h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Pedro. I shan't add the info. about Colossus as it's very incidental to the story anyway. I ended up just deletingg the sentence where I'd mentioned 'Turing Machine'

Entry: Prime Numbers - < A25209047 >
Author: Big Al - Member, Wessex Researchers Group, Keeper of Mnemonics, Patron Saint of Left Handers - < U723247 > (watching night television )

Places where I got lost:

Gauss's chart. What is the second column about?


Riemann's landscape. I understand the 3D graph, but *landscape* of numbers? Huh? How?


The description of Hardy: you didn't do the bio thing for anyone earlier. And his logic is .

The idea behind the 'landscape' term is that, if you draw a 3D graph, you end up with something which looks like a mountain. Now, 'landscape of numbers' is not an official terminology.

Would 'scalar field' do?

'Number field'?

One hump? Two? To me, landscape has a mountain range with several peaks in the background. A description of the "landscape" would help understanding the zeros business.

Content:

"After this one needs to use special cases of Lagrange's Theorem from group theory". -- There are plenty of ways of finding primes bigger than 10,000. I could name at least three, and I've never heard of Lagrange's Theorem, so I think this statement doesn't add to the Entry at all.

The paragraph about the zeta function, which starts with "At Gottingen" is really not very explanatory. I think you could explain it better.

the sum of two cubes in two different ways .. you might like to add in a footnote, that Ramanujan is pointing out that 1729 = 1^3 + 12^3 = 9^3 + 10^3. There's a code for a raised three, but I can't remember it.

"Note that only 11 digits are required to express the total number of atoms in the universe." -- I still think this is wrong. I'm not great on chemistry but I think a litre of water has more than 10^23 atoms, which is a number of 23 digits. I'm sure you can work it out.

Dyson sphere - I understand that the Dyson sphere is a solid shell around a star, not orbiting satellites.

Nitpicks:

Man has been interested... -- it's not considered polite to use "Man" in this way anymore. Say "Humankind" instead.

e.g. Just when one thinks -- there's no need for e.g. here.

It wasn't until the late 18th Century when -->
It wasn't until the late 18th Century that

I don't know why you used the sharp s symbol in Gauss's name. It is always written with two s's in English.

(that is, 1G = ...) this would be better if you omitted "that is".

then, if one picks a number at random within each range, then -- that's too many thens

show an interest mathematics -->
show an interest in mathematics

At age sixteen -- not wrong, but I'd prefer "At sixteen"

when, it is said, that he read an entire -->
when, it is said, he read an entire

But in Germany. this notion -- change the full stop to a comma

The sentence "Riemann also discovered something else" is misleading because it is a long way from a description of what he discovered. A casual reader might think that it is the 3-dimensional landscape that Riemann discovered.

GH Hardy, alone of these academics ... You've mentioned Hardy's name a number of times at this point, so you don't need to provide his initials here.

naivity --> naivet&eacute;

2 May 1918 --> 2 May, 1918
27 February 1919 --> 27 February, 1919

the key role he played the development -->
the key role he played in the development

December 15, 1923 --> 15 December, 1923

Traveller in Time watching the blue mountains
"They imaged the zeros as deep depressions along a mountain ridge, the slopes still continuing in front of the holes.

I do think anyone would call the graph display of mountains

Search: < Riemann mountain > and you will find many sites referencing to the graph as mountains. Perhaps this is not a pure mathematical term, it is how you would discribe the shape of the graph.

< http://math-it.org/Mathematik/Riemann/Riemannia.html >

__/\/\__ "

The second column merely tells you how many primes there are between 1 and 10, 1 and 100, 1 and 1000 etc..

Reason for the Hardy biography is because it IS , and therefore interesting. He was totally eccentric - and I have a kind of empathy with his eccentricities

After this one needs to use special cases of Lagrange's Theorem from group theory". -- There are plenty of ways of finding primes bigger than 10,000. I could name at least three, and I've never heard of Lagrange's Theorem, so I think this statement doesn't add to the Entry at all.

See for example:

http://primes.utm.edu/notes/13466917/index.html, where

Under the sub-header 'A Little Theoty aNever Hurts', it says,
'Large numbers need more complicated tests that usually involve a form of Lagrange's Theorem.

See also

http://primes.utm.edu/largest.html
A

"between 1 and 10, 1 and 100, 1 and 1000"

- oh - I wasn't sure if it was 1 and 100 or 10 and 100. Which is why I got confused - the increasingly rising numbers didn't jive with the text.

No, I just realised that a few minutes ago and corrected the text

ARef Gnomon's Post 50:

"After this one needs to use special cases of Lagrange's Theorem from group theory". -- There are plenty of ways of finding primes bigger than 10,000. I could name at least three, and I've never heard of Lagrange's Theorem, so I think this statement doesn't add to the Entry at all.
I disagree with this. See my Posts 51 and 52

The paragraph about the zeta function, which starts with "At Gottingen" is really not very explanatory. I think you could explain it better.
I've changed this slightly.

'the sum of two cubes in two different ways .. you might like to add in a footnote, that Ramanujan is pointing out that 1729 = 1^3 + 12^3 = 9^3 + 10^3. There's a code for a raised three, but I can't remember it.
Done

"Note that only 11 digits are required to express the total number of atoms in the universe." -- I still think this is wrong. I'm not great on chemistry but I think a litre of water has more than 10^23 atoms, which is a number of 23 digits. I'm sure you can work it out.
I'd already done this but it somehow got deleted. Done it again now > 80 digits.

Dyson sphere - I understand that the Dyson sphere is a solid shell around a star, not orbiting satellites.
A Type 1 Dyson Sphere does consist of orbiting satellites (see the h2g2 EGE on Dyson Spheres, which I've linked to.

Nitpicks
'Man has been interested... -- it's not considered polite to use "Man" in this way anymore. Say "Humankind" instead.

'fraid I'm not going to succumb to this kind of assinine, crass, politically-correct pomposity.

e.g. Just when one thinks -- there's no need for e.g. here.
Done

It wasn't until the late 18th Century when -->
It wasn't until the late 18th Century that
Done

I don't know why you used the sharp s symbol in Gauss's name. It is always written with two s's in English.
Well, another Researcher just did in the Entry on Gauss integers. I will probably change mine, I was just experimenting with the code and found that it worked for the Subheader but not for the main text

(that is, 1G = ...) this would be better if you omitted "that is".
Done

then, if one picks a number at random within each range, then -- that's too many thens
Done

show an interest mathematics -->
show an interest in mathematics
Done

At age sixteen -- not wrong, but I'd prefer "At sixteen"
What, sixteen bananas?

when, it is said, that he read an entire -->
when, it is said, he read an entire
Done

But in Germany. this notion -- change the full stop to a comma
Done

The sentence "Riemann also discovered something else" is misleading because it is a long way from a description of what he discovered. A casual reader might think that it is the 3-dimensional landscape that Riemann discovered.
Done

GH Hardy, alone of these academics ... You've mentioned Hardy's name a number of times at this point, so you don't need to provide his initials here.
Done

naivity --> naivet&eacute;
Done

2 May 1918 --> 2 May, 1918
27 February 1919 --> 27 February, 1919
Done

the key role he played the development -->
the key role he played in the development
Done

December 15, 1923 --> 15 December, 1923
Done

'The description of Hardy: you didn't do the bio thing for anyone earlier.'


... also, I wanted to get the anecdote about the in , and I couldn't do it in isolation .

Very instructive

a typo
>>that is the size of the gaps been successive prime numbers is very arbitrary<<
been -> between
Also, I would suggest 'seems very arbitrary' because at this point it does seem so. Then when you later write
>>The primes aren't just unpredictable, they really do behave as if each prime number is picked at random, with a calculable probability -almost as though they were chosen with a weighted coin.<<
there is an 'aha' moment.


>>3-dimensional graphs have an extra z-axis going backwards into the page.<<
This is confusing in two ways. First, there is only one z-axis, so the 'extra' makes it sound like you mean there are two of them. Second, the direction of the z-axis is purely a matter of convention - I'm used to a right hand system where the z-axis is positive pointing out of the page. You describe it as going into the page, but then talk about mountains, which one would visualise as rising from the page - I think you must mean the z-axis to point out of the page for this to be the case. Suggest:
->3-dimensional graphs have an added z-axis with the convention that it points up from the page.<-

The 'Modern Application' is a very good addition to this entry

Excellent

I see that you've taken that sentence about Lagrange's theorem from that website, but even on that website, it gives many different ways of finding larger primes, and doesn't mention Lagrange at all, so I really don't think the line makes your entry any more explanatory.

See http://primes.utm.edu/prove/merged.html where many different ways are discussed.

>>'fraid I'm not going to succumb to this kind of assinine, crass, politically-correct pomposity

I consider it simple politeness towards 50% of the human race. I also don't slap children or send them up chimneys.

But leave it there and see does it offend anybody else.

Pallaway. I've taken on board all your points.

Ref the 3-D graph, I am used to the z-axis projecting both from the page and behind the page, but I found that difficult to describe. So opted for 'projecting behind the page'. I've now done as you suggested and went for 'projecting out of the page'.

Ref the image.model of a 3-D landscape. I had in mind the 3-D maps we used to make from papier mache in geography lessons/Scouts etc (to illustrate contour lines). I was trying to recall if we referred to them as some particular name ...