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Studiot's five minute course in thinking and proof.

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This thread was inspired by the recent long philosopy thread and by Edward De Bono.

The discussion is about the difference between mathematical proof and scientific proof.

 

One form of proof that is available in Mathematics but best avoided in Science is that of showing the negation of a proposition leads to a contradiction vis-a-vis some more basic statement.

For example the proposition that gravity causes objects to fall to the ground is false.

I struggle up a podium lugging a large ball.
I stretch, holding the ball out and shout to an assistant standing below "Catch"
I then drop the ball

But instead of falling the ball shoots upwards.

Therefore gravity is false.

 

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The subject is an interesting one, but I need a little more padding in that to understand the point.

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Scientific questions are multi faceted with an unlimited amount of inputs to a situation whilst  logic and maths attempts to clear the scenario of extraneous inputs?

For logic to be correct it only needs to be self consistent whilst that is just a necessary requirement for physical/scientific questions

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2 hours ago, studiot said:

One form of proof that is available in Mathematics but best avoided in Science is that of showing the negation of a proposition leads to a contradiction vis-a-vis some more basic statement

The equivalent of showing a logical contradiction in mathematics is to show a contradiction with observations in physics.

Quote

But instead of falling the ball shoots upwards.

Therefore gravity is false.

In reality, the ball doesn't shoot up and therefore the hypothesis "the proposition that gravity causes objects to fall to the ground is false" (reductio ad absurdum) is shown to be false. 

Edited by Strange

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6 minutes ago, Strange said:

The equivalent of showing a logical contradiction in mathematics is to show a contradiction with observations in physics.

In reality, the ball doesn't shoot up and therefore the hypothesis "the proposition that gravity causes objects to fall to the ground is false" (reductio ad absurdum) is shown to be false. 

If the large ball is filled with helium it does shoot up,surely.

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1 minute ago, geordief said:

If the large ball is filled with helium it does shoot up,surely.

This is what I mean by thinking. +1

(This harps back to an Edward De Bono demonstration)

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25 minutes ago, studiot said:

This is what I mean by thinking. +1

(This harps back to an Edward De Bono demonstration)

It is quite relatively  easy to find holes in others' reasoning but much harder ,I believe to find them in your own.

That may be a platitude.

 

EDIT: that may be back to front as  I just edited my post (so  I did find my own mistake)  whereas  I actually rarely find logical mistakes in others' reasoning :I  generally object to what they say and try in vain  to  work out where they are wrong.

Edited by geordief

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5 minutes ago, geordief said:

If the large ball is filled with helium it does shoot up,surely.

I thought that too, but thought it too obvious. Also "I struggle up a podium lugging a large ball" negates that possibility because you would not have to lug it.  Anyway, it still conforms to the proposition, because it is the heavier air that falls, not the ball.

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Your path up to the podium could be encumbered. It could feel like lugging if it was just awkward.

 

Hope we are not going to fall out over this;)

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2 hours ago, geordief said:

Your path up to the podium could be encumbered. It could feel like lugging if it was just awkward.

 

Hope we are not going to fall out over this;)

Can't see any of us falling out over this so long as the new troll stays out of this thread.

I described a situation in which I was deliberately tricking you by pretending to lug the ball.

You can't do this in Mathematics 'proofs', only Science ones.

There was also a hint in the De Bono reference and the thread title was taken from his book 'A Five Day Course in Thinking'

https://www.google.co.uk/search?q=edward+de+bono&ie=utf-8&oe=utf-8&client=firefox-b&gfe_rd=cr&dcr=0&ei=w2HSWbDHEpyq4gTeq6xY

 

One of De Bono's demonstrations went thus:

In front of the lecturer was a table.

On the table was a nearly cubical opaque box. (I can't remember if he brought it in or it was there at the start)

The box was ignored by the lecturer, but partway through it toppled over onto its side on the table with a loud bang and just laid there.

The lecturer continued to ignore the box until the end of the lecture when he said

"You all saw what happened. Why did the box topple over?"

 

One of his books goes through in excruciating detail the why mechanisms proposed by many famous physicists could not produce the observed action.

 

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3 minutes ago, studiot said:

"You all saw what happened. Why did the box topple over?"

 

All I can think of is a firework attached to one side which explodes, thrusting burnt gunpowder sideways. This would give an impulse which would topple the box (with a bang). This would of course only work if the box is not airtight. (Reminding me of the lorry with a 5 ton load limit, carrying 6 tons of birds.....)

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I should have said there was no visible action other than the box falling over.

And there were no hidden jacks poking the box over the table was an ordinary classroom table.

As far as I am aware, DE Bono never revealed the mechanism, which must have been inside the box.

Edited by studiot

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I obviously completely missed the pint of the initial example. (And I still don't get it.) I thought it was supposed to show that you can't prove or disprove a physics hypothesis by pure reason.

36 minutes ago, studiot said:

As far as I am aware, DE Bono never revealed the mechanism, which must have been inside the box.

There was no box and so no mechanism to reveal.

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On ‎2‎-‎10‎-‎2017 at 1:12 PM, studiot said:

The discussion is about the difference between mathematical proof and scientific proof.

I don't think you can make a real distinction between math and science, they are too intertwined...every science uses mathematical concepts. Take E=mc² for example. The logical interpretation of this concerns physics yet you use Math to make a derivation from this equation.

*You can not say that you're good in Science if you don't know how to use its Language which is Math *

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On 02/10/2017 at 5:54 PM, Strange said:

There was no box and so no mechanism to reveal.

Where do you know this from?

 

2 hours ago, Itoero said:

I don't think you can make a real distinction between math and science, they are too intertwined...every science uses mathematical concepts. Take E=mc² for example. The logical interpretation of this concerns physics yet you use Math to make a derivation from this equation.

*You can not say that you're good in Science if you don't know how to use its Language which is Math *

Is your position that there is no difference between 'proof' in Mathematics and 'proof' in Science?

The example I gave arises because Mathematics is built on axioms and propositions, proof is a process of verification of the consistency of any proposition with what precedes it in the structure.

Scientists do not have this absolute luxury since there may be a scientific phenomenon beyond their knowledge that negates their prediction.
As a result of this scientific 'proof' is really about the verification of a prediction.

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30 minutes ago, studiot said:

Where do you know this from?

Occams Razor. As it is attributed to an unnamed professor from an unnamed university it sounds like an urban myth. SO I assume it is just a thought experiment.

 

2 hours ago, Itoero said:

I don't think you can make a real distinction between math and science, they are too intertwined...every science uses mathematical concepts. Take E=mc² for example. The logical interpretation of this concerns physics yet you use Math to make a derivation from this equation.

You can prove things is mathematics without reference to anything in the real world. You can't do that in physics.

However, one thing they both have in common is that they both look like plurals but are singular nouns.

Edited by Strange

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36 minutes ago, Strange said:

Occams Razor. As it is attributed to an unnamed professor from an unnamed university it sounds like an urban myth. SO I assume it is just a thought experiment.

So you were just guessing.

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13 minutes ago, studiot said:

Is your position that there is no difference between 'proof' in Mathematics and 'proof' in Science?

I suppose it's about whether the mathematical concepts which are used have a physical meaning or not. When you proof a mathematical concept with a physical meaning then proof in math and science are the same thing. You have the density matrices, metrics...

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6 minutes ago, Itoero said:
1 hour ago, studiot said:

Is your position that there is no difference between 'proof' in Mathematics and 'proof' in Science?

I suppose it's about whether the mathematical concepts which are used have a physical meaning or not. When you proof a mathematical concept with a physical meaning then proof in math and science are the same thing. You have the density matrices, metrics...

Perhaps you could explain to me how this is an answer to either my question directly to yourself or to the original post?

Either the 'proof' is the same in Mathematics and Physics or it is not.

You seemed to me to be asserting that it is the same so I asked for confirmation since My OP operates from the premise that it is not the same and furthermore I offered one example of difference.
I do not claim it is the only example.

Edited by studiot

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6 minutes ago, studiot said:

So you were just guessing.

Just like all the other suggested solutions. 

6 minutes ago, Itoero said:

I suppose it's about whether the mathematical concepts which are used have a physical meaning or not. When you proof a mathematical concept with a physical meaning then proof in math and science are the same thing. You have the density matrices, metrics...

You can mathematically prove a physical theory but that doesn't tell you if it is correct or not 

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10 minutes ago, studiot said:

Perhaps you could explain to me how this is an answer to either my question directly to yourself or to the original post?

Either the 'proof' is the same in Mathematics and Physics or it is not.

You seemed to me to be asserting that it is the same so I asked for confirmation since My OP operates from the premise that it is not the same and furthermore I offered one example of difference.
I do not claim it is the only example.

It can be the same, I suppose it's about whether the mathematical concepts which are used have a physical meaning or not.(Isn't this a direct answer on your question?) I don't understand why you make such a distinction between math and science.

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1 hour ago, Itoero said:

 I don't understand why you make such a distinction between math and science.

Because a valid mathematical proof might not describe the real world.

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13 hours ago, Strange said:

Because a valid mathematical proof might not describe the real world.

That's true but math is used in nearly all sciences. The M-theory is in a sense a mathematical description. For people that believe in M-theory then math with a physical meaning is their evidence for the existence of strings.

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40 minutes ago, Itoero said:

The M-theory is in a sense a mathematical description.

Not just in a sense. :)

Quote

For people that believe in M-theory then math with a physical meaning is their evidence for the existence of strings.

Nope. The existence of the math is not evidence of anything. The only way you can know if the math describes reality is to test it against reality. 

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