Tuesday, May 02, 2006

If we were to say that a definition only applies to a specific time, does that mean that the trash can we had on monday is not the same as the one we have now? Most people would agree that it is in fact the same trash can, so it seems this is not the case in practice.

Also, for what quantum of time does the definition hold? If the properties given to a trash can only apply at the current moment, is the trash can the same for this second? This hour? This day? If time is continuous, we could divide infinitely and show that this definition can never be applied to a precise moment because there was always a smaller moment in which it could have been assigned to, so it in a way expired. If time is discrete, we would have to determine how long a definition is good for - and why would that be the case? It doesn't seem like a natural way to think about an object


Blogger Undercover Sheep said...

It's important to recognize that it may have a different amount of particles or a different arrangment of particles, but as the object could be seen on a time line, it is still the same object. Its "worm", or path through time, is still the same. So it's not about defining it in one instant, but instead through time. As it changes through time, it gains 4th dimensional parts, but it is still the same trashcan with the same past and present. Just as some objects are tall, others wide, and others deep, some objects have big temporal parts, others have smaller ones.

10:13 PM  
Blogger linford86 said...

I do not agree with those who hold that definitions can change; that being said, if it was the case that they could, it would appear to me then that it might also be the case that the time over which the definitions hold depends upon the term being defined. A single atom in a vacuum has a very small chance of ever changing at all - therefore, its definition would never change. But a river, which is constantly changing, would have a definiton that changed extremely fast, possibly even infinitely many times per second.

By the way, whether or not a given thing is natural or intuitive to believe doesn't mean that its true. There are plenty of ideas which are difficult to fathom but are true none the less. If it were the case that only things that came to us naturally were true, then we'd never have quantum mechanics.

1:46 PM  
Blogger Undercover Sheep said...

that is a good point. i've never thought about it that way.

9:13 PM  
Blogger johnnyrobe said...

"By the way, whether or not a given thing is natural or intuitive to believe doesn't mean that its true. There are plenty of ideas which are difficult to fathom but are true none the less. If it were the case that only things that came to us naturally were true, then we'd never have quantum mechanics."

While I agree with the first sentence and maybe agree with the second sentence, I am skeptical of the implications of this third sentence. Now, I know absolutely nothing about quantum mechanics but it sounds pretty mathy/sciencey/engineering-like and my following criticism is directed towards math, science, and engineering as a whole and not specifically to quantum mechanics. Simply because there is some collection of coherent properties and theorems in quantum mechanics does not make it true. Experiments/whatever one does with quantum mechanics will, presumably, produce consistant and true results if and only if quantum mechanics is true. In years to come, maybe someone will provide evidence that elicits some flaw in quantum mechanics. If this seems implausible to you, then consider that perhaps quantum mechanics relies on something like gravity. While we have many perceptions that would lead us to believe that gravity exists, I think you would agree that perception does not necessarily imply that something exists, and so it is POSSIBLE (however unlikely this possiblity may be) that gravity does not exist.

So, I agree with the general point you were trying to make, but I think you should reconsider what makes something true instead of highly likely.

11:55 PM  
Blogger linford86 said...

Your criticism of quantum mechanics is almost completely unfounded. To believe that quantum mechanics accurately describes nature, you simply have to believe this:

1. Physical reality exists; i.e. we aren't all living in the Matrix and this isn't one giant dream. Arguably, the only thing that I know with 100% certainty is that I exist - "Cogito ergo sum". But presumably, it is absurd for me to actually believe that you don't exist, or that the bed I am sitting on as I write this doesn't exist.

2. The physical reality that exists can be known by the human mind. That is, we can find meaningful patterns in nature that allow us to actually comprehend nature.

Next, I wish to address your problem with mathematical theorems. A mathematical theorem is the result of a mathematical proof; if it is the case that the axioms of a mathematical proof are sound, and it is the case that the proof is logical (which, if written correctly, then it is) then it must also be the case that the conclusion is sound. If the conclusion is sound, then by transistivity of identity the theorem must be sound (i.e. the conclusion of a proof is identical to the theorem.) In fact, mathematics is so rigorous when stated properly that mathematicians will not accept the statement that "1+1=2" were it not for the Peano axioms of arithmetic (or some other equivalent set of axioms.) I posted the Peano axioms elsewhere on this blog, so, if need be, refer to them there. In fact, there is almost universal agreement amongst scientists, mathematicians, and philosophers that the only statements other than those pertaining to self existence (i.e. "cogito ergo sum") that can be said to be known to be true with 100% certainty are mathematical theorems. They are the closest to absolute truth that mankind will ever get no matter what. Unfortunately, high school and even introductory college math classes usually do not do a great job at presenting this whole idea of a mathematical proof or the idea of a formal logical language. That being said, what I can say about them is that the purpose of a proof is to formulate a given argument in such a way that it would be logically impossible for it to be false. In this sense, all correctly stated theorems must be true. Of course, since humans are the ones who write proofs, it is still possible to have incorrect proofs, and a number of these are circulating the internet. They usually conclude things like 1=2. But these proofs usually just result from some trivial algebraic error, albeit that the error is usually pretty well hidden under all the formality.

As for quantum mechanics, however, it is an experimental science. Specifically, it is the branch of physics that deals with sufficiently small objects. However, in over 500 years of doing physics, nothing has ever been found that contradicts or could not be explained (eventually) in terms of quantum mechanics. In fact, the entire computer revolution that has taken place over the course of the last 50 or so years is a direct result of quantum mechanics, whose byproducts include both the vacuum tube and the transistor. It would appear to be the case that the only reason you're able to read what I post here is due to the fact that quantum mechanics is so well understood. All of chemistry and biology and most, if not all of engineering, hinges on quantum mechanics being true. At laboratories like CERN, it is possible to gather millions of data points per day. In fact, quantum mechanics is one of the best tested theory in all of science, if not the single best tested theory. It is entirely internally consistent, and produces experimentally reproducible results (as I already said, it's tested millions of times per day, and not one single contradiction or error has shown up yet.)

That being said, it could be the case that, as you said, quantum mechanics is "like gravity". That we might think it exists only because we percieve it as existing. However, that would contradict (1) and (2) above - that is, if gravity is actually just some really elaborate illusion, then the physical reality that we see around us cannot actually be understood by the human mind. In turn, that is because in order to comprehend this external physical reality we must accept that it is not just some elaborate illusion, that when we do test a given scientific hypothesis, the data we gather over a sufficiently long period of time and in sufficiently large numbers doesn't lie to us. Surely, if there was some way of showing that gravity doesn't actually exist, it would have been done by now.

However, if you are unwilling to accept that even mathematics is capable of describing truth, then I have this to say: no discipline can. The methods for describing truth in mathematics and physics are so rigorous that no other discipline can ever even come close to having this level of accuracy. So, either it is the case that nothing can ever be known to be true, or it is the case that atleast math and physics are true.

As an example of this, let's compare psychological research to physics research. Suppose that we had the best psychological research program in the entire world - we are going to give surveys to every person planet Earth (all 6 billion or whatever) and that every person on Earth is willing to truthfully fill out those surveys and return them to us. Even then, psychology would not even come close to being able to produce the kind of data that is yearly gathered by physics laboratories. In a more reasonable case, it is possible to take about 1 survey per hour, while it is possible to gather thousands of data points in a physics laboratory in the same amount of time.

8:31 AM  

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