The idea of exceptions

[Boojatta]

Given an object or rule that is somewhat complicated, we may find ourselves thinking of a simpler object or rule together with the notion that there are some exceptions to the simpler object or rule.

For example, imagine a list of numbers. The nth entry in the list is the number n, with the following exceptions: the 203rd entry in the list is the number 200, the 1,037th entry in the list is the number 100, and the 5,003rd entry in the list is 150.

Even people who claim that there can be no violation of a law of nature should be able to imagine such a list of numbers.

Now, just as we can define a particular list of numbers by combining a simple rule with some information about exceptions to the rule, isn't it conceivable that the sequence of real events could be described by a combination of simple rules and exceptional incidents that violated those simple rules?

[trotsky]

1. Bacon. n/t

[Silent3]

4. Perilous hopscotch even beside ermine.

Sanction whatnot, universal tirade over said latent kowtow. Undulate. Persist. The overreaction congeals heedlessly.

[Random_Australian]

2. Yes. It is conceivable. It does NOT change the fact that until there was evidence

for those exceptions actually existing, it would be irrational to believe in them.

[Boojatta]

3. What counts as evidence?

Many people accept that Fermat's Last Theorem is true, not because they have personally checked an attempted proof and confirmed that it's correct, but because they trust people who say that there is a good proof.

Now, in the case of a conjecture with a tricky proof, it's possible that completely honest experts in math have failed to notice a subtle gap and that the conjecture is actually false. For various kinds of miracles, such a misunderstanding is very unlikely, so there is reliance upon the honesty of people who claim to have witnessed miracles, but not necessarily reliance upon an assumption of impressive performance by people who claim to have witnessed miracles.

[Random_Australian]

5. Mainly because they don't care that much.

In fact, if it was life-shattering to someone, they would probably get someone to explain the proof of Fermat's last theorem every step of the way. I certainly would.

But more to the point, rather than "because they trust people who say that there is a good proof", it's a matter of "they know the people who are saying there is good proof are using standards of proof and evidence that they can themselves can examine for incorrectness".

ie. if a person were to use the scientific method to show that some obscure thing were true, and others concluded that they had, in fact, used the scientific method correctly, we would believe them.

If a person were to make claims about things at random without any real way of checking it, we would not believe them. (Well, unless you wanted to believe them)

So rather than trusting a person, we trust a method that we can check ourselves, even if checking everything would be far beyond our cognitive abilities.

[Boojatta]

6. Does a particular application of the scientific method rely upon nothing but the scientific method?

ie. if a person were to use the scientific method to show that some obscure thing were true, and others concluded that they had, in fact, used the scientific method correctly, we would believe them.

Why do you think that you can avoid the question of the trustworthiness of particular people and focus entirely on the question of the reliability of the scientific method? Isn't it possible that a particular application of the scientific method might rely upon records of some observations that were allegedly made?

If you suspected that someone used 1.5 cups of salt and one teaspoon of sugar when making a cake, then would you be willing to eat the cake provided that you first had an opportunity to investigate just one thing: the quality of the oven that was used to bake the cake?

[Random_Australian]

9. Ah, but what if I had the opportunity to investigate stupid misleading analagies?

I wasn't avoiding any damn questions at all.

On one hand, there is never an issue of "trust" when it comes to the method used, you check that yourself.

As for people making things up, until you have evidence of a vast, shadowy conspiracy that has thus far left no trace, it is fairly unreasonable to assume there is one and fairly reasonable to assume that when various people from all over the place replicate someone's work, they checked it as best they could.

And as for your wonderfully stupid analagy, a more true one would be "if I suspected that someone used 1.5 cups of salt and one teaspoon of sugar when making a cake, would I then be willing to eat the cake provided that you first had the opportunity to find out one thing: when tested several independent groups of chemists, what salt content did they find?"

In other words, I said we check the method people used to come to the conclusions they did. We both know damn well that looking at an oven in no way tests whether or not someone's conclusion about the salt content of a cake is valid.

[Boojatta]

10. "when various people from all over the place replicate someone's work"

It sounds as though you're narrowing the focus. Aren't there some kinds of scientific observations that can't be replicated at will, but require an indefinite amount of waiting?

[Random_Australian]

11. No.

[Boojatta]

12. What about the study of supernovas that are a hundred times as energetic as the average supernova?

[Random_Australian]

13. It's quite simple. We have this thing called the null hypothesis.

It contains variables that have already been established.

For instance, something falling and accelerating with a = (acceleration due to gravity) - (retardation from air resistance) would be evidence for absolutely nothing, as we expect it to do just that.

If something is in the null, it is rational to believe it. Science exists to bring evidence against the null. (More or less).

Now we go to a particular example: If those supernovas were what you would expect once you had worked out the relevant physics, then it it would be rational to believe in them. If not, it would be irrational.

In neither case were their actual observations of those supernovas.

Also, we've never observed something falling on the 17th of March, 2008. But because it is in the null, it is rational to believe it.

[Boojatta]

14. This discussion is becoming a bit disconnected.

Now we go to a particular example: If those supernovas were what you would expect once you had worked out the relevant physics, then it it would be rational to believe in them. If not, it would be irrational.

My question isn't whether or not it's rational to believe in them. My question is: can such explosions be replicated at will or are we forced to wait for them?

In neither case were there actual observations of those supernovas.

What about this:

NASA's Chandra Sees Brightest Supernova Ever

The brightest stellar explosion ever recorded may be a long-sought new type of supernova, according to observations by NASA's Chandra X-ray Observatory and ground-based optical telescopes. This discovery indicates that violent explosions of extremely massive stars were relatively common in the early universe, and that a similar explosion may be ready to go off in our own galaxy.

"This was a truly monstrous explosion, a hundred times more energetic than a typical supernova," said Nathan Smith of the University of California at Berkeley, who led a team of astronomers from California and the University of Texas in Austin.

Source:
www.nasa.gov/mission_pages/chandra/news/chandra_bright_supernova.html

[Random_Australian]

15. We ultimately arguing about what it is rational to believe.

So my points were still valid.

But more to the point of the discussion: Was that a single observation? No. Any single detected blip is to be assessed for accuracy, and is to be challenged if it presents data outside the null. (And not to be let go if it gives you data within the null, either :)).

In this case, there were many observations by different people. Of the same event. The same cake in the previous analagy.

Even if something like the CERN LHC (which runs experiments no-one else can replicate) were to produce unique results, if it did it just once then we would not believe it.

[Boojatta]

19. "In this case, there were many observations by different people. Of the same event."

How many observations by different people would be enough to authenticate a single miraculous event?

[Random_Australian]

21. We require that the observation has

for it to be considered statistically significant.

Of course, since human brains are outside resolution, we can't calculate this too exactly when humans are involved, but the answer to your question remains "the minimum number such that we assess the chance of them not screwing up the result as less than the required 0.05"

That is only to get statistical significance, though. If you want evidence, you have to repeat. Usually 3 to 5 times is enough (depending on various things).

So, for a single event you need "the minimum number such that we assess the chance of them not screwing up the result as less than the required (0.05)^3 to (0.05)^5.

Note: Actual numbers of people have nothing to do with it. If 500 people "witnessed" a water powered car, that would mean nothing. If 5 different telescopes all see God mooning the earth, we'd probably believe something was going on.

[edhopper]

7. I find the trick to making really good pesto

is that the basil has to be very fresh and don't combine the parmigiana until after you've blended everything else together.

[Boojatta]

8. We're talking about cake, not pesto.

[edhopper]

16. I like cake.

[Realityhack]

17. So?

Do you have some kind of point? If so please make it.

The fact of the matter is that (as I am sure you know) for any finite series of numbers X,X1,X2...Xn there exists a formula that will produce that series of numbers.

Now obviously there can be situations where the formula is very complex but a very simple formula with a couple of exceptions would produce the same results.

But um... so the fuck what? If we are back to your completely BS definition of a 'law of nature' than what you are ACTUALLY describing is

Complex formula = law of nature
Simple formula = man's approximation of the law
Exceptions = flaws in man's understanding of nature

You still fail by definition.

[Boojatta]

18. "The fact of the matter is that (as I am sure you know) for any finite series of numbers..."

Well, I don't claim to know that, but I'm glad you raised the issue and I'm glad that you were careful to include the word "finite."

Is the goal of scientific studies simply to find a formula that fits some particular finite pile of data? I thought that one important goal of scientific studies is to develop theories that can be used to make good predictions.

Now obviously there can be situations where the formula is very complex but a very simple formula with a couple of exceptions would produce the same results.

What if, whenever people think of a complex formula and then wait for more data to test the complex formula, they find that such a formula generates predictions that are no more accurate than the predictions made by the simple formula?

[Realityhack]

20. ug.

You seem to be intentionally misunderstanding in an intellectually dishonest attempt to 'prove' your previous theisis that natural laws can be violated.

If the REAL formula for the series is:
For n!=(203,1037,5003) Fn=n
For n=203 Fn=200
For n=1037 Fn=100
For n=5003 Fn=5003

Then that is the only 'Law of Nature'. The formula
Fn=n is just a human approximation.
When we test n=1037 we get a strange result we don't understand and rework our understanding of the law.

Thats it. No miracles that violate the law.

We KNOW Newtonian physics is flawed. But for many purposes nothing is gained by adding in the complexity of relativity. No better results are obtained. So we use Newtonian physics. but we don't go 'oh my gosh... a miricle' when we observe something very fast that does not behave in accordance with Newtonian physics.

BTW Did you ever bother to define a law of nature for us?

[Boojatta]

22. "If the REAL formula for the series is:..."

For n!=(203,1037,5003) Fn=n
For n=203 Fn=200
For n=1037 Fn=100
For n=5003 Fn=5003

Are you sure that for n=5003, Fn is equal to 5003?

A more important question...

Suppose G is a function such that:
If n<5004 and n!=(203,1037,5003), then Gn=n
For n=203 Gn=200
For n=1037 Gn=100
For n=5003 Gn=150.

What can you tell me about Gn for n>5003?

[Realityhack]

23. Um

Gn >5003 = n according to the formula you provided. If we find exceptions we modify our 'human approximation' of the formula or we come up with a more complex formula that may predict future deviations from the genera Gn=n rule of thumb

[Boojatta]

24. "Gn >5003 = n according to the formula you provided."

I thought that you gave the name "F" to the function that I originally provided, so I gave some information about a function "G". Are you, for some reason, assuming that G is equal to F?

If we find exceptions ...

If you look at the information I provided about G, you will see that I provided information about Gn only for n less than 5,004. Thus, your talk about "exceptions" seems premature.

[Realityhack]

25. I stand corrected...

Nothing and you know it.

Now. Unfortunately...

The 'real' rule (not 'man's approximation of it') for G cannot exclude ranges of n where Gn exists.
Therefore you are missing part of the 'real' rule, or no such function exists beyond that point.

So you successfully demonstrated that man's approximation != the real rule
Congratulations you defined that as the fact in the first post of your other thread.

[Realityhack]

26. let me try to get this back to your original post

Given an object or rule that is somewhat complicated, we may find ourselves thinking of a simpler object or rule together with the notion that there are some exceptions to the simpler object or rule.

so we KNOW for a FACT that the simpler rule is WRONG in some cases... like say Newtonian physics. ok.

For example, imagine a list of numbers. The nth entry in the list is the number n, with the following exceptions: the 203rd entry in the list is the number 200, the 1,037th entry in the list is the number 100, and the 5,003rd entry in the list is 150.

Check.

Even people who claim that there can be no violation of a law of nature should be able to imagine such a list of numbers.

Yes.

Now, just as we can define a particular list of numbers by combining a simple rule with some information about exceptions to the rule, isn't it conceivable that the sequence of real events could be described by a combination of simple rules and exceptional incidents that violated those simple rules?

Yes. See Newtonian physics.
However, we KNOW for a FACT that n=n is NOT a 'law of nature'. We KNOW it's a quick rule of thumb that doesn't always get the right answer. Therefore it is NOT a law of nature.

You keep intentionally trying to claim that there are 'laws of nature' to which there are exceptions. These are not 'Laws of nature' by anyone else's definition, because by definition there are no exceptions.
Our shortcut of n=n is NOT a law of nature. We know this for a fact. So what is your point?
That when we use a rule of thumb for which we know there are exceptions their exist exceptions to our rule of thumb?

[Boojatta]

28. "You keep intentionally trying to...

... claim that there are 'laws of nature' to which there are exceptions."

Can you quote where I tried to make such a claim?

[Realityhack]

29. Well...

assuming your last two topics actually HAVE some point (which is quickly becoming debatable) you are clearly attempting to continue your attempts to make room for miricles by showing there can be exceptions to natural laws from your previous topic.

As usual you are trying to dodge around the issue and generally obfuscate what it is you are getting at. Which BTW is terribly anoying and you have been called on it numerous times. Hence the discussions of eggs and bacon in your topics.

So go back to your other thread and find the posts yourself.

[Boojatta]

31. "find the posts yourself."

You made a claim and now you expect me to search for evidence to support your claim?

Okay, then I will claim that there are flaws in your arguments designed to demonstrate that miracles never occur. Mind you, I'm not claiming that your conclusion is false. I'm claiming that there are flaws in your arguments. Now, you will search for flaws in your arguments and then post them here in this thread. Goose, gander, and all that.

[Realityhack]

32. here

This whole thread was all about your trying to re-define natural laws
http://www.democraticunderground.com/discuss/duboard.php?az=show_mesg&forum=214&topic_id=163476&mesg_id=163618

BTW did you ever get around to comming up with a coherent answer?

[Boojatta]

34. I'm interested in an actual quote of me making the claim you said I made.

Providing your own interpretation of the "whole thread" doesn't provide a quote of the kind required.

[Realityhack]

35. Boojatta you are being intentionaly intelectualy dishonest.

You posted an entire thread that had to do with 'miracles' occurring outside the laws of nature. You where repeatedly told that by definition this was impossible. You continuously challenged the definition of a law of nature but flatly to this day refuse to provide whatever you are working off of as far as a definition.
Now you start this topic where you try to rephrase the question in terms of numbers saying if the patten is x then the law would be y and you can violate the law.
We have repeatedly shown you that this is by definition not the case.

You are are being downright dishonest in claiming that is not what this thread and the thread I linked to are about.

furthermore you continue to refuse to answer the simple question of what your personal definition of a 'law of nature' is. thus intentionally confusing the debate.

You are playing word games where you allude to a topic or position while refusing to actually stat it then demanding exact quotes of your position. It is quite clear to any reasonable observer that both in this thread and the one I linked to that you are discussing the possibility of 'real miracles' occurring. Your logical errors have been repeatedly pointed out and you have consistently failed to respond.

If you want to have a serious debate you need to be honest about your position and actually respond to the criticisms of it.

So start with these questions.
1. Do you actually dispute that the subject of this poll http://www.democraticunderground.com/discuss/duboard.php?az=show_mesg&forum=214&topic_id=163476&mesg_id=163476 and the following discussion starting here http://www.democraticunderground.com/discuss/duboard.php?az=show_mesg&forum=214&topic_id=163476&mesg_id=163519 is wither there can exist 'real miracles'?
2. Do you dispute that your position was that there can be? If you do, on what grounds, and what IS your position?
3. Have you provided at any point an answer to the repeated question of what definition you are using for a 'law of nature' as opposed to mans understanding of a law?
4. For about the 10th time. What 'definition' are you using for a 'law of nature'?
5. Why have you not responded to post 25?

[Boojatta]

36. Can you provide one example of this?

Your logical errors have been repeatedly pointed out and you have consistently failed to respond.

Are you saying that I have stated some assumptions and that I have provided faulty reasoning based on my stated assumptions? If I did that and you know where I did it, then you should be able to copy and paste it.

furthermore you continue to refuse to answer the simple question of what your personal definition of a 'law of nature' is. thus intentionally confusing the debate.

When I create a thread, I might on occasion inadvertently presume something about word meanings that conflicts with your word usage preferences. However, I'm perfectly willing to use whatever definitions you like, provided that no substantive assumptions are smuggled in along with the definitions. If there's a substantive dispute, then it will not dissolve merely because I choose to accommodate your word usage preferences.

[Boojatta]

37. Request for clarification.

Your logical errors have been repeatedly pointed out and you have consistently failed to respond.

Do you mean I expressed ideas that you consider to be errors, but you admit that the ideas are logical?

If you mean that I relied upon some assumptions and arrived at a conclusion that cannot be reasonably obtained from those assumptions, then I would appreciate one clear example of where I made such an error in this thread or in the other thread or threads that you have in mind.

[Realityhack]

33. oh and this as well

from your OP in THIS thread:
"Even people who claim that there can be no violation of a law of nature should be able to imagine such a list of numbers."

You are clearly setting up an argument that there can be exceptions to a 'law of nature' based on the fact that you are arguing against the opposite position.

Now are you going to start being honest? How about you define what a 'Law of nature' is for us.

[edhopper]

27. When I make chopped liver

should I use one egg or two per lb.?

[Realityhack]

30. deleted

[smoogatz]

38. The idea of erections.

If one neighbor has reliable erections 85% of the time, and the other neighbor has reliable erections only 37% of the time, but the neighbor with less reliable erections has a sperm count 42% higher than average, which neighbor is more likely to accidentally impregnate Mrs. Torvald, the accountant's wife? Bear in mind that it's the height of tax season, that the Torvalds are Catholic, and that Mrs. Torvald prefers the "doggy" position.

[Boojatta]

39. Kick

[Boojatta]

40. Kick

[HamdenRice]

41. Blue cheesecake. A silver spoon in the sand. The seaweed barks at me.

[Boojatta]

42. Exploration can provide fresh air and a cure for an unhealthy obsession.

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[Boojatta]

43. Kick

[ZombieHorde]

44. I suppose then we would do well to remember

the example is not the situation or object.

[Boojatta]

45. Kick

[westerebus]

46. Bacon, definitely bacon. n/t

[Boojatta]

47. Kick

[gcomeau]

48. Allow me to sumarize your argument.

"Couldn't there be stuff we don't know?"

Yes.

If you want to make claims there's something specific of that nature however, demonstrate it.

[Boojatta]

49. I think that your summary omits some essential ideas.

[gcomeau]

50. I don't.

[Boojatta]

51. This thread has more life in it than some threads half its age.