Comments on: Clock for geeks http://boingboing.net/2009/01/29/clock-for-geeks-1.html Brain candy for Happy Mutants Sat, 25 May 2013 06:29:00 +0000 hourly 1 http://wordpress.org/?v=3.4.1 By: Antinous / Moderator http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393217 Antinous / Moderator Wed, 30 Nov -0001 00:00:00 +0000 #comment-393217 Bathblogger, I've suspended you for repeated blogwhoring. Write me if you'd like to explain. Bathblogger,

I’ve suspended you for repeated blogwhoring. Write me if you’d like to explain.

]]> By: Thad http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-636161 Thad Wed, 30 Nov -0001 00:00:00 +0000 #comment-636161 1 = .999... Proof: 1 = 1/3 + 1/3 + 1/3 1/3 = .333... Therefore, 1 = .333... + .333... + .333... 1 = .999... Q.E.D. 1 = .999…

Proof:

1 = 1/3 + 1/3 + 1/3

1/3 = .333…

Therefore,

1 = .333… + .333… + .333…

1 = .999…

Q.E.D.

]]> By: dougrogers http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393225 dougrogers Wed, 30 Nov -0001 00:00:00 +0000 #comment-393225 Maybe the little black line marking 6.9 is actually imperceptibly ever so slightly moved in the anti-clockwise direction, so that it does mark 6.9 rather than 7? Maybe the little black line marking 6.9 is actually imperceptibly ever so slightly moved in the anti-clockwise direction, so that it does mark 6.9 rather than 7?

]]> By: retchdog http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393752 retchdog Wed, 30 Nov -0001 00:00:00 +0000 #comment-393752 #38: The people who are bickering about the 7, don't actually understand the 2 and thus accept it on faith of authority (probably because it explicitly incorporates a formal expression). #38: The people who are bickering about the 7, don’t actually understand the 2 and thus accept it on faith of authority (probably because it explicitly incorporates a formal expression).

]]> By: dougrogers http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-392995 dougrogers Wed, 30 Nov -0001 00:00:00 +0000 #comment-392995 Repost :-) Repost :-)

]]> By: michaeltheotherone http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393766 michaeltheotherone Wed, 30 Nov -0001 00:00:00 +0000 #comment-393766 #35 js7a / #36 coreymaley : js7a's notation is nonsensical, but we can ask: does 2 - 0.999... == 1? And the answer is yes. #35 js7a / #36 coreymaley : js7a’s notation is nonsensical, but we can ask:

does 2 – 0.999… == 1?

And the answer is yes.

]]> By: Ceronomus http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393000 Ceronomus Wed, 30 Nov -0001 00:00:00 +0000 #comment-393000 Best clock EVER! Best clock EVER!

]]> By: sabik http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393513 sabik Wed, 30 Nov -0001 00:00:00 +0000 #comment-393513 @anonymous #22, it's because 2*4=1 (mod 7). It's all in how you define division. One definition of a/b is "what number, multiplied by b, gives a?". Here, we have 1/2; in other words: "what number, multiplied by 2, gives 1?" When working with integers modulo 7, the answer is 4 (as above). When working with ordinary integers, there is no such number (the answer doesn't exist). With integers modulo 8, there is also no such number. When working with fractions or reals, the number is a half. The practical importance of this is mostly in cryptography; several well-known ciphers (including RSA) rely on related facts about modular arithmetic. @anonymous #22, it’s because 2*4=1 (mod 7).

It’s all in how you define division. One definition of a/b is “what number, multiplied by b, gives a?”. Here, we have 1/2; in other words: “what number, multiplied by 2, gives 1?” When working with integers modulo 7, the answer is 4 (as above).

When working with ordinary integers, there is no such number (the answer doesn’t exist). With integers modulo 8, there is also no such number.

When working with fractions or reals, the number is a half.

The practical importance of this is mostly in cryptography; several well-known ciphers (including RSA) rely on related facts about modular arithmetic.

]]> By: mightymouse1584 http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393003 mightymouse1584 Wed, 30 Nov -0001 00:00:00 +0000 #comment-393003 http://en.wikipedia.org/wiki/Geometric_series for a more specific, albeit not as funny, explanation of 2. http://en.wikipedia.org/wiki/Geometric_series
for a more specific, albeit not as funny, explanation of 2.

]]> By: noen http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393006 noen Wed, 30 Nov -0001 00:00:00 +0000 #comment-393006 I bet we can get a good argument going over "does 6.999... really equal 7.0? and is it really a different number". I bet we can get a good argument going over “does 6.999… really equal 7.0? and is it really a different number”.

]]> By: arkizzle http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393010 arkizzle Wed, 30 Nov -0001 00:00:00 +0000 #comment-393010 Curses! Noen, I just wrote: In before arguments about "0.9999.. = 1" MeFail Curses!

Noen, I just wrote: In before arguments about “0.9999.. = 1″

MeFail

]]> By: retchdog http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393015 retchdog Wed, 30 Nov -0001 00:00:00 +0000 #comment-393015 Obscure; shallow; and ugly. If I wanted to see that everyday, I'd hang a mirror. Also, 6.999... is not a "different number than 7", it is 7. Obscure; shallow; and ugly. If I wanted to see that everyday, I’d hang a mirror.

Also, 6.999… is not a “different number than 7″, it is 7.

]]> By: arkizzle http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393016 arkizzle Wed, 30 Nov -0001 00:00:00 +0000 #comment-393016 ..or Auto-Fail ..or

Auto-Fail

]]> By: Anonymous http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393274 Anonymous Wed, 30 Nov -0001 00:00:00 +0000 #comment-393274 More precisely, 4 is the multiplicative inverse of 2 in Z^x_7 : 4 mod 7 * 2 mod 7 ≡ 1 mod 7, so 4 mod 7 ≡ 2^-1 mod 7. The additive inverse in Z_7 would be -2 mod 7 ≡ 4 mod 7. More precisely, 4 is the multiplicative inverse of 2 in Z^x_7 : 4 mod 7 * 2 mod 7 ≡ 1 mod 7, so 4 mod 7 ≡ 2^-1 mod 7. The additive inverse in Z_7 would be -2 mod 7 ≡ 4 mod 7.

]]> By: js7a http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393285 js7a Wed, 30 Nov -0001 00:00:00 +0000 #comment-393285 Whenever this .999... thing comes up, I like to ask this: does 1.000...0001 = 1? Whenever this .999… thing comes up, I like to ask this: does 1.000…0001 = 1?

]]> By: brooklyntwang http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393033 brooklyntwang Wed, 30 Nov -0001 00:00:00 +0000 #comment-393033 if you believe 6.999... is equal to 7, then it is the same number. Two equivalent numbers are the same number. If they are not equivalent, then they are not the same number. But I bet we all agree (except for Mark, maybe) that you can't have two quantities that are equal but not the same number. No need to debate the 0.999... = 1 thing. if you believe 6.999… is equal to 7, then it is the same number. Two equivalent numbers are the same number. If they are not equivalent, then they are not the same number. But I bet we all agree (except for Mark, maybe) that you can’t have two quantities that are equal but not the same number. No need to debate the 0.999… = 1 thing.

]]> By: arkizzle http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393038 arkizzle Wed, 30 Nov -0001 00:00:00 +0000 #comment-393038 "<i>No need to debate the 0.999... = 1 thing.</i>" Ah ha ha hahah hah ha... Are you new to this, or have you just suppressed the horror? “No need to debate the 0.999… = 1 thing.”

Ah ha ha hahah hah ha…

Are you new to this, or have you just suppressed the horror?

]]> By: coreymaley http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393298 coreymaley Wed, 30 Nov -0001 00:00:00 +0000 #comment-393298 @JS7A Unfortunately, 1.000...0001 is a nonsensical notation. The "..." ellipsis doesn't stand for some really large number, like what you're suggesting. It's infinite. So it doesn't make sense to have an infinity of 0's, and then something after that. It's not the name of any number, and so it's not a number at all. @JS7A

Unfortunately, 1.000…0001 is a nonsensical notation. The “…” ellipsis doesn’t stand for some really large number, like what you’re suggesting. It’s infinite. So it doesn’t make sense to have an infinity of 0′s, and then something after that. It’s not the name of any number, and so it’s not a number at all.

]]> By: Takuan http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393043 Takuan Wed, 30 Nov -0001 00:00:00 +0000 #comment-393043 this enrages me since I am too stupid to understand it! this enrages me since I am too stupid to understand it!

]]> By: coreymaley http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393047 coreymaley Wed, 30 Nov -0001 00:00:00 +0000 #comment-393047 I think the best way to express the 6.99... and 7 thing is to say that they're different names for the same number, much like 0.5 and 1/2, or 111 (base 2) and 7 (base 10). A lot of confusion can be avoided by carefully distinguishing the expressions we use to refer to the numbers (the numerals, along with decimals and slashes), and the numbers themselves (whatever kind of abstract object those are). I think the best way to express the 6.99… and 7 thing is to say that they’re different names for the same number, much like 0.5 and 1/2, or 111 (base 2) and 7 (base 10).

A lot of confusion can be avoided by carefully distinguishing the expressions we use to refer to the numbers (the numerals, along with decimals and slashes), and the numbers themselves (whatever kind of abstract object those are).

]]> By: spazzm http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393048 spazzm Wed, 30 Nov -0001 00:00:00 +0000 #comment-393048 6.999... is equal to 7, but it is a different symbolic representation. So same value, different representation. Sort of how 0.0, -0 and 0 all have the same value, but are different symbolic representations. Since one definition of 'number' is 'symbolic representation', then yes - different numbers. The whole thing hinges on whether you believe that a symbol and the value it represents are two different things or not. Ceci n'est pas une pipe. 6.999… is equal to 7, but it is a different symbolic representation.

So same value, different representation.

Sort of how 0.0, -0 and 0 all have the same value, but are different symbolic representations.

Since one definition of ‘number’ is ‘symbolic representation’, then yes – different numbers.

The whole thing hinges on whether you believe that a symbol and the value it represents are two different things or not.

Ceci n’est pas une pipe.

]]> By: Avram / Moderator http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393059 Avram / Moderator Wed, 30 Nov -0001 00:00:00 +0000 #comment-393059 A friend of mine has a similar, but not identical, clock. If I remember correctly, it also uses various geekish symbols such as scientific constants and mathematical symbols, but doesn't constrain itself to the traditional twelve clock positions. So it's got π instead of three, but slightly past the three position (because it's 3.14...). A friend of mine has a similar, but not identical, clock. If I remember correctly, it also uses various geekish symbols such as scientific constants and mathematical symbols, but doesn’t constrain itself to the traditional twelve clock positions. So it’s got π instead of three, but slightly past the three position (because it’s 3.14…).

]]> By: barnaby http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393320 barnaby Wed, 30 Nov -0001 00:00:00 +0000 #comment-393320 To quote a former bar patron of great renown: SEMANTICS! To quote a former bar patron of great renown:

SEMANTICS!

]]> By: ReboundDesigns http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393064 ReboundDesigns Wed, 30 Nov -0001 00:00:00 +0000 #comment-393064 Here's another <a href="http://www.etsy.com/view_listing.php?listing_id=18965031" rel="nofollow">geek clock</a> on etsy, I got this one for my Nobel Laureate physicist father for Christmas. He got a big kick out of it. Then again, physicists are not known for having the best taste in home decor. Here’s another geek clock on etsy, I got this one for my Nobel Laureate physicist father for Christmas. He got a big kick out of it. Then again, physicists are not known for having the best taste in home decor.

]]> By: mdh http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393068 mdh Wed, 30 Nov -0001 00:00:00 +0000 #comment-393068 re: 6.99999 vs. 7 it's a math clock, not an atomic clock. One significant digit please. re: 6.99999 vs. 7

it’s a math clock, not an atomic clock. One significant digit please.

]]> By: Anonymous http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393843 Anonymous Wed, 30 Nov -0001 00:00:00 +0000 #comment-393843 Easy proof that 0.999~ does not = 1. Let's compare repeating digits in decimal and hexadecimal notation. Hex numbers are preceded by h; decimal by d Assertion: h0.FFF~ = 1 (By similar rule that d0.999~ = 1) hF > d9 (Hope you agree) but h0.FFF~ = d0.999~ (Wait, I thought F > 9...) Worse yet... hE < hF (Hope you agree) h0.EEE~ < h0.FFF~ (Hope you agree) hE > d9 (You see where I'm going here...) h0.EEE~ < d0.999~ (???) ==== Zeno's Paradox approach: You need to get to one. I give you 9/10. Now you need an additional 1/10. I give you 1/100. And so forth. Doing this an infinite number of times is <i>not going to help</i>. And, no, I'm not talking about the number moving or approaching anything, I'm talking about how to determine where that point is by evaluating its representation. I get the feeling that some refutations confuse these two points. The problem is that saying "an infinite number of nines" is equivalent of saying "and then a miracle occurs". Yes, there is a place on the number line that represents 1/3, you just can't accurately express where that place is with base ten digits, <i>no matter how long you try</i>. Claiming that it works out if you go to infinity doesn't help. In short, a repeating decimal is not a number any more that 1/0. It may be used as a shorthand for a concept, but you can't do real math with it because it's inherently inaccurate. Or, if you insist, show your work. Easy proof that 0.999~ does not = 1. Let’s compare repeating digits in decimal and hexadecimal notation. Hex numbers are preceded by h; decimal by d

Assertion: h0.FFF~ = 1 (By similar rule that d0.999~ = 1)

hF > d9 (Hope you agree)

but

h0.FFF~ = d0.999~ (Wait, I thought F > 9…)

Worse yet…

hE < hF (Hope you agree)

h0.EEE~ < h0.FFF~ (Hope you agree)

hE > d9 (You see where I’m going here…)

h0.EEE~ < d0.999~ (???)

====

Zeno's Paradox approach: You need to get to one. I give you 9/10. Now you need an additional 1/10. I give you 1/100. And so forth. Doing this an infinite number of times is not going to help.

And, no, I’m not talking about the number moving or approaching anything, I’m talking about how to determine where that point is by evaluating its representation. I get the feeling that some refutations confuse these two points.

The problem is that saying “an infinite number of nines” is equivalent of saying “and then a miracle occurs”. Yes, there is a place on the number line that represents 1/3, you just can’t accurately express where that place is with base ten digits, no matter how long you try. Claiming that it works out if you go to infinity doesn’t help.

In short, a repeating decimal is not a number any more that 1/0. It may be used as a shorthand for a concept, but you can’t do real math with it because it’s inherently inaccurate. Or, if you insist, show your work.

]]> By: Anonymous http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393333 Anonymous Wed, 30 Nov -0001 00:00:00 +0000 #comment-393333 I think it's really odd that people happily accept the infinite sum used on this clock for 2, but not the one for 7. They're completely analogous situations. I think it’s really odd that people happily accept the infinite sum used on this clock for 2, but not the one for 7. They’re completely analogous situations.

]]> By: arkizzle http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393081 arkizzle Wed, 30 Nov -0001 00:00:00 +0000 #comment-393081 Takuan, take your pick, they disagree. http://en.wikipedia.org/wiki/0.999... http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0.999eq1/ http://www.straightdope.com/columns/read/2459/an-infinite-question-why-doesnt-999-1 Takuan, take your pick, they disagree.

http://en.wikipedia.org/wiki/0.999…

http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html

http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0.999eq1/

http://www.straightdope.com/columns/read/2459/an-infinite-question-why-doesnt-999-1

]]> By: eagleapex http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393083 eagleapex Wed, 30 Nov -0001 00:00:00 +0000 #comment-393083 Hey I got Boinged! If you want to buy one they are currently sold out. But as soon as I can I will repost more quantities of math clocks Sweet. Hey I got Boinged! If you want to buy one they are currently sold out. But as soon as I can I will repost more quantities of math clocks
Sweet.

]]> By: UncleBaggy http://boingboing.net/2009/01/29/clock-for-geeks-1.html#comment-393087 UncleBaggy Wed, 30 Nov -0001 00:00:00 +0000 #comment-393087 this is just the kind of NERDiculator I've been looking for. FWIW, 6.9... is not the same number as 7, but it does have the same value. To say 6.9... = 7 is correct, but 6.9... == 7 is not. this is just the kind of NERDiculator I’ve been looking for.

FWIW, 6.9… is not the same number as 7, but it does have the same value. To say 6.9… = 7 is correct, but 6.9… == 7 is not.

]]>