ian@psuvax1.UUCP (Ian Parberry) (09/17/85)
Great Moments in the History of Mathematics:
I heard the following story while an undergraduate in Brisbane in the late
seventies. (It involves the well-known fly-and-bicycle problem, which
has for some time been a fashionable example of "lateral thinking".)
A graduate student of a respected mathematician poses the following
problem to the great man (hoping to catch him out):
"A cyclist is exactly x miles from home. She rides home at a constant
speed of c miles per hour. At the exact instant she starts out, a fly
leaves the front wheel of her bicycle at i miles per hour (i>c),
heading towards home. When it reaches there, it turns around (in zero time)
and heads back to the bicycle. It flies backwards and forwards at the
same speed between the bicycle and the house until the rider gets home.
How far does the fly fly?"
The Master replies, without pause, "ix/c miles". Deflated, the student
observes that "a surprising number of people miss the easy solution, and
try to sum the infinite series of distances flown by the fly". To which
the puzzled mathematician replies, "But I did!".
Can anyone answer the following questions:
1. Is this a true story, or just a piece of mathematical folk-lore?
2. What is the origin of the fly-and-bicycle problem? Assuming the story
is true, did the student make it up? If not, who did?
3. Who was the great mathematician? (I've forgotten).
4. Who was the student? (I was never told).
5. When and where did this (alleged) conversation occur?
6. How was the original problem stated? For example, every time I've heard the
fly-and-bicycle problem, the person telling it has used different values
for i, c and x.
-----------------------------------------------------------
Ian Parberry.
<allegra,ihnp4,atcgva,burdvax,purdue>!psuvax1!ian
Dept. of Computer Science, Penn. State University.gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (09/18/85)
Who knows? I believe it has appeared in a reputable semi-popular book by a real mathematician. This might have been Hugo Steinhaus's "Mathematical Snapshots" or some such similar work; I've forgotten. > 3. Who was the great mathematician? (I've forgotten). John Von Neumann. > 4. Who was the student? (I was never told). I thought it was a colleague, not a student.
norman@lasspvax.UUCP (Norman Ramsey) (09/20/85)
The story is often told about John von Neumann. I have no idea whether it's
true. Someone at the Institute for Advanced Study might know.
--
Norman Ramsey
ARPA: norman@lasspvax -- or -- norman%lasspvax@cu-arpa.cs.cornell.edu
UUCP: {ihnp4,allegra,...}!cornell!lasspvax!norman
BITNET: (in desperation only) ZSYJ at CORNELLA
US Mail: Dept Physics, Clark Hall, Cornell University, Ithaca, New York 14853
Telephone: (607)-256-3944 (work) (607)-272-7750 (home)judith@proper.UUCP (Judith Abrahms) (09/23/85)
In article <> ian@psuvax1.UUCP (Ian Parberry) writes: >Great Moments in the History of Mathematics: > ... > > "A cyclist is exactly x miles from home. She rides home at a constant > speed of c miles per hour. At the exact instant she starts out, a fly > leaves the front wheel of her bicycle at i miles per hour (i>c), > heading towards home. When it reaches there, it turns around (in zero time) > and heads back to the bicycle. It flies backwards and forwards at the > same speed between the bicycle and the house until the rider gets home. > How far does the fly fly?" > > The Master replies, without pause, "ix/c miles". Deflated, the student > observes that "a surprising number of people miss the easy solution, and > try to sum the infinite series of distances flown by the fly". To which > the puzzled mathematician replies, "But I did!". > >Can anyone answer the following questions: >1. Is this a true story, or just a piece of mathematical folk-lore? It was told to me as a true story. >3. Who was the great mathematician? (I've forgotten). I was told it was Steinmetz, but I've been shot down on my other Steinmetz story, so don't take my word for it. >6. How was the original problem stated? For example, every time I've heard the > fly-and-bicycle problem, the person telling it has used different values > for i, c and x. The way I heard it, there were two trains on a collision course, and a bee flying back & forth between them until they met and pureed it. I don't remember the exact values stated. >Ian Parberry. ><allegra,ihnp4,atcgva,burdvax,purdue>!psuvax1!ian >Dept. of Computer Science, Penn. State University. Judith Abrahms {ucbvax,ihnp4}!dual!proper!judith ------------------------------------------------------------------------------ A man who is a genius and doesn't know it probably isn't. -- Lec ------------------------------------------------------------------------------
granvold@tymix.UUCP (Tom Granvold) (09/23/85)
-
I first heard the fly and bicycle problem given by one of my high
school teachers. That would be in 1963, give or taken two years.
Therefor the problem is at least that old.
Tom Granvold
ucbvax!allegra!oliveb!tymix!granvoldleimkuhl@uiucdcsp.CS.UIUC.EDU (09/23/85)
I have heard it was Von Neumann. (Raymond Smullyan, <<What is The Name Of This Book?>>) But you know, famous academicians tend to become the focus of an abundance of jokes, mythical conversations, and legends. My theory is that they are 99% crap. Some scientists seem even to propagate these stories themselves; Feynmann, for example, seems to be trying to bury himself in fiction. Partly this is great egotism--by encouraging myths that call attention to his peculiar genius, Feynmann appears larger than life, and probably some of those anecdotes will still be in vogue when his work on quantum chromodynamics is ancient history. Witness this story about the young Gauss: as an elementary school pupil, his teacher is said to have become exasperated with the class and as a punishment, ordered them to sum the integers from 1 to 100. A few minutes pass and Gauss (the worst of the brats) cheerily announces the answer. He is said to have recognized the trick of forming the pairs (100+1), (99+2),..,(51+50), and so to have seen that the answer was just 50*101--this for the first time! I don't know whether this is true or false--there's no doubt that Gauss at age ten was a far better mathematician than most of us will ever hope to be--but notice how this story is still quite popular. Such stories tend to cling to great men--the greater the man, the more stories are told about him. I think Einstein had a particular problem with being made the center of stories--his famous line "God doesn't play dice with the universe" may not have been his. (He is said to stated this at a banquet in an argument with a quantum theorist.) -Ben Leimkuhler
kanner@tymix.UUCP (Herb Kanner) (09/24/85)
In article <320@proper.UUCP> judith@proper.UUCP (judith) writes: >In article <> ian@psuvax1.UUCP (Ian Parberry) writes: >>Great Moments in the History of Mathematics: >> >... >> >> "A cyclist is exactly x miles from home. She rides home at a constant >> speed of c miles per hour. At the exact instant she starts out, a fly >> leaves the front wheel of her bicycle at i miles per hour (i>c), >> heading towards home. When it reaches there, it turns around (in zero time) >> and heads back to the bicycle. It flies backwards and forwards at the >> same speed between the bicycle and the house until the rider gets home. >> How far does the fly fly?" >> >> The Master replies, without pause, "ix/c miles". Deflated, the student >> observes that "a surprising number of people miss the easy solution, and >> try to sum the infinite series of distances flown by the fly". To which >> the puzzled mathematician replies, "But I did!". >> >>Can anyone answer the following questions: >>1. Is this a true story, or just a piece of mathematical folk-lore? >It was told to me as a true story. > >>3. Who was the great mathematician? (I've forgotten). >I was told it was Steinmetz, but I've been shot down on my other Steinmetz >story, so don't take my word for it. > >>6. How was the original problem stated? For example, every time I've heard the >> fly-and-bicycle problem, the person telling it has used different values >> for i, c and x. >The way I heard it, there were two trains on a collision course, and a bee >flying back & forth between them until they met and pureed it. I don't >remember the exact values stated. > >>Ian Parberry. >><allegra,ihnp4,atcgva,burdvax,purdue>!psuvax1!ian >>Dept. of Computer Science, Penn. State University. > >Judith Abrahms >{ucbvax,ihnp4}!dual!proper!judith >------------------------------------------------------------------------------ >A man who is a genius and doesn't know it probably isn't. -- Lec >------------------------------------------------------------------------------ This story was kicking around the University of Chicago circa 1960. The scenario as I remember it was two trains and the mathematician was allegedly John von Neumann. -- Herb Kanner Tymnet, Inc. ...!hplabs!oliveb!tymix!kanner
johnl@ima.UUCP (09/25/85)
The fly-and-bicycle story was often told about Von Neumann, though it was usually phrased as two trains heading toward each other and a bumblebee flying back and forth. According to people I know around Princeton (I grew up there) in later years people would ask Von Neumann if the story were true, and he'd say "Yes, but the numbers were harder." There are many well-documented stories about Von Neumann's amazing calculating abilities, so it probably is true. John Levine, ima!johnl PS: If you care, see "The Computer from Pascal to Von Neumann" by Herman H. Goldstine, who worked closely with Von Neumann for many years.
ttp@kestrel.ARPA (09/26/85)
In article <9600018@uiucdcsp>, leimkuhl@uiucdcsp.CS.UIUC.EDU writes: ** are mine. ttp > But you know, famous academicians tend to become the focus > of an abundance of jokes, mythical conversations, and legends. **My > theory is that they are 99% crap.** It would be nice to know if such legends did, in fact, happen. > Some scientists seem even to propagate these stories themselves; > Feynmann, for example, seems to be trying to bury himself in fiction. > Partly this is great egotism-- **by encouraging myths that call attention > to his peculiar genius, Feynmann appears larger than life** .. I think Feynmann, in his book "Surely you're joking, Mr. Feynmann" is NOT trying to make himself larger than life. I think it is remarkable that he admits that he liked to impress others with his brilliance, and then describes several schemes that he had that would make him appear brilliant: e.g. rattling off the answer to a problem he had previously solved without adding that he'd seen it before. I wish this book had been available when I was at CalTech, where Feynmann was a God. His book conveys only that he's very sharp and quirky, but understandably human. > ordered them to sum the integers from 1 to 100. > A few minutes pass and Gauss (the worst of the brats) cheerily announces > the answer. He is said to have recognized the trick of forming the > pairs (100+1), (99+2),..,(51+50), and so to have seen that the answer was > just 50*101--this for the first time! > I don't know whether this is true or false--there's no doubt > that Gauss at age ten was a far better mathematician than most of us > will ever hope to be--but notice how this story is still quite popular. The one mentioned for Gauss was recounted in modified form in the book "Men of Mathematics" by E.T. Bell. There was an emphasis on addition training, and the sums were separated by a fixed number, not 1. Maybe Gauss had already solved this problem. Maybe he hadn't. Perhaps the reason it is still quite popular is that this derivation for the sum of the integers is very intuitive, so perhaps lends verisimilitude to the idea that a 10 year old developed it. A slight generalization allows one to express the sums of certain powers in terms of sums of lower powers. > I think Einstein had a particular problem > with being made the center of stories--his famous line "God doesn't > play dice with the universe" may not have been his. (He is said to > stated this at a banquet in an argument with a quantum theorist.) > -Ben Leimkuhler Notice that this story makes Einstein look stodgy, because, if one accepts quantum mechanics, "God" DOES play dice with the universe. So why is this saying famous? Because it sounds good to people ignorant of quantum mechanics? -tom
dgary@ecsvax.UUCP (D Gary Grady) (09/26/85)
In reference to the story about the bird and the bicyclists, allegedly
solved by the brilliant mathematician not by seeing the trick but by
summing up an infinite series in his head...
I heard this as a John von Neumann story in a film biography of von
Neumann. Allegedly it happened at the Institute for Advanced Study and
my recollection is that it was told by another inmate of that
institution, which lends some credibility to it.
Another tale in the same film (told by a witness, I think) had it that
someone had been cranking through the terms of a fairly complicated
sequence using a mechanical calculator. He had stayed up all night and
had gotten through about 5 or 6 terms. Von Neumann came in the next
morning and asked what was up. The other guy told him. Von Neumann
said something about that being interesting, stared off into space, and
started outputting terms at intervals of about a minute. The other guy
said nothing, but when von Neumann got up to term 8 or so he got up and
went home...
--
D Gary Grady
Duke U Comp Center, Durham, NC 27706
(919) 684-3695
USENET: {seismo,decvax,ihnp4,akgua,etc.}!mcnc!ecsvax!dgaryyena@pur-ee.UUCP (Anthony T Yen) (09/26/85)
The problem was given to me in my freshman physics class and stated as a bird flying between two trains which are running to collision. There was no mention of the Great Mathematician, though. I think it is a problem from Halliday & Resnick's "Physics", but I don't have the book anymore (sold it for thirty bucks), so I can't really check. ------------------------------ Hao-Nhien Qui Vu ( pur-ee!vu )
usenet@ucbvax.ARPA (USENET News Administration) (09/27/85)
>> I think Einstein had a particular problem >> with being made the center of stories--his famous line "God doesn't >> play dice with the universe" may not have been his. (He is said to >> stated this at a banquet in an argument with a quantum theorist.) > >Notice that this story makes Einstein look stodgy, because, if one >accepts quantum mechanics, "God" DOES play dice with the universe. >So why is this saying famous? Because it sounds good to people >ignorant of quantum mechanics? Another way of looking at this may be that Einstein had philosophical objections to assuming that randomness is an inherent property of events. Perhaps Quantum physics can be looked at as a model rather than a true description. I personally have never been able to accept the premise that randomness truly underlies anything, but it is easy to accept as long as it is seen as part of a model rather than truth.
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (09/27/85)
> > I think Einstein had a particular problem > > with being made the center of stories--his famous line "God doesn't > > play dice with the universe" may not have been his. (He is said to > > stated this at a banquet in an argument with a quantum theorist.) > > -Ben Leimkuhler > > Notice that this story makes Einstein look stodgy, because, if one > accepts quantum mechanics, "God" DOES play dice with the universe. > So why is this saying famous? Because it sounds good to people > ignorant of quantum mechanics? Einstein most assuredly did not personally accept that there was an inherent, unavoidable, fundamental randomness in the laws of physics. For many years he played devil's advocate to try to identify flaws in the foundations of quantum theory, and Bohr and others would soon come up with answers to Einstein's objections. So it is no wonder that in this regard Einstein would look stodgy. The quotation, whether it is worded accurately or not, is indicative of Einstein's personal belief, and therefore has been used as a famous example of how even great minds could reject new theoretical discoveries. Having said all that, I must say that I am on Einstein's side in this issue. It is certainly a minority opinion among physicists today.
southard@unc.UUCP (Scott Southard) (09/28/85)
In article <10480@ucbvax.ARPA> tedrick@ucbernie.UUCP (Tom Tedrick) writes: >>Notice that this story makes Einstein look stodgy, because, if one >>accepts quantum mechanics, "God" DOES play dice with the universe. >>So why is this saying famous? Because it sounds good to people >>ignorant of quantum mechanics? > >Another way of looking at this may be that Einstein had philosophical >objections to assuming that randomness is an inherent property of >events. Perhaps Quantum physics can be looked at as a >model rather than a true description. I personally have never >been able to accept the premise that randomness truly underlies >anything, but it is easy to accept as long as it is seen as part >of a model rather than truth. Quantum physics seems to deal more with probabilities than randomness, since events can happen spontaneously without cause, but the event that occurs occurs with a certain probability. This is not true randomness, since it is probability that guides what events occur. Nevertheless, it is disturbing that events can occur without prior cause. It seems that God does play dice with the universe, but the numbers that come up on the dice are inevitably decided by probability. It seems I'm getting off the subject of math.... Scott Southard <southard@unc>