Who turned out the light?

tdb

@tdb said:
@bstorer said:
@rohypnol said:
We all agree mathematics are right and the same everywhere in the known and unknown Universe
That doesn't mean that our mathematics are right. Math is no more inherently true than anything else we've discovered. It's a shame we don't still refer to them as part of natural philosophy.
I would like to offer a different point of view to this. Mathematics is an exact science. It consists of symbols (numbers) defined by us and rules for how to manipulate them (operators and functions), also defined by us. We can take a simple statement we know to be true (either by definition or by earlier proof), and derive more complex statements from it. Such proofs are absolute truths within our set of rules (provided that it has been proven correctly). Even if someone else defines mathematics with different rules, that doesn't make ours any less correct.
Rohypnol wants to claim that there is a universal mathematics that is right everywhere. Depends how you interpret "right", I suppose. Does he mean that there is one system of symbols and rules which encompasses everything in this universe? Such a thing either leads to unprovable statements or paradoxes. Or does he mean, as you suggest, that given the numbers 1 through 4 and addition, 2 + 2 always equals 4? That's a valid interpretation, but it doesn't tell you anything. It doesn't allow you shed any new light on the universe. Whitehead's problem (Different Whitehead this time) can be either true or false depending on what axioms you add to ZFC set theory. But which one is right?

So he does. I won't say that such a claim is true or false - I say it does not make any sense to begin with, since mathematics is independent of space and time. It is pure logic. As you have noted, mathematics alone does not tell us anything of the universe. 2 + 2 does equal 4 under our selection of symbols and rules, but we can as well take other symbols and say that squiggle plus squiggle equals gobba. Theorems may be wrong, but axioms, by definition, never are. Whether a set of them is consistent is another matter.

@bstorer said:

@tdb said:
Now, it's important to note that pure mathematics is different from for example physics, which uses mathematical truths to arrive at theories about the universe. Those theories may be incomplete or even incorrect, but tat doesn't make the underlying mathematics any less true - perhaps the mathematilcal truths were applied incorrectly. And with a different kind of mathematics, also physics needs to be different.
Ah, now we come to the rub: which system are we using? When you go to model the universe, which axioms are you picking? Will you make Whitehead's problem true, or false, or undecidable?

An interesting point. I think that as long as we stick to a consistent set of axioms to base our physics on, we are in the safe zone. If we use an unproven theorem, we must document that we used it and acknowledge that our new laws of physics may or may not hold.

I have to say that I'm hard pressed to find a disputed theorem in mathematics that would have use in physics. But then again, I'm by no means knowledgeable enough in either of those fields to say that such theorem does not exist.

alegr

@morbiuswilters said:

Just like when Newton fell out of that apple tree and invented carbon dating!

Morbs,

We need to stay with dating carbon forms of life. Screwing silicon-based things is unhealthy.

CDarklock

@boh said:

@CDarklock said:

TRWTF would be if he said this while actually understanding that we dismiss all those other gods because God said "thou shalt have no other gods before me".

"...but you may have them after I'm done with them", is that correct?

No, no, no. Not "before" as in the opposite of "after", but as in the opposite of "behind". We can only have other gods when He's not looking.

And we have to use a condom.

CDarklock

@rohypnol said:

Our whole technology is based on scientific discoveries.

Let me explain the problem people have with carbon dating, since you don't seem to understand it. We start from two things.

1. Carbon-14 decays at a fixed rate.

2. Every currently living and breathing thing is acquiring carbon-14 at a fixed rate.

Therefore, over the course of an animal's life, it will acquire carbon-14 in direct proportion to its lifespan. When it dies, the carbon-14 begins to decay, and we can determine two more things.

3. Because we can identify how much of the carbon-14 has decayed, we can determine how long ago it died.

4. Because it decays into nitrogen-14, we can identify the total amount of carbon-14 there was when it died, and therefore how long it lived.

There are some obvious flaws in this hypothesis.

The flaw in proposition (2) is the implied acceptance that the rate of carbon-14 acquisition has never changed.

The flaw in proposition (4) is the assumption that ALL nitrogen-14 in a fossil previously existed as carbon-14.

However, the hypothesis is simplified. Without advanced understanding of the chemistry involved, which I do not have, it is extremely difficult to explain WHY it is extraordinarily unlikely that the rate of carbon-14 acquisition has changed markedly, or HOW we can identify nitrogen-14 as being specifically the result of carbon-14 decay. But we can. This is the fact of the matter: these flaws do exist in the hypothesis as explained to the layman, but to a scientific professional qualified to carbon-date a specimen - those flaws do not exist. So the argument that carbon-14 dating suffers from these flaws is fundamentally ignorant, and the scientific community ignore it.

@rohypnol said:

The only alternative I can see is to say that carbon dating was given by the devil

Oh, ye of little imagination.

Posit: the rate of carbon-14 decay is not constant.

During the early days, carbon-14 was taken on in the same proportions as we see today, but decayed much more rapidly. So while we can accurately determine that a given fossil died at a given age, our backward projection of WHEN it died is hopelessly off-base.

A curve can be plotted which identifies how the rate of carbon-14 decay would need to change over the lifetime of the Earth, matched to the data points for any and all known fossils, then stretched or compressed to any arbitrary scale. In this way, one could accurately - and scientifically - posit that the Earth is of any arbitrary age.

Six thousand. Four billion. Twelve billion. Two thousand. Pick a number. Any number. You could be right. The data could show that you are right. All you have to do is draw the curve.

For convenience, scientists assume the rate does not change at all, ever. This is probably correct. (Ockham's razor: do not multiply entities unecessarily.) If this assumption is wrong, we will discover it over time - after all, if the decay rate has changed this much in six thousand years, we will see the decay rate change a corresponding amount in the next couple hundred. At that point, the flaw in the hypothesis will be corrected, science will issue a mea culpa, and the curve will be plotted appropriately. We will then know from scientific analysis and empirical research the actual age of the Earth.

And if you actually care about truth, you will accept this whatever the findings. Those who claim it is some conspiracy or coverup are simple nutjobs.

morbiuswilters

@tdb said:

@bstorer said:
@tdb said:
@bstorer said:
@rohypnol said:
We all agree mathematics are right and the same everywhere in the known and unknown Universe
That doesn't mean that our mathematics are right. Math is no more inherently true than anything else we've discovered. It's a shame we don't still refer to them as part of natural philosophy.
I would like to offer a different point of view to this. Mathematics is an exact science. It consists of symbols (numbers) defined by us and rules for how to manipulate them (operators and functions), also defined by us. We can take a simple statement we know to be true (either by definition or by earlier proof), and derive more complex statements from it. Such proofs are absolute truths within our set of rules (provided that it has been proven correctly). Even if someone else defines mathematics with different rules, that doesn't make ours any less correct.
Rohypnol wants to claim that there is a universal mathematics that is right everywhere. Depends how you interpret "right", I suppose. Does he mean that there is one system of symbols and rules which encompasses everything in this universe? Such a thing either leads to unprovable statements or paradoxes. Or does he mean, as you suggest, that given the numbers 1 through 4 and addition, 2 + 2 always equals 4? That's a valid interpretation, but it doesn't tell you anything. It doesn't allow you shed any new light on the universe. Whitehead's problem (Different Whitehead this time) can be either true or false depending on what axioms you add to ZFC set theory. But which one is right?
So he does. I won't say that such a claim is true or false - I say it does not make any sense to begin with, since mathematics is independent of space and time. It is pure logic. As you have noted, mathematics alone does not tell us anything of the universe. 2 + 2 does equal 4 under our selection of symbols and rules, but we can as well take other symbols and say that squiggle plus squiggle equals gobba. Theorems may be wrong, but axioms, by definition, never are. Whether a set of them is consistent is another matter.

In my mind, the biggest place where rohypnol's dogma breaks down is that even if mathematics is "universally true" and consistent within the formal system, that still does not mean that the real world maps to that system in a necessarily meaningful way. Logic is a creation of man (or, at least, our interpretation of it is) and it is demonstrably limited in its ability to be both complete and consistent, as you noted. However, how we apply mathematics to the physical world is even more "squishy". Integers are a concept but within physical reality what does "oneness" mean? Are discrete components of the universe a matter of "absolute truth" or simply a limitation of our perception? In other words, math might help us navigate the conceptual space of the physical realm, but who's to say that the universe actually obeys those mathematical truths? Perhaps our notions of space and time are completely screwy. When it comes to "absolute truth", this matters because scientific theory simply cannot (and should not) be considered authoritative. On the other hand, engineering is about "just working" which was my original point. Math helps us organize our theories regarding the natural world and those theories help us advance our ability to manipulate said world. However, assuming that the theories themselves must be absolutely true just because engineering works and mathematics comprises a consistent formal system is absurd.

tl;dr That scientific theory is absolute truth does not follow from the functionality of engineering and the logical consistency of mathematics.

DaveK1

@belgariontheking said:

@rohypnol said:
whatever
You say that like you would actually listen and not dismiss his views because he disagrees.

Since you proudly point out that you didn't listen to what he was saying, you're guilty of a PKB there.

DaveK1

@morbiuswilters said:

@bstorer said:
@morbiuswilters said:
@bstorer said:
Merely that you cannot necessarily know all the rules of the game from inside it.
Your axioms are showing!
*falls out of tree*
Just like when Newton fell out of that apple tree and invented carbon dating!

Nah, just like his ancestors did. Evolution, remember?

DaveK1

@morbiuswilters said:

@tdb said:
@bstorer said:
@tdb said:
@bstorer said:
@rohypnol said:
We all agree mathematics are right and the same everywhere in the known and unknown Universe
That doesn't mean that our mathematics are right. Math is no more inherently true than anything else we've discovered. It's a shame we don't still refer to them as part of natural philosophy.
I would like to offer a different point of view to this. Mathematics is an exact science. It consists of symbols (numbers) defined by us and rules for how to manipulate them (operators and functions), also defined by us. We can take a simple statement we know to be true (either by definition or by earlier proof), and derive more complex statements from it. Such proofs are absolute truths within our set of rules (provided that it has been proven correctly). Even if someone else defines mathematics with different rules, that doesn't make ours any less correct.
Rohypnol wants to claim that there is a universal mathematics that is right everywhere. Depends how you interpret "right", I suppose. Does he mean that there is one system of symbols and rules which encompasses everything in this universe? Such a thing either leads to unprovable statements or paradoxes. Or does he mean, as you suggest, that given the numbers 1 through 4 and addition, 2 + 2 always equals 4? That's a valid interpretation, but it doesn't tell you anything. It doesn't allow you shed any new light on the universe. Whitehead's problem (Different Whitehead this time) can be either true or false depending on what axioms you add to ZFC set theory. But which one is right?
So he does. I won't say that such a claim is true or false - I say it does not make any sense to begin with, since mathematics is independent of space and time. It is pure logic. As you have noted, mathematics alone does not tell us anything of the universe. 2 + 2 does equal 4 under our selection of symbols and rules, but we can as well take other symbols and say that squiggle plus squiggle equals gobba. Theorems may be wrong, but axioms, by definition, never are. Whether a set of them is consistent is another matter.
In my mind, the biggest place where rohypnol's dogma breaks down is that even if mathematics is "universally true" and consistent within the formal system, that still does not mean that the real world maps to that system in a necessarily meaningful way. Logic is a creation of man (or, at least, our interpretation of it is) and it is demonstrably limited in its ability to be both complete and consistent, as you noted. However, how we apply mathematics to the physical world is even more "squishy". Integers are a concept but within physical reality what does "oneness" mean? Are discrete components of the universe a matter of "absolute truth" or simply a limitation of our perception? In other words, math might help us navigate the conceptual space of the physical realm, but who's to say that the universe actually obeys those mathematical truths? Perhaps our notions of space and time are completely screwy. When it comes to "absolute truth", this matters because scientific theory simply cannot (and should not) be considered authoritative. On the other hand, engineering is about "just working" which was my original point. Math helps us organize our theories regarding the natural world and those theories help us advance our ability to manipulate said world. However, assuming that the theories themselves must be absolutely true just because engineering works and mathematics comprises a consistent formal system is absurd.

I believe the take-home point of Godel's theorem is that /all/ formal systems are equally universally true yet equally flawed. Nonetheless, you skate over a point there. It's a hell of a supposition that it's mere coincidence that mathematics (in whatever formal scheme) should serve to represent the universe so adequately, yet it's not a given - so why? A lot of the early-to-mid-20th-century debate over the Copenhagen vs. realist/Newtonian-Einsteinian interpretations of QM was about whether we're really describing the universe and processes within it using our maths, or whether it's merely a back-formation, a retrospective projection of the constructs that our own minds employ to describe the universe. And although it would have been reassuring to a lot of people to hope that the wierdness of QM was only a reflection of our imperfect knowledge of the universe, the current best evidence - coming from experimental tests of the Bell inequality - is that that structure really IS out there in the universe, not just in our heads.

@morbiuswilters said:

tl;dr That scientific theory is absolute truth does not follow from the functionality of engineering and the logical consistency of mathematics.

No argument there, that is of course a truism and I'm trying to discuss whether maths is a model of the universe or a model of our understanding of the universe, not whether or not his argument is justifiable but the grounds and basis underlying the concepts we're so freely flinging around in this discussion.

CDarklock

@DaveK said:

I'm trying to discuss whether maths is a model of the universe or a model of our understanding of the universe, not whether or not his argument is justifiable but the grounds and basis underlying the concepts we're so freely flinging around in this discussion.

This rather begs the question:

Is it at all possible to construct an accurate model of something we do not understand?

I would argue that it is the scientific equivalent of playing the lottery. You can construct a model that appears to be accurate, but it is only accurate insofar as your understanding permits. Beyond that point, there be dragons. It's pretty trivial to construct a list of numbers and ask what comes before and after it:

?, 3, 5, 7, ?

Which demonstrates that if you don't understand the system, you can't answer that accurately. You can only guess that it's a list of odd numbers:

1, 3, 5, 7, 9

But it's equally likely to be a list of prime numbers:

2, 3, 5, 7, 11

And there's always the chance you're looking at the middle of a ZIP code, in which case no rule of logic or reason can ever reliably determine the other two digits. You can reduce it to nine possibilities if you know the digits are sorted (six if you know whether 0 is the lowest digit or the highest), but what if they're not? In the absence of additional information, we have 101 possibilities. (Why isn't it 108? Discuss.) So maths, while intended to be a representation of the universe as it is, can only be a representation of the universe as we understand it.

bstorer

@CDarklock said:

@DaveK said:
I'm trying to discuss whether maths is a model of the universe or a model of our understanding of the universe, not whether or not his argument is justifiable but the grounds and basis underlying the concepts we're so freely flinging around in this discussion.

This rather begs the question:

Is it at all possible to construct an accurate model of something we do not understand?

I would argue that it is the scientific equivalent of playing the lottery. You can construct a model that appears to be accurate, but it is only accurate insofar as your understanding permits. Beyond that point, there be dragons. It's pretty trivial to construct a list of numbers and ask what comes before and after it:

?, 3, 5, 7, ?

Which demonstrates that if you don't understand the system, you can't answer that accurately. You can only guess that it's a list of odd numbers:

1, 3, 5, 7, 9

But it's equally likely to be a list of prime numbers:

2, 3, 5, 7, 11

And there's always the chance you're looking at the middle of a ZIP code, in which case no rule of logic or reason can ever reliably determine the other two digits. You can reduce it to nine possibilities if you know the digits are sorted (six if you know whether 0 is the lowest digit or the highest), but what if they're not? In the absence of additional information, we have 101 possibilities. (Why isn't it 108? Discuss.) So maths, while intended to be a representation of the universe as it is, can only be a representation of the universe as we understand it.