Tuesday, April 15, 2008

What Do Trees and Math Have in Common?

After watching "A Beautiful Mind," I got to thinking about how weird it would be to not be able to discern between reality and delusion. I started thinking about certainty. This got me to thinking about trees.

You have heard the old question:
"If a tree falls in the forest, but no one is there to hear it, then does the tree make a sound?"

I'm sure you've thought about this question at some point or another. It gets at the idea that we can't have complete certainty of something's existence (in this case, sound) without perceiving it ourselves.

In one of the discussion-based philosophy courses that I took, we talked about knowledge and certainty, and this same question came up. However, the professor changed it up a bit. He and a student in the class had the following discussion in class (a paraphrase):
Professor: "If tomorrow, at noon, humanity ceased to exist, then would mathematics also cease to exist?"
Student: "Yes, because mathematics is a creation of humanity."
P: "So are you arguing that all creations cease to exist when their creators cease to exist?"
S: "Uh, yah, I guess so."
P: "Ok. Tell me something. Is your great grandmother still alive?"
S: "No."
P: "When she passed away or ceased to exist here on earth, did your grandmother (her daughter) also cease to exist?"
S: "Ok, I see your point. But humans are different from things."
P: "Alright then, lets look at the creator of this building. Do you suspect that when he or she ceases to exist, that this building will consequently cease to exist?"
S: "No, I guess not. What I was trying to say is that math only exists in peoples' thoughts. When people cease to exist, so do their thoughts. Therefore so does math."
P: "What do you mean when you say mathematics exists only in thoughts?"
S: "Well, take the number 3 for example. The word 'three' and the symbol '3' are just constructions, created by humans for the purpose of explaining certain occurences in nature. So in essence '3' means nothing without a human to give the symbol significance."
P: "Oh I see. So you are not saying that the occurence, for which the symbol '3' was created, would cease to exist as a result of humanity ceasing to exist. Just the significance of the symbol '3' would cease to exist."
S: "Thats right."
P: "Lets look at a particular mathematical truth: 1+1 = 2 . So when humans cease to exist tomorrow at noon, the symbols '1', '+', '=', '2' would lose their meaning. But would the principal that underlies the sybols cease to exist. Lets look at another example: the standard gravity constant, 'g', which is used to explain the acceleration due to gravity on earth. Once again, when humans cease to exist, so does the significance of the symbol 'g'. But does that mean that gravity itself ceases to exist? Would the old rule of 'what goes up must come down' cease to exist?"

Would love to continue discussion on these questions.


Haseeb A. said...

I believe that once facts are created they remain permanent forever until someone comes along to challenge those facts.

If someone wrote the number 3 on a piece of paper, and then everyone (humanity) died, then that symbol would lose its meaning. however the symbol would still exist.

Jay said...

Yeah clearly the study of mathematics would cease to exist if no people were around to think about it, but obviously the universe it was used to describe would remain unchanged and thus the underlying concepts would still be valid, there would just be no one around to muse about them.

Kyle Caffey said...

Phew... I'm glad to hear that we believe in an objective reality. There are some that believe that "perception is reality." In this case, with out human perception, math (and reality for that matter) wouldn't exist.

Alyssa said...

my 2 cents:
I guess I believe in an objective reality simply because I cannot deny it. In fact I think it would be foolish to deny it. But observation does not define reality, it distorts reality. If humanity ceased to exist so would our theories of mathematics. But the affects of our use of math that remained would still be part of reality. The characteristics of reality on which we based our patterns and laws of math would also still exist. Humanity and its understanding of math would be part of the history of reality, and although reality is a product of history as we observe it, or time, reality does not include history.

Oh and my answer to the old adage about a tree in the woods has generally been: Sound is created by waves that are interpreted by the physical faculties of an organism. Surely the tree would fall, but if no creatures remain that have ears or similar organs, the only affect felt would be vibrations and a visual change. The concept of sound requires an interaction of physical elements attuned to one another. So yes, a tree would fall exactly the same, to the same laws of gravity and all the other affects I do not know the technical terms of...that change which we perceive as sound would still exist, but it wouldn't exactly be sound.

I like thinking about observation a lot, like Turing Machines and the observation of a particle necessarily moves it with the light you use to see.

Kyle Caffey said...

I think it is interesting that you mention the past not being a part of reality. Do you believe that the future is a part of reality? If not, then I guess you believe that only the present is a part of reality.

It could be argued that there is no such thing as the present. The reasoning for this is that time is constantly moving and it is impossible to define a value of time precise enough to call "the present".

The Proof that the present doesn't exist: Let us define "the present" as all events that are happening right now. Let us define "the past" as all events that has already happened. Let us define "the future" as all events that will but have not happened yet. Now let the length of time that "the present" lasts equal n seconds for any positive real number n. Notice that n/2 seconds after "the present" starts, roughly half of "the present" has already happened and is in "the past", and roughly half of "the present" will but has not yet happened and is in "the future". So almost the entire time interval that we defined as "the present" was either a part of "the future" or "the past". Therefore, since we chose an arbitrary n, there is no time interval that precisely measures our definition of "the present".

In conclusion, if only "the present" is a part of reality, and "the present" doesn't exist, then reality doesn't exist.

Blackout said...

Based on the discussion I'd say the tree still makes a sound.