tag:blogger.com,1999:blog-3758330678390419129.post8741487794385233989..comments2023-12-05T21:51:32.788-05:00Comments on EconomicPolicyJournal.com: Going Deep with David GordonRobert Wenzelhttp://www.blogger.com/profile/14296920597416905488noreply@blogger.comBlogger28125tag:blogger.com,1999:blog-3758330678390419129.post-2061308327188447632012-04-12T22:27:34.854-04:002012-04-12T22:27:34.854-04:00Mark,
Haven't we been through this before? Mi...Mark,<br /><br />Haven't we been through this before? Mises wrote a book, not a passage. If you read beyond class probability, you will encounter case probability. And, yes, numerical probabilites can be assigned, but they are metaphor ...I'll stop there since I don't want to spoil the ending for you.Jim Fedakohttps://www.blogger.com/profile/16380143827895514714noreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-48187245884333974172012-04-06T17:59:56.068-04:002012-04-06T17:59:56.068-04:00My probability math may be rusty.... but here is m...My probability math may be rusty.... but here is my sense of this.<br /><br />Infinity in a set of points on a real curve is just a non-real abstraction. In reality if we imagine a real dart, and a real set of points in a possible space that it can strike, then the larger the number of points (and the finer the point of the dart) then the smaller the probability of hitting any designated point. Stephan Kinsellahttps://www.blogger.com/profile/07986650653184633661noreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-23909411528034394812012-04-06T03:32:19.652-04:002012-04-06T03:32:19.652-04:00What's the probability that anyone except Murp...What's the probability that anyone except Murphy and Gordon actually read Callahan's droolings?Liberty Jerknoreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-53456715100527330022012-04-05T09:18:47.162-04:002012-04-05T09:18:47.162-04:00You're trying to apply reasoning of discrete e...You're trying to apply reasoning of discrete events to your analysis of the continuous. You're making the ill fated logical jump from the finite to the infinite that led to erroneous mathematics for so many years.<br /><br />These are not mathematical "tricks". They're perfectly valid techniques that allow for a systematic study of probability. This is not leading to Equalityhttps://www.blogger.com/profile/15557728134298301835noreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-21179090599834837912012-04-05T09:12:57.402-04:002012-04-05T09:12:57.402-04:00I'm a big fan of the blog, but I have to say t...I'm a big fan of the blog, but I have to say that Richard and Gene are perfectly right here. <br /><br />An event occurring with probability zero would never happen if we are dealing with a discrete distribution. However, Gene's thought experiment involves a continuous distribution, in which we general say an event with probability zero happens "almost never". <br /><br />The Equalityhttps://www.blogger.com/profile/15557728134298301835noreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-38076853084495209772012-04-04T22:49:00.361-04:002012-04-04T22:49:00.361-04:00David K,
I have a problem with point (2) of your ...David K,<br /><br />I have a problem with point (2) of your statement. Is it really possible that 0.5 will be chosen? it seems to me that the dart will be guaranteed to hit a transcendental number, which form an uncountable set along the real number line. Since there are infinitely more non-algebraic numbers along the line, you'll be guaranteed to hit one of them (ie. you'll be guaranteedAntony Zegershttps://www.blogger.com/profile/06249086850664272661noreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-28493309678523068512012-04-04T22:17:52.981-04:002012-04-04T22:17:52.981-04:00It's the study of logic. Which underpins econ...It's the study of logic. Which underpins economics and political philosophy. You won't get to correct answers in advanced sciences like economics or political philosophy if you don't master the basics.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-44167248105412630092012-04-04T22:11:43.968-04:002012-04-04T22:11:43.968-04:00Scholasticism is one of the great intellectual ach...Scholasticism is one of the great intellectual achievements in the west, and as Rothbard argued was an essential underpinning to the natural rights theories that gave rise to the cultural acceptance of capitalism, and of the acquisition and investment of wealth. You might consider reading something about it beyond pulp fiction.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-38119665377007874492012-04-04T22:00:29.042-04:002012-04-04T22:00:29.042-04:00Dan, are you seriously suggesting that it is liter...Dan, are you seriously suggesting that it is literally impossible to hit the number you chose when you toss the dart? If so, then how can that outcome be considered part of the sample space, and thus be part of the probability calculus at all? <br /><br />The same question applies to Dr. Gordon's comment here. How can we say that Callahan's statement was true (as Dr. Gordon says here) Mark Crovellinoreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-42973355971031475692012-04-04T21:34:30.263-04:002012-04-04T21:34:30.263-04:00Jim, I'm surprised that you of all people are ...Jim, I'm surprised that you of all people are not jumping to the defense of the Mises-Rothbard theory of probability here. Why is it suddenly possible to calculate a probability a priori in this example? There is no "class" involved, as Ludwig von Mises puts it, so why is it suddenly ok to assign a numerical probability in this case? <br /><br />I'm just curious.Mark Crovellinoreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-81864952308274217622012-04-04T19:22:23.228-04:002012-04-04T19:22:23.228-04:00I intended my first interpretation to be a probabi...I intended my first interpretation to be a probability before the experiment, not after it.David Gordonhttps://www.blogger.com/profile/03491884384604322669noreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-15357145364660461092012-04-04T19:19:32.144-04:002012-04-04T19:19:32.144-04:00My objection to Gene Callahan's post isn't...My objection to Gene Callahan's post isn't based on the mathematics of probability but rather on the meaning of the sentence he wants to challenge. Gene wants a counterexample to "0% chance X will happen per definition means X will never happen." Suppose someone predicts that, when Gene's dart is tossed, it will land on the number 0.5 The prediction has a 0% chance of David Gordonhttps://www.blogger.com/profile/03491884384604322669noreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-81318921013467605562012-04-04T19:03:02.749-04:002012-04-04T19:03:02.749-04:00Every paradox is the result of at least one false ...Every paradox is the result of at least one false premise -- always. So why the discussion.<br /><br />BTW: The false premise is the infinitely fine pointed dart. Go find me one.Jim Fedakohttps://www.blogger.com/profile/16380143827895514714noreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-29841322428687944062012-04-04T16:16:15.460-04:002012-04-04T16:16:15.460-04:00But the probability in 1 is not exactly zero. It ...But the probability in 1 is not exactly zero. It approaches zero as the fineness of the measurement increases. But there is no perfectly fine measurement in real life, no matter how close we come in theory. So there is always a positive nonzero probability, no matter how close to zero it is.<br /><br />There are ~7 billion people in the world. The chances of anyone being the best at anything Richardhttps://www.blogger.com/profile/16192630129745886988noreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-88539461147926236972012-04-04T14:24:06.921-04:002012-04-04T14:24:06.921-04:00What interests me most of all about this discussio...What interests me most of all about this discussion is that no Austrians are screaming and moaning about the method for generating probability that Callahan uses. Austrians of the Mises-Rothbard bent have followed Richard von Mises in claiming that the a posteriori relative frequency method is the ONLY method for generating legitimate numerical probabilities. They have, moreover, argued that Mark Crovellinoreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-2887078743850656892012-04-04T14:22:21.813-04:002012-04-04T14:22:21.813-04:00David K,
As a math student, you should know that...David K, <br /><br />As a math student, you should know that to talk about the probability of hitting a point in a continuous distribution is nonsensical. Gordon is saying that if it is possible for the dart to hit a number, then the probability of that event cannot be zero. If the probability of hitting a specific number is exactly zero, then it must also be true that the probability of hitting marketsclearnoreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-2587093704249594742012-04-04T14:05:09.056-04:002012-04-04T14:05:09.056-04:00What I gather he is saying is that the description...What I gather he is saying is that the description is not actually any sort of paradox, it's just two separate statements that aren't actually related to one another. If you choose a number and then throw your dart at the number line it will not land on the number you picked, ever. There is a zero percent chance it will happen. The fact that it lands on a number is irrelevant since that Dan Boninhttps://www.blogger.com/profile/17256402324432330811noreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-67928761341760820492012-04-04T13:58:37.663-04:002012-04-04T13:58:37.663-04:00If I understand David correctly, I agree with him....If I understand David correctly, I agree with him. Actually, it was the first thing I thought when I read the post. I think what David is saying, put more simply, is this: If you're throwing the infinitely-tiny-pointed dart with the INTENTION of hitting the number 0.23929398492839489283984982983949384982, then there is a 0% probability that you will succeed. But, to the contrary, if the Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-25231492016643716732012-04-04T13:11:23.789-04:002012-04-04T13:11:23.789-04:00What exactly is the relevance of all this to econo...What exactly is the relevance of all this to economics or political philosophy?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-61785530331850426002012-04-04T12:59:49.269-04:002012-04-04T12:59:49.269-04:00Would NSA bureau(c)rats even know what you are tal...Would NSA bureau(c)rats even know what you are talking about? Liberty? Private Property? Self-responsibility? WHATZ THAT???<br /><br />Even if a few NSA drones could be found who wanted to co-operate with you to uncover and publish recordings of conversations of David Gordon with Robert Nozick and Murray Rothbard, I doubt very much if they would know how to access the relevant files.<br /><br />David K.Mellerhttps://www.blogger.com/profile/01748020826341596745noreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-61723117739504793862012-04-04T12:49:57.158-04:002012-04-04T12:49:57.158-04:00One other note about the classical method Callahan...One other note about the classical method Callahan is using. The classical method STARTS from the assumption that each POSSIBLE outcome in the sample space has an equal likelihood of occurrence. In other words, the method itself takes as given that each outcome IS possible. Callahan could have saved his breath by just pointing this out (i.e., that every outcome IS possible according to the Mark Crovellinoreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-599745675651069392012-04-04T12:42:07.770-04:002012-04-04T12:42:07.770-04:00...isn't there a difference between 'appro......isn't there a difference between 'approaches' and 'reaches'? The limit of 1/n as n approaches infinity - a concept, let us remember, not a number - is 0, as you say, but I was under the impression that the whole point of a limit is that it isn't ever *actually* reached, just approached. In practical use, it may be fine not to make a distinction between 'Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-90905674519034628282012-04-04T12:36:22.443-04:002012-04-04T12:36:22.443-04:00David,
One thing you neglect to note is that both...David,<br /><br />One thing you neglect to note is that both you and Callahan are calculating the probability for the event occurring a priori using the so-called "classical method" by assuming each outcome has equal likelihood of occurring. Frequentists like Richard von Mises (and many Austrians, unfortunately), however claim that there can be no such thing as a probability until the Mark Crovellinoreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-53303885284925401172012-04-04T12:30:36.879-04:002012-04-04T12:30:36.879-04:00OK, riddle me this: Does an an infinitely deep we...OK, riddle me this: Does an an infinitely deep well have a bottom?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3758330678390419129.post-56200568928651814072012-04-04T11:58:45.932-04:002012-04-04T11:58:45.932-04:00Here's my take on this (I'm a graduate stu...Here's my take on this (I'm a graduate student of mathematics):<br /><br />As a Rothbardian, I have my disagreements with Gene Callahan, but in this case, he is 100% correct. He's simply stating a very basic fact about probability theory.<br /><br />"0% chance X will happen per definition means X will never happen."<br />There is no such definition.<br /><br />"And withDavid K.https://www.blogger.com/profile/16353503547913857327noreply@blogger.com