Math feels like discipline with no reward.

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iamnotaparakeet
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11 Feb 2012, 12:59 am

RushKing wrote:

Math is the only subject my brain won't gain pleasure from for some reason. How can I gain pleasure from just memorizing, following rules and steps? It makes my mind feel like a slave. I learn allot quicker when I gain pleasure from knowledge, maybe that’s why I fail at math.

Study mathematics in conjunction with a study of physics then, since you'll be able to see how incredibly useful the mathematics really are.

monkeykoder
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11 Feb 2012, 1:14 am

iamnotaparakeet wrote:

RushKing wrote:

Study mathematics in conjunction with a study of physics then, since you'll be able to see how incredibly useful the mathematics really are.

You're confusing Mathematics with the application of Mathematics.

marshall
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11 Feb 2012, 1:15 am

Declension wrote:

monkeykoder wrote:

Here we may contend with differing definitions of the word "true" or "truth"

I think so. For me, a claim can only be true or false when it refers to objects in "reality".

So for me, mathematical claims cannot be true or false, because there are no mathematical objects in reality for them to refer to.

However, metamathematical claims can be true or false, because they refer to proofs, and proofs exist in reality.

e.g. "There exists an empty set."
-mathematical claim
-neither true nor false

e.g. "In ZFC, the statement "there exists an empty set" is provable."
-metamathematical claim
-true

I do feel that ZFC is arbitrary to some degree, but I do think certain things arise more naturally than others. You can play around with axioms but in the end there is a strong sense that "all roads lead to Rome". If some other intelligent life forms came up with their own mathematics I have a strong feeling they would have similar axioms and proofs. The more controversial matters concerning axioms mostly crop up at a level that has less connection to the physical world. The existence of certain pathological mappings and structure of higher order transfinite numbers is very sensitive to the axiomatic framework, but the part of set theory needed to do calculus and differential equations is a bit more settled.

Declension
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11 Feb 2012, 1:25 am

marshall wrote:

You can play around with axioms but in the end there is a strong sense that "all roads lead to Rome".

I definitely agree that aliens have the concept of natural numbers. That is an extremely "natural" concept (as the name implies!)

Also, aliens are studying the same physics as us, so presumably the mathematics that they use to model the physics is isomorphic in some sense.

However, I strongly suspect that there are some fields of mathematics that are "cultural", i.e. if we thought of mathematics from a different viewpoint, it would never occur to us to study them. I have no idea which fields these are, because I cannot escape from my assumptions.

monkeykoder
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11 Feb 2012, 1:33 am

marshall wrote:

Declension wrote:

monkeykoder wrote:

Here we may contend with differing definitions of the word "true" or "truth"

I believe contrary to popular thought that reality does not create truth but rather truth creates reality. ALL that is true exists. EVERY axiom is true in it's own space. Physics/Biology/Science in general are merely languages to describe the consequences of a given set of axioms that gave rise to us.

monkeykoder
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11 Feb 2012, 1:50 am

Declension wrote:

marshall wrote:

You can play around with axioms but in the end there is a strong sense that "all roads lead to Rome".

I am at this exact moment trying to postulate an alien race that has no concept of natural numbers. It might take me a few weeks to break that far out of my limited human brain.

monkeykoder
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11 Feb 2012, 1:59 am

Dang I've come up with a few thought processes which might come to the conclusion of having an alien being that has no concept of the natural numbers but I don't know that I could get anyone to perceive it as "alive".

ruveyn
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11 Feb 2012, 11:51 am

monkeykoder wrote:

Do newborn babies have any concept of number? No. But they eat and eliminate. Yup. They are alive.

ruveyn

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11 Feb 2012, 12:08 pm

ruveyn wrote:

monkeykoder wrote:

Do newborn babies have any concept of number? No. But they eat and eliminate. Yup. They are alive.

ruveyn

I guess I have to amend that to say "mature sentient alien being". I think I am narrowing down to a perception of the universe that would actually forbid a concept of the natural numbers. Of course my usual thought experiments can get a little too far out there to actually be useful for the conversation.

Ancalagon
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11 Feb 2012, 2:52 pm

marshall wrote:

There are actually a lot of fractal software programs that contain their own language and compiler that will do high precision floating point math on complex numbers very efficiently.

True, and if you just want to make fractal images, grabbing an already-written program is more efficient. But he did say he wanted to write that code, and simple code to do just that can be written in 15 lines or so. Writing code that does something that cool (even if you got the recipe from somewhere else) is pretty cool itself.

I first wrote that code in an interpreted BASIC on a very slow computer by following the code from a book. I started playing around with it, and images sometimes took hours to make. Then I tried out a free software package (fractint) and it did things almost instantly on the same computer (at least if you weren't zoomed in a lot).

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marshall
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12 Feb 2012, 7:32 pm

Ancalagon wrote:

marshall wrote:

There are actually a lot of fractal software programs that contain their own language and compiler that will do high precision floating point math on complex numbers very efficiently.

Yea. The pseudo-code in c would be something like...

bound = 4.0;

for ( x_grid = 0; x_grid < x_gridsize; x_grid++)
for ( y_grid = 0; y_grid < y_gridsize; y_grid++) {

x = grid2float(x_grid)
y = grid2float(y_grid)
z1 = 0.0
z2 = 0.0
bail = false;

for ( i = 0; i<256; i++ ) {

new_z1 = z1*z1 - z2*z2 + x;
z2 = 2*z1*z2 + y;
z1 = new_z1;

if (bound < z1*z1 + z2*z2) { bail = true; break; }
}

if (bail) { colorgrid(x_grid, y_grid, color( i ) ); }
else { colorgrid(x_grid, y_grid, "black"); }
}

iamnotaparakeet
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13 Feb 2012, 5:00 pm

monkeykoder wrote:

iamnotaparakeet wrote:

RushKing wrote:

Study mathematics in conjunction with a study of physics then, since you'll be able to see how incredibly useful the mathematics really are.

You're confusing Mathematics with the application of Mathematics.

No, I'm not. Seeing the application of mathematics to reality was a great encouragement to me to keep learning more in the field of mathematics, and seeing how everything behaves in a mathematical manner allows for a better understanding of the mathematics itself.

Zorae
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15 Feb 2012, 12:47 am

iamnotaparakeet wrote:

monkeykoder wrote:

iamnotaparakeet wrote:

RushKing wrote:

Study mathematics in conjunction with a study of physics then, since you'll be able to see how incredibly useful the mathematics really are.

You're confusing Mathematics with the application of Mathematics.

Realizing that everything behaves in a mathematical manner fascinated me and made me value math much more. But I do feel a bit of distain towards physics as it is inductive and therefore impossible to be absolutely true (just very likely that it's true). Math, however, is absolute. If the constants of the universe were to change, then all of our current knowledge of physics would be wrong and new laws/rules would have to be written. But no matter what they are, 1+1=2. Math isn't just true everywhere in this universe, it's true in every universe, and that's a godly quality in my eyes.

Math's consistency is what I love about it. It's not subjective like english or history. If you follow the correct steps, you'll always get the correct answer. Because math itself is logical, the steps you need to apply are usually logical themselves (yes usually, partial differential equations can go f*** themselves). I love working on a hard math problem. The amount of focus and energy you put in it makes the moment when you have an epiphany/finally get the correct answer very rewarding.

Also, fractals are beautiful and awesome!

marshall
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16 Feb 2012, 6:13 pm

Zorae wrote:

I agree with most of that.

As for math being absolutely true in every universe I'm not so sure. Not all mathematical logicians have made up their mind on whether the axiom of choice is "true". Then there's still something logically disconcerting about the concept of infinity. Godel's incompleteness theorem showed that any axiomatic system that hypothesizes the existence of the set of all integers allows for certain statements that must be either true or false in reality but cannot be proven either way.

Declension
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16 Feb 2012, 6:29 pm

marshall wrote:

As for math being absolutely true in every universe I'm not so sure. Not all mathematical logicians have made up their mind on whether the axiom of choice is "true".

I don't think that the axiom of choice is the sort of thing that is either true or false. However, the statement "in ZF, the axiom of choice is equivalent to the well-ordering principle" is true in every possible world. Metamathematics is absolutely true.

kxmode
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16 Feb 2012, 9:49 pm

RushKing wrote:

Let Jack Black show you how math can be fun!
[youtube]http://www.youtube.com/watch?v=aa8U0nL-KXg[/youtube]

Beyond that you can go to http://www.khanacademy.org/ There are videos for virtually EVERY aspect of math from basic all the way up to the very advanced. Also the exercises are presented like a game. You earn achievements and level up as you progress! Check out the video below to get an overview.

[youtube]http://www.youtube.com/watch?v=hw5k98GV7po[/youtube]

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