

Mysterious number 6174 - imgabe
http://plus.maths.org/issue38/features/nishiyama/

======
jdoliner
It's not so much a question of mathematical use. In mathematics ideas are
normally judged for implications for the rest of the field. This leads to a
self perpetuating notion of what's important (things are important simply
because they are). The notion of rearranging the digits of an integer has
absolutely no mathematical significance. Because we represent numbers by
strings of digits it's a very intuitive idea but I can promise you it will
never lead to "significant results" as pe the current academic notion of
mathematics. Furthermore mathematics has always been a search for generality.
The more general a concept is the more cases to which it can be applied and
normally the more impressive it is the mathematical community. I personally
find this substantially more reasonable. Rearranging the digits of a number
isn't even general to the concept of integers. It's dependent on the fact that
we write our numbers in a base of ten. If this theorem held in other bases
(like binary numbers) then that would be kind of cool.

On another note the author uses the word kernel when I think he wants "fixed
point". Kernel doesn't really have a meaning in this context.

~~~
Shamiq
To jdoliner:

Please add some information to your profile so I can place your comment in
some kind of reference. I love that you write clearly and to my untrained,
therefore naive, eyes your arguments seem valid. But without an understanding
of where you are coming from, I do not want to necessarily accept what you say
on face value.

I mean no insult, I just want more information.

Cordially,

Shamiq

~~~
jrockway
What difference do his credentials make?

If you want to know if something is true, do research, don't just assume that
someone's credentials make everything they say true.

~~~
RiderOfGiraffes
Personal opinion coming up ...

I find this attitude an incredible strength in the hacker community, but also
occasionally a real weakness. It leads to a complete dismissal of a source of
information, and that, surely, can't be right - namely, the mindset and
knowledge of the person making the statements. When making decisions you
should use all the information available.

Yes, some information should be tagged as "hearsay" (you can't check the
person's credentials) and some should be marked as "suspicious," but simply
throwing it out is wrong.

When you teach or train it is critical that you know people's background so
you can pitch the explanations and demonstrations at the right level. When you
listen to someone, you should assess what level of confidence to place in what
they say.

Work since Shannon has shown that the most efficient communication of
information (as opposed to data) is achieved when the sender has an effective
model of the receiver, _and the receiver has an effective model of the
sender._

Certainly many advances in breaking ciphers are achieved by knowing more about
the source. Cryptographers know not to throw away information, even when it is
suspect.

You can dismiss this, or go and research it. Does it sound interesting? Should
you ignore it? Modern information theory says you shouldn't. You don't know my
credentials, so you have to make that decision in a void. If I told you my
credentials, would your opinion remain completely unchanged? Modern
information theory says it shouldn't.

Yes, be skeptical, but use what information you have.

All of it.

~~~
jacquesm
ah, but then there is google:

<http://www.google.com/search?q=riderofgiraffes>

"User Profile for: riderofgiraffes UserID: 383529 Name: Email: Registered:
1/11/07 Occupation: Mathematician Location: UK Total Posts: 350"

So much for that vague reputation, unless of course you've been fibbing ;) and
/ or someone else liked your moniker as much as you did, but I somehow doubt
there are multiple riders of giraffes.

I fully agree with the above by the way, it feels just right.

I always tell my kid to distrust all sources of information, including his dad
(there is a pardox in there somewhere) and to gather his own facts if the
issue warrants the effort.

~~~
RiderOfGiraffes
But such a search is uninformative for the author in question. If I had used a
pseudonym you would have had no such additional information.

My point remains. With no credentials, with no idea of the author's
background, you must perform independent verification. With some idea of the
author's background, you have more information, and can decide whether the
information is likely to be trustworthy, or at least worthy of pursuit or
verification.

I am concerned that hacker culture teaches "Trust no one, verify everything."
I think it is thereby unnecessarily impoverished.

~~~
Shamiq
I typed up a similar response.

<http://news.ycombinator.com/item?id=481272>

------
jerf
What would an "explanation" be? An explanation with lower Kolmogorov
complexity than the operation itself. That system of equations is probably all
the "reason" you're going to get, since it's hard to get simpler than that.

If you're looking for something more humanly profound, how about this:
"Arbitrary operations on integers can yield arbitrary results." That's
actually profound (in the Zen-like way a tautology can still be profound) in
the context of "human understanding" and how people argue with numbers, but it
would take a long time to explain why, if you don't already know.

------
huhtenberg
Interesting.

Feels like a more mysterious version of Collatz conjecture :) which is - start
with a positive integer, iterate as such:

    
    
      x = (x & 1) ? (3*x + 1) : (x/2);
    

and you will eventually end up at 1.

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

------
euroclydon
Call me naive, but I have always doubted the mathematics significance of
rearranging the digits of an integer. When you rearrange 1234 to be 3241, you
have lost all meaning.

What _real_ mathematical operation involves rearranging digits in an integer?

~~~
fiaz
Who ever thought that x^3 transformed into 2x^2 would be useful one day? Of
course I'm being facetious in this example, but the simple rearrangement of
the mathematical expression above has profound implications for how we
interact with the world.

Yes I know that there is a whole derivation to the simple derivative example
I've given, but who is to say that the 6174 transformation might have preceded
an actual use?

Who's to say that this odd mathematical transformation actually leads to
something useful one day?

~~~
euroclydon
I don't really see the connection. Your example is the derivative of a
function, and what I am saying is that rearranging 1234 to 3421 doesn't mean
anything to me.

Now you have some new number who's only relationship to the old number is that
it's one of (4 _3_ 2)-1 possible permutations of it. Other than that, what's
the significance?

~~~
imgabe
The numbers in the article aren't rearranged arbitrarily, they're sorted to
ascending and descending order.

------
Eliezer
The meaningfulness of rearranging the digits in a base-10 representation is
fully and sufficiently demonstrated... by coming up with an interesting non-
obvious mathematical fact that depends on rearranging the digits in a base-10
representation. Meaning is something you get out of a math trick, not
something you put into it.

------
fh
Downvoted for implying there's anything mathematically special or interesting
about base 10. Okay, I can't really downvote, but you get the idea.

~~~
jacquesm
first off, this is not about 'base 10', it is about interesting patterns found
in series of digits, similar (but different) interesting patterns can be found
in series of digits in other bases.

Secondly, if every time a mathematically oriented person stumbles upon
something interesting instead of figuring out why they would respond like you
just did mathematics would grind to a halt really quickly. After all, that's
how math started - that curiosity about patterns - and mathematicians really
can't help it but they have to figure out what causes this. There may be a
trivial answer, or something profound may be found out, who is to know in
advance what will come of it.

To everybody else the circumference of a circle may as well be three times its
diameter.

------
daveparker
"...it also has one more surprise up it's sleeve..."

Fail.

