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johncarlosbaez.wordpress.com

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Re: 42

#51
post #31

Earlier quoted context omitted.

I second that: I definitely remember reading something in which Douglas Adams explained that he chose 42 arbitrarily. And I think he was surprised at and amused with everyone’s theories of the significance of the number.

What if it turns out that 42 really is the answer? :)

Then "The Simpsons" would be right about the one true religion being a mix of an amazon tribe belief and Mormons... and we are all going to hell...

Re: 42

#52

Earlier quoted context omitted.

42 digits in base 10 though, and base 10 is just an arbitrary convention. It can be more or less in other equally valid bases.

Yes, but the other number will have a similar number of digits in whatever base you choose. More precisely, the number of digits will be multiplied by ln(10)/ln(base) for both numbers.

I see what you mean, sounds right

Re: 42

#53

Earlier quoted context omitted.

42 digits in base 10 though, and base 10 is just an arbitrary convention. It can be more or less in other equally valid bases.

Yes, but within that base it's significant. Just as within other bases the corresponding number would be significant. This is important because if you operate a system universally with the same base, the significant number begins to take on an objective importance intra-system. Stated another way, it's mathematical semantics, the same as arguing an idea is not significant because you can express it in a multitude of…

I didn't really consider it like that, interesting

Re: 42

#54
post #34

I always thought that this was interesting... I am sure that many of you are familiar with Dr. Feynman's 7-part lecture series entitled The Character of Physical Law , which were part of the "Messenger Lectures" [1], given at Cornell University in 1964. In the first lecture, Law of Gravitation - An Example of Physical Law , Feynman states the following: "Question: what is the ratio of the gravitational force to the e…

42 digits in base 10 though, and base 10 is just an arbitrary convention. It can be more or less in other equally valid bases.

All bases are base 10 within that base. So actually, base 10 is about as non-arbitrary as it gets.

Re: 42

#55
post #34

I always thought that this was interesting... I am sure that many of you are familiar with Dr. Feynman's 7-part lecture series entitled The Character of Physical Law , which were part of the "Messenger Lectures" [1], given at Cornell University in 1964. In the first lecture, Law of Gravitation - An Example of Physical Law , Feynman states the following: "Question: what is the ratio of the gravitational force to the e…

Isn't the universe still growing? Which means that at some point in the very far off future, the ratio of of the diameter of the universe to the diameter of a proton will be 43 digits? Passing thought -- since 42 _is_ the the answer to the Great Question of Life, etc., perhaps only a universe with this ratio of certain length can support life, e.g. when the universe becomes too large, there will be too much entropy i…

let's wait and see if proton grows too to keep the equation!

Re: 42

#56

Earlier quoted context omitted.

42 digits in base 10 though, and base 10 is just an arbitrary convention. It can be more or less in other equally valid bases.

Yes, but within that base it's significant. Just as within other bases the corresponding number would be significant. This is important because if you operate a system universally with the same base, the significant number begins to take on an objective importance intra-system. Stated another way, it's mathematical semantics, the same as arguing an idea is not significant because you can express it in a multitude of…

"Just as within other bases the corresponding number would be significant."

Numbers are independent from any base. You may mean the numeral in another base, which would have a different number of digits.

But what is more important, note that not necessarily the two ratios from the quote will have the same number of digits in another base.

Re: 42

#57

Earlier quoted context omitted.

Isn't the universe still growing? Which means that at some point in the very far off future, the ratio of of the diameter of the universe to the diameter of a proton will be 43 digits? Passing thought -- since 42 _is_ the the answer to the Great Question of Life, etc., perhaps only a universe with this ratio of certain length can support life, e.g. when the universe becomes too large, there will be too much entropy i…

let's wait and see if proton grows too to keep the equation!

Of course it grows. Accelerated growth even. How else would you explain that when walking out a window the earth grows to meet you?

Re: 42

#58

Earlier quoted context omitted.

Yes, but within that base it's significant. Just as within other bases the corresponding number would be significant. This is important because if you operate a system universally with the same base, the significant number begins to take on an objective importance intra-system. Stated another way, it's mathematical semantics, the same as arguing an idea is not significant because you can express it in a multitude of…

"Just as within other bases the corresponding number would be significant." Numbers are independent from any base. You may mean the numeral in another base, which would have a different number of digits. But what is more important, note that not necessarily the two ratios from the quote will have the same number of digits in another base.

Yes, the numeral representation of the number is exactly what I mean, you clarified my comment perfectly. Numbers are independent from any base.

Re: 42

#59
post #54

Earlier quoted context omitted.

42 digits in base 10 though, and base 10 is just an arbitrary convention. It can be more or less in other equally valid bases.

All bases are base 10 within that base. So actually, base 10 is about as non-arbitrary as it gets.

http://math.stackexchange.com/questions/166869/is-10-a-magic...

Re: 42

#60
post #34

I always thought that this was interesting... I am sure that many of you are familiar with Dr. Feynman's 7-part lecture series entitled The Character of Physical Law , which were part of the "Messenger Lectures" [1], given at Cornell University in 1964. In the first lecture, Law of Gravitation - An Example of Physical Law , Feynman states the following: "Question: what is the ratio of the gravitational force to the e…

42 digits in base 10 though, and base 10 is just an arbitrary convention. It can be more or less in other equally valid bases.

Irrelevant. Two numbers with the same number of digits when expressed in base 10 will necessarily be within a factor of 10 of each other. This is just a different way of saying these numbers are close.
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