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Zinjanthropos
Post  Post subject: Math and Theory Questions  |  Posted: Thu May 12, 2016 2:53 pm
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If I develop a theory and can provide the mathematics then have I really proven anything? A theory being a testable hypothesis formulated through use of the best observational techniques known to man. However from what I understand, a theory basically describes what should happen but doesn't guarantee it will.

So what does that mean for any equation I develop to support the principles of my theory? Does it mean the equation is always in doubt (stands to be corrected) and if so then does it mean I could develop an equation for just about any theory, even an incorrect one? Let's say my theory has a hole in it or is missing some unknown component, there is an equation that fits regardless?

If an equation can be developed for any good theory then does it only imply the theory is correct? To be able to produce an equation for something that could be totally wrong strikes me as a rather useless pursuit. It's like interpreting religious text so that it suits your belief.

If I have to plug in theoretical numbers to have an equation satisfy the theory then shouldn't that be a sign the theory is probably wrong?

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iNow
Post  Post subject: Re: Math and Theory Questions  |  Posted: Thu May 12, 2016 6:08 pm
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If you develop a mathematical proof, then you will have proven something.
If you develop a scientific theory using math, then you will have created a model that is subject to forecasts and testing.
In science, however, you don't ever prove anything. You only ever accumulate additional evidence of its veracity / disprove it when evidence shows it to be flawed.
Nothing is ever certain in science. Nothing is ever proven (though, for many circumstances, for simplicity we generally assume it is given overwhelming weight and consistency in the evidence).

Zinjanthropos wrote:
So what does that mean for any equation I develop to support the principles of my theory? Does it mean the equation is always in doubt (stands to be corrected)

Yes

Zinjanthropos wrote:
Let's say my theory has a hole in it or is missing some unknown component, there is an equation that fits regardless?

Encourage you to explore this same phenomenon when looking at gravity from a Newtonian perspective versus an Einsteinian one. Both are correct, given specific circumstances, and the math is extremely powerful and helpful, but clearly have holes in other circumstances (quantum level, for example).

Zinjanthropos wrote:
If an equation can be developed for any good theory then does it only imply the theory is correct?

Having an equation is often necessary, but never sufficient.

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Zinjanthropos
Post  Post subject: Re: Math and Theory Questions  |  Posted: Fri May 13, 2016 1:01 am
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Why is mathematics so spectacularly successful at describing the cosmos? Brian Greene

Quoting a book review written by Greene. The book's author is Max Tegmark, someone who claims the universe IS mathematics.

Up until recently I thought that everything could accurately be explained mathematically. In the "Does Space Move" thread I was very interested in what SpeedFreek had to say about scientific observation in an future isolated galaxy. The intimation was that an observer could formulate a legitimate theory for his galaxy universe despite not ever having key pieces of contrary evidence that unbeknownst to him is gone forever. That theory would undoubtedly have a mathematical equation associated with it. This tells me that there is a fundamental error with using equations, not that they can be unknowingly wrong, but also if you work on it long enough you can devise one that fits the observation.

As of now I'm finding it difficult to trust equations attached to theories. 1+1=2 is more trustworthy to me than an equation with many variables. It's as if mathematicians are capable of assembling equations for just about anything by merely plucking and plugging in numbers until it works. I used to be in awe of these guys but now I'm starting to wonder.

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iNow
Post  Post subject: Re: Math and Theory Questions  |  Posted: Fri May 13, 2016 1:26 am
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I suppose it's harder for us to trust things we don't really understand and with which we're unfamiliar or can't easily validate ourselves.

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Zinjanthropos
Post  Post subject: Re: Math and Theory Questions  |  Posted: Fri May 13, 2016 3:03 pm
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Is there any way mathematicians can prove their equations are not just something that works in certain situations? Is it generally accepted in the scientific community that if there is an equation that fits then the theory is sound, despite the fact a theory is not solid proof?

Mathematicians do not seem to face the same scrutiny that a scientist might, IMHO. I stand to be corrected on that.

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iNow
Post  Post subject: Re: Math and Theory Questions  |  Posted: Fri May 13, 2016 7:56 pm
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Zinjanthropos wrote:
Is there any way mathematicians can prove their equations are not just something that works in certain situations?

I'm not sure I follow. Math proofs are not the same as science and context-dependent predictions and experiments.

Zinjanthropos wrote:
Is it generally accepted in the scientific community that if there is an equation that fits then the theory is sound, despite the fact a theory is not solid proof?

Not really, no. It still has to hold up against reality.

Zinjanthropos wrote:
Mathematicians do not seem to face the same scrutiny that a scientist might, IMHO.

Apples and oranges, really. If the math is internally consistent and rooted in valid rules and premises, then no issue, but that's separate from science, which sometimes involves math but should not be conflated with it.

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Olinguito
Post  Post subject:   |  Posted: Tue May 24, 2016 4:18 pm
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Zinjanthropos wrote:
Mathematicians do not seem to face the same scrutiny that a scientist might, IMHO. I stand to be corrected on that.

Mathematicians generally use deductive reasoning whereas a scientific theorist generally uses inductive reasoning. A mathematical theorem, or a mathematical result that is proven to be true, is true for all eternity. That 1 + 1 = 2 has always been true, is still true, and will always be true, whatever happens in the Universe. With a scientific theory, on the other hand, we can only say that it is "true" (if we accept it) with a probability that may be close to 100% but never equal to 100%. Now matter how much a theory has stood the test of time, no matter how many countless times it has been confirmed by experiment, it can never be true in the same way that 1 + 1 = 2 is true. One exception is all it takes to bring a lofty theory to its knees – and it may be that we have yet to encounter the exception. For example, it used to be thought that Newton's laws had the final say on the motion of all bodies in the Universe. The theory however could not account for the results of the Michelson–Morley experiment, which showed that the speed of light is independent of the relative motion between source and observer. This was subsequently explained by Einstein's theory of relativity, showing that Newtonian theory broke down for speeds close to the speed of light. Newtonian theory is therefore only an approximation, not the absolute truth that 19th-century scientists thought it to be.

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Zinjanthropos
Post  Post subject: Re: Math and Theory Questions  |  Posted: Sat Jul 16, 2016 9:38 pm
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My point is that we don't know what or if anything happened prior to the BB. Since we cannot observe it nor do we have any evidence of there ever being a time or whatever before the BB, one could take the same stance as someone who million of years from now is staring at an empty expanse beyond the galaxy and theorizing on its origin with key evidence gone forever. If there's an equation that fits the isolated galaxy scenario then is any equation re the universe worth the paper it's written on?

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"Science is much better than religion because our faith is shakeable. There can be something I believe with all my heart to be absolutely true, and the minute there's evidence that it isn't true, I throw it out like yesterday's garbage"-Krauss


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