed highly arbitrary and more like an organizational framework of expressing things in columns and rows. Matrices were invented so that you have less strain on your eye and brain. I'm sorry to say that matrices, as useful as they may be in quantum mechanics, are the poor physicists' crutches.

Mathematics is expressed in the way that it is most convenient for everyone. It is a language that is used to communicate and express ideas to others as well as being a tool to discover the mechanics of nature. You are not going to convince anyone that quantum mechanics is broken with pseudo-logic.

Am I the only one in the world who feels that in a world without intuition, one with complete pandemonium, as described by quantum mechanics, there's not much room left for the excitement of knowing that individual opinions matter? That the universe is just uninteresting and unexplorable by human-granted knowledge. That there's nothing to look forward to, that you can never do your part, because reality just doesn't work how you expect it to. The show's over, folks. Reality is unyielding to the human experience. Everyone can just go home now.

At least I know a great genius with whom I share the same views on intuition and quantum mechanics.

Einstein - "I cannot bear the thought that an electron exposed to a ray should by its own free decision choose the moment and the direction in which it wants to jump away. If so, I'd rather be a cobbler or even an employee in a gambling house than a physicist."

 

[Chairman Lmao]

Never heard of ladder operators. Again, I didn't like much matrix mathematics as it seemed highly arbitrary and more like an organizational framework of expressing things in columns and rows. Matrices were invented so that you have less strain on your eye and brain. I'm sorry to say that matrices, as useful as they may be in quantum mechanics, are the poor physicists' crutches.

It's pretty clear your opinions are fixed and we sadly can't convince you otherwise. What do you want from us again?

 

[CyberShot]

It's pretty clear your opinions are fixed and we sadly can't convince you otherwise. What do you want from us again?

I'm sorry that I'm making personal attacks; you must understand that it's the inevitable consequence of semesters of frustration with professors and the fraudulence of physics graduate schools.

Nonetheless, that's besides the point.

What I do require from you, however, is to tell me why you think that any physical problem that requires numerical answers in the universe can't be found by adding or subtracting a bunch of quantities? If they can be, then they're the most fundamental. If they're the most fundamental, then they come pre-packaged, if you will, with reality.

 

[axiomatic7777]

What I do require from you, however, is to tell me why you think that any physical problem that requires numerical answers in the universe can't be found by adding or subtracting a bunch of quantities? If they can be, then they're the most fundamental. If they're the most fundamental, then they come pre-packaged, if you will, with reality.

Well, find me the http://en.wikipedia.org/wiki/Anomalous_magnetic_dipole_moment" of the electron, I dare you, with just addition of numbers. The anomalous magnetic dipole moment of the electron is a number, and it has been experimentally verified to an incredible precision.

You sound incredibly arrogant. Fraudulence of physics graduate schools? I hope you do know that without those graduate schools and their research, every remotely technologically-related aspect of your life would be impossible, including the computer you type your posts with, or the car you drive, or the electricity in your sockets, etc.

It happens even to the best of us physicists that the first time we see some new abstraction - be it calculus, or quantum mechanics, or quantum field theory, or string theory, or general relativity - we may get lost in the new symbols being used. Instead of writing ignorant and/or stupid rants such as yours, we try to understand the new concepts and sooner or later we acquire intuition of some sort on those new concepts/abstraction.

I do hope that you give up physics (or indeed, any technical or even humanities disciplines), because based on what you wrote so far, academia and universities can do so much better without people like you who seem to think they are the brightest human beings ever lived.

 

[Ryker]

Take for example my reductionist argument :

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.

-----
If A, then B

A.

Therefore, B.

-----

The above is a tautology. The one above the above is a bunch of statements I've made to conform to the tautology.

The argument seems to make as much, if not more, sense about the world as physics does.

* I've just thrown in multiplying and dividing for the sake of completeness, but they themselves are really just built on addition and subtraction


Why do you require an actual study? Studies are sometimes flawed. All it sometimes takes is just one counter-example that any individual could come up with to invalidate things and shed some light on others.

Well, since you're good with logic, you probably know that if a premise (A) is false, any statement (B) correlated to it can be proven true. Hence, you are right in everything you say.

 

[Fizex]

Am I the only one in the world who feels that in a world without intuition, one with complete pandemonium, as described by quantum mechanics, there's not much room left for the excitement of knowing that individual opinions matter? That the universe is just uninteresting and unexplorable by human-granted knowledge. That there's nothing to look forward to, that you can never do your part, because reality just doesn't work how you expect it to. The show's over, folks. Reality is unyielding to the human experience. Everyone can just go home now.

That's because intuition and opinion aren't science. The former expect an outcome based upon nothing at all while science doesn't expect a set outcome. Quantum mechanics is in essence a description of nature and it wasn't invented by anyone. It was discovered. It's a part of nature. You can't take away it's inherent probability. You clearly don't have the mind-set of a scientist. The excitement in physics comes from finding out something you didn't expect. You should switch majors immediately.

What I do require from you, however, is to tell me why you think that any physical problem that requires numerical answers in the universe can't be found by adding or subtracting a bunch of quantities? If they can be, then they're the most fundamental. If they're the most fundamental, then they come pre-packaged, if you will, with reality.

Once again, for I think the 4th time now, no one is debating that the + and - aren't inherent of reality. And again, the symbols are just algorithms for these operations.

Stop making the same argument over and over while ignoring advances in the current discussion. Such practice is called trolling and no one will tolerate it.

 

[Klockan3]

Am I to assume the balloon hovers in the same y-position above the floor before the train accelerates and does not move after that? If so, then the back of the train will soon meet the balloon, consistent with intuition.

Why did none else catch up on this? You are wrong here, the balloon will fly forward inside the train car till it hits the front, it won't touch the back of it at all. The reason he stated that example is to show you how your intuition doesn't work everywhere. You can look it up on google if you wonder how it works. A hint though, the reason it is moving forward in the car is the same reason it is moving upwards even though there is a gravitational force acting downwards on it, if your intuition was as great as you claim then you would have caught this one. And to be fair, if it actually had just the correct density to hover in place then it wouldn't move at all but we are assuming that its height is fixed by some frictionless thing or something.

Am I the only one in the world who feels that in a world without intuition, one with complete pandemonium, as described by quantum mechanics, there's not much room left for the excitement of knowing that individual opinions matter? That the universe is just uninteresting and unexplorable by human-granted knowledge. That there's nothing to look forward to, that you can never do your part, because reality just doesn't work how you expect it to. The show's over, folks. Reality is unyielding to the human experience. Everyone can just go home now.

At least I know a great genius with whom I share the same views on intuition and quantum mechanics.

Einstein - "I cannot bear the thought that an electron exposed to a ray should by its own free decision choose the moment and the direction in which it wants to jump away. If so, I'd rather be a cobbler or even an employee in a gambling house than a physicist."

Quantum is intuitive, it is just that particles aren't small balls like you imagined them to be. If you instead accept the plethora of evidence suggesting that particles are inseparable waves then most of it falls into place.

Never heard of ladder operators. Again, I didn't like much matrix mathematics as it seemed highly arbitrary and more like an organizational framework of expressing things in columns and rows. Matrices were invented so that you have less strain on your eye and brain. I'm sorry to say that matrices, as useful as they may be in quantum mechanics, are the poor physicists' crutches.

With your approach science wouldn't have evolved past the 15th century, Newton would be stuck calculating infinite sums etc. Back when I was in middle school I had your views, but then I realized while solving some harder problems that the formulas are the same thing as skipping calculation steps since you already know all of them. If I ask you "What is 1234+1234", do you take 1234 and add 1 to it 1234 times or do you skip steps, because 1234+1234 isn't intuitive, intuition gets you up to roughly 4-5 elements... If you skip these steps then why would it be so bad to skip other steps that you have already done?

For example when integrating I have already proved that the area under the curve of f(x)= x is x squared through 2 (From using infinite sums etc), why can't I use that result later on when I need it? Forcing yourself to always make every step will just stunt your development, so please stop with that and instead try to understand what the more complex structures actually mean. What makes our minds powerful is our ability to generalize, we are really weak in things like adding numbers, without learning to think more abstractly you will always be this feeble not being able to understand more than the most simple of Newtonian physics.

 

[DDTea]

To quote Richard Feynman regarding quantum mechanics and its lack of intuition, "If you don't like it, go somewhere else. Try a different universe."

:)

 

[ZapperZ]

What I do require from you, however, is to tell me why you think that any physical problem that requires numerical answers in the universe can't be found by adding or subtracting a bunch of quantities? If they can be, then they're the most fundamental. If they're the most fundamental, then they come pre-packaged, if you will, with reality.

This is now off topic to Academic Guidance forum. If you wish to do that, please continue in the General Discussion forum.

This thread is closed.

Zz.