Extraordinary claims require extraordinary proof

[CFLarsen]

Scientists used to think that life did not exist beneath the photic zone. Then they dredged deep sea sediments, and they found organisms. In your example, the problem is that the observations are not complete.

Exactly. The point is that our observations are formed by the tools by which we measure the world around us.

That's a "negative" claim - one which can be disproven with a single counterexample. Such claims are extremely difficult to establish, because you must test and rule out all possible counterexamples.

Yeah. But how will you find a counterexample if your net doesn't catch anything smaller than 5 cm? Or if you don't even realize that it is the net size that determines the size of your captured specimens?

The existence of DM is a positive claim. If is far easier to establish, and in fact it already has been by multiple lines of independent evidence - including the direct observation of its gravitational lensing effects.

Look - there is a (reasonably) unambiguous mathematical formalism for handling this question of what is extraordinary and what is not. You can take either a Bayesian or frequentist approach, but they both give the same result - DM is by far the least extraordinary theory we have. Until or unless someone comes up with an alternative, it will remain so.

I'm not arguing against DM.

I reject that.

How long have we been using telescopes? A few hundred years. How long has a well codified scientific method been actively used. A few hundred years.

And you think that it is surprising that we are discovering new "stuff". That is an extraordinary view.

Absolutely.

We are not uncovering the last remnants of knowledge about the universe. We have merely begun to scrape the surface of what can be found.

 

[ynot]

You are joking, I hope? I admit that some models are inaccurate, but we know that they are inaccurate because someone tested them. Other models make predictions, which then prove to be quite accurate when tested.


As to the existence of 0 (if this is meant as a serious problem with math), how many elephants are standing on your computer right now?


As an aside, the Mayans counted up from 0 instead of 1. They held 0 in a special regard, almost to the extreme Pythagoreans held the number 10.

Didn’t say that 0 is problem with math. Just that 0 is a completely abstract concept that has no existence in actual reality. It’s only a problem if 0 is claimed as an actual reality.

There are no elephants standing on my computer right now. The relationship between my computer and elephants is therefore completely imaginary and abstract. Are you saying that there is a 0 elephant standing on my computer, and that this 0 elephant has actual existence?

 

[ynot]

I find it so ironic that you could possibly make such a statement using a piece of technology that is based directly upon that supposedly "woo-physics/science"...

For the record, the science of quantum mechanics (which we used to make computers, etc) is extremely mathematical in nature. But, seeing as how you made such an inane statement using a computer, you're shooting yourself in the foot.

May I suggest ditching the Internet all together and sticking with smoke signals from now on?

Quite so, didn’t mean all of science, just some just some branches that I would wrongly describe as new age theoretical.

Puff, puff, . . . puff, puff, puff, puff . . . puff . . . puff, puff, puff . . . if you see what I mean

 

[MattusMaximus]

Quite so, didn’t mean all of science, just some just some branches that I would wrongly describe as new age theoretical.

Puff, puff, . . . puff, puff, puff, puff . . . puff . . . puff, puff, puff . . . if you see what I mean

A bit more clarity on your part would be useful, y'know.

 

[m_huber]

Didn’t say that 0 is problem with math. Just that 0 is a completely abstract concept that has no existence in actual reality. It’s only a problem if 0 is claimed as an actual reality.

There are no elephants standing on my computer right now. The relationship between my computer and elephants is therefore completely imaginary and abstract. Are you saying that there is a 0 elephant standing on my computer, and that this 0 elephant has actual existence?

You are getting into the question of "does a number exist?" 0 is a special number, and there are 0 elephants on your computer right now. That is describing something very real. You also have (I will assume) 5 fingers. A "seven" doesn't exist, but neither does a "green." That is not to say that 7 and green are not real, only that they do not fit in the "thing" category.

 

[ynot]

You are getting into the question of "does a number exist?" 0 is a special number, and there are 0 elephants on your computer right now. That is describing something very real. You also have (I will assume) 5 fingers. A "seven" doesn't exist, but neither does a "green." That is not to say that 7 and green are not real, only that they do not fit in the "thing" category.

That there are 0 elephants (and 0 entire objects of the universe that aren’t on my computer) on my computer. This is a real situation. But there is no real thing that is a 0 elephant that is on my computer. 0 elephants (or 0 anything) only exist as an abstract mathematical concept to describe a situation, not a thing.

 

[sol invictus]

That there are 0 elephants (and 0 entire objects of the universe that aren’t on my computer) on my computer. This is a real situation. But there is no real thing that is a 0 elephant that is on my computer. 0 elephants (or 0 anything) only exist as an abstract mathematical concept to describe a situation, not a thing.

But you think there's such a thing as 1 elephant?

How many are there if I cut the poor thing in half?

You see, numbers themselves are abstractions. What they really are are symbols which allow us to manipulate expressions according to the rules of logic. Since the world appears to operate according to the rules of logic, a correct input, manipulated correctly, yields a correct output.

It makes no difference whatsoever whether the symbols you use themselves have any "reality" - it just matters that the rules they transform under (formal logic) are true.

 

[ynot]

But you think there's such a thing as 1 elephant?

How many are there if I cut the poor thing in half?

You see, numbers themselves are abstractions. What they really are are symbols which allow us to manipulate expressions according to the rules of logic. Since the world appears to operate according to the rules of logic, a correct input, manipulated correctly, yields a correct output.

It makes no difference whatsoever whether the symbols you use themselves have any "reality" - it just matters that the rules they transform under (formal logic) are true.

An elephant that has actual existence can be abstractly defined mathematically as being a 1 elephant (or any other number). It may be also defined as a 2 or 3 elephant etc if it’s part of a herd. How numbers are applied in an abstract mathematical system is completely arbitrary. A situation where an elephant doesn’t have actual existence is a situation where there are 0 elephants. 0 defines that an elephant doesn’t exist in a particular situation, not that it does.

 

[m_huber]

An elephant that has actual existence can be abstractly defined mathematically as being a 1 elephant (or any other number). It may be also defined as a 2 or 3 elephant etc if it’s part of a herd. How numbers are applied in an abstract mathematical system is completely arbitrary. A situation where an elephant doesn’t have actual existence is a situation where there are 0 elephants. 0 defines that an elephant doesn’t exist in a particular situation, not that it does.

No, an elephant can be "number 1" or you might see "1 elephant," but you do not see a 1 elephant. That makes no sense syntactically. If you are describing a number of objects, you might see any number from 0 to infinity (you might say that you see an infinite number of subatomic particles, for instance).

Numbers act as descriptors and placeholders. Your argument is tantamount to saying that green doesn't exist. Have you ever seen a green? No? But you have seen the color green. Both green and numbers relate to real things in the real world.

 

[ynot]

No, an elephant can be "number 1" or you might see "1 elephant," but you do not see a 1 elephant. That makes no sense syntactically. If you are describing a number of objects, you might see any number from 0 to infinity (you might say that you see an infinite number of subatomic particles, for instance).

Numbers act as descriptors and placeholders. Your argument is tantamount to saying that green doesn't exist. Have you ever seen a green? No? But you have seen the color green. Both green and numbers relate to real things in the real world.

I said “an elephant” (not a “1 elephant”) can be defined as being “1 elephant”, not that it is a 1 elephant.

 

[ynot]

double post

 

[Reality Check]

Getting away from elephants:

Wasn’t questioning math per se, just the way it sometimes appears to be used. Seems to me that some conclusions are entirely the result of abstract math, yet these conclusions seem to be readily accepted as being actual reality. If a conclusion is purely mathematical, how is it known if it’s actual or abstract?

The conclusions are accepted as actual reality because we compare them to reality and they match. For example: I want to build a steel wheel of a certain radius. "Abstract math" tells me that I need steel of a certain length to form the outside circle. I try to build the wheel. If the wheel can be built this confirms the abstract math. If the wheel cannot be built then the abstract math is disproved.

 

[ynot]

Getting away from elephants:

The conclusions are accepted as actual reality because we compare them to reality and they match. For example: I want to build a steel wheel of a certain radius. "Abstract math" tells me that I need steel of a certain length to form the outside circle. I try to build the wheel. If the wheel can be built this confirms the abstract math. If the wheel cannot be built then the abstract math is disproved.

But are they always compared with actual reality? What actual reality is the math of the theoretical (mythical) light clock compared with?

In the expanding balloon/universe analogy, the outer surface of the balloon exists in reality, but it doesn’t exist in isolation from the rest of the balloon. The outer surface is only an abstract part of the actual reality of the total balloon, and is therefore only an abstract reality.

Expanding rasin bread is a better analogy to represent uniformly expanding space. Trouble is bread always has a crust.

 

[Reality Check]

But are they always compared with actual reality? What actual reality is the math of the theoretical (mythical) light clock compared with?

In the expanding balloon/universe analogy, the outer surface of the balloon exists in reality, but it doesn’t exist in isolation from the rest of the balloon. The outer surface is only an abstract part of the actual reality of the total balloon, and is therefore only an abstract reality.

Expanding rasin bread is a better analogy to represent uniformly expanding space. Trouble is bread always has a crust.

I will guess that "math of the theoretical (mythical) light clock" is Special Relativity. In that case the actual reality is a multitude of things, e.g. every physics experiment using high energy particles.
The "expanding balloon/universe analogy" is an analogy. It is not "abstract math". Get an actual balloon and try it out. An analogy is not the actual thing. No one is arguing that the universe is actually a balloon.

You still have not given us your definition of "abstract math". Is "1 + 1 + 2" abstract? How about "E=mc²"?

 

[ynot]

I will guess that "math of the theoretical (mythical) light clock" is Special Relativity. In that case the actual reality is a multitude of things, e.g. every physics experiment using high energy particles.
The "expanding balloon/universe analogy" is an analogy. It is not "abstract math". Get an actual balloon and try it out. An analogy is not the actual thing. No one is arguing that the universe is actually a balloon.

You still have not given us your definition of "abstract math". Is "1 + 1 + 2" abstract? How about "E=mc²"?

All languages and systems, including mathematics, are abstract.

 

[Jeff Corey]

Except for those that are concrete.

 

[ynot]

Except for those that are concrete.

A concrete example is?

 

[GreyICE]

Why are we positing dark matter to explain matter we can't observe when we have a perfectly good culprit - black holes? We already know they can pull stars into orbit around them when they're large enough, and they are seemingly a perfectly good reason for there to be literally 'missing mass' in that they can only be observed by inference (there's an incredibly dense lump of mass somewhere - exactly what we're seeing).

So why posit dark matter when we have black holes?

 

[ynot]

How about "E=mc²"?

E=mc² . . .

Einstein - E = Energy, M = Mass and C = speed of light

Theist - E = Existence, M = Miracle, and C = Creation

Relativity Sceptic - E = Einstein, M = Mathematical and C = Conjurer

Ancient Romans - E = 10,000,000, M= 1,000 and C = 100 (hope that’s correct)

 

[Reality Check]

Why are we positing dark matter to explain matter we can't observe when we have a perfectly good culprit - black holes? We already know they can pull stars into orbit around them when they're large enough, and they are seemingly a perfectly good reason for there to be literally 'missing mass' in that they can only be observed by inference (there's an incredibly dense lump of mass somewhere - exactly what we're seeing).

So why posit dark matter when we have black holes?

The initial reason that dark matter was needed is because galaxies rotate slower than they should according to the visible matter that we see. This means that galaxies have more mass at their edges and that this mass is not visible (thus "dark matter"). See the Wikipedia article for other observations that dark matter is needed.
I believe that the reason that dark matter is not considered to be conventional black holes is that black holes are actually quite detectable, e.g. through their interaction with interstellar gas. It is also hard to think of a mechanism to create many black holes on the galatic edges that did not also create them in the body of the galaxy.