How Long is a Piece of String?

How Long is a Piece of String?

2009, Science  -   56 Comments
Ratings: 7.17/10 from 35 users.

How Long Is A Piece Of String?Alan Davies discovers that answering that question is much harder than he originally thought after visiting mathematician Marcus du Sautoy to help him find an answer. However, this creates more questions, which requires a trip to a place dedicated to measurement, the National Physics Laboratory.

Finding out the exact length of the string proves even more troublesome when Marcus proposes the string could be infinitely long, thanks to the theory of fractals. After leaving Marcus, Alan visits a physics teacher to see if measuring the string in atoms can help him find an answer. However, this means exploring Quantum Mechanics.

Alan goes to a lab to explore the theory of Quantum Mechanics in more detail to see if his string can be in two places at once, confusing him even further. Still no closer to an answer Alan is introduced to the theory that his string may have multiples lengths at the same time, all with the help of a stuffed cat. Alan doesn't believe Quantum Mechanics is important on a basic scale, but photosynthesis and the ability to smell might just change his mind.

If Alan was to find the most accurate way of measuring his string he could theoretically create a black hole. Trying to find the solution to this question has been a philosophical journey for Alan, but he still visits Marcus du Sautoy to tell him his personal answer.

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56 Comments / User Reviews

  1. Victor Redlick

    My beloved mother of blessed memory received her elementary school education in eastern Europe in the 1920s and 30s. When, one day, I interrupted her by asking "How long is a piece of string?", in reference to something she had been saying, her matter-of-fact response was, ".. from one end to the other."
    The following is an excerpt of an email I sent to a friend:
    This Sunday evening, at 7:00 p.m., I happened to switch to TVOntario and there was a promo for a show coming up called, HOW LONG IS A PIECE OF STRING?, with the foremost mathematicians in the world answering the question, according to their expert abilities.
    I just thought you may like to let the producer of the piece know that all they would have had to do is ask Ruth z"l. You could have saved all that time and documentation by calling her.
    Or me. I heard her.

    How Long Is A Piece Of String? - Top Documentary Films › Science

  2. darransus

    Half as long as its length

  3. Defrim

    The answer is 2?r. Why - take your string form it into a circle , then the circumference of the circle is the length of the string I.e 2 x ? x r. .... Defs Theorem

  4. Carla Mclachlan

    I was a bit frustrated at watching this as I now have a whole bunch of questions - it starts with the laser beam and showing it in 2 places at once when passed through 2 slits. I can see the end measurement with the stripes, but what happens if you were to measure the start, what does that look like? Is it actually just one particle? Or are there many particles in that one ray? Anyone??

  5. Sean Scott

    I have known the answer to this since I was 10: How long is a piece of string? Exactly twice as long as half its length.

  6. devlinwaugh

    on my last comment basically if you are allowed to be your own judge juror and critic exuberant mathematical calculations allow anything to be possible(run away science) and community getting a lot of funding.I cannot pass through a wall even tho my mass is 100000000000000000 times smaller than a pin head.But it cannot be proven why i cannot pass through a wall so i can state that mathematically and prove it is possible in numbers but not reality,i hope you get my drift and hope that science moves on quickly.Nothing has been discovered in science other than e=mc2 i cant wait for the next genius,all we have are people walking down streets coming back with the answers that were given by Albert .The true scientists even say we have come to a dead end now we need to manipulate what we know and let the rest go,one said we have matter manipulation and if we invested all our resources we could in 400 years make anything we wanted by the click of a switch.

  7. devlinwaugh

    watched this a year ago Alan Davis is a cute comedian none welsh of middle class education, from a good background but lacked the lust of education like many in youth.Most adults in later life strive for education leaving others behind and more elders should go back into education just for the exam pass to be speculative of the run away mathematical lies that are prevalent at the moment in all science..

  8. Cabot Circus

    Does anyone know where can I watch "Alan and Marcus Go Forth and Multiply"?

  9. Aaylsworth

    Not bad, covers some interesting theories and mathematics... 7/10.

  10. VoxFox

    The concept of fractals is a purely mathematical idea based on the bogus idea of 'real' numbers (numbers with an infinite number of digits). The real world is discrete - there are only a finite number of atoms in a piece of any matter - including string. There is a finite distance between atoms, so there is a finite length to the string. All the rest is pseudo-science, mumbo-jumbo built on Platonic idealism. Time to upgrade to reality.

  11. Erik van den Enden

    Seriously watching the first 10 minutes of a guy saying "look I have string, or do I?"
    Really doesn't make it easy to watch.
    Making it understandable okay, but dumbing it down that bad is just horrible.

    1. yLordy

      Would that be Schrödinger string?

  12. za

    A great approach to science and math teaching. Get a witty skeptic to say all the things we would say, presented with the seeming silliness of science, and tear down all that you can, to leave what's really worthy of it.

    Should be done with religion too. Actually, has been.

  13. Amabio

    topographical => topological...sorry, my mind wonders while I speak/type sometimes.

  14. Amabio

    Before you begin, the mathematical 'lengths' discussed at the beginning were topographical lengths. Actual, measurement of those in the real world does not apply; a coffee cup is equivalent to a donut.

  15. Amabio

    Luckily, they focused on physicist; this program would have been over, before it began with mathematicians on a piece of string. The string is L in length; yes, but I have a different piece of string; so, that's L1 and L2, problem solved. But, long is it? It's L.

  16. Amabio

    I meant literal blind, btw.

  17. Amabio


    You have an extra closed parenthesis in your equation...jacking it up. As you must know (unless you are blind), there are no videos for experts; only videos to inspire people to become experts. Experts are made through study of books.

  18. Amabio

    I loved how they archived the piece of string, Indiana Jones style, at the end. Very excellent vid and series, I've seen it before. Hopefully, it has encouraged someone, or two, to venture into the incredible realms of maths and science, and help all of us along our journey of discovery.

  19. azilda

    hum! ha ha ha ha

  20. Mantram

    How do you know you are alive? Maybe we all are dead cats dreaming we are people? : D

  21. Mantram

    : D

    But I am serious; Of course the cat knows if it´s alive or dying/dead? Then the cat´s consciosness of course make that observation (and the "probabilty waves" break down) before we open the box!! I think it´s strange that no-one in all books I´ve read in this matter ever have understood this! : )

    (English is not my native tounge...)

  22. Achems Razor


    Ha,Ha, need some humour once in a while, tell me, how will the cat know that it is dead??

  23. Mantram

    I think the cat knows if it´s dead or alive and that makes the prob. wave break down. : )

  24. charles1957b

    BBC the real weight (mass) of matter IS in the atomic center, the nucleus, with it's protons and neutrons, and at the same time if we only took that portion of the all the atoms of Earth (nuclei), they could fit into something like the size of say an orange, but it would still have the weight of the whole earth. What we see and feel with the spread out nuclei in our spread out world, I like to visualize as energy fields. The field associated with objects repels physical penetration and various energy penetrations such as an apple reflecting red light in the visible light spectrum. Chemical bonds between atoms present these barriors to sight and touch, and give us the structure of objects that we sense. I hope this helps clarify for you.
    We as humans can only sense through touch and site only extremely large numbers of these repelling bonds, even for the smallest objects we can see or feel. I guess with the exception of smelling at the sub-atomic level, which I never knew before.

    Karen I've always understood black matter to be collections of protons/neutrons stripped of their associated electrons via tremendous gravity, like the Earth reduced to the orange size described above. It's been a long time since I've been to school, so these ideas may have been long since surpassed, by new visualizations. The tremendous gravitational effects of black matter however attest to it's presence.

  25. Coyote03

    Informative and entertaining, definitely worth a watch! :)

  26. Karen

    Nobody understands black matter yet. That's why it's called black matter. They know it is there, there is a lot of it but you can't see it or precisely measure it.

  27. Nobodies Right

    Gotta check your formula again Yvanna, shouldn't 6 O's be going to water? Cancel that hydrogen gas?

  28. BBC

    Thanks everyone for the help. I read some stuff from NASA astrophysicists, and well it is non-comprehendable on my part. Where does this energy that holds the atoms together come from? Do the atoms themselves create this energy?

  29. Yavanna


    It seems Alan is now starting to get involved in documentaries. I`ve found one more so far:

    "Go forth and multiply" It's on You Tube but I will submit it to Vlatko for upload.

  30. Mahesh

    I really enjoyed the simplicity of this doc trying to explain a complex theory.
    Interstingly 2500 years ago Buddah has stated that,
    '.......all things have no fixed identity ('inherent existence') and are are in a state of impermanence - change and flux - constantly becoming and decaying. Not only are all things constantly changing, but if we analyse any phenomenon in enough detail we come to the conclusion that it is ultimately unfindable, and exists purely by definitions in terms of other things - and one of those other things is always the mind which generates those definitions...'

  31. Yavanna


    You wont find Davies in any documentaries - he is a comedic actor. Whilst very well known in the UK for being in a panel show called QI: his only other claim to fame is being a sort of magician in a BBC series called "Jonathon Creek" If you like him search YouTube for "QI."

  32. Tara

    What other documentaries has Davie's been in? He said he'd been in one previously but I've search and cannot find a thing!

  33. Yavanna

    I forget the site name but achems sent me to a really good one that showed very simple explanations of QT. It had a cartoony professor explaining it all.

  34. Joe_nyc

    I am downloading this doc so I can show to my 11year old son later.
    Hopefully, he can grasp the idea of "existing in different places at same time" better than me.

  35. Yavanna

    Well you caught me on the hop there with my sweeping statement! I was thinking about the Quantum theory stuff but I suppose this doc does also touch on fractals etc.... and by "out there" I meant on TDF....

  36. Joe_nyc


    "Any ways an entertaining doc but there are better out there."

    Do tell us what others(docs) are out there.

  37. Yavanna

    It was a custard explosion Eric. "Dude" got it - I suspect he cheated and watched the show previously :)

    Blax but how far down the rabbit hole should we go?

  38. Erik

    oxidation of glucose into carbondioxid and hydrogen gas?^^

  39. blaxparx

    Shows like this are just silly. Maybe good for a laugh or two. To ask physicists about such things is very silly. Do you actually believe that in a thousand years people will believe what these people have to say? That we'll still have these same concepts of reality? I hardly think so. Quantum mechanics will be a footnote in the history books by then. Other, more elegant, ideas will come along and they, too, will end up being footnotes along the way. Do you want to be entertained? Go read Alice in Wonderland...

  40. Achems Razor

    You can also Google, Wikipedia- "Electromagnetic Force"

    Electromagnetic force holds all matter together.

    If you want to delve deeper Google- "Quantum Theory-Mozilla Firefox".

  41. Yavanna

    Well without watching the Doc again I imagine what you are referring to is the convergence of atoms to former dense matter. It is explained that atoms are mostly empty space. If atoms are bombarded together their ions get stuck. They effectively clump together. Imagine snowflakes falling around you then gathering lots up then squeezing them in your hand. What was once mostly air is now condensed into a much denser material.

    I`m not particular scientifically minded perhaps someone else could explain better.

    I could cut and paste the real science here; but easier for you to google "how does dense matter form."

  42. BBC

    I'm confused, is that not what they are trying to show?

  43. Yavanna

    100 Bonus points to Dude! (There are QI clips on youtube - great show)

    BBC empty space does not form dense matter, Where did you get that idea from.

  44. Dude

    @ Yavanne
    is it custard exploding?

  45. BBC

    How can empty space form dense matter?

  46. Achems Razor

    @ Yavanna:


  47. Yavanna

    Hint - fermentation would be too slow a process. No MORE HINTS!

  48. Achems Razor


  49. Yavanna

    OK hint

    You have identified ONE ingredient. But you miss the obvious which is the reaction.

  50. Achems Razor


    Da*n it!...BEER!

  51. Yavanna

    You are close you exquisite googler! I`ll allow a few days for the real answer

  52. Achems Razor

    Liked the doc. simple and funny.

    @ Yavanna: Your formula, something to with glucose, at least the first part. Sugar?

  53. Yavanna

    Alan Davies is a well known comedic actor in the UK, probably best known as playing the layman on the panel show hosted by Stephen Fry - Qi (Quite interesting) in which some really tough often ridiculously hard questions are asked. The winner is generally the panellist who has the least points deducted!

    For instance: What does this chemical formula mean...


    Any ways an entertaining doc but there are better out there.

  54. BBC

    So according to this video there is an unseen world around us?

  55. Tyler

    What I had assumed was going to be a fairly dry repeat of general physics turned out to be very informational. It's told like a story thats actually quite funny, and not dry at all. Well done.

    And complete with light jazz. :)