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Math is not Science / Was Euler Wrong?

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Math is not Science / Was Euler Wrong?

Postby GenePeer » Jul 5th, '11, 17:46

EminemBase, if you are a troll then congratulations! You've really got me riled up on this.

Now please first throw your bullshit English dictionary and get a fucking scientific dictionary to explain this TECHNICAL terms.

Science is the area of knowledge where people use the scientific method as a way of knowing/learning. It's as simple as that. So what is the scientific method? It's usually broken down to four stages:

1. Make a "generalisation" based on experience and observations, this is the theory
2. Create a hypothesis from this generalisation
3. Make predictions based on this hypothesis
4. Experiment and see if hypothesis is right!

If hypothesis is right, you make a new hypothesis and start from 2 again. If the experiment fails, revise your generalisation and start from 1. This is the key part, you will never say the theory is correct because it hasn't passed all possible tests yet! In fact, there are infinitely many tests to logically you will never now if it's right!

I really don't have the time to give example of how this really works but thats it. If it doesn't follow those steps, there is no way you can call it science.

Now in math, you don't need to do any observations, any experiments, and any predictions! You simply prove a theory and you know it's correct. Therefore it isn't a science!

Side note: Science isn't just physics, chemistry, and biology. There's also things like Political Science or Economics.
Last edited by GenePeer on Jul 12th, '11, 13:56, edited 1 time in total.
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Re: Math is not Science

Postby EminemBase » Jul 5th, '11, 17:55

^ Maths ISSSSSS a science.

You're going to make yourself look extremely stupid when people who are more knowledgable about this than I am come in on this. You're now disputing a history of definition and a known fact, based on your absolute arrogant ignorance.

You think you can just bluff your way through defining things and that they're true because you think they're true.

Science is knowledge. It organizes knowledge in the form of tests and explanations about the world around us, it proves things with reason and LOGIC.

Maths is a strain of science. It's not a separate thing. There's a lot of science that is more provable than other science. Some science is purely theoretical and even the top in the field aka Quantum Physics basically don't fully understand it.

But they use maths in conjunction with it, to know that it's true. Maths is used in science and IS a science. That's just a fucking fact and you're now disputing... not me or my opinion, you're disputing a basic truth. You may as well say English is not a language, you moron.

Also maths does use predictions, as it leverages theories and helps create predictions through its foundation. There are laws of mathematics the same as there are laws of physics. And you make predictions and equations out of those laws. Maths isn't exempt from experiment. There are absolute truths to it, but that doesn't mean it's not a science lmao. You're such an idiot man.

Maths is studied as a science at university and is used in conjunction with other areas of science. Science isn't one thing, it's a collection of ideas and ever-progressive methods. Are you now saying universities have it wrong too.
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Re: Math is not Science

Postby EminemBase » Jul 5th, '11, 18:04

Amadeo wrote:Name me one mathematical theorem that wasn't founded upon experiment/observation and I will kill my mother.


:laughing:
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Re: Math is not Science

Postby GenePeer » Jul 5th, '11, 18:07

Do you know the proof of pythogarus' theorem? There's absolutely no prediction or testing in it.

Proof by mathematical induction uses no testing in it! e.g. 1 + 2 + 3 + ... + n = n(n+1)/2

Proof by contradiction uses no testing in it! e.g. Square-root of 2 is irrational.
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Re: Math is not Science

Postby GenePeer » Jul 5th, '11, 18:47

Ok, let's see if this type of so called "experimentaion/testing" is the same. The result in math becomes immortalized, whereas in science (biology, chemistry, physics, economics, etc) the result is only there until further notice.

One experiment is by letting nature you don't and are trying to understand do everything, while you observe.
The other experiment is by letting pure logic do everything, while you "observe".

If you can't see that you're reaching by claiming those "testings" are the same then I don't know what to say.

In fact, I don't see how it's "experimenting" when I say "if x=3, then 2x=6". And it's only these types of statements that are used when proving in math!
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Re: Math is not Science

Postby GenePeer » Jul 5th, '11, 19:46

Amadeo wrote:The result is only there until further notice if scientists are approximating something. Sorry, but approximating things is usually more practical and useful and actually helps humanity progress.

The very point I tried to make in the last thread is scientists are always approximating. Sooner or later what scientists thought was right will eventually fail one of their tests. I have nothing against approximation but if all the other science subjects are approximating and mathematics is not, don't you think there's something wrong with the categorization?

Mathematical concepts aren't just innate. They are all fundamentally based on experience and observation.

When you were first taught math, yes! But it has absolutely lost all it's characteristics to nature. I no longer imagine a bundle of stick doubling, when I multiply by two. The last time I did that I was probably in grade 2/3. I don't even remember! Things like complex numbers have no relation to real life quantities whatsoever! In fact, excuse the use of hypothetical cases, if I was a math whiz capable of serious mental calculations, and all of a sudden I lost all my senses (sight, hearing, taste, touch, smell), it wouldn't stop me from doing math! I no longer need reality-comparisons to explore new things in math! There's nothing stopping me from proving the irrationality of the root of 2 if I didn't know so already. But can you really say the same about any "other" science? Can someone really test their new theories without their senses? No.

Again, if all the other science subjects require empirical evidence and mathematics does not, don't you think there's something wrong with the categorization?
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Re: Math is not Science

Postby GenePeer » Jul 6th, '11, 09:07

It's simply because it wasn't such an important thing, and was not really investigated by mathematics. No one was going to through all tons of papers Euler wrote just to make sure they are all correct. It's more of a math thing Euler was trying to formalize but people already knew there was something not right with square-root of -1! It's like I write a blog and in one of my entries there's a mistake. This particular entry isn't adding anything new to math, so no one will notice! However, if I claim to have solved one of the millennium problems, the mistake will certainly be noticed!

You are also completely misusing the word experiment! In science, you use the experiment to collect empirical data. Not once in math will a proof require empirical data! So saying you're experimenting like science is stretching the limits of definitions. Just because you tried to solve, doesn't qualify as a scientific experiment!

Amadeo wrote:Don't get the idea that mathematics is always right. Read up on Godel's incompleteness theorem, please.

And what has that got to do with mathematics being a science? All of a sudden we gather empirical data and make approximations like the rest of science?

I really don't get what the whole big deal is, with this! Math is just statements like

if this is true, then that is true, if that is true, then that is true, etc...

And if we are going to assume, the very first if clause as false, you're not doing anything interesting! Fine, all mathematics is false (still doesn't make it a science)! What's interesting is if you assume just this small set of carefully crafted axioms to be consistent, then you're open to a whole new world of exploration and wonder! But never will you reach a point, where you prove one thing to be both right and wrong (since the first assumption was the axiom is consistent)!

You can't draw the same comparison to science! In science, theories are constantly evolving due to conflicts.

Amadeo wrote:TL;DR : They both do the same thing, except using different methods.

If mathematics specifically uses different methods from all the other science subjects, then putting it under science is a stretch!
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Re: Math is not Science

Postby GenePeer » Jul 6th, '11, 10:48

Chemistry: 3mm^3 of H20 was produced in ten seconds.
Biology: The number/mass of bacteria doubled in a day.
Physics: Ten complete oscillations of the pendulum took 14s.
Psychology: In 2 weeks, 75% of the patients given nothing but placebo show improvement.
Economics: The increase in prices by 10% has created an increase profit of 20%.
Math: When I was small, in a time I can now barely remember, I saw that 3 people giving me 4 apples each meant I had 12 apples in total.

They all use empirical data indeed.
----------------------

You now what I said, those experiment are totally different because for one, I can test the validity of n^2 - n + 41, without the use of any of my senses! No emprical data gathered. Tell me how you can claim to have a new theory in science without showing data?

----------------------

Approximations are made in math, if there's PROOF that it is actually an approximation. Like using taylor series to approximate sin and cosine function.

If you have proof that the approximation is always within a certain range from the real value, and can easily show that some other factor is way beyond that approximation, then it's obviously also way beyond that actual value.

But not once will it be accepted in a mathematical proof that since plotting a graph of the number of primes less than x against x produces a curve close to ln(x)/x, that this is now the official approximation to be used for even greater values of x that haven't been graphed yet!

If someone starts chanting numbers and from the very beginning goes on saying "1, 1, 1, 1, 1, 1, 1,...". Science will accept the next number to be one until something happens, and many theories will be based on this. In math, no theory would ever be based on this and accepted because there's no guarantee that the next number x is with the range 1-a<1<1+a, for a fixed real positive number a.

Justifiable approximation (in math) is very different from approximation used in science.

Amadeo wrote:Approximations are made in mathematics all the time. All the time.

Nobody knows how to integrate x^x exactly. Nobody knows the exact values of the normal distribution. Nobody knows the exact solution to x * e^x = 1

It can be proven that x is within a given range from the proposed solution/approximation with use of taylor expansion. And x can be found with arbitrary precision. You want it to 5 decimal places? No problem, 100 decimal places possible. It's an irrational number so trying to find the exact form in decimal form is pointless as it has infinite numbers, just like pi or root of 2.

But here's another place where math differs from science again, the exact value of this solutions isn't that important. It's only important when scientist want to use math to understand their observations! Mathematician are simply creating tools for solving equations through theorems, and it's upto scientists to come up with the usefulness in real world.

Just because I'm creating a car, it's doesn't automatically make me a driver!
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Re: Math is not Science

Postby SajN » Jul 6th, '11, 11:11

Eminem fans aren't supposed to be math-geeks :'(
! Is He Nuts? No, He's InSajN !
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Re: Math is not Science

Postby GenePeer » Jul 6th, '11, 11:26

The ultimate example I can think of: Circumference of a Circle!

Science:

I get this idea that there should be a relation between a circles radius and it's circumference. So when I'm toying around with the idea, I get a compass and draw three circles of radius 1cm, 2cm, 4cm. Measuring the circumference, 3.14, 6.28, 12.56, and I see that each time the circumference is doubling when I double the radius! This must mean the circumference is directly proportional to radius. Which is written as:

C = kr (k being constant of proportionality.)

Now to find the value of k, I draw many more circles with all various radii, and the plot a graph of Circumference against radius. Due to experimental error, the points don't line on a perfect line, so I draw a line of best fit. This line is the best approximation of the above relations.

We know that the gradient is the coefficient of what goes on the x-values (radius in this case) so, the gradient must be equal to the constant of proportionality. I find the gradient is 3.14 and I call it pi.

Now I write to the scientific community saying I've found a new theorem: C = pi*r, and the data above is my evidence. This will be accepted and if lucky I get a nobel prize for it.

But simply because the finite number of circles I plotted were (nearly) on a line, it doesn't mean all circles will be. So IT IS NOT A MATHEMATICAL THEORY YET!!

Math:
But it was given as a formula? So it must have something mathematical truth to it, while we're not sure if it's true or not C=pi*r is a conjecture.

Now, I'm now the other guy's twin I'm trully intrigued by his new discovery. However, I'm not convinced yet. I want to prove it!

Using calculus/limit theory, I'm able to prove that indeed C = kr. With respect to my inspiration I also call it pi, and to help my dear twin brother, I come up with a method of finding the value of pi to arbitrary precision.

Once I submit this to the mathematics community, I've found proof for the conjecture!

Conclusion: Real-life observations can inspire math theories, but when it comes to math, they lose all attributes to real-life and are purely abstract. Science is for real-life, math is abstract! This is a difference big enough to disqualify it from science.

Edit: Even though, it's always been called Fermat's Theorem, it was always a conjecture and became a theory once it was proven.
Last edited by GenePeer on Jul 6th, '11, 11:29, edited 1 time in total.
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Re: Math is not Science

Postby GenePeer » Jul 6th, '11, 11:32

Now you're crossing the blurred line between computer science and mathematics.
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Re: Math is not Science

Postby GenePeer » Jul 6th, '11, 12:39

My bad with this formula, but you got my point!

Amadeo wrote:the scientist in your example, as long as the experimental conditions were controlled well enough, did nothing wrong. He was being a scientist, and approximating the circumference of a circle. In the absence of any theoretical equations that math can give him, he should model it empirically...that's what he did.

Exactly, that's what he did because he's a scientist. No mathematician would do that and expect it to be accepted as a math theory.

Amadeo wrote:The mathematician (who came up with the EXACT formula) also did nothing wrong. He was being a scientist.

He threw away all of the earlier data given and started from scratch trying to prove the formula. At that particular moment, even if he's normal a physicist, he stops being one, and turns into a mathematician. A scientist will never say, I don't care about that data! A mathematician will. Look at the Erdos-Straus conjecture for instance, a computer search has shown that it is right for n up to 10^14, but mathematicians still don't care.

When Archimedes came up with the principle of buoyancy, he was being a scientist. When Archimedes proved that A=pi*r^2, he was being a mathematician. He then approximated it to 22/7 to help the rest of his calculations in SCIENCE! Math and science help each other, but that doesn't mean they're one and the same!
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Re: Math is not Science

Postby EminemBase » Jul 7th, '11, 05:19

Amadeo wrote:Mathematics relies on the other sciences just as much as other sciences rely on mathematics.


:y: Brilliant sentence.
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Re: Math is not Science

Postby Mahmoud48 » Jul 7th, '11, 05:58

2+2 doesnt always equal 4???
can u nerds tell me how
jk i really wanna know :shakehead:
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Re: Math is not Science

Postby GenePeer » Jul 8th, '11, 17:21

I don't know how I missed this when you posted it. Maybe your confidence fooled me or I'm just bad at noticing errors.
Amadeo wrote:The square root of -1*-1 isn't -1.

Really?

EminemBase wrote:
Amadeo wrote:Mathematics relies on the other sciences just as much as other sciences rely on mathematics.

:y: Brilliant sentence.
GenePeer wrote:Math and science help each other, but that doesn't mean they're one and the same

:coffee:
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