The Secret Number(strangehorizons.com)
strangehorizons.com
The Secret Number
http://www.strangehorizons.com/2000/20001120/secret_number.shtml
23 comments
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.
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.
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.
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.
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?
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?
Actually, if you look at the original version of that page (http://en.wikipedia.org/w/index.php?title=Archimedean_proper...), it doesn't mention the word "axiom" at all. Someone edited the page at some point to introduce this concept! It seems to have been done in a somewhat anonymous fashion, lending credence to Natsu's theory that there's a conspiracy involved here.
> Why not have number systems where infinitesimals are allowed?
There are. A few of them, in fact. Look up the hyperreals.
There are. A few of them, in fact. Look up the hyperreals.
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).
I think you might like this:
http://www.cut-the-knot.org/WhatIs/Infinity/9999.shtml
http://www.cut-the-knot.org/WhatIs/Infinity/9999.shtml
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).
but 0.999... /is/ 1. That is, they are equal (this still sounds like a lie to me and I constantly think about "what if our numbers are wrong".)
> what if our numbers are wrong
In mathematics, a definition cannot be 'wrong'; it can lead to an inconsistency, but that isn't the same thing.
The definition of the real numbers (the set of numbers where 0.999... == 1) does not lead to any inconsistency. However, there are other consistent definitions of sets of numbers where (the equivalent of) 0.999... does not equal (the equivalent of) 1. Those sets of numbers have values mathematicians call 'infinitesimals', which do not exist in the set of the real numbers. The hyperreals are one such set of numbers.
http://www.swaytts.org/blog/?p=1567
http://en.wikipedia.org/wiki/Hyperreal_number
In mathematics, a definition cannot be 'wrong'; it can lead to an inconsistency, but that isn't the same thing.
The definition of the real numbers (the set of numbers where 0.999... == 1) does not lead to any inconsistency. However, there are other consistent definitions of sets of numbers where (the equivalent of) 0.999... does not equal (the equivalent of) 1. Those sets of numbers have values mathematicians call 'infinitesimals', which do not exist in the set of the real numbers. The hyperreals are one such set of numbers.
http://www.swaytts.org/blog/?p=1567
http://en.wikipedia.org/wiki/Hyperreal_number
Apparently it has been made into a film (12 minutes, mind you):
http://secretnumber.colinlevy.com/
http://secretnumber.colinlevy.com/
Hey, that's my cousin! He's working at Pixar now actually. Check out sintel on youtube if you want to see some of his other work.
Too bad the kickstarter project didn't offer a reward at a donation of $bleem.
Link to the kickstarter project, http://kck.st/vvTBR9
Is the film available online?
It looks like he still hasn't finished the film.
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.
Could Pi somehow actually be Bleem, hiding in plain sight all this time?
Pi is not an integer.
Or is it....
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.
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.
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.
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.
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?").
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?").
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...
See also http://en.wikipedia.org/wiki/Non-standard_model_of_arithmeti...
Sorry, I should have been clearer -- I meant arithmetic with Peano's original axioms (i.e., with 2nd-order induction).
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.
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.
Depends what your definition of < is. Some definitions leave unspecified what the relationship between two values not in {0, 1, 2, ...} is.
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?
I am reminded of Ramanujan's proof that the sum of all positive integers is -1 / 12. The Wikipedia article has a fascinating excerpt from his letter to Dr. Hardy:
http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%80%...
http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%80%...
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).
-the Laundry novels (Charlie Stross). Here's one novella: http://www.goldengryphon.com/Stross-Concrete.html
-Luminous/Dark Integers (Greg Egan).
Here's another great Laundry story: http://www.tor.com/stories/2008/07/down-on-the-farm
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
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
(Though here's a link to a synopsis of Luminous): http://kasmana.people.cofc.edu/MATHFICT/mfview.php?callnumbe...
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.
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).
EDIT: Sorry; on looking closer, it's clearly Gardner's "The No-Sided Professor" (http://en.wikipedia.org/wiki/Fantasia_Mathematica).
I thought 137 was the secret number? Feynman, Heisenberg, Weisskopf and Pauli were intrigued by it.
http://www.1377731.com/137/
http://www.1377731.com/137/
The current recommended value of α is 7.2973525698(24)×10−3 = 1/137.035999074(44).
I prefer to read this as a parody of science fiction lacking internal consistency (e.g. most stories about time travel).
Wow, that story captured me! I want more.
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
http://downlode.org/Etext/nine_billion_names_of_god.html
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.
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.
Another classic short story that gave me chills is Isaac Asimov's The Last Question (1956):
http://www.multivax.com/last_question.html
http://www.multivax.com/last_question.html
Great story, indeed.
Sadly, it seems Igor only wrote that one, almost 12 years ago, and stopped writing on that website. You can read some more from him at http://www.stanford.edu/~teper/writing.html
Well, I can give you a different take on the same idea. http://scp-wiki.wikidot.com/scp-033
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...
I don't really get this...can someone explain (in 6 year old terms please) what the hell it actually means?
This is great. It reminds me of Ted Chiang's short story "Division By Zero".
Reminds me a bit of something I wrote a few years ago: https://md401.homelinux.net/fiction/sample%20%2327.html
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.
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.
Who is more insane: a madman, or a sane man who invents a madman?
This looks like a fun list too of math movies: http://www.qedcat.com/moviemath/index.html
Bleem is three itself. Because three is more than an integer, or any number.
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.
Bleem (in the story) = 3 + i?
Nothing profound to add, just thanks for sharing!