# extend beyond the proof

#### gatoran

##### Senior Member
What is meaning of "extend beyond the proof" in the following sentence, please:

But while we do not know all the laws, we can use some to make guesses at theorems which extend beyond the proof.

From "The Character of Physical Law," by Feynman.

• #### Barque

##### Senior Member
The word "proof" here means (WR dictionary): a sequence of steps, statements, or demonstrations that leads to and establishes a valid conclusion. It's a word often used in maths/physics contexts.

I'm not sure what "extend beyond" means here however.

#### gatoran

##### Senior Member
Thank you Barque. Could it mean that when we compare the theorems with their proofs, the applications of the theorems are so far reaching that they become much more important than their proofs.

#### Barque

##### Senior Member
Theorems are more important than their proofs.

I agree it's probably something to do with the applicability of the theorems, however. Hopefully someone will come along and explain it.

#### gatoran

##### Senior Member
I thank you very much Barque.

#### hanapb151

##### Member
It means these theorems cannot be proven ("beyond the proof") by, for example mathematics, because we do not know everything yet.

#### Barque

##### Senior Member
I'm not sure I've understood. If the theorem can't be proven, that means there's no proof. The original sentence suggests that there are proofs.

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#### suzi br

##### Senior Member
What is meaning of "extend beyond the proof" in the following sentence, please:

But while we do not know all the laws, we can use some to make guesses at theorems which extend beyond the proof.

From "The Character of Physical Law," by Feynman.
We know some laws of physics. We do not know them all. (We can prove some of them.) We can use what we are sure about to make up theorems which go beyond what we know how to prove.

Is that clearer?

#### srk

##### Senior Member
"The Character of Physical Law" is a three-part lecture given by Feynman at Cornell University in 1964. I found video recordings under that title online. The quote comes at minute 32:45 of the video of the second lecture and appears on page 50 of a 176 page transcript online. Shortly after the quote, he says "... the laws often extend beyond the range of their deductions."

I think the words "extend beyond the proof" and "extend beyond the range of their deductions" are both hard to understand. I think they were substitutes for ones that may have eluded him in the middle of an hour-long extemporaneous lecture. "... extend beyond what can be inferred from the nature of their derivation" might have been better.

For example, he talks about using Newton's law of gravitation to derive Kepler's second law of planetary motion, and he wonders aloud about which of these two laws might be considered axiomatic in physics. Because the second can be derived from the first, it might be assumed that the first is more fundamental. However Kepler's second law is more clearly related to the law of conservation of angular momentum, which does not depend on the law of gravitation as a basis: Spinning skaters spin faster as they draw their limbs inward, and this effect has nothing to do with gravity.

#### gatoran

##### Senior Member
Thanks srk for your detailed and enlightening explanation. There are seven parts to Feynman's Messenger Lectures. But what bothers me still is the meaning of the words extend and beyond in this context.

#### suzi br

##### Senior Member
Say there is a point in the ground and you want towards it. If you go past that point you have goen BEYOND it.

To extend is slightly different, it suggests more like the thing itelf stretches, maybe like piece if elastic.

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