

The Secret Number - nyellin
http://www.strangehorizons.com/2000/20001120/secret_number.shtml

======
timsally
Strage Horizons is a fantastic speculative fiction publication. They're
considered a professional market and pay their authors at professional rates.
The archives are worth checking out. Clarkesworld is another similar
publication and has won the Hugo award for best semi-pro zine two years in a
row (<http://clarkesworldmagazine.com/>). If you enjoy this type of writing,
support these places! They're run by small communities and often do quite a
bit of independent publishing.

------
te_platt
Only bleem is not the secret integer between 3 an 4 but the smallest real
number greater than zero. Yes, I know real analysis and all about supremum and
coverings and epsilons and all the other ways to hide its existence. John
Conway gets close in "On Numbers and Games" (there is some of the secret in
non-standard analysis) but the conspiracy pushed him off into knot theory when
he got too close... Still if you drop the real number line from (0,1)
something has to hit the ground first. Bleem.

~~~
Natsu
No, no, no. See, I think it's between 0.99999999_ (repeating) and 1. I mean,
something has to go between the two, or people will think they're secretly the
same number. But they're not. Numbers can't be Superman. They can't just
change costumes in the blink of an eye. They should always look the _same_ ,
dammit.

Sure, you can multiply 1/3 (== 0.33333_) by 3 and make it look like they're
the same, but there's really a tiny little epsilon of something that's getting
zeroed out.

It's a conspiracy I tell you! They hide all the cool stuff with infinity and
you can't see it any more, then it's like it never existed.

~~~
kalid
Hrm, I can't tell if you're joking, but the existence (or non-existence) of
infinitesimals is an axiom:

<http://en.wikipedia.org/wiki/Archimedean_property>

It took thousands of years to accept that the parallel postulate might not be
required, and lots of neat geometry emerged. Why not have number systems where
infinitesimals are allowed?

~~~
derleth
> Why not have number systems where infinitesimals are allowed?

There are. A few of them, in fact. Look up the hyperreals.

~~~
kalid
Yep, exactly :). (Should have made it more clear that I was referring to other
systems like surreals and hyperreals, but wasn't clear whether the parent was
joking or not).

~~~
Natsu
I think you might like this:

<http://www.cut-the-knot.org/WhatIs/Infinity/9999.shtml>

~~~
kalid
Thanks for the pointer! I enjoy discussions about .999... because it really
makes us question what we mean about infinity (and assumptions about the
reals).

------
BlackJack
Apparently it has been made into a film (12 minutes, mind you):

<http://secretnumber.colinlevy.com/>

~~~
ph0rque
Too bad the kickstarter project didn't offer a reward at a donation of $bleem.

~~~
esalazar
Link to the kickstarter project, <http://kck.st/vvTBR9>

------
gk1
That's a great short story. It reminds me of the movie Pi, in which a man
obsessively searches for a secret number, to the point of debilitating
paranoia. If you enjoyed this short story even slightly, then I highly
recommend watching Pi.

~~~
malingo
Could Pi somehow actually be Bleem, hiding in plain sight all this time?

~~~
WiseWeasel
Pi is not an integer.

~~~
rgbrgb
Or is it....

~~~
seanp2k2
I've always thought about stuff like this; a numerals system based upon
quantities appearing in nature. 3.1415... is silly. Make that 1 or 4, and see
where everything else "fits", or something similar based on a universal
constant as the base.

~~~
JadeNB
But, in your number system where π is 4, what is e?

More to the point, we aren't just making up numbers here to enjoy infinite
decimal expansions; the reason is that you can wrap the radius of a circle
around its circumference more than 3 times (or, if you don't like numerals, as
many times as letters in 'pie'), but fewer than 4 (not as often as letters in
'easy')—and no changing of units is going to get around that.

------
esalazar
Very cool short story. One of the lessons I got from it is that you should
never consider somebody crazy for having a crazy idea. Some of our most
brilliant scientists, mathematicians, entrepreneurs, etc have been called
crazy fools for having radical ideas (That ended up being right). Our society
needs radical thinkers to shake things up, and revolutionize the world. Next
time somebody tells you about their own "bleem" just consider it, and don't
throw them to the street as a heretic.

~~~
cperciva
_Next time somebody tells you about their own "bleem" just consider it, and
don't throw them to the street as a heretic._

Mathematicians are aware of bleem. It's what you get when you remove the
induction axiom from Peano arithmetic: A number which is not in the set {0, 1,
2, ...}.

In general the higher up you go in academia the more open people are to
"variant realities". Most of our analysis of curved space-time comes to us
thanks to mathematicians who thought they were playing with entirely
theoretical constructs ("what happens if we remove the parallel postulate?").

~~~
metashurick
You actually do not have to remove any axioms from Peano arithmetic to prove
that a model of PA with such a 'bleem' exists. It is a straightforward
consequence of the compactness theorem: just enrich PA with a new constant c
and an infinite series of axioms 'c != N' for every numeral N. For any finite
set of these new axioms a model exists (just set c to a large enough number),
therefore by the compactness theorem there exists a model which satisfies all
our new axioms.

See also [http://en.wikipedia.org/wiki/Non-
standard_model_of_arithmeti...](http://en.wikipedia.org/wiki/Non-
standard_model_of_arithmetic)

~~~
cperciva
Sorry, I should have been clearer -- I meant arithmetic with Peano's original
axioms (i.e., with 2nd-order induction).

~~~
shasta
Except the number you get this way is not between 3 and 4. It's essentially
infinite with no functions in the model that separate it from the finite
numbers (and this can be proven in PA: if a number isn't 0..N, then it's
greater than N).

Generally, I don't think it's fair to characterize this story as something
studied by mathematicians. Really, it's an exercise in reasoning about
nonsense.

~~~
cperciva
Depends what your definition of < is. Some definitions leave unspecified what
the relationship between two values not in {0, 1, 2, ...} is.

~~~
shasta
Inequality can be defined in Peano arithmetic in a total way. Maybe you're
talking about defining some relation on the model? But what justifies calling
such a relation an inequality?

------
zmj
The "applied" number theory reminds me of a couple other stories:

-the Laundry novels (Charlie Stross). Here's one novella: <http://www.goldengryphon.com/Stross-Concrete.html>

-Luminous/Dark Integers (Greg Egan).

~~~
zmj
Here's another great Laundry story: <http://www.tor.com/stories/2008/07/down-
on-the-farm>

------
jblow
Greg Egan has written a couple of less-jokey stories that deal with a related
idea (that is more plausible).

The first story is "Luminous" from 1995, but I don't have a link to a free
copy.

The second is "Dark Integers" which you can find here:
<http://www.asimovs.com/_issue_0805/DarkINtegers.shtml>

~~~
jblow
(Though here's a link to a synopsis of Luminous):
[http://kasmana.people.cofc.edu/MATHFICT/mfview.php?callnumbe...](http://kasmana.people.cofc.edu/MATHFICT/mfview.php?callnumber=mf19)

------
ithought
I thought 137 was the secret number? Feynman, Heisenberg, Weisskopf and Pauli
were intrigued by it.

<http://www.1377731.com/137/>

~~~
windsurfer

        The current recommended value of α is 7.2973525698(24)×10−3 = 1/137.035999074(44).
    

<http://en.wikipedia.org/wiki/Fine-structure_constant>

------
jarin
This reminds me of a short story I read when I was a kid, where a guy
discovered a shape with zero sides. I think at the end he made his boss
disappear by folding him into the shape.

~~~
JadeNB
This story is in either "Fantasia Mathematica" or "The Mathematical Magpie",
both edited by Clifton Fadiman. I don't have my copies here to check, but a
look at the table of contents suggests that it might be "The Hermeneutical
Doughnut", by H. Nearing Jr. (Even if it's not, it's worth picking up the
books to look; anyone who liked this story is guaranteed to like them.)

EDIT: Sorry; on looking closer, it's clearly Gardner's "The No-Sided
Professor" (<http://en.wikipedia.org/wiki/Fantasia_Mathematica>).

------
shasta
I prefer to read this as a parody of science fiction lacking internal
consistency (e.g. most stories about time travel).

------
foxhop
Wow, that story captured me! I want more.

~~~
xxdiamondxx
one of my favorite sci-fi short stories is The Nine Billion Names of God by
Arthur C. Clarke

<http://downlode.org/Etext/nine_billion_names_of_god.html>

~~~
foxhop
Thanks I saved both of these stories off after reading them. This story gave
me the chills. I have NO idea how the author made me feel like the narrator.

I was absorbed with the story and I could feel the silence of my companion as
he traveled behind me gazing at the disappearing stars.

~~~
cpeterso
Another classic short story that gave me chills is Isaac Asimov's _The Last
Question_ (1956):

<http://www.multivax.com/last_question.html>

------
lukas
Anyone that liked that story should pick up a copy of Mathenauts - an
anthology of Mathematics themed short stories put together by Rudy Rucker.
Many of the stories have a similar feel to that one. You can find it on Amazon
here: [http://www.amazon.com/Mathenauts-Mathematical-Wonder-Rudy-
Ru...](http://www.amazon.com/Mathenauts-Mathematical-Wonder-Rudy-
Rucker/dp/0877958904)

------
wdewind
I don't really get this...can someone explain (in 6 year old terms please)
what the hell it actually means?

------
DanBC
This is great. It reminds me of Ted Chiang's short story _"Division By Zero"_.

------
lmm
Reminds me a bit of something I wrote a few years ago:
<https://md401.homelinux.net/fiction/sample%20%2327.html>

~~~
computator
I read the story above and I did like it. It has a blend of math, insanity,
and consciousness like the story in the main article.

A synopsis for others to decide if they want to read it: Chloe is a beautiful
humanoid companion. Deliberately implanted in the programming of her mind is a
minor reasoning defect. Whereas an ordinary person could live with it, and
perhaps not even be aware of it, Chloe cries and has fits whenever she becomes
aware of the flaw in her chain of thought. A psychologist is brought in to
figure things out.

By the way, "Sample 27" is the title and not the 27th sample story from the
author as I originally thought.

A suggestion to the author: You might want to either not use HTTPS or buy a
certificate. I don't think it's a barrier to Hackernews readers but most
people won't get past the browser's security exception box.

------
ctdonath
Who is more insane: a madman, or a sane man who invents a madman?

------
nate
This looks like a fun list too of math movies:
<http://www.qedcat.com/moviemath/index.html>

------
NHQ
Bleem is three itself. Because three is more than an integer, or any number.

------
dhughes
As I was reading I imagined at the end Dr. Tomlin back home found the bag of
jelly beans he emptied onto the table still in his pocket only he would find
one jelly bean still in it.

------
oikjbniojszdio
Bleem (in the story) = 3 + i?

------
mathattack
Nothing profound to add, just thanks for sharing!

------
hackermom
Professor Ersheim = John Titor.

~~~
phoopee3
+1

