The Scientific method and Math Dogma.

I would like to start a topic that shows a conceptual inconsistency between the philosophy of science and math.

If you consider the math operation of dividing by a fraction such as 1/(1/2)=2, although this is accepted math, this operation has no physical basis in reality, because it violates the conservation of energy.

For example, if I had one gallon of gasoline and divide by a 1/2 , I now have two gallons of gasoline. This math operation could solve the world's energy crisis and implies perpetual motion is possible. Science would say this is in violation of energy conservation and would be called perpetual motion. How can science continue to use that math operation knowing it cannot be proven in the lab?

My explanation was this math operation appeared before science knew about energy conservation. Since science was young, the operator may have appeared valid, when science was just cutting its teeth. It became a tradition.

In the bible, Jesus feeds thousands with just a few fish and loaves of bread. Conceptually all he needed to do was divide by a fraction, such as 1/500 and he got the math and science accepted multiplier. So it is valid, or is there a dual standard as to who is allowed to use perpetual motion, extras, to solve equations and problems.

 

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Q: How many halves are in a whole?
A: Two

What do you find difficult about this?

 

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And your "explanation" is nuts. Of course math was being developed long before the concept of conservation of energy - but that has nothing to do with your problem in this area.

The whole problem here is that you simply do not understand math and it's operations! <shrug> I'd be willing to bet you don't believe in negative numbers either.

 

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You don't understand what math is.

If you try to use the wrong wrench to turn a bolt and the bolt doesn't turn, it isn't the fault of the wrench or the bolt, it is YOUR fault.

Math is just a tool.

 

No, you have two half-gallons.

 

If I have X gallons and I divide it by two, I have X half gallons. Conceptually, the result, the half-gallon, multiplied by the divisor, leave you with the original X gallons.

BUT, if I have X gallons and I divide it by one half, what do I have? In that case, you can conceptualize the answer in a similar way. The answer has to be a number (Let's say "Y") such that Y * 1/2 = X. That means Y=2X

Math and science are different, certainly, in that math is pure logic. Math must be true always and without exception. Science cannot say that, as scientific conclusions proceed from the assumption that if a thing happens to have been true in the past, it will continue to be true in the future. While that's a reasonable assumption quite often, obviously it's not always true. Even if conservation of energy is a "law" and has held in every case since the beginning of the universe, that is not an ironclad logical proof that it won't be violated in the next time you check. That said 1 divided by 1/2 will always equal 2, even a trillion years from now.

 

You forgot step (2).

(1) Y * 1/2 =X
(2) (Y * 1/2)*2=2*X
(3) Y = 2*X

 

wrong.
let's replace the numbers with letters, makes it easier to understand.
a/b=c, where b is a fraction.
you will have the number c of b fractions.
in your cited example 2 one half gallons.
if b was 1/10 then you will get 10 because there are ten 1/10 in a whole.

just because you do not understand what you are saying doesn't mean the fundamental laws of math will change.

i just proved it to you above, and probably every other poster in this thread has too.

the operation appeared as soon as fractions came on the scene.

. . . should be the last place to look to find answers to math problems
problem solved.

 

You guys are defending a math religion dogma, that appears before modern science, but have yet to prove this operation can occur in reality. If you replace numbers or physical things with letters you can hide the magic trick with the smoke of an abstraction. Show us with a real example. The operation does not work with real things in hard reality. Science has to deal with reality, with energy conservation one aspect of reality. If I have one gallon of gasoline and divide by 1/2 I get 2 gallons. If we assume this is possible, the operation of dividing by half, in this case, would need at least the energy of a gallon of gasoline. I could use the first gallon to boil crude oil and distill two gallons. But the operation does not tell us any of this.

One compromise is this operation cannot be used unless you can show the source of energy and a possible process. When Jesus divided a few fish and bread by a fraction, to feed thousands, he used this math operation, but with the assumption God has access to whatever energy is needed. The actual energy materialization process for fish and breads us still unknown, but is it accepted via this math operation? The answer is no since science will not support perpetual motion unless it uses the operation.

Math is not as pure as the sales pitch. Some math dogma started before modern science and was never questioned; allows fantasy science. Don't get me wrong, practical results can be useful. It does not matter if we use irrational dogma and get useful result. But when we want to model reality, this math dogma needs to be justified so we are not getting hidden perpetual motion using real things.

 

why do you even bother buying gasoline then?
just buy yourself a thimble full and divide it up into 1000s of gallons.
damn dude, you just solved the energy crisis

will this work for money too?
you mean i can get rich just by dividing my penny?

you cannot possibly be serious about this.

 

I was demonstrating how this math operator leads to fantasy results. I assume mathematicians came up with this before science defined the conservation of energy. This may have been possible in the middle ages since unicorns could help using magic. It is not natural, in the modern world, but since it does not work with anything real.

But I also said, practical results do not have to be real to be useful. Just if we use this operator to define the hard reality of nature, there is a problem, since there is a magic step that make use of unicorn magic.

 

Your example is incorrect and I suspect its due to confusion concerning division and linguistic terminology. Maybe this will clear it up for you.

When you say: "I had one gallon of gasoline and divide 'by a' 1/2"
This means: "I had one gallon of gasoline and divide 'by a' 1/2 a gallon of gasoline"

The result of dividing a gallon of gasoline 'by a' 1/2 a gallon of gasoline is "2 times", not "2 gallons". Similarly, if you divide a gallon of gasoline 'in half' then you get 2 half-gallons of gasoline.

 

It does work with crumbs.

If I divide one crumb by 1/2, I will have two crumbs.

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If we pour both 1/2 gallons back into a container it adds to one gallon. You do not violate energy conservation, because 1 gallon divided by (1/2) still equals one gallon of actual product. The operator says 2 gallons.

If we have one apple and divide by 2 we get 1/2. We separated the apple into two halves, but we only look at one half which has separated. If we take one apple and divide by 1/2, we don't cut all the way through, or that would be divided by 2. We only cut part way. If we look at each piece, since both are still connected each piece appears to be the entire apple, since it is still attached via the uncut half. It is still one, but might appears like two if we add both sides. If we add the entire apple grabbing one side with the entire apple grabbing the other side, it looks like two. But again that is a perpetual motion, since we still only have one apple with a partial cut.

 

This is the same interpretation problem that you have been running into.

Dividing a gallon by half a gallon = 2 times (not 2 gallons).
1gal / .5 gal = 2 (times)

Re-arranging the terms gives us an identity:

1 gal = 2 x .5 gal

 

Not really familiar with the unit of measure "times." The only unit being discussed is gallons, so how do you arrive at the unit "times?"

 

Now on the other hand if you meant:

1 gal divided into 2 equal parts is equal to .5 gallons per part, so 1 gallon/2 parts=.5 gallons/part, then you would be correct.

But that's not what you meant, is it, Crunchy Cat?? Then there's the fact that in reality you can't physically divide a gallon of gas into two equal parts, can you, Crunchy Cat?

 

Logic, term cancellation, reality, you name it. How many times do we have to add half gallons to get a full gallon? 2 times. The issue that wellwisher is running into is that he is setting up an equation where he is mistakenly adding a gallon to his existing gallon while thinking he is mathematically dividing his existing gallon into smaller pieces but getting a result that violates reality.

 

From post #12: "Similarly, if you divide a gallon of gasoline 'in half' then you get 2 half-gallons of gasoline."

At some point I did; however, I am trying various approaches to show the OP errors. And yes, I don't think it's possible for humans to physically divide something into objectively equal parts, but we can certainly come close.

 

the only fantasy here is you saying you will get 2 gallons by dividing 1 gallon by one half.