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johncarlosbaez.wordpress.com

41–50 of 62 posts

Re: 42

#41

Is this guy a, genius?

Every number has special properties :) Edit: In fact, I'd be astounded to encounter a number that did not exhibit any special properties. Until, of course, one makes "having no special properties" a special property. In that case, I would no longer be astounded.

I can't find it on the net, but in Umberto Eco's 'Foucault's Pendulum' the final monologue by the wife illustrates that really well.

Re: 42

#43
post #25

Earlier quoted context omitted.

We proceed by induction. Clearly n =1 is special, as it divides every integer. Assume k is special. If k +1 is not special, then it is special, as it is the first non-special number to come after a special number. This is a contradiction; then k +1 is special. ■

Can you categorize the next non-special number in the same way? Now k+1 is no longer non-special, but the reason why it is special still exists, so you can't use it a second time.

I think it was meant to be in jest.

Re: 42

#44
Wow all these numbers put me into an endorphine rush, I love these kind of posts!! Keep them coming, it's no as theoretical as you may expect, it's applications are endless.

    42, (Endo-)Fullerenes, the Omega Particle.
Do you remember the Star-Trek series that was about the Omega Particle? Isn't it crazy that they were right?!

They actually exist. https://en.wikipedia.org/wiki/Fullerene https://www.youtube.com/watch?v=454uu96gFzU

Re: 42

#46
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.

Re: 42

#47
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.

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 different languages, each having an arbitrary words.

Developing via Django (Python) or Rails (Ruby) is similarly predisposed to making one think it's all relative, but when you look closely, the framework doesn't matter at all - there are universal abstractions inherent in web development.

The representation is arbitrary and insignificant, what is significant is what the number or word represents, and what you can do by unraveling it.

Re: 42

#48
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.

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.

Re: 42

#49
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 in the universe for life?

Re: 42

#50
This is where I point out that the answer was wrong.

In HHGTG, a massive computer was built to answer the Question. The computer spent millions of years calculating, and arrived at the answer "42". The problem, it said, was that the Question had never been formulated. The computer then designed another computer to calculate the Question. After millions of years of calculation, this computer was inadvertently destroyed. The last remnants of the computer were only able to provide the question "What is six times nine?"

Also, knowing the answer without knowing the question is Jeopardy!

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