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New Technology Breeds New Vices:

A correspondent reports:

No doubt you have seen that a lot of the law reviews now have pocket parts, debate sections, web publications, etc. People are now writing on their resume that they published in the main line law review, without any indication that it was not in the hardcopy traditional publication. Does this seem right to you?

No, it doesn't. If I saw this on a resume, assumed that the person had published in the main journal, and then realized that he'd published in a separate online publication that the journal runs, I'd count that strongly against him. The Pocket Part is a great publication, and it's run by The Yale Law Journal, but it's not the same publication, it doesn't have the same selection pool, and it shouldn't be listed as -- or count as -- the same credential.

anonVCfan:

People are now writing on their resume that they published in the main line law review, without any indication that it was not in the hardcopy traditional publication. Does this seem right to you?


I wonder if your correspondent has any documentation for this. The Yale Pocket Part has 25 essays and 9 "commentaries," and other journals' special online sections have similarly small numbers of "publications." I'd be mildly surprised if it turned out that this was actually happening. Which "people" are in fact doing this?
9.8.2006 4:17pm
cirby (mail):
If someone can't manage to fit that half-sentence into the description of what they did on their resume (especially some younger folks), then how good would their regular work be?

Or how honest?
9.8.2006 5:36pm
Elliot Essman (mail) (www):
Once you learn resume-integrity, you're on the road to general integrity in all aspects of life. Resume assets must be earned. Ambiguity as to pocket parts and other transactional facets should be resolved in favor of non-inclusion.

Even worse, try asking someone who claims to speak a certain language, say the ubiquitous French, to carry out an actual conversation in real terms and in real time. After nineteen years of effort and expense I do speak this language, and I am constantly catching people. The truth shall set you free.
9.8.2006 6:06pm
Brezh (mail):
How about a law school where anyone who applies gets to write for law review (not necessarily be published)? I went to a school consistently ranked by US News as Top 20 for close to 20 years.

While the notation on the resume looked nice, the non-selectivity eviscerated any meaning from the implied accomplishment. I chose to obtain writing credits under direct faculty supervision. When I explained the situation during interviews, it clearly was not something they previously had been aware of and they seemed somewhat disconcerted by it.

Are there other schools that do this?
9.8.2006 6:08pm
Jeremy T:
I think this is much ado about nothing. It reminds me of when we were told in law school that if you have a 3.4999, you can't put on your resume that you have a 3.5. I once asked the career services people if they realized that the set of numbers represented by the number "3.5" unambiguously includes all numbers in the set (3.45, 3.55), of which 3.4999 was an element. The idiots had no idea what I was talking about.
9.8.2006 8:51pm
none (mail):
I'm not sure how this could even happen. Wouldn't you put the westlaw/lexis cite along with the name of the article you published? Do pocket parts and other non-traditional journal publications have such a citation? If someone claims to have published something on a resume but does not tell me how I can find that document, I don't trust them anyway.
9.8.2006 10:04pm
Edd (mail):

I once asked the career services people if they realized that the set of numbers represented by the number "3.5" unambiguously includes all numbers in the set (3.45, 3.55), of which 3.4999 was an element. The idiots had no idea what I was talking about.


I'm a grad student in math and I have no idea what you're talking about. This idea that there's a mathematical foundation for publishing 3.47 as 3.5 is just plain wrong. That said, it is true that 3.4999 . . . (with the "9" repeating forever) is the same number as 3.5.
9.8.2006 10:45pm
Lev:

"3.5" unambiguously includes all numbers in the set (3.45, 3.55), of which 3.4999 was an element.


So, when the legislature wanted to define Pi as 3.14, it was unambiguously correct.


That said, it is true that 3.4999 . . . (with the "9" repeating forever) is the same number as 3.5.


I'm not the godlike being, a grad student in math, but I wonder anyway, is that really correct, that something that, what, asymptotically approaches a number is that number? Or is it, instead, actually correct, in a mathematical sense, to say something like


the limit as x approaches infinity of 3.4(9)subscript x, is 3.5?



How about a law school where anyone who applies gets to write for law review (not necessarily be published)? I went to a school consistently ranked by US News as Top 20 for close to 20 years.


I don't see how this is different from the Volokh pocket parts, except that maybe it is done with the law school connivance.
9.9.2006 12:05am
Edd (mail):

I'm not the godlike being, a grad student in math, but I wonder anyway, is that really correct, that something that, what, asymptotically approaches a number is that number? Or is it, instead, actually correct, in a mathematical sense, to say something like the limit as x approaches infinity of 3.4(9)subscript x, is 3.5?


I'm sorry if my post came off as arrogant, as it wasn't intended that way. I only wanted to establish that I do in fact have some math training and am not just speculating. That said, 3.499 . . . does equal 3.5 according to accepted definitions of real numbers. Below I'll describe why, although it might get somewhat technical.

Let's define real numbers in a simple, rigorous way. Consider an infinite set S of rational numbers with the property that for any 2 rational numbers x and y, if x is in S and y < x, then y is in S. Now consider the set consisting of all sets with this property. This "set of sets" is the real numbers. The natural correspondence is that the real number x corresponds to the contained set of rational numbers for which it serves as the least upper bound, i.e., x corresponds to { y such that y is rational and y<=x }.

The real number 2 corresponds to the set of all rationals less than or equal to 2. The real number sqrt(2), which is not rational, corresponds to the set of all rationals less than sqrt(2). As an aside, notice how naturally addition and multiplication of real numbers spring out of this definition.

The reason 3.4(9) is equal to 3.5 is that their corresponding sets are the same. There is no element of the set corresponding to 3.5 that is not contained in the set corresponding to 3.4(9).

Alternate definitions of equality which say 3.4(9) doesn't equal 3.5 suffer from serious defects. Presumably you'd set 3.5 - 3.4(9) equal to some distinct element z. Now is z*z < z? Is 3.5 - z/2 = 3.4(9)? What's sqrt(z)? What's 2*sqrt(z)? Does z/2 have a decimal expansion distinct from z? These are just a few simple, non-technical problems. When you get to defining limits, forget about it - pretty quickly we're moving away from math and into philosophy.

These sorts of "gray areas" may go over alright in law, but math's a different story. If that last part sounds arrogant, well, I personally wouldn't dream of arguing points of law with a law student.
9.9.2006 1:10am
Lev:

rational numbers


That obviously excludes anything having to do with the federal budget.


the real numbers


Same for that.


The reason 3.4(9) is equal to 3.5 is that their corresponding sets are the same. There is no element of the set corresponding to 3.5 that is not contained in the set corresponding to 3.4(9).


But, it seems to me, 3.5 is not in the set corresponding to 3.4(9) because it is not less than 3.4(9) - "if x is in S and y < x, then y is in S", but y, 3.5, is greater than x, 3.4(9), therefore they are not equal.


There is no element of the set corresponding to 3.5 that is not contained in the set corresponding to 3.4(9)


Sure, but there is one "element" of the set corresponding to 3.5 that is not in the set corresponding to 3.4(9), and that is 3.5.

Which means, it seems to me, that 3.4(9) equals 3.5 and 3.5 does not equal 3.4(9).


I personally wouldn't dream of arguing points of law with a law student.


Me either, because, while lawyers know more about everything than nonlawyers, and judges know everything about everything, law students know even more than there is to know about everything, which is why they edit law reviews.
9.9.2006 2:29am
Edd (mail):
You're right, I wrote "less than or equal" when what I meant was "strictly less than". Then 2 corresponds to the set of rationals upper bounded by (but not including) 2, sqrt(2) to the set of rationals upper bounded by sqrt(2), and so on.

You might be interested in reading about the surreal numbers, a field described by the mathematician John Conway which behaves consistently in a way similar to what you describe. But this is very different from the real number system. I can basically say with absolute confidence (and yes, as a graduate student of mathematics) that no serious mathematician would challenge the idea that 3.4(9) and 3.5 are equal real numbers.


Me either, because, while lawyers know more about everything than nonlawyers, and judges know everything about everything, law students know even more than there is to know about everything, which is why they edit law reviews.


I never said anything like what you're suggesting. But it does require a certain level of arrogance to argue with someone over a subject he's devoted years of his life to and you clearly know nothing about.
9.9.2006 3:01am
Lev:

But it does require a certain level of arrogance to argue with someone over a subject he's devoted years of his life to and you clearly know nothing about.



You're right, I wrote "less than or equal" when what I meant was "strictly less than".


There seems to be some sort of disconnect there.

-----------------------------

"strictly less than". Then 2 corresponds to the set of rationals upper bounded by (but not including) 2, sqrt(2) to the set of rationals upper bounded by sqrt(2), and so on.


So then 3.4(9) corresponds to the set of rationals bounded by but not including 3.4(9), and which obviously does not include 3.5.

and then 3.5 corresponds to the set of rationals bounded by but not including 3.5, but which includes 3.4(9)

I don't see how that gets you out of 3.4(9) equals 3.5 and 3.5 does not equal 3.4(9).


I can basically say with absolute confidence (and yes, as a graduate student of mathematics) that no serious mathematician would challenge the idea that 3.4(9) and 3.5 are equal real numbers.


That is argument by appealing to authority.


But it does require a certain level of arrogance to argue with someone over a subject he's devoted years of his life to and you clearly know nothing about.


And that is argument by personal attack.
-----------------------------


I never said anything like what you're suggesting.


Did I say you did? I was explaining why I agreed with your statement:


I personally wouldn't dream of arguing points of law with a law student.



surreal numbers


Now you're talking federal budget.
9.9.2006 3:22am
lucia (mail) (www):
Math, schmath. By convention, when rounding to two significant figures 3.47 is rounded to 3.5. If a person has a 3.501 gpa, and they want to make sure someone doesn't think it's a 3.451 they can write 3.50. Or heck, if they want credit for every single possible crumb of GPA those who really don't want to round down can write 3.50001. (At which point, whoever reads the resume will think they are a weenie. They will not based their opinion on any sophisticated mathematical argument.)

If the career services people advocate a rule requiring 3 significant figures, they should insist everyone include 3 significant figures regardless of whether their GPA is 3.501. 3.499 or 3.472.

When written to two significant figures 3.47 correctly becomes 3.5. It's a convention taught in grade school, programmed into calculators and generally used.
9.9.2006 11:49am
Edd (mail):

So then 3.4(9) corresponds to the set of rationals bounded by but not including 3.4(9), and which obviously does not include 3.5.

and then 3.5 corresponds to the set of rationals bounded by but not including 3.5, but which includes 3.4(9)

I don't see how that gets you out of 3.4(9) equals 3.5 and 3.5 does not equal 3.4(9).


3.4(9) is not a rational number, and so not a member of either of the 2 associated sets. To see this, imagine (for the sake of argument) that 3.4(9) = x/y, where x and y are integers. Then 3.5 - 3.4(9) = 7/2 - x/y = (7y - 2x)/2y, which is clearly some rational number that may or may not be 0, but certainly is not some bizarre number that sometimes behaves like 0 and sometimes not. That is, unless you're going to set y to infinite, claiming infinite as an integer (it's not), and set x to 3.4(9) * (infinite), another made-up integer.


That is argument by appealing to authority.


In general, I don't see anything wrong with arguing by appealing to authority. I'm a doctor, I have 20 years of experience, and you simply don't have cancer. That seems pretty convincing, at least when the expert has no incentive to lie.
9.9.2006 12:03pm
Lev:
----------3.4(9) is not a rational number,-----------


I can see how it would be not rational with (9) meaning it is repeated infinitely. The drill would be to have an integer [7 x (10 exp x)]/[2 x (10 exp x) + 1]. As x gets larger and larger, the number of nines after the decimal point gets greater and greater, but at some point with any discrete integer no matter how large, eventually some digit other than nine fall out of the division. [Conceptually, however, it also seems to me that if x is an infinitely large number, then the numerator and denominator are both infinitely large but different integers, and (9) is achieved. But then who understands infinity anyway.]

So what I gather, is that so long as there is a 3.4(9)subscript x where x is not infinity, then 3.4(9)subscript x is a rational number, produced by the ratio of two integers, and is not equal to 3.5. But 3.4(9)subscript x where x is infinity is equal to 3.5. Although that sounds to me like one of Zeno's paradoxes.

Perhaps my problem is this:

----------The natural correspondence is that the real number x corresponds to the contained set of rational numbers for which it serves as the least upper bound, i.e., x corresponds to { y such that y is rational and y<=x }. The real number 2 corresponds to the set of all rationals less than or equal to 2. The real number sqrt(2), which is not rational, corresponds to the set of all rationals less than sqrt(2).--------------------

What does "correspondence" mean.

-----------------In general, I don't see anything wrong with arguing by appealing to authority. I'm a doctor, I have 20 years of experience, and you simply don't have cancer. That seems pretty convincing, at least when the expert has no incentive to lie.-----------


Suit yourself, but I would rather be sure the doctor actually is an expert in cancer and diagnosing it, has done all the appropriate tests and interpreted them correctly, and can explain them.
9.10.2006 12:11am
DK:
Edd, it is a contradiction for you to claim that 3.4(9) is not a rational number and to simultaneously claim that it equals 3.5. Perhaps everyone here should take a deep breath.

The truth here is that Edd is completely right that 3.5 = 3.4(9), these are really just two different ways of writing down the single number 3.5, a number which can also be written as 7/2 and which is therefore rational as well as real. None of this can be proven because it is a definition, not a proof; there happens to be a redundancy in the way people write numbers, so that 7/2 and 3.5 and 3.4(9) are all synonyms.


Edd has above given a correct set-theoretical definition of the real numbers. When he says that this is accepted by all serious mathematicians, he is not making an argument by authority, but simply stating a definitional fact -- i.e. just as doctors write an (unprovable) definition of cancer, mathematicians define numbers, and if you prefer to use your own nonstandard definitions, you are in 2+2=5, love is hate, war is peace territory.

Limits BTW don't matter for this equality. The numbers 3.49, 3.499, 3.4999, 3.49999 ... converge to a single limit which equals 3.5 and equals 3.4(9) simultaneously.
9.10.2006 12:25pm
Edd (mail):

Edd, it is a contradiction for you to claim that 3.4(9) is not a rational number and to simultaneously claim that it equals 3.5. Perhaps everyone here should take a deep breath.


You're right, I do need to take a deep breath. I meant if we assume (for sake of contradiction) that 3.4(9) doesn't equal 3.5, then 3.4(9) isn't rational. I agree with everything else written here.

Sure, in a sense this is a semantic argument. But if Lev wants to demonstrate a (not unusual or even problematic in itself) ignorance of basic college-level math by arguing that 3.4(9) is distinct from 3.5, and then stubbornly dismiss any correction from a practicing mathematician, I feel a duty to set the record straight lest math become seen like so many other academic disciplines; groundless, devoid of formal frameworks, built up on fads, etc.

If I, a non-lawyer, were to walk into a courtroom and argue that the 4th amendment protected my right to free speech, I would (rightly) be laughed at. Similarly, I think it's important to mock people like Lev for a few reasons. For one thing, it provides an incentive for people to learn some math before entering into math discussions, or at least to exercise a bit of humility. For another thing, it re-affirms that math, unlike perhaps other fields, really is a hard subject with a strong analytic base. Finally, it just plain feels good.

So here goes. Lev, you are an idiot. You know nothing about math. What's worse, you're belligerent and too damn cocky to realize you know nothing about it. You don't engage other arguments except to try to poke holes in them. You love arguing, but would never actually read a book on analysis, because that would require challenging yourself.
9.10.2006 5:25pm
Lev:
DK


just as doctors write an (unprovable) definition of cancer



I would guess they would write one as including something such as "...the presence of observed cancer cells...." And the absence of cancer as including something such as "...the absence of observed cancer cells...". Neither of these is "I am the doctor with twenty years experience and I say you don't have cancer." The conclusion, cancer/no cancer, must be based on actual data demonstrating one or the other proposition.


correct set-theoretical definition of the real numbers. When he says that this is accepted by all serious mathematicians, he is not making an argument by authority,


Perhaps I am being picky, but it is, and this is why.


1 - under the set theory definition of real numbers, 3.4(9) is equal to 3.5, and this is how that result is arrived at under set theory: explanation

2 - all serious mathematicians agree that 3.4(9) is equal to 3.5


In the former, the opinion of mathematicians is irrelevant to the conclusion, in the later, it is the basis for the conclusion. Perhaps in your mind they mean the same thing......but the expression is different.


Limits BTW don't matter for this equality. The numbers 3.49, 3.499, 3.4999, 3.49999 ... converge to a single limit which equals 3.5 and equals 3.4(9) simultaneously.


I understand the limit, which is why I mentioned it earlier.


None of this can be proven because it is a definition, not a proof; there happens to be a redundancy in the way people write numbers, so that 7/2 and 3.5 and 3.4(9) are all synonyms.


That isn't what what Edd said, so far as I can figure out. It sounded to me as if he was saying it was something that could be proved.
9.11.2006 1:18am
Lev:
Edd


So here goes. Lev, you are an idiot.


If you are so very smart, how is it you are contradicting yourself


Edd, it is a contradiction for you to claim that 3.4(9) is not a rational number and to simultaneously claim that it equals 3.5.


Answer that one. How can I understand what you are trying to communicate, when you contradict yourself, and, as you said earlier, were incorrect in how you worded something? That kind of performance is not calculated to lend confidence in your statement that "all serious mathematicians" agree on something.


But if Lev wants to demonstrate a (not unusual or even problematic in itself) ignorance of basic college-level math by arguing that 3.4(9) is distinct from 3.5, and then stubbornly dismiss any correction from a practicing mathematician, I feel a duty to set the record straight lest math become seen like so many other academic disciplines; groundless, devoid of formal frameworks, built up on fads, etc.


I have been looking for an explanation that makes sense. You haven't been able to provide one, and because you haven't, you call me names. Maybe you should reinforce your explaining instead of raising your voice.

I was in college 40 years ago, and my calculus, differential equations, linear algebra etc. math electives did not have any "set theory" in them.


What's worse, you're belligerent and too damn cocky to realize you know nothing about it.


I guess, brainchild, that is why I asked you:


What does "correspondence" mean.


It appears you can't explain that either.


If I, a non-lawyer, were to walk into a courtroom and argue that the 4th amendment protected my right to free speech, I would (rightly) be laughed at. Similarly, I think it's important to mock people like Lev for a few reasons. For one thing, it provides an incentive for people to learn some math before entering into math discussions, or at least to exercise a bit of humility. For another thing, it re-affirms that math, unlike perhaps other fields, really is a hard subject with a strong analytic base. Finally, it just plain feels good.


There is one big fat problem with that formulation bright boy, the math analog for mathematicians to "a courtroom" for lawyers would not be The Volokh Conspiracy, unless I am greatly mistaken. Unless I am mistaken, I would think that it would be a math conference of some sort. If I am mistaken, we are in a heap of trouble. Do you feel The Volokh Conspiracy is a math conference?

]You love arguing, but would never actually read a book on analysis, because that would require challenging yourself.

Now you read minds and know people you have never met. What arrogance.
9.11.2006 1:33am
Lev:
DK

I wonder if you could explain something that occurred to me with respect to this:


None of this can be proven because it is a definition, not a proof; there happens to be a redundancy in the way people write numbers, so that 7/2 and 3.5 and 3.4(9) are all synonyms.


At what point does a number become sufficiently different from 7/2 and 3.5(0) [with, in my layman's language, 3.5(0) meaning 3.5(0)subscript x where x is infinitely large or alternatively where the 0 repeats itself infinitely]?

For example, you have said that under set theory 3.4(9) is defined as being the same as 3.5.

1. What about 3.4(9)8? In my layman's language, 3.4(9)8 meaning 3.4[(9)subscript x]8 where x is infinitely large, or alternatively, 3.4(9)8 is 3.4(9) except that instead of the "last" digit being a 9, it is an 8.

Or 3.4(9)7?

2. On the other side of the ledger but similarly, does set theory define 3.5(0)1 as 3.5? And how "far away" from 3.5(0) does a number have to be to no longer be defined as 3.5?

It seems to me, using limits, that if 3.4(9) is 3.5, then so should 3.5(0)1. As "x approaches infinity" the limit each approaches is 3.5.
9.11.2006 2:08am
DK:
Lev,
0. You asked "At what point does a number become sufficiently different from 3.5?". For two numbers to be different, you must be able to identify a finite, nonzero number 1e-X such that number A - number B > 1e-X, where 1e-X means 0.(X 0's) followed by a 1.
1. It is not possible to write a number 3.4(9)8, because there is no "last" digit, there is only an infinite series of 9's. If you wrote the series 3.498, 3.4998, 3.49998 ..., this series would converge to the limit of 3.4(9) = 3.5. The same would apply to the series 3.491, 3.4991, 3.49991 or 3.490, 3.4990, 3.49990, etc.
2. As you write it, 3.5(0)1 would also be 3.5. You have to have a difference at a finite digit in order to get a different number. As Edd mentioned, it would be possible to define a different number system with different rules, but that is headed into increasingly bizarre territory.
9.11.2006 9:22am
Lev:
DK

Let me restate what you said to make sure I understand it. The problem with something such as 3.4(9)8 is that because (9) means an infinite number of 9s, you never get to the "last 8" that would make the number different from 3.5.

In order to have a number sufficiently different from 3.5 that it is not 3.5, one would have to use notation such as 3.4[9subscript x]8 where x is a specific finite number, no matter how large, that specifies the specific number of 9s that go before the 8.

I see that.


If you wrote the series 3.498, 3.4998, 3.49998 ..., this series would converge to the limit of 3.4(9) = 3.5. The same would apply to the series 3.491, 3.4991, 3.49991 or 3.490, 3.4990, 3.49990, etc.


I was thinking about that later, and see that too.


2. As you write it, 3.5(0)1 would also be 3.5.


That's what I thought it should be since it merely the "mirror image" around 3.5 of 3.4(9), one being
3.5 - 0.0(0)1, the other being 3.5 + 0.0(0)1, using my layman's notation. From what Edd was saying it sounded to me as if the 3.5 limit could only be approached from the low side, which is why I asked you the question.

I don't know how much longer this thread will live, or if you will check back, but I have another question.

In a different place and a different time, a person said to me that "mostly includes all" mathematically speaking. It was in the context of trace contaminants, you know ppm lead, ppb, arsenic things like that. It seems to me that "mostly" means, at least, 50%
In view of our discussion, what would your view on that be if you care to say?
9.12.2006 2:55am
Lev:
DK

ahh problems with the carats I should have used preview, this should be better

In a different place and a different time, a person said to me that "mostly includes all" mathematically speaking. It was in the context of trace contaminants, you know ppm lead, ppb, arsenic things like that. It seems to me that "mostly" means, at least, 50% < x < 100%, and that the other person was saying mostly means 50% < x < =100%. To me, 50% < x < =100%, means "mostly or all." It seems to me that something is only 100% pure if there are no detectible impurities at all, and if there are detectible impurities, then it is mostly or almost pure - that is leaving aside a physical definition that says substance x is defined as pure if total trace impurities are less than a specific percent, whether expressed as percent, ppt, ppm, ppb etc.
9.12.2006 3:00am