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ICOT:
1) Yes.
2) Yes. Also, I meant to say that Y stays on the boundary of the circle.
Yes also to your square question – in fact, this strategy works in any compact metric space. (My square visualization hint at the beginning was correct given the assumption on X and Y’s optimal strategies. It turns out, though, that Y has an optimal strategy that does not necessarily maximize the distance from X.)
Radius vector – this is just the line drawn from the center of the circle to Y.
{t_1, t_2, t_3, …} – I don’t know if it’s possible to do math type here, but the “_number” is supposed to mean subscript. The number just identifies the time period, so t_1 is the first period of movement and so on.
ith – “i” just means that it refers to any number. It could refer to t_1 or t_2 or t_557 or anything you want. So using “i” instead of a number is a generalization. So if the ith time period happens to be t_557, then the (i+1)th time period is t_558. But “i” can be any number.
half-plane – in our example of a closed circle, we were using R^2 space, i.e. your standard 2-dimensional metric space. R^2 is the metric space that children do math in for all of grade school; when you draw a graph with an x-axis and y-axis, this is R^2 space. The whole R^2 space makes up a plane. If I only consider everything above the x-axis, then I am considering a “half-plane.”
So in the context of the problem, we could consider Y’s radius vector as dividing the “world” in half. By imagining that the vector actually is a line rather than a line segment, everything to one side of the line would constitute a half-plane whereas everything to the other side of the line would constitute the other half-plane.
The Pythagorean Theorem is actually quite easy; draw a line from the center of the circle to where Y is located. This is Y’s radius vector. Now Y is moving perpendicular to his radius vector, so draw a small line segment perpendicular to the radius vector that begins at Y’s current location. This line segment represents Y’s movement. Now connect the other end of the segment to the center of the circle. This will be Y’s new radius vector after moving. Note that since the original radius vector is perpendicular to the line segment of movement, we now have a right triangle, where the new radius vector after moving is the hypotenuse of the triangle.
The boundedness of the radii is a bit more difficult, but basically the idea is that in order for the strategy to work, Y cannot make “too big” of moves or else the strategy will require him to leave the circle, which he is not allowed to do.
frummy in the tummy: If I understand your kasha (which I might not), you are concerned that Y does not know where X is heading necessarily, so he cannot know which half-plane to choose.
Y does not need to know X’s direction; Y only needs to know X’s location.
ICOT: This riddle became popular in the early 1930s, and if it were before 1952, you would not only have the correct answer, but you also noted within your answer the correct strategy X would use to catch Y.
Namely, X could be guaranteed to catch Y by staying on the same radius as Y. In other words, X moves at top speed in such a way that X always lies on the radius vector from the center to Y. If we assume without loss of generality that X stays on the boundary of the circle, then it is easy to check that X does now catch Y in
finite time. Indeed, in the time that it takes Y to run a quarter-circle at full speed, X (say starting at the center) performs a semicircle of half the radius of the disc, thus catching Y.
However, in 1952, it was proven that Y need not stay on the boundary and in fact can survive forever in a closed circle. The clever proof is as follows:
First, I establish a winning strategy for Y, and then I will establish that it is feasible, i.e. Y does not leave the closed circle.
Let T = {t_1, t_2, t_3, …} be a sequence of time periods of equal length. At the ith time period, Y runs in a straight line that is perpendicular to Y’s radius vector at the start of the period. Y runs into the half-plane that does not contain X (if X is on the radius then Y may choose either half-plane). Certainly, X does not catch Y in this time period.
Let Y repeat this procedure for all time periods. As long as T is an infinite sequence, Y is never caught.
Now, I must show that this strategy is feasible. Note that if R_i is the distance of Y from the center at the start of the ith time period, then (R_i+1)^2 = (R_i)^2 + (t_i)^2. (This is just a simple application of the famous Pythagorean Theorem.) If the sum of (t_i)^2 is finite, then the R_i’s are bounded so that (multiplying by a constant if necessary) Y does not leave the closed circle. Let t_i = 1/i.
Then, Y is never caught and never leaves the closed circle.
OOM: I was reading it like you did as well… however, I think where the OP refers to the child as a ‘him’ is actually referring to the father, i.e. the father’s parents never showed compassion to the father when the father was a child.
yekke2: Consider an economy where one can buy 1 kipa for $1.
Then, due to the government printing money, suppose there are twice as many dollars in the economy. Now, you would think that this is a good thing. In fact, it would be if the population grew and there were more valuable services created. However, in the absence of such modifiers, now $1 is worth half as much as before. So the same kipa now costs $2 instead of $1.
This is what happened in the Weimar Republic after WWI. They owed so much to other countries from the Versailles Treaty that they printed money to pay their debt. As a result, there was hyperinflation, which caused their currency to become virtually worthless. Aside from the economic consequences, the poor state of the economy made way for a young, charasmatic politician named Adolf Hitler Y”S to capture the hearts and minds of the German people. I don’t need to tell you the rest of the story.
Now, I assume you may be asking because of the talk about “quantitative easing.” In a recession with periods of deflation, it is possible to increase the money supply without causing inflation. In the liquidity trap of 2008-2011, the Bank of England pursued quantitative easing (increasing the money supply), but this only had a minimal impact on underlying inflation. This is because although banks saw an increase in their reserves, they were reluctant to increase bank lending.
However, if a Central Bank pursued quantitative easing during a normal period of economic activity like our fictitous economy above, then it would cause inflation.
In the U.S., the question is really about number crunching. The United States is not experiencing deflation, but inflation is virtually 0. So the inflationary results of quantitative easing might not be so drastic.
Curiosity: Sorry for not being so clear. Perhaps this will clarify…
Consider a closed unit circle centered at the origin (0,0) in the Cartesian coordinate system in the Euclidean plane (i.e. your standard unit circle). Now, consider two different points in the closed unit circle (these points can be inside the circle or on the boundary of the circle, but since the circle is closed, they can never be outside the circle). Let’s call these points A and B, respectively.
Now, assume A and B move freely in the closed circle with equal maximum speed. A tries to “catch” B by getting to the same location as B (i.e. A catches B if both A and B have the same exact coordinates at any given time). B tries to “evade” A.
Assuming A and B play optimal strategies (i.e. A and B make the best possible moves at all times in accordance with their goals), does A “catch” B? If so, how can A be guaranteed to “catch” B? If not, how can B be guaranteed to “evade” A?
To make it more interesting for non-math-oriented people, I had called A the rodef and B the nirdaf since in a literal sense this is the case (i.e. A is the chaser and B is the chased). However, you correctly point out that from a halachic standpoint, the din of rodef and nirdaf is more complex. I apologize for the confusion.
Aside (if it’s confusing, just ignore): This is an example of a pursuit-evasion game. There are several interesting properties of these games in general, but there is something particularly interesting about this game.
One of the basic properties of these types of games is to note the path that the chaser takes to catch the chased. This path is called a pursuit curve, which is aptly named because the path of pursuit need not be straight. For example, if a mother is chasing a little child running straight in some direction, chances are that the mother is faster, and she can get onto the child’s path of travel and then follow the child’s path until she catches him. However, if she runs at the same speed as the child, then she cannot just follow the child’s path because she will never catch up. Instead, the mother runs to where the child is heading and intercepts him at some point. If the child changes direction during the chase in response to the mother’s chase, then the mother’s path of pursuit will be curved. Hence the term pursuit curve.
moskidoodle: I don’t know how today’s posts will turn out, but tomorrow’s (on the Jewish calendar) posts will be me’ein olam haba.
Curiosity: the rodef and nirdaf are each a single point in a closed circle. A single point can’t carry a gun (since a single point has no dimension, and hence no mass). Alternatively, shooting the nirdaf would violate the given assumption that both move with the same maximum speed.
Here’s a hint for how to visualize the problem:
Let’s assume for a moment that we have a closed square with vertices at (0,0),(0,1), (1,0) and (1,1). This is a simple unit square. Now, assume the rodef begins at one corner of the square, say (1,1), and the nirdaf begins at the opposite corner (0,0). So the nirdaf is sqrt(2) units away from the rodef.
Now, as a conjecture, it would be a reasonable assumption that the rodef and nirdaf would have opposite strategies; namely, the rodef wants to minimize distance between the rodef and nirdaf while the nirdaf wants to maximize distance between the rodef and nirdaf.
In this example, the nirdaf actually has no incentive to move whatsoever. This is because (0,0) is as far as the nirdaf can get from (1,1) where the rodef is. So the nirdaf is maximizing distance from the rodef by remaining at (0,0). The rodef’s optimal strategy from (1,1) is to move in a straight line towards (0,0) because the shortest distance between two points is a straight line (extra credit to whoever proves that the shortest distance between two points is a straight line).
Since the nirdaf will never have an incentive to move given the rodef’s strategy (moving away from (0,0) at any time will shorten the distance with the rodef), and the rodef continually gets closer, then it is clear to see that the rodef will eventually “corner the nirdaf” and catch the nirdaf at (0,0).
So in this contrived example, the rodef catches the nirdaf regardless of what the nirdaf tries to do. The riddle, though, is what happens in a circle?
Another hint:
The optimal strategy for the rodef to minimize distance to the nirdaf is to move along the straight line connecting the rodef’s location on the circle with the nirdaf’s location on the circle.
bpt: Correct me if I’m mistaken, but in dinei nefashos, wouldn’t any number of votes not guilty and 1 vote guilty result in a din of not guilty?
A rodef and a nirdaf (each viewed as a single point) are in a closed circle. They both move with the same maximum speed. Can the rodef catch the nirdaf?
If so, how does the rodef catch the nirdaf?
If not, how does the nirdaf avoid capture by the rodef?
Wow, I responded al regel ahas… I need to correct a few errors in my response (and stop responding al regel ahas so often):
First, just delete what I wrote in parentheses in my previous post regarding mitzvah to marry. That opens up a can of worms (well, actually rishonim, but anyhow it’s not shiach to the point).
Second, I should just clarify that taka yes, “a woman is her husband’s field” does refer to r’shus issues… meaning that yes, the wife enters the husband’s r’shus and not vice versa. However, she cannot be sold like a field, so one must understand there are limitations to this statement.
Thirdly, I meant to only bold the “in this case”… meaning that a woman’s status as her husband’s field refers to r’shus as I said, so since she enters his r’shus and becomes zocheh to his providing for her (and not the other way around), the man cannot claim that her mazal is at fault.
Anyhow, it still has nothing to do with ishto k’gufo. And regardless, I should’ve mentioned before, but you haven’t showed how my original logic was a boich svara. You’ve just brought a Tosefos and tried to equate it to ishto k’gufo.
Goldenpupik: the only boich svara here is yours. You are taking that Tosefos grossly out of context.
What is Tosefos’ kasha? In this case, his opening line reveals the implicit kasha: why can’t the man claim that the woman’s luck caused her to be sick (and therefore he shouldn’t have to feed her)?
The first answer accepts the validity of the kasha and says because since she’s not obligated in pru u’rvu, she can’t be punished (in other words, there’s no mitzvah for her to marry).
The second answer, per Tosefos’ M.O., rejects the validity of the kasha. A woman is her husband’s field and not the other way around, which in this case means that the obligation is on the man to feed the woman, not on the woman to be fed by the man.
This has nothing to do with ishto k’gufo. I don’t know your husband, and I’m not impugning his status, but in this case what you have said in his name is wrong.
Additionally, in light of the explanantion of this Tosefos, your “stira” in your second post doesn’t begin.
And of course there’s the famous joke:
When a husband goes missing, the wife is an agunah. When he’s not missing, the husband is an agun.
On a serious note, though, bnei Torah should always have hakares hatov to bnos Yisroel, and the best way to show that is for bnei Torah to express it directly to their wives, mothers, etc. and to hold up their end of the bargain in the beis.
on the ball: see Kiddushin Daf 2 Amud 2 – the mishna says HaIsha Niknis to teach us that this “acquisition” requires the woman’s consent.
Goldenpupik: your husband’s diuk does not make sense. ishto k’gufo, as you said, means his wife is like his body. So a husband and wife are like one body. So of course a husband’s body is like his wife… they are like one body! I assume (and everyone knows what happens when you assume) that the diuk was made in jest; I’m just pointing out a response…
If I were a mod, I would simply enforce the rules that Y.W. Editor posted 3 years ago. For some reason unbeknownst to me, the current mods don’t do their job of enforcing the rules (particularly preventing posts of loshon hara against posters, rabanim, and groups of Jews). So I’d also have them all stripped of moderator status. In that vain, I’d also have some sort of warning system where egregrious posters would be warned and subsequently banned for offensive submissions.
It really is sad that the rules aren’t enforced. I have read posts on the forum for a while now, but I only recently started taking an active role. However, the sina that is allowed through by the moderators is appalling, and I am contemplating leaving based upon these tragic circumstances.
I remain for now because every once in a while there is an interesting Torah discussion, and I suppose I hope that after Tisha B’Av, and with Elul around the corner, that posters and moderators will contemplate the seriousness of this matter.
557: We don’t count Jews.
I don’t think stating how many children are in one’s family is included in that Issur. And I don’t think the Mods EDITED all the numbers because of that. I think s/he was/is having fun.
You obviously don’t appreciate dry humor.
Kozov: Sorry, but I just don’t know exactly what we are arguing about, if anything.
ohr chodesh
+557
Whatever you would do if you saw your neighbor eating a cheeseburger with shrimp you should do if you saw your neighbor in public with above her knees showing.
That’s a boich svara; nobody even has the hava amina that eating a cheeseburger with shrimp is mutar.
What in the EDITED world happened to this tread??!!
We don’t count Jews.
and assuming you were being sarcastic, it’s not funny.
+557
shlishi: You have not shown how my assumptions were incorrect. I don’t disagree with your last post.
Bustercrown: I’ve already explained why one should assume that the tochachah will go unheeded. As far as being so sure that she got a psak, again, like I said, it’s dan l’chaf z’chus, which one is obligated to do for a stranger.
Kozov: I’m not sure what your first sentence is arguing on. As for your second sentence, while there are mamrei razal that say such things, it is not for us to make the cheshbon of how quickly moshiach will come. I feel like this was addressed in a recent thread someone.
Anyway, since we don’t know when moshiach will come, it is impossible to know the extent that our tzedakah (in your example) hastens his coming. We have emunas chochamim that it will hasten his coming because razal said so. But how much so is impossible to determine. So our job is to learn Torah and do mitzvos and trust in Hashem. Moshiach will come when Hashem is good and ready for him to come.
you really have an unfounded negative opinion about jewish women which borders on loshon hora
Mammele, if you want to accuse someone of loshon hora, please understand the implications of your accusation being incorrect (even if well intentioned). This discussion has been (IY”H) l’shem shamayim, but accusations like that tend to kill the productivity of a torah discussion. My very well-founded opinion, as you’ll see below, if anything is a shevach about jewish women. Also, note Curiosity’s response to your case (not to mention that it was also a woman who gave you tochachah).
There is every chance she will heed the Torah once advised that she is acting improperly.
Although the statement itself is true, this is where your logic fails. To see this, note that a)her husband and rav know that she covers her hair this way (dan l’chaf zchus – you must assume this for a stranger) and b)she is following her husband or rav’s opinion, even if it is wrong (again, you must assume she is following an opinion because of dan l’chaf zchus combined with the knowledge that there are rabanim, even if wrong, who say that covering the hair less than fully is fine). There are entire communities whose rav does not correct them on this (again, I’m not saying it’s right or wrong, I’m saying that they rely on their rav).
So therefore, when a stranger approaches this jewish woman and gives her tochachah, she will not accept it because a)her husband and rav haven’t corrected her and b)she is following a psak (not necessarily yours, but a psak nonetheless). She will rightfully get defensive because who is some stranger to come tell her that her husband or rav is wrong? Therefore, you see, it is not proper for a stranger to give tochachah in this case.
And Mammele, now you see that this is a shevach of jewish women for assuming that they listen to their rabanim on matters of halacha.
The Tzitz Eliezer is a big Talmid Chacham, but he is not in the league of Rav Moshe and the Gedolei Hador, and surely not of the previous generation(s).
Who decided/decides that? You?
That is 100% correct. And if he does not know it will go unheeded, and certainly if there is even a small chance it will be heeded, he is obligated to give the tochacha.
Right. And of course there is no chance that an aishes ish will heed tochachah from a complete stranger that her head isn’t covered enough or not covered in the proper manner. So it is settled.
There are maamorei razal that tell us that if we do something it will hasten moshiachs coming. For example gidola tzdaka shemikareves es hageula. What do you think that was for, informational purposes only?
Gedolim stories are not tzedaka.
Ya right.
+557
Ah, I see. Okay, I completely misread the original post. For some reason I thought he was looking for the source of the bad smell to complain to them or something.
Tochacha is an obligation incumbent and halachicly binding upon every Jew towards every other Jew. Not limited just for their immediate family and talmidim. Whether it is a violation of pritzus or thievery.
If one knows in advance that his tochacha will go unheeded, he is not obligated to go through with it.
See Rambam, Sefer Hamitzvos, ‘Aseh no. 205; Hilchos Deos 6:7; Semag, Mitzvah no. 11; Rashi, Yevamos 65b, s.v. lomar davar hanishma’; Rif and Me’iri on Yevamos 65b; Rosh, Beitzah 4:2; Tosafos, Bava Basra 60b, s.v. mutav; Shabbos 55a, s.v. ve’af ‘al gav; Ra’avid, cited in Chida, Machazik Brochah, Orach Chaim 208; Shitah Mekubetzes, Bava Metzia 31a; Sefer Yere’im Hakatzar, no. 37; Hagahos HaGra, Orach Chayyim 608:4; Sefer Hachinuch, no. 239; Sefer Chasidim, no. 413, Magen Avraham, Orach Chaim 608:3.
Also, see Targum Onkeles, Ibn Ezra, and Ramban on Vayikra 19:17, as well as Rabbeinu Yonah, Sha’arei Teshuva 3:59, 72, 196, and of course don’t forget Shabbos 54b-55a.
think one day is hard try 9 in a row
Shabbos. Twice this year.
It’s incumbent on all of us to inform those who are unknowledgable about this issue to advise them that they are not at all coving their hair if they’re not doing it so it more than a tefach shows.
No, it’s incumbent upon their husbands and rabonim. Not us.
Kohanim have to be Mafrish and burn Challah too?
What? What do kohanim have to do with this?
Iy”h by doing this it will speed Moshiach’s arrival!
Moshiach will come when Hashem is good and ready for him to come. Our job is to learn Torah and do mitzvos and trust in Hashem. Period.
I’ve heard about this alleged pillar, and the pillar is salt (though it’s covered in dirt, so it doesn’t look spectacular or anything), but I’ve heard from multiple sources that it was unsubstantiated rumor that the pillar was actually Lot’s wife.
That’s nice.
Yasher koach! I’m very impressed by the London asifa: practical, down-to-earth, and thoughtful approach to a serious issue without the drama and political nonsense.
Fact is, most rabbonim I know are on a much, much higher madreiga than lowly me. I’m talking people who haven’t got a clue what “vacation” means or what “bein hazmanim” stands for and where kids have never heard of the word “camp”.
Vadei words of the yetzer hara…
If so, what’s the problem with having a “shvitzy” pair and washing it like we do to our T shirts and sports clothing?
I’m not saying those rabanim are right or wrong, but the difference from using the bathroom and playing sports is obvious. Having the use the bathroom is involuntary, but playing sports is voluntary. Obviously you don’t hold that this difference is relevant, and perhaps you are correct, but the point is that there are those who would make the chiluk.
Should it become extremely hot, there is always the option to put them in my backpack.
Doesn’t that contradict what you said earlier: However, every serious frum rov will simply tell you if you ask him, that in that case, you simply shouldn’t do that sport/activity. Obvious solution.
Lessen, don’t eliminate.
dash, although your statement seems perfectly logical, this is not necessarily correct. To see this, take a look at the Mishna Berurah 551:1, sif katan aleph. The shaar hatzion on that Mishna Berurah brings down a way to see things your way, but also a way to see things the Mishna Berurah’s way.
I have heard rabanim say that if one is going to play sports or do manual labor where they will be shvitzing a lot, then it is not mechubadige to do so while wearing tzitzis.
Hate to break this to you, but this was proven never to have happend
Of course it didn’t, but unfortunately that doesn’t stop people from this shtus.
I always knew that looks are important to men. But this thread is scaring the daylights out of me! Why would a man want other men to check out his wife?! A woman should always dress in a way that is pleasing to her husband, but to attract the attention of other men?! I’m glad i’m not their wife!
There needs to be a delicate balance. In general, what is attractive to her husband will also be attractive to other men as well.
The woman must not dress provocatively, and other men must control their yetzer haras. What that balance is exactly… well, I suppose it depends on who you ask.
a) too many tzedaka phone call
b) too many tzedaka letters
c) too many baalei tzedaka collecting in shuls
d) too many baalei tzedaka collecting at their houses
They derogatorily refer to these people who give them so many golden opportunities to get the mitzvah rabba of giving tzedaka and saving themselves from death and negative decrees as “schnorers”.
See what R’ Elazar says at the top of Kesubos 68a.
The last sentence was the following:
I have got the fattest wife in town.
great explanation, for a man so vociferously outspoken, you are a man with little solid information beyond the bravado.
I would venture to guess that PBA wants you to focus on the last sentence in BS’s post. Either way, I stand by my previous post.
What is wrong with you all? Way to show some ahavas yisroel.
This is hypocritical. To see this, note that your esteemed brother wrote “I spit on this dor.” This is sinas chinam mamish.
Yes, it makes you look like a moron.
More sinas chinam.
Why does this have to be all the man’s fault or all the woman’s fault?
Women ought to dress modestly, and men ought to have enough self control to avoid looking.
The “source” is from the Torah (Bereishis 24:65), where Rivka Imanu covered her face when meeting Yitzchok Avinu. It is also brought down in the Gemorah (Ketubos 17b, Rashi ad loc).
This is incorrect. To see this, note that nowadays the choson bedeckts the kallah. However, as you wrote, Rivka Imanu was bedeckt herself. So if this were true, as most people beleive, then the kallah should bedeckt herself.
Neither the gemorah nor Rashi say that the choson bedeckts the kallah. All that is said is that the kallah wears a veil.
As you noted, the Tur and Tosefos hold that today’s bedecken would actually be the chupah. The Bach does state the we try to be yotzei all shittos, but note that bedecken today wouldn’t be yotzei the Tur or Tosefos’ shitah.
To see this, note that nisuin can take place only after kiddushin. Since at the time of bedecken, kiddushin has not yet taken place, it would be an invalid nisuin.
I apologize, however, in that I should have been more clear. The gemorah IS the source for wearing a veil, and you correctly stated the opinions of the rishonim. What I was trying to say was that the custom of bedecken as it is performed today is baseless. It couldn’t accomplish nisuin, so it is ineffective.
I retract. Apparently Rashi proved that nisuin can precede kiddushin. He brings the following case: The arranged marriage of an orphaned ketana by her mother must be repeated after she is a gedola, but her chuppah need not be repeated. It’s like people say: you learn something everyday or you don’t. I had been told by a former maggid shiur that bedecken was pointless, but I can no longer find a limud z’chus to that in light of this teshuva from Rashi (I believe it’s from a Hagahot Mordechai that was maybe quoted in the Kehillas Yaakov)
I work in a retail store & when I answer the phone, to “hey do you guys have……..” I usually hang up on them.
If your boss didn’t give you permission to hang up, you are stealing from your employer, which is an issur d’oreisa.
In the town of Rabbi Akiva Eiger there lived a very wealthy man who was very stingy and would charge interest when lending money to his fellow Jew. When he died, the Chevra Kadisha in revenge for his wicked behavior, charged an exorbitant price to bury him far more than they usually charged to even the wealthy residents of the town. His children protested bitterly, to no avail. Ultimately the feuding sides went to the Rov of the town, Rabbi Akiva Eiger, to hear his thoughts on the matter.