When a blogger named Zeno proudly announces that his blog, Halfway There, is about to reach the landmark of 250,000 hits, doesn’t that imply that he’ll never ever reach 500,000 hits?

Here is what is being proposed to be cut from the bill, according to TPM:
NASA exploration $750,000,000 = 50% NSF $1,402,000,000 = 100%
NOAA $427,000,000 = 34.94%
NIST $218,000,000 = 37.91%
DOE energy efficiency & renewable energy $1,000,000,000 = 38% DOE office of science $100,000,000 = 100%

I am sorry this is OT, and I don’t mean to hijack this thread, but I was shocked.

Dutchdocsays

As any good scientist who ever looked at Zeno’s paradox and then PERFORMED THE ACTUAL EXPERIMENT knows, the answer to the stated question is “NO”.

When a blogger named Zeno proudly announces that his blog, Halfway There, is about to reach the landmark of 250,000 hits, doesn’t that imply that he’ll never ever reach 500,000 hits?

Hahahahahahaha!

As every moment goes by, I come closer and closer to my death and thus the prospect of heaven. But as more and more of my life is lived, there seems less objective evidence for a supernatural realm than before. One could then conclude that I will die, but never get any closer to heaven. I must alert Jerry Coyne!

Hit #250,000 was scored by a pharynguloid at the University of Maryland (perhaps you know who you are). Now that PZ has stirred things up, I suppose I’ll have to report on who scored hit #500,000 by the end of the day.

I may have to raise the level of my game now.

Davidsays

Why 500,000? Is that the goal?

If the goal is, say, 3,141,592,653,589 hits then he can go MUCH further before slowing down to where the blog will only accept fractional hits….

Awesome Robotsays

“As any good scientist who ever looked at Zeno’s paradox and then PERFORMED THE ACTUAL EXPERIMENT knows, the answer to the stated question is “NO”.”

That’s because it turns out distance isn’t infinitesimal. You can’t travel half a planck length.

Bodachsays

+1 to highlycaffeinated for the Pratchett reference.

Christophersays

@8:

That’s a lot of pi’s.

SteveMsays

That’s because it turns out distance isn’t infinitesimal. You can’t travel half a planck length.

That isn’t the solution. It does not depend on any “granularity” of space or time. Zeno just could not accept or prove that an infinite series could sum to a finite value.

'Tis Himselfsays

Zeno,

I tried to put a comment on your blog but the software didn’t recognize my google account.

The comment was that mortgage companies and banks often put the loan money into checking accounts. When I bought my present house the bank put just under $200K in my checking account. At the closing, I wrote a personal check to the seller. But it was nice knowing that for a few days I was a multi-thousandaire.

SteveMsays

As any good scientist who ever looked at Zeno’s paradox and then PERFORMED THE ACTUAL EXPERIMENT knows, the answer to the stated question is “NO”.

That is what makes it a paradox. Obviously motion is possible so a mathematical proof of its impossibility is a paradox.

DaveHsays

#2 “There’s good eatin’ on those”

and would the gentleman at comment #3 please report to the testing station and pee into the receptacle provided. Thank you.

Well played Zeno!

Christophe Thillsays

A mathematical view of the impossiblity of movement is only a paradox as long as mathematics remain primitive. When it has made enough progress, it clearly appears as just an error. Later still, when philosophers still brandish the “intuitive” reasoning now that we know it’s false, it becomes sophistry.

That isn’t the solution. It does not depend on any “granularity” of space or time. Zeno just could not accept or prove that an infinite series could sum to a finite value.

Arrg, maties! I say we make Awesome Robot walk the planck. ;-) After all, when you think about it, what’s the harm?

Zeno’s “Dichotomy” paradox is perhaps a little more interesting. Here, before Achilles can go half the distance to the tortoise, he has to go a quarter the distance. Before he can do that, he has to go one eighth the distance; before that, one sixteenth the distance; and so on. Achilles is liable to spend infinitely long thinking along these lines, without ever working out how long his first step has to be.

Calculus can tell us about summing infinite series, sets without minima, bounds that are never actually attained, etc, but I think it still leaves a little something in the Dichotomy for us to philosophise about. Or maybe I’m just as thick as two short Plancks.

Lee Brimmicombe-Woodsays

PZ and Pharyngulites in general, lend me your ears! (Not literally, that would be gross.)

Dr. Ben Goldacre, writer of the UK Guardian newspaper’s ‘Bad Science’ column, has been threatened with legal action for posting a file of a radio program on his blog that highlighted the on-air rantings of anti-MMR vaccination campaigner Jeni Barnett. You can find more of the story at Ben’s blog here:

Some folks are already offering to help Ben out, but as he is a poor scientist he might find the offer of a few quid (or dollars or shekels) to be of invaluable assistance.

It’s time to help one of our own.

PZ, any chance of a blog on this?

RamblinDudesays

“. . . Doesn’t that imply that he’ll never ever reach 500,000 hits?”

Simple solution: just raise the goal to 1,000,000!

Actually many philosophers (arrghhh!) consider it possible to go through an infinite series itself (not just cheat by saying you’re covering the continuum and the series is just a mathematical fiction.) IOW, look up “supertasks”. Supertasks do use the Zeno series or similar, but you define an idealized event (rather than a proportional distance etc.) at t = 1/2, 3/4, 7/8, … and so on to cover an infinite set (Aleph null, not the continuum) in a finite time.

It is also possible to compress infinite space or time by transformation into a finite extent, using for example x’ = ATan (x) or x’ = x/sqrt(1 + x^2). That means, if we accept mathematical transformation as “real”, that even if our space is infinite, “something” can be beyond it … really. Even the singing green alien can’t get out there. Hey, that’s where God lives! ;-)

Hey, don’t mess around with the Zeno paradox. I used that to prove to myself that I am never going to die!

SC, OMsays

Congratulations, Zeno! :)

jaysays

no, it implies he’ll not reach 500,001. If I give you $50 and say that’s half of it, $100 is all of it, and anything MORE we will not reach. ‘>=’ ^= ‘>’. And I’m not even a math teacher!

Valor Phoenixsays

Zeno’s Paradox is basically like Discovery Institute smoke and mirrors. Take for instance the two trains math problem cliche where two trains leave at certain speeds and times and we’re asked when they meet/collide/pass-each-other.

Basic motion in physics is solving for a certain velocity over a certain time giving a certain distance(eg 60 mph for 2 hours giving 120 miles distance).

Zeno’s Turtle relies on misdirection by stating that Achilles is progressively going half-way to the turtle, but because the turtle moves just a little bit further, Achilles doesn’t even reach the proposed halfway point. (eg as pointed out above, if the turtle is 100, halfway is 50, but the turtle is already at 101 or more by the time Achilles approaches 50, so that is no longer the halfway point. Basically auto-moving goalposts.)

This implies that somehow Achilles can’t catch the turtle because he can’t even achieve the halfway point.

However back to the science, the solution becomes obvious when using basic physics of motion and ignoring the philosophical smoke and mirrors.

Turtle has a headstart of 50m and a movement rate of 1m/s(very generous) while Achilles starts at 0m but has a movement rate of 10 m/s. At five seconds Achilles is at 50m and the turtle at 55m, at six seconds Achilles is at 60m and the turtle at 56m. Achilles passes the turtle somewhere between 5 and 6 seconds after the race starts.

Indeed, Zeno’s Paradox sounds a lot like Creationist claims against Macroevolution while accepting Microevolution. The creationists basically claim that evolution somehow slows down at a certain boundary, like they’re looking at the race track and always arranging it so Achilles is apparently behind Zeno’s Turtle, when in fact Achilles has lapped it many times already.

Sure the officials have ‘evidence’ of Achilles completing laps and passing the turtle multiple times, but they just trot Zeno’s dead corpse back out on stage as rebuttal.

nothing's sacredsays

no, it implies he’ll not reach 500,001. If I give you $50 and say that’s half of it, $100 is all of it, and anything MORE we will not reach. ‘>=’ ^= ‘>’. And I’m not even a math teacher!

If you were, you might realize that you have no clue what people are discussing here.

My usual blog traffic is around 200 hits per day. Thanks to PZ’s plug, today is closing in on 2000.

PZ: the magical order of magnitude boost!

Can’t package it, though.

Many thanks to all of today’s visitors, especially the ones who left amusing comments. PZ’s minions are nothing if not witty (and I count myself among them, of course).

Bill Dauphin says

Is the blog written by a tortoise?

highlycaffeinated says

“A very useful philosophical animal, your average tortoise.”

Achilles says

I totally won that race, dude.

Kausik Datta says

It’s “half”way there…

Zeno is a math teacher, after all…

BTW, this morning I came to Pharyngula to see if PZ has taken notice of this event: …efforts underway this morning to zero out a large portion of the science funding from the Senate American Reinvestment and Recovery Act as a part of a $77.9B reduction effort led by Senators Ben Nelson (D-NE) and Susan Collins (R-ME). (Via ScienceDebate2008)

Here is what is being proposed to be cut from the bill, according to TalkingPointsMemo:

Here is what is being proposed to be cut from the bill, according to TPM:

NASA exploration $750,000,000 = 50%

NSF $1,402,000,000 = 100%NOAA $427,000,000 = 34.94%

NIST $218,000,000 = 37.91%

DOE energy efficiency & renewable energy $1,000,000,000 = 38%

DOE office of science $100,000,000 = 100%I am sorry this is OT, and I don’t mean to hijack this thread, but I was shocked.

Dutchdoc says

As any good scientist who ever looked at Zeno’s paradox and then PERFORMED THE ACTUAL EXPERIMENT knows, the answer to the stated question is “NO”.

Scott Hatfield, OM says

When a blogger named Zeno proudly announces that his blog, Halfway There, is about to reach the landmark of 250,000 hits, doesn’t that imply that he’ll never ever reach 500,000 hits?Hahahahahahaha!

As every moment goes by, I come closer and closer to my death and thus the prospect of heaven. But as more and more of my life is lived, there seems less objective evidence for a supernatural realm than before. One could then conclude that I will die, but never get any closer to heaven. I must alert Jerry Coyne!

Seriously, Zeno…congrats!

Zeno says

Hit #250,000 was scored by a pharynguloid at the University of Maryland (perhaps you know who you are). Now that PZ has stirred things up, I suppose I’ll have to report on who scored hit #500,000 by the end of the day.

I may have to raise the level of my game now.

David says

Why 500,000? Is that the goal?

If the goal is, say, 3,141,592,653,589 hits then he can go MUCH further before slowing down to where the blog will only accept fractional hits….

Awesome Robot says

“As any good scientist who ever looked at Zeno’s paradox and then PERFORMED THE ACTUAL EXPERIMENT knows, the answer to the stated question is “NO”.”

That’s because it turns out distance isn’t infinitesimal. You can’t travel half a planck length.

Bodach says

+1 to highlycaffeinated for the Pratchett reference.

Christopher says

@8:

That’s a lot of pi’s.

SteveM says

That’s because it turns out distance isn’t infinitesimal. You can’t travel half a planck length.That isn’t the solution. It does not depend on any “granularity” of space or time. Zeno just could not accept or prove that an infinite series could sum to a finite value.

'Tis Himself says

Zeno,

I tried to put a comment on your blog but the software didn’t recognize my google account.

The comment was that mortgage companies and banks often put the loan money into checking accounts. When I bought my present house the bank put just under $200K in my checking account. At the closing, I wrote a personal check to the seller. But it was nice knowing that for a few days I was a multi-thousandaire.

SteveM says

As any good scientist who ever looked at Zeno’s paradox and then PERFORMED THE ACTUAL EXPERIMENT knows, the answer to the stated question is “NO”.That is what makes it a paradox. Obviously motion is possible so a mathematical proof of its impossibility is a paradox.

DaveH says

#2 “There’s good eatin’ on those”

and would the gentleman at comment #3 please report to the testing station and pee into the receptacle provided. Thank you.

Well played Zeno!

Christophe Thill says

A mathematical view of the impossiblity of movement is only a paradox as long as mathematics remain primitive. When it has made enough progress, it clearly appears as just an error. Later still, when philosophers still brandish the “intuitive” reasoning now that we know it’s false, it becomes sophistry.

Kristine says

That isn’t the solution. It does not depend on any “granularity” of space or time. Zeno just could not accept or prove that an infinite series could sum to a finite value.Arrg, maties! I say we make Awesome Robot walk the planck. ;-) After all, when you think about it, what’s the harm?

Fun thread.

Glen Davidson says

He can, however, come arbitrarily close to that limit.

Glen D

http://tinyurl.com/6mb592

Alex. says

@8: The joke is that he’s at 250,000 and the blog’s name is “Halfway There.”

Vole says

Zeno’s “Dichotomy” paradox is perhaps a little more interesting. Here, before Achilles can go half the distance to the tortoise, he has to go a quarter the distance. Before he can do that, he has to go one eighth the distance; before that, one sixteenth the distance; and so on. Achilles is liable to spend infinitely long thinking along these lines, without ever working out how long his first step has to be.

Calculus can tell us about summing infinite series, sets without minima, bounds that are never actually attained, etc, but I think it still leaves a little something in the Dichotomy for us to philosophise about. Or maybe I’m just as thick as two short Plancks.

Lee Brimmicombe-Wood says

PZ and Pharyngulites in general, lend me your ears! (Not literally, that would be gross.)

Dr. Ben Goldacre, writer of the UK Guardian newspaper’s ‘Bad Science’ column, has been threatened with legal action for posting a file of a radio program on his blog that highlighted the on-air rantings of anti-MMR vaccination campaigner Jeni Barnett. You can find more of the story at Ben’s blog here:

http://www.badscience.net/

Some folks are already offering to help Ben out, but as he is a poor scientist he might find the offer of a few quid (or dollars or shekels) to be of invaluable assistance.

It’s time to help one of our own.

PZ, any chance of a blog on this?

RamblinDude says

“. . . Doesn’t that imply that he’ll never ever reach 500,000 hits?”Simple solution: just raise the goal to 1,000,000!

Congrats Zeno

Neil B ☺ says

Actually many philosophers (arrghhh!) consider it possible to go through an infinite series itself (not just cheat by saying you’re covering the continuum and the series is just a mathematical fiction.) IOW, look up “supertasks”. Supertasks do use the Zeno series or similar, but you define an idealized event (rather than a proportional distance etc.) at t = 1/2, 3/4, 7/8, … and so on to cover an infinite set (Aleph null, not the continuum) in a finite time.

It is also possible to compress infinite space or time by transformation into a finite extent, using for example x’ = ATan (x) or x’ = x/sqrt(1 + x^2). That means, if we accept mathematical transformation as “real”, that even if our space is infinite, “something” can be beyond it … really. Even the singing green alien can’t get out there. Hey, that’s where God lives! ;-)

Tom says

Hey, don’t mess around with the Zeno paradox. I used that to prove to myself that I am never going to die!

SC, OM says

Congratulations, Zeno! :)

jay says

no, it implies he’ll not reach 500,001. If I give you $50 and say that’s half of it, $100 is all of it, and anything MORE we will not reach. ‘>=’ ^= ‘>’. And I’m not even a math teacher!

Valor Phoenix says

Zeno’s Paradox is basically like Discovery Institute smoke and mirrors. Take for instance the two trains math problem cliche where two trains leave at certain speeds and times and we’re asked when they meet/collide/pass-each-other.

Basic motion in physics is solving for a certain velocity over a certain time giving a certain distance(eg 60 mph for 2 hours giving 120 miles distance).

Zeno’s Turtle relies on misdirection by stating that Achilles is progressively going half-way to the turtle, but because the turtle moves just a little bit further, Achilles doesn’t even reach the proposed halfway point. (eg as pointed out above, if the turtle is 100, halfway is 50, but the turtle is already at 101 or more by the time Achilles approaches 50, so that is no longer the halfway point. Basically auto-moving goalposts.)

This implies that somehow Achilles can’t catch the turtle because he can’t even achieve the halfway point.

However back to the science, the solution becomes obvious when using basic physics of motion and ignoring the philosophical smoke and mirrors.

Turtle has a headstart of 50m and a movement rate of 1m/s(very generous) while Achilles starts at 0m but has a movement rate of 10 m/s. At five seconds Achilles is at 50m and the turtle at 55m, at six seconds Achilles is at 60m and the turtle at 56m. Achilles passes the turtle somewhere between 5 and 6 seconds after the race starts.

Indeed, Zeno’s Paradox sounds a lot like Creationist claims against Macroevolution while accepting Microevolution. The creationists basically claim that evolution somehow slows down at a certain boundary, like they’re looking at the race track and always arranging it so Achilles is apparently behind Zeno’s Turtle, when in fact Achilles has lapped it many times already.

Sure the officials have ‘evidence’ of Achilles completing laps and passing the turtle multiple times, but they just trot Zeno’s dead corpse back out on stage as rebuttal.

nothing's sacred says

no, it implies he’ll not reach 500,001. If I give you $50 and say that’s half of it, $100 is all of it, and anything MORE we will not reach. ‘>=’ ^= ‘>’. And I’m not even a math teacher!If you were, you might realize that you have no clue what people are discussing here.

Zeno says

My usual blog traffic is around 200 hits per day. Thanks to PZ’s plug, today is closing in on 2000.

PZ: the magical order of magnitude boost!

Can’t package it, though.

Many thanks to all of today’s visitors, especially the ones who left amusing comments. PZ’s minions are nothing if not witty (and I count myself among them, of course).