Happy 2 year anniversary! At the time my channel was very small and people asked why I would even make a video, so let me share the history. The topic was trending and Buzzfeed posted a reaction video that racked up 450,000 views. I thought the topic was a great way to teach some math and topology. It is now 2 years later...Buzzfeed's video has 566,000 views, my video has 800,000 views, and a video by VSauce on the topic is trending right now with over 3 million views (search for how many holes does a human have). It is often said math is not popular, but it seems math and science are Buzzworthy topics after all!
Nice one Presh, I think your graphical explanation for the 1 hole answer is easier to see than trying to explain the imposibility to (continously) shrink any closed curve over the straw's surface down to a point...and this reminded me of the poincare conjecture that perelman proved true in 2003
I think the main confusion comes from the fact that "hole" can mean different things. If you think about a hole as an opening, it's 2 If you think about a hole as a tunnel, it's 1 If you think about a hole as a defect, it's 0. Of course mathematically there's 1 hole.
Here's how I explain it: A donut has one hole, right? Imagine you could stretch a donut so it's taller so that it looks like a straw. If you believe a donut has one hole and a straw has two holes, at some point when you stretch that donut, it must go from having one hole to two, which doesn't make much sense.
LimeGreenTeknii My thoughts where someone along does line but I came at zero holes, since a doughnut to have a hole, it's surface being a 3d object must have at least two holes. The surface of a doughnut has no holes thus the doughnut has no holes.
That seems to be his explanation above, but without food. It might help this topololgy discussion to define a solid blob (even with profound depressions but no perforations, as an object with no holes. The human body, (barring fistulas or artificial perforations) has 4 openings, all connected at the back of the throat: 2 nostrils, a mouth, and anus. How many 'holes' is that? (Ears, eye sockets, eustachian tubes, sinuses, bladders, etc are just 'depressions' that don't 'go thru'.) PS: English is used by many people with different cultures. A topologist has a useful definition for 'hole', and so does a farmer with a post hole digger, who also has a different term; 'thru-hole' (also used by machinists & commercial engineers). If either is 'wrong', it is a matter of context & code-switching. Does topology have a name for a post-hole? If not, does that make it the more limited context? Our minds are certainly flexible enough to manage multiple, sometimes contradictory definitions for many words.
Well I am not sure if doughnut (or circle) does have a hole since the shape is kind of defind without the hole. I would agree that the straw is just really long doughnut, but the question is whether the doughnut has hole or not and how is the hole actually defined.
Donuts have 2 holes. Coffee Mug has 1. The issue with this problem is that no one is making a distinction between intentional holes and unintentional holes.
+shyhalu Coffee Mugs (with handles that loop back to the body of the mug) and Doughnuts are the same (topological) shape - a ring with blobby bits. A good test for whether something has a (topological) hole is whether you could take a length of elastic, wrap it loosely around the object in some way, attach the ends of the elastic together to form a closed loop, and then be unable to separate the elastic from the object without either breaking the loop, or breaking the object. So you can form the loop so that you can't separate it from a doughnut, or the handle of a coffee mug, but no matter how you arrange the elastic, you'll always be able to get it away from a wineglass. That doesn't settle how many holes something has, just whether it has any, but it's a starting point.
A physicist could argue that it has an infinite number of holes aligned beside each other. Or be like vsauce, use his reasoning with the "How many holes does a donut have?" video.
I've listened to 1:56 and have this to say: It depends on your definition of "hole" and of "straw." If you start with a rod and drill a hole through its center along its long axis, then it has one hole, (like a reusable metal drinking straw). If the straw is formed by winding a flat material in a spiral and glueing the edges where they meet, (as in a paper drinking straw), you could say it has no holes.
It doesn't matter how the "straw" is made. The end result is the same - a long tube. As a tube, it's a length of hollow material with both ends open. It has one hole.
To make a hole material has to be removed in such a fashion that material is surrounded by the voided space. A straw, tube and a hose by it's nature has a voided space. I firmly believe there is no holes in such things. Unless damage has occurred or someone willfully makes one. Drilling a hole in a rod merely speaks to the manufacturer of the straw. I don't understand the quotation marks around the words hole and straw in your comment.
@@oldfart1079 Some people might define a "straw" as a water resistant paper tube formed by coiling and glueing paper around a rod shaped mandrel, or as an extruded plastic tube. Some may include a glass or metal tube in the definition of a straw. Some may define "hole" as an empty space formed by removing material. So if they define "straw" by the first definition and use the definition of "hole" I gave, they would say a paper straw didn't have a hole, but a stainless steel straw made on a lathe in a machine shop does.
@@billvojtech5686 yes there a multiple ways to manufacturer a straw. Nature herself can in deed manufacturer straw's and holes. Not all holes persist through an object, a cup or drinking glass are good examples of such holes commonly referred to as a "blind" hole. In manufacturing "blind" holes are used for screw fasteners and through holes are for bolt and nut fasteners.
I explain it like this. If you cut a hole in a paper it makes one hole. It you thicken the paper, say a block of wood and cut a hole, there will still be one hole. So a straw is basically a super tall but skinny piece of paper with 1 hole.
+Juan Carballo If you poke a hole all the way through a ball so that it breaks on through to the other side, that's the same as a straw, one hole. If you poke a "hole" halfway through a ball, it's not a "hole" topologically speaking, just an "indentation", which does not alter the topology of the ball.
From a manufacturing standpoint, a paper straw has zero holes. It is a rhombus spindled around a cylinder and glued into place. The rhombus remains intact, thus no holes.
@@ukulelevillain4170 The doughnut does indeed not have a hole. The doughnut is wrapped around a hole. Oh wait, it's not, there's no hole to wrap around. Anyway, the nut is the part of the doughnut that was the hole, but and so it's the nut is in quantum entanglement with the hole.
Pio Lio: then people are wrong. If you make a hole in a door to put a handle, you make one hole that you can see from both side, Nobody would say they made 2 holes. The lenght / depth of the hole has no impact on the number of holes.
Just to be anarchic about it, if you take a solid 3-d structure and drill a hole in it, you seem to have made one hole; but, by the definition given in the video, you have not made a hole at all, unless you go all the way through. However, if you take a 2-d piece of paper and connect one end to the other creating a tube (straw) then there is no hole in the paper, so that structure could readily be said to have no holes. Alternately, if you take your 3-d solid, and drill two holes, one in each end, and they eventually meet, does one of the holes cease to exist. Create a set of axioms or definitions that will support your conclusions and you can get any conclusion you like.
If I have a piece of wood, and drill a hole through it, it has one hole. If I carve the outside of the wood down until it's a tube (a straw), it still only has one hole. Not too complicated.
If you're going to be clever, you need to call it a "through hole", not just a hole. Besides, you're overcomplicating it. Topologically it's just like taking that straw and morphing it into a flat disc. It'll still retain the one through hole.
Here's ALL the correct answers : Straws have one hole, topographically speaking - but only because, in the field of topology, a hole has a very specific meaning and we're considering the straw to be an ideal mathematical surface (which it clearly isn't) Then there's semantics... one can dig a hole in the ground but it is not (topographically speaking) a hole - however it IS still a hole according to the english language. How many of these non-topological holes a straw has is merely a question of scale... since the surface of a straw is not an ideal surface. So, the answer is likely to be between zero and trillions. Then there's the functional answer. Having defined the object to be a straw - how many holes does the STRAW have? None... it is a perfect straw. If it had a hole it wouldn't work very well. This is a logical statement based upon types, equivalent to asking whether a bicycles inner tube has a hole in it ... the concept of the item itself establishes the baseline of form, and this ideal conceptual form is then compared to the item under test. Then there's the material sciences answer. A straw has enough tiny (and, indeed, also properly topological) holes in it to lose water/gas molecules by osmosis, so again the answer is trillions. This IS still a topological answer, but one properly recognising that the straw is NOT some ideal mathematical surface as those weird beardy mathemagicians would have you believe. Then there's a pragmatic materialists answer... there IS no straw, just a collection of atoms which are held in proximity but never touch. The concept of holes cannot be reconciled with this view. Which brings us neatly to the Zen answer: Mu! Clearly one needs to first : - define a straw that we can all agree on. - define a hole that we all can agree on. - define a scale that we can all agree on. Only then, can a proper answer be attempted. To hold out that a hole is a strictly topographic feature and that we should imagine a straw to be an ideal surface - is a cartoonish simplification. Similarly, one could establish how many sheep can fit in a field by first considering all sheep to be perfect spheres... ... by doing so, we answer an *entirely different question* - and usually one which is more comfortable to work on. But yes, I'd also default to claiming that a straw only has one hole... and, probably, later get arrested for brawling with pragmatists in the car park.
RealRupert topologically, there is no difference between a hole and a "tunnel" as you call it. If a circle with no depth drawn on a piece of paper is a "hole" then more accurately it is a hole with no depth. An open cylinder or "tunnel" is therefore a hole with depth L. It's less accurate to say a tunnel is not a hole than it is to say all tunnels are just holes with depth
My first thought was to define a hole. It must have some height, so any solid with a change in surface height downwards must be a hole. After that I struggled with all sorts of counter definitions. It was a really interesting exercise. Thanks.
We must first define what is a straw. Could the straw have a cross section structure inside to support the wall? Creating four paths for fluid to flow? Would it still be a straw? Does the word straw actually just define how an object is used? "a thin hollow tube of paper or plastic for sucking drink from a glass or bottle". This may be the common image of what we think a straw is. But how does this explain if I use a short section of a thin wall tube or pipe as a straw. My answer is there is no answer. A straw can have as many holes as anybody wants to design into it. I remember as a kid straws that had basically two in one twisted around each other. But to define a hole. Can a hole have a hole in it? Or would that just be one hole with variable dimension?
If you had an infinitely thin plane and there was an area which lacked material where you could go from one side of the plane to the other, wouldn't that be a hole?
By that logic (and dont get me wrong there is nothing wrong with that logic) holes as we usually think they are can not exist. Since you can allways travel on the edge of the "hole" and end up on otherside of that "hole" which is still on The same infinitely thin plane. This is why my reaction to this riddle was that this can not be answered before The question defines "a hole".
The reason why people "debate" about it, is because it is a debate about the meaning of language words, which is defined by the people, and not by experts. What is a "hole", anyway.
there's a topological definition for it which ought to be used in mathematics. but in real life its not practical. e.g. if you dug a hole in your backyard, the topological definition would say that you haven't added a hole at all.
Gustavo The question wasn't "how many holes does THIS straw have" but "how many holes does A straw have" meaning, if in your definition of straw you consider it an object with a hole, then the answer to those question would be 1, not 0.
Taping the ends together changes the topology of object. You cannot change the number of holes in an object without fusing two separate ends together or tearing apart two ends that are connected.
Interesting. I was looking at it geometrically, without the mathematic elements. I figured a straw was basically a hollow cylinder so it was pretty much a rod with a single hole inside. I came up with the same answer by intuition instead of math.
I came up with the same answer based on how I could create a straw in cad. Create a solid cylinder and use the hole command to create 1 hole through the entire thing.
Non mathematically speaking it must have only one hole for engineers. Because if you drill 16 Holes into a metal plate with a regular drill to put screws inside its still just 16 holes and not 32. If you would tell 1000 handcrafters to drill 16 holes they would all drill only 16 holes, no matter how long or wide the object is they drill into. I think this is the only explanation as to why its only one hole for the majority of people.
there are two correct answers to this problem, depending on your starting point. As illustrated if the starting point is a circle then the straw has 1 hole, but if the starting point is a parametrized continuous surface in R^3 which curves back on itself, then the answer is 0 holes. The apparent paradox is due to the lack of initial definition.
Morphing the shape of the straw like you did is the most intuitive way (for me) of looking at the problem. A good way to illustrate this is with the similar question of how many holes a tea cup with a closed loop for a handle has. Morphing the cup into a toroid gives a strong intuitive basis for working out similar problems in the future.
@@SimGamerTV from a topological viewpoint, yes, a hollow sphere with two holes top and bottom has one hole. Similarly a hollow sphere with on hole in its surface has zero holes. If you stretch it out, you will see it has the same topology as a disk, with the edges of that single "hole" now forming the circumference of the disk.
@@AlDunbar similarily if you stretch the two opening sphere you will get a disc with one opening the circumference edge and the other opening the hole in the middle. So back to the straw (cylinder) , if you slit it lengthwise and roll it out it will form a rectangle with no hole , just as if you started with an unclosed circle it would not have a hole till it was closed.
Love this channel. As a patent lawyer, I actually have to consider questions quite similar to this on a routine basis. "Is this two holes? Or one long hole? Or if I call this a 'straw' then is it implied there is a hole, and if I say there is a hole, then am I saying there's two holes?" The process of drafting a good patent claim is bit like doing math in words.
What if you define a straw as an area rolled up into a cylinder? As a hole is a perforation, and straws are made not by punching holes in matter, but by wrapping sheets or extrusion, they don't really have "holes" in them.
@@rhodesj1893 But if it's a tube then it's debatably not a hole, for the reason mentioned above. there's a reason those two things are different words.
@@Person01234 By rolling a sheet of paper into a tube, you break the rules of homeomorphism. A sheet of paper has no hole. You can‘t flatten a strawhat and make the hole vanish while following the rules of homeomorphism.
I think much disagreement comes from how hole is defined in regular language and how it is defined in mathematics. In real life you can dig a hole in the dirt, but a mathematician would say it is not a hole, but an insignificant dent. Likewise the interpretation of the word hole can lead to disagreement in this conundrum. But the straw has 1 mathematical hole, that is for sure.
Turns out "hole" is not defined mathematically, and by some definitions a real drinking straw that exists in the real world would have 2 holes, and depending on how you idealize the drinking straw it can have 1 or 3 holes.
I feel like a similar thing happens when using the word "theory." Scientifically for something to be a theory there are defined standards that have to be met. Problem is when most of us (and I'm guilty too) say theory, at best what we're describing is a hypothesis. In everyday speech people have "theories" about everything... No, no we don't, we've mostly got ideas and an occasional hypothesis. So then when an article is published regarding say gravity, and it's referred to as a theory, people misinterpret. Establishing definitions is paramount before a dialogue can take place.
Depends on your reference surface. If you consider only the surface of the dirt in an arbitrary circle around the point of interest, what you end up with is what one may consider a "hole" mathematically speaking. After all, you can technically go through surfaces as if the yaren't there. A surface is just a set of points. It has no specific physicality.
I think what made me decide on one hole is that the wall thickness of the straw is measurable. even if its just a few thousandths that makes it a side/face that you would use to calculate the surface area. so basically you have a cylinder with a hole through it, even if the hole is near the size of the outside diameter and the straw was manufactured by extrusion.
there are different types of holes and you must consider the second hole the torus surrounds so they are no topologically equivalent i.e T^2 is isomorphic to S^1 x S^1 not S^1 X R like the straw is here in the video.
I agree. It would have been nice to see an application of its mathematical use. Otherwise I’m left thinking the mathematician has just defined it their way without respecting another perspective. I do however accept that there is just one hole, mostly because I would consider that if the tube was bent into a continuous circle there would be only one hole.
I've never done something in that field but here is my explanation so far: Assuming that you take a piece of paper without holes. You have an area with 0 holes. If you create a hole in there, you have a plane with a hole but notice that the amount of borders that exist has increased by 1. Instead of having just 1 border, you end up with 2. This can be translated to any surface I assume. Second, I imagined a cup. Nobody would ever say that a cup has a hole. It's just a shaped surface. Now, if you remove the bottom of the cup, you will have a cup with a hole on one side which is pretty much a straw. Therefor a straw has only 1 hole.
If you punch a whole through thin piece of dry wall, that's 1 hole. It has the entry and exit but is considered 1 hole in the wall. Same as if you ram an iron rod through many pieces of dry wall, creating a long straw shape. Still 1 hole. But what if you dig a cave-like hole in the side of a mountain. It has no exit. 1 hole. You start another hole on the other side of the mountain. That's 2 separate holes. You then connect the 2 tunnels in the middle, is there still 2 holes or did you just reduce the holes from 2 to 1? Anyways it all depends how you're defining the word hole to begin with.
johnny_schwifty.soundcloud as soon as they connect then you’re back to having one hole as you can’t define where one hole is and whether the other is, separate to it, ergo it’s only got one hole
johnny_schwifty.soundcloud what about ur mouth and ur ass. They're both connected with a long tunnel of an entry and an exit and people considered them two different holes
Johnny - You have TWO holes until they meet. Note that "hole" is simply a word, while the math itself doesn't change. If you apply your logic about the iron rod and the drywall to it. Think of this. When the "Chunnel" was being built, they bored from both ends. There were two distinct holes. You couldn't go from one side to the other without exiting one hole and entering the other. Once the two holes met, they became one hole. Here's another way of thinking about it. You take an ice cube in each hand, allow them to melt a bit, then you hold them touching each other and allow them to freeze together. How many ice cubes do you now have?
PewDiePie 3 is right, this video is not really about a clever insight in math, but about how the mathematical definition of "hole" differs from the everyday (pluriform) use of the word "hole" in English. Sure, the topological "hole" is specifically defined so that it serves a useful and meaningful mathematical purpose, but this video doesn't show us anything of that purpose. For the casual viewer, the way mathematics chose to define "hole" seems just arbitrary.
well so basically it depends on the definition of a hole. the topological definition would give the answer 1. if you define a hole intuitively, not mathematically, as any entrance into the object's 'core', then it has 2 holes.
This is how I have explained the 1 hole answer: imagine a sliver of wood as thin as a piece of paper with a single hole punched in it, now make the wood thicker, still only one hole. No matter how you change the shape of the surrounding wood, it will just be one hole, so if you had a very thick piece of wood, and then shaved off the excess and just leave a thin bit around the hole, you have a straw!
It's an intriguing one by the way that if you were to make a straw with 3 ends, you would say it had 3 holes since there were 3 places a substance could come out of the containment of the straw. If you then remove 1 of the holes, for example return it back into the original straw, surely it would now have 2 holes. Just like if I asked how many holes are in a regular t-shirt. You would say 4: the 2 sleeves, the collar and the base. If I sew up the sleeves, you would say it had 2 holes: the collar and the base. But it's still topologically the same shape as a straw. However, the straw having 1 hole totally makes sense; it is all the same space all the way through. So does that mean that a t-shirt really just has 1 massive hole? It's all the same space. Or does it mean that a straw has 2 holes? I think it always depends on how you define the terms in the question. Just like you can't assume an angle in a triangle is a right angle because it looks like it, you also need to set the parameters of the question. And therefore the answer is there isn't really a correct answer
You are interchanging hole with opening or orifice... and they are not the same thing. A Door is not a Hole in your house... Neither is a window. Your sewage drain is a hole in the floor to the city sewage or your septic tank... sure. Your Radiator has an inlet, outlet, petcock drain, and burp bleed-off tube.... but only ever has a "hole" if it is leaking. Words need to be used appropriately and correctly.
1 hole is probably the most practical answer. The material used to make the straw, which effectively is the entirety of the straw - has 0 holes, but that material was formed specifically to create an aperture, which now meets the definition of "hole" The less compelling answer could be 2 unique openings, where the materials seems to open up And no longer restrict the contents of the straw, so 2 holes
How many holes are there on an 18 hole golf course? How much dirt is in a 1m x 2m x 3m hole? Are any of the holes that the movie "Holes" is named for actually holes? Could there be a hole in the definition of hole, rather than a hole in people's logic? Topologically speaking I should be able to eat as many donut holes as I want and never gain weight!
@@liamg1706 How can you not see there’s a third one right there? It’s literally right there in plain sight and you can’t see it. Are you messing with me?
@@hydropage2855 for a 3rd to exist it would have to be seperate from the other 2 which in this case there is no seperate hole just one either end of the hollow tube
@@spaghettiking653 It was a bit of an exaggeration, but non-experts are brought on news shows way more than experts, and when experts are brought on, it is much more likely there will also be a non-expert to contradict the expert.
Great videos, thanks Presh! Another intuitive way to look at this is as follows. Imagine that you have a small metal cylinder 2cm diameter and 3cm long. You place it standing upright in a bench drill and drill a 5mm hole in the center of the round face through to the other face. (You now effectively have a "straw".) How many holes did you drill in the cylinder? Just one! This logical answer is independent of the dimensions (and material) of the original cylinder.
Or you have one piece of paper with no holes. You roll it upon itself and secure it with adhesive. Still a piece of paper with no holes, just rolled to form a straw.
If you drill the hole almost halfway through the cylinder, and drill a second hole from the other end, you have two holes. Now if you complete the drill through, you have now only one hole. So by drilling a 'third' hole, you've subtracted a hole?
Before I watch the video I'm going to say no holes. The mathematical definition of a hole is very precise. For polyhedra the definition is Euler's Formula for Polyhedra. I started looking a little closer at topographic analysis, and even then by strict definition there are no holes. It's basically a plane that has been curved (revolved) along an axis. The plane is continuous, so there are no holes geometrically speaking.
I think the confusion comes from differences in basic language and in topology. Let me give an example, if we take a balloon and ask any average person, now many holes does this balloon have they will say one. If you ask someone that deals with topology, they may say one, as it's a common excepted answer. However topologically a balloon has 0 holes unless we poke one in it to complete the hole. In topology any object with 0 holes can be transformed into any other object with 0 holes. (Paper, Balloon, Cup, Fork, etc.) The same is true of an object with 1 hole. (Donut, Coffee Cup, Straw, Ring, etc.) So it really comes down to whether we are speaking in basic language, or topology. So both 1 and 2 are correct, we just need to agree on which system is being used.
All three answers are correct when given the right definition of hole. If a hole has to be intentionally added to a complete object, then zero is also an exceptionable answer. For example, if someone said, "This straw doesn't work. It has a hole in it". That implied that in language, the word straw is a complete object and any descriptor is in addition to that object. Just thought I'd help complete your point for all three answers.
Derek Gooding I think the implication of that statement is that the straw has an [extraneous] hole, therefore it doesn’t work. Not that the straw had no holes prior and now that it does have one, ceases to work. So in that sense the meaning of straw already implies a hole to begin with, otherwise it would just be a solid stick or a stick with a deep depression (ie a long and thin cup).
If I'm understanding you correctly, this is in line with my way of thinking. I consider it a cylinder if the center of the straw is not "missing". Therefore, my answer is that a straw has no holes until one occurs through the side-wall. By name, a "straw" starts as a whole, not holey.... ;)
netrogue1 I don’t think we’re saying the same thing entirely. We both agree that by definition a straw comes with a hole. That means a complete and functional straw is an object that inherently embodies a hole. For me that means the identity of the whole object contains a hole. That hole is what makes it a straw. So for us to call it a straw, there must be one identifiable hole. So when someone states there is a hole in their straw, they are imo implying that this hole is extra to the one that makes the straw a straw. They need not describe the extraneous hole as a second hole since that meaning is implied.
Gerry Iles That is, until you realize that objects made of atoms dont give a crap about the silly rules of topology. Good luck at stretching a blind hole in real life.
+Mahikan Nakiham objects do give lots of crap about topology. solid state physics, biology, quantum field theory, and data analysis etc. there's a reason Nobel Prize was given for it.
Your content is very interesting. Thank you for posting. I initially thought a straw would have infinite holes. Why? - A straw can be thought of as infinite number of 2-D circles stacked together - each circle having 1 hole. :)
One I saw a chair with a mustache on it and then a dancing water bottle went up to the to me to you and said hey, why don't we see some picture frames fall out to the ceiling tonight
This is actually pretty close to what he did. The difference is that the correct way is not to add the circles (and it's holes), but to multiply the circle. Also the multiplication is not by infinity, but by the straw's length :)
I thought of relating to doorways. Doorways are basically holes into another room. If you 2 doors in one room, regardless of the size or shape of the room, each doorway is a separate "hole" into that room; an entry point. The room inside is just the space between the entry points.
Its flawed because that's nothing like how actual holes work. And using your flawed logic the answer would be 2, not 1. Doors open into 3d spaces, and aren't passages through planes...so that analogy is totally flawed when talking about topology.
I think a more suitable approach for people who don't know much about mathematics and who think that it's two holes would be to ask them: "How short would a straw have to be in order to have just one hole?" This way you could lead their claim about two holes ad absurdum.
Panulli4, I think your question is absurd because in y6our context, there's no such thing. To anyone who thinks it is two holes, if it were short enough to have just one hole, it is no longer s straw. The circle in the explanation is a two dimensional object, and I defy you to suck up a drink with it.
James, just like everyone else, you are living in Fantasyland and not in the real world. Haven't you ever seen a door that says "exit only"? Not every door has an entrance. Did you ever hear of P.T. Barnum? He had one of these extraordinary doors in his museum in New York City. It was designated by a sign saying "To the Egress". Look it up, it's a fascinating story. It might even give you a perspective on real life.
As soon as the straw is shorter than it's diameter it has one hole. When the length of the straw is longer than the diameter there are two holes. Where is the ad absurdum?
But is it more like a sealed tube that has both ends cut off? If you take a long thin ketchup sachet and cut opposite ends off will most people say it has one hole or 2?
Using the formula you provide, S X ("0",L), the 2-dimensional circle has "0" holes, since the L=0, and S X "0" = "0". You only introduce a "hole" when "L" becomes a positive number.
I am guessing 1. But really, the answer is: "It depends on how you define hole". And no, we don't need profesionall mathematicans to explain this. Because you don't have to use the mathematical definition for "hole".
IMO, it depends on how the straw in manufactured (ignoring classical topology because this is a straw, not a hypothetical shell in Euclidean space). The most common way to mass produce a straw is to create one long cylinder and then cut at regular intervals. For this explanation, I'll define a hole as an opening created in a closed shell. Imagine an infinitely long straw. At that point, you would be forced to say there are no holes, as the surface is completely self-enclosed. If I cut it in half, making it only infinite in one direction, it would have one hole. In the same way, if I were to cut it twice, it would have two separately created holes. A less common method of manufacturing straws is folding a rectangular strip into a cylinder. In this case, the straw has no holes, as it is an undamaged rectangle morphed into the third dimension. For there to be only one hole, the straw would a) have to be made by punching a long hole in a cylinder or b) never be created, existing just because it does. In the second case, we have traditional topology. All answers are equally right, depending on how you view this straw puzzle.
My first thought was that the answer depends on the definition of what we actually call a "hole". Starting from the one-dimension space a "hole" could be defined as a discontinued object, a gap of a line. In the 2D space, a hole can be easier identified, since we're more familiar with it. Well, a hole in the 2D space could be defined, as before, as a lack of space INSIDE a 2D object. For instance, think o a piece of paper with a hole in the middle. You wouldn't call it a "hole" if a piece of this paper was missing from the edges, right? Staying in the same line, a hole in a 3D object would be a lack of material INSIDE a solid 3D object. Otherwise, a hole could be a called a bubble in the cake, or INSIDE a piece of cheese. So from this point of view, a straw could have a hole if there was a discontinuity in its material or a "bubble" inside it. Therefore I assume that a usable straw has no holes or else you wouldn't be able to use it.
0 holes is also a good answer. Think of a straw that starts out as a sheet with 0 holes. Then you wrap a sheet into a cylinder and attach one end to the other. The sheet still has no holes, but now they inscribe a space inside it. 2 holes is definitely wrong any way you construct it.
topology is really weird, and in there, if you connect something you're changing the object basically. If you connect a cylinder, you're making something different, which is an object with 1 hole
Why would the properties of a straw formed by joining two sides of a rectangle be any different from the properties of a straw formed by the topological product of a circle and an interval? Contrary to what your math teacher may have told you, it's the end result that matters, not how you got there. It's kinda like thinking the result of 2² is a square number, but the result of 2+2 isn't.
This comment is what more people should have said. Even if it's not very clear in this video, "this object has n holes" is a perfectly defined topological proposition. Search for "homotopy between curves".
2016: Actually smart people 2017: *plays with fidget spinner* 2018: How many holes are in a straw? 2018: *chewing Tide Pods* 2018: Stephen Hawking dies 2019: *humanity ends*
I would say it depends on how the straw was made. Most plastic straws are a product of a long cylinder of plastic getting a hole punched in it and being cut and results in 1 hole. If a straw was made from a piece of plastic or paper that was rolled/folded and then sealed along the length, I'd say that it has 0 holes as it is not a circle/tube/cylinder, but a rectangular surface that has been rolled.
The math solution was more math than I expected lol. Once you said topology I thought you were gonna show a straw is topologically equivalent to a donut, which people unquestionably believe has only one hole.
I have a follow-up question: if you drill a hole into the straw in the middle, how many holes does the object have now? I'd say it is 3 then but not sure...
Topologically speaking, there is only one type of hole, which is a through hole that goes all the way from one side of an object to the other. In that case, as the video demonstrated, a straw has only one hole. Many commenters claim that if you use the everyday definition of a hole, then there are two holes. We talk about things like holes in the ground even though the hole does not go all the way through the Earth, making it not fall under the topographical definition of a hole. However, even under the colloquial definition of a hole that we use more regularly, there is still only one hole in a straw. This is because there are two types of holes. There are through holes, which go all the way through the object, and there are blind holes, which do not go all the way through. Holes in the ground are an example of blind holes. A straw does not have two blind holes, because the hole never stops. It goes all the way through the straw, making it a through hole. Straws would be completely pointless if they had two separate blind holes, because then the beverage would never make it from your drink to your mouth. Side question for people who still think there are two holes: At what point when you are sucking the drink through the straw does the drink switch from one hole to the other?
Colloquial basically means ordinary or familiar conversation. In other words, conversation that people use when they are just talking to each other in a casual manner. In a casual conversation, most people would say a straw has two holes, therefore, *by definition of the word colloquial*, a straw has two holes, in a colloquial context. In other words, many people say it has two holes, therefore, for those people, it does have two holes. Just like a large hill could be called a mountain because the locals call it a mountain. Or, a tomato is a vegetable because plenty of people call it a vegetable, or because it's used like one in cooking. Or that, for many people, Pluto is still a planet, because they call it a planet.
What about a hole that doesn't go through all the way? For example, if either I puncture a side of a cube without going all the way, or I take away one whole side of a cube, does it count as hole? I could argue that a straw is just a really thin cylinder that is missing both sides. If it's just missing one side, does that count as a hole?
to me, people trying to say its 2 holes are like flat earthers, who dont think and only use what they see at face value. its obviously 1 long hole when you actually think about it.
Take a piece of PRINTER paper. Stab it with a pencil. I think we can all agree it has one hole. Shape wise, the only difference between that paper and a straw is the straw is thinner, longer, and circular. Straws have one hole.
Joseph Stalin but what if you got that undamaged piece of paper and rolled it up into a straw... it originally had no holes and it remains undamaged so is there a hole?
Nice one. I guess you could've mentioned that the (physical) straw is also topologically equivalent to a "donut" (torus). And also show some object with two actual holes.
I don't see how, Alan. Could you clarify your observation? For me, an object with two holes could be reshaped into the form of the number eight, "8", and anything with a single hole into the form of the number zero, "0". How can you continuously transform the soccer ball into any of those?
actually nevermind a torus has 2 holes, technically. A 'hole' in mathematics is what you'd call an equivalence of loops. The 2 holes in the torus comes from the two circles being producted.
Before watching the video, my opinion is that the answer is pretty clearly 1. If you drilled through any other 3D object from one surface to another, it would be one hole. It just so happens that this hole takes up like 99% of the volume and runs lengthwise through the long axis of the object. Now, to see if Presh can make any compelling argument to *consider* other possible answers...
At the end of the video, I can see a small argument in favor of 0 (with the definition of "hole" being something that was not intended to be a part of the design). I can't see any in favor of 2 ("hole 1" and "hole 2" are clearly connected to each other and in fact it's impossible to specify the boundary between the two of them).
If you take the convex hull of a straw, there are two compact regions where the material of the straw is significantly distant from that surface. Two gaps in the surface.
Can't you say that a straw is just a plane that is folded in such a way that its long sides meet. This way the "hole" we see in the straw is just a byproduct so there isn't an actual hole. That's why i'd say a straw has 0 holes as it's the middle section is not part of the actual straw.
+Jose Hoyos chinareds54 asked how people could argue for 2 holes. I gave an example of a way to get the number 2. If you want to get into the physics of it, the straw, like almost all matter, is mostly empty space. When you talk about a "solid object", you're talking about either an abstract approximation, or a statistical feature of a large collection of subatomic particles. Depending on how you choose to model it, a straw can be a curved 2-dimensional surface, or a solid cylinder with a cylindrical tunnel passing through it leaving only fairly thin walls, or something with a complicated surface that's approximately a thin-walled, open-ended hollow cylinder, or... +TTeaMeister Inspector Tea You could say that, but that "long sides meet" means the topological properties of the shape change. In particular, if you run some elastic through a straw then tie the ends together so that it forms a slack loop, you can't get the elastic away from the straw without either breaking the loop, or breaking the straw, while with the plane folded so that the sides don't quite meet, you can slip the elastic out through the gap. It's not like a hollow object which actually partitions space - but it does divide loops into different categories - those that are entangled with the straw and those that aren't.
If you polled topologists, I would expect you get different answers depending on whether they think a drinking straw is a cylinder with no end caps or a long torus. Those shapes have different topologies and have different numbers of "holes".
My thoughts are along the lines of: if you start with a sphere, you need to cut two circular holes in it (then squish the middle portion) to get it to be a straw shape. The only way 1 hole makes sense is if a sphere has -1 holes, which is clearly wrong. Therefore, a straw has 2 holes.
01 - We can close one of the two holes and leave the other open : so there are two holes 02 - If the straw is conical : we will say that one hole is larger than the other : so there are two holes 03 - What if the straw is Y-shaped : will we say that it has 2 or 3 holes (knowing that we only added one hole) : so the original one has two holes
When a solid stick has a long longitudnal hole from one end to other then it becomes a straw. So a straw does not has holes it is the stick which has a hole
# Bob Silver: According to Quantum mechanics, nothing is the world is tangible. So, there is no actual atom. Atom is not a solid thing. Atom consists of particles which are actually clouds/cyclones of energy.
It all depends on your perspective(s) and what is the definition of a word or concept to you. What is a hole? (in your own point of view) The "one-hole thing" is based on a mathematical (dunno what branch) perspective, as he'd said earlier.
To my mind it has no holes and two openings, it is a hollow tube. A hole has a bottom which defines the term hole, as in dig a hole. If you dig a hole deep enough, or long enough you get a tunnel which is a tube. If you make a hole then that has no bottom, unless in your jeans or underwear, but the that is then not a straw.
you're describing a blind hole. there are blind holes and through holes. a straw has one through hole, as does a donut, as does a piece of paper with a hole in it, etc.
I think it is wrong say that there is a right answer to this question. There are different ways to interpret a straw and a hole mathematically, and a reasonable answer would acknowledge this and discuss the various interpretations.
Eli Damon There are different ways to interpret a straw and a hole. There however is only one mathematical way to interpret a straw and a hole. Math does not deal with language and thus the only way to interpret a straw is as a topological shape. A hole actually does have a mathematical definition and thus is interpreted as such: "A hole in a mathematical object is a topological structure which prevents the object from being continuously shrunk to a point." mathworld.wolfram.com/Hole.html
Taking forward the example in this video, instead of stretching the 2 dimensional circle-with-1-hole to form a straw-length, we could consider the length of this straw being composed of an infinite number of such 2D circles stacked together. The straw then has an infinite number of holes! Now, since the group of the 2D circles result in a single straw, the group of those infinite holes collectively become 1 single hole. On the other hand, if a paper sheet were to be rolled into a cylinder/straw, it could be said that there are no holes as there wasn't any to begin with, nor has the paper been punctured. Yes, there would be inner and outer 'space' within and around the straw.
Happy 2 year anniversary! At the time my channel was very small and people asked why I would even make a video, so let me share the history. The topic was trending and Buzzfeed posted a reaction video that racked up 450,000 views. I thought the topic was a great way to teach some math and topology. It is now 2 years later...Buzzfeed's video has 566,000 views, my video has 800,000 views, and a video by VSauce on the topic is trending right now with over 3 million views (search for how many holes does a human have). It is often said math is not popular, but it seems math and science are Buzzworthy topics after all!
Congrats
Congrats
Hey couldn’t you say that the straw has infinite holes because there are infinite circles? Continue making your videos Great job 💪🏻.
Can you use dark background .
Nice one Presh, I think your graphical explanation for the 1 hole answer is easier to see than trying to explain the imposibility to (continously) shrink any closed curve over the straw's surface down to a point...and this reminded me of the poincare conjecture that perelman proved true in 2003
I think the main confusion comes from the fact that "hole" can mean different things.
If you think about a hole as an opening, it's 2
If you think about a hole as a tunnel, it's 1
If you think about a hole as a defect, it's 0.
Of course mathematically there's 1 hole.
gratz. you just put in words what everyone was thinking but couldn't formulate. you win
this is the most comment of the entire century
@@GDPlainA definitely the most comment
It's just a rearranged donut....
Mathematically holes are tunnels so Yes
Before I watch: one.
After I watch: yes
What
I thought it would be 2
M'Games U.K ßßß I always thought it was 1 because it’s one continuous hole.
If you take a cylander and push the middle out you have only created a single hole.
Lol same.
1903: i bet there will be flying cars in the future
2018: how many holes does a straw have?
iHoRst2000 Dude lol. I need 2 vape now
Humanity is evolving
Not liking
iHoRst2000 10000BC: What's the meaning of life?
2018AD: what's the meaning of life?
This makes no sense
1898: let's try heroin cough syrup
2018: let's definitely not try heroin cough syrup.
UA-cam poll brought me here
ME TOO
We might be from the same Poll
Me too
Yes.
I literally saw that post like 17 hours ago, and it’s been on my mind since,, so now I’m here...
Here's how I explain it: A donut has one hole, right? Imagine you could stretch a donut so it's taller so that it looks like a straw. If you believe a donut has one hole and a straw has two holes, at some point when you stretch that donut, it must go from having one hole to two, which doesn't make much sense.
LimeGreenTeknii My thoughts where someone along does line but I came at zero holes, since a doughnut to have a hole, it's surface being a 3d object must have at least two holes. The surface of a doughnut has no holes thus the doughnut has no holes.
That seems to be his explanation above, but without food. It might help this topololgy discussion to define a solid blob (even with profound depressions but no perforations, as an object with no holes.
The human body, (barring fistulas or artificial perforations) has 4 openings, all connected at the back of the throat: 2 nostrils, a mouth, and anus. How many 'holes' is that?
(Ears, eye sockets, eustachian tubes, sinuses, bladders, etc are just 'depressions' that don't 'go thru'.)
PS: English is used by many people with different cultures. A topologist has a useful definition for 'hole', and so does a farmer with a post hole digger, who also has a different term; 'thru-hole' (also used by machinists & commercial engineers). If either is 'wrong', it is a matter of context & code-switching. Does topology have a name for a post-hole? If not, does that make it the more limited context? Our minds are certainly flexible enough to manage multiple, sometimes contradictory definitions for many words.
Well I am not sure if doughnut (or circle) does have a hole since the shape is kind of defind without the hole. I would agree that the straw is just really long doughnut, but the question is whether the doughnut has hole or not and how is the hole actually defined.
Donuts have 2 holes. Coffee Mug has 1.
The issue with this problem is that no one is making a distinction between intentional holes and unintentional holes.
+shyhalu
Coffee Mugs (with handles that loop back to the body of the mug) and Doughnuts are the same (topological) shape - a ring with blobby bits.
A good test for whether something has a (topological) hole is whether you could take a length of elastic, wrap it loosely around the object in some way, attach the ends of the elastic together to form a closed loop, and then be unable to separate the elastic from the object without either breaking the loop, or breaking the object. So you can form the loop so that you can't separate it from a doughnut, or the handle of a coffee mug, but no matter how you arrange the elastic, you'll always be able to get it away from a wineglass.
That doesn't settle how many holes something has, just whether it has any, but it's a starting point.
Never thought a straw could stir such a philosophical conversation
*touché.*
Was that a pun?
get out
Over many a Martini, I'm sure.
this was the last straw
Normal person: 2 holes
Mathematician: 1 hole
Philosopher: 0 holes
Me: Infinite holes
Any normal person says there's 1 hole...
A physicist could argue that it has an infinite number of holes aligned beside each other.
Or be like vsauce, use his reasoning with the "How many holes does a donut have?" video.
@@ariesmars29 so am i a physicist? 🤔🤔
Neo: There is no straw.
I've listened to 1:56 and have this to say: It depends on your definition of "hole" and of "straw." If you start with a rod and drill a hole through its center along its long axis, then it has one hole, (like a reusable metal drinking straw). If the straw is formed by winding a flat material in a spiral and glueing the edges where they meet, (as in a paper drinking straw), you could say it has no holes.
I believe the mathematicians would tell you that gluing the edges together is not a continuous transformation and so you have in fact added a hole.
It doesn't matter how the "straw" is made. The end result is the same - a long tube. As a tube, it's a length of hollow material with both ends open. It has one hole.
To make a hole material has to be removed in such a fashion that material is surrounded by the voided space. A straw, tube and a hose by it's nature has a voided space. I firmly believe there is no holes in such things. Unless damage has occurred or someone willfully makes one.
Drilling a hole in a rod merely speaks to the manufacturer of the straw.
I don't understand the quotation marks around the words hole and straw in your comment.
@@oldfart1079 Some people might define a "straw" as a water resistant paper tube formed by coiling and glueing paper around a rod shaped mandrel, or as an extruded plastic tube. Some may include a glass or metal tube in the definition of a straw. Some may define "hole" as an empty space formed by removing material. So if they define "straw" by the first definition and use the definition of "hole" I gave, they would say a paper straw didn't have a hole, but a stainless steel straw made on a lathe in a machine shop does.
@@billvojtech5686 yes there a multiple ways to manufacturer a straw. Nature herself can in deed manufacturer straw's and holes. Not all holes persist through an object, a cup or drinking glass are good examples of such holes commonly referred to as a "blind" hole.
In manufacturing "blind" holes are used for screw fasteners and through holes are for bolt and nut fasteners.
Wait-wait-wait
Do you really expect Buzzfeed to do something reasonable?
Is there a spider on your ceiling or something?
They just create buzz and then feed it.
HOLYCRAP! Names amirit?
Ball Juice Of Zeus xD
Nah
You have 16 subs for some reason.
I explain it like this. If you cut a hole in a paper it makes one hole. It you thicken the paper, say a block of wood and cut a hole, there will still be one hole. So a straw is basically a super tall but skinny piece of paper with 1 hole.
What does this have to do with astronomy?
+potato man Star or straw? There's a difference.
Okay imagine a ball and you poke a hole right? And then you poke a hole on another random spot so does that still make it one whole? No it's two
Juan Carballo unless you poke on hole all the way through or you poke two that meet in the middle
+Juan Carballo If you poke a hole all the way through a ball so that it breaks on through to the other side, that's the same as a straw, one hole. If you poke a "hole" halfway through a ball, it's not a "hole" topologically speaking, just an "indentation", which does not alter the topology of the ball.
From a manufacturing standpoint, a paper straw has zero holes. It is a rhombus spindled around a cylinder and glued into place. The rhombus remains intact, thus no holes.
thats not what a hole is. a donut is made with dough and that dough remains intact, so therefor a donut doesn't have a hole?
@@ukulelevillain4170 The doughnut does indeed not have a hole. The doughnut is wrapped around a hole. Oh wait, it's not, there's no hole to wrap around. Anyway, the nut is the part of the doughnut that was the hole, but and so it's the nut is in quantum entanglement with the hole.
A donut has pi holes.
@@ukulelevillain4170 Some commercial donuts have the holes punched in them, then those are sold separately.
+1 manufacturing mind
Me at 2 AM: I need to go to sleep
My brain: No, you need to find out how many holes a straw has
a hole is through something not interested something, spread the word
One hole, two openings.
puttesla intxtbks But ppl would think hole is equal to opening...An entrance hole/opening and an exit hole/opening
Pio Lio: then people are wrong. If you make a hole in a door to put a handle, you make one hole that you can see from both side, Nobody would say they made 2 holes. The lenght / depth of the hole has no impact on the number of holes.
How many openings does a doughnut have?
puttesla intxtbks well done you answered it in four words👍👍👍
Just to be anarchic about it, if you take a solid 3-d structure and drill a hole in it, you seem to have made one hole; but, by the definition given in the video, you have not made a hole at all, unless you go all the way through. However, if you take a 2-d piece of paper and connect one end to the other creating a tube (straw) then there is no hole in the paper, so that structure could readily be said to have no holes. Alternately, if you take your 3-d solid, and drill two holes, one in each end, and they eventually meet, does one of the holes cease to exist. Create a set of axioms or definitions that will support your conclusions and you can get any conclusion you like.
0 holes proof: "Waiter! My Straw has a hole in it!" - Waiter brings new straw. Q.E.D.
Will Mack my underwear have 3 holes
Vipul Mehta That's 3 than it should have.
“QED” lol!! Nice proof
Well, common sense makes you interpret the statement as "one hole that shouldn't be there".
Vipul Mehta no, that's one hole
If I have a piece of wood, and drill a hole through it, it has one hole. If I carve the outside of the wood down until it's a tube (a straw), it still only has one hole. Not too complicated.
If you're going to be clever, you need to call it a "through hole", not just a hole. Besides, you're overcomplicating it. Topologically it's just like taking that straw and morphing it into a flat disc. It'll still retain the one through hole.
One entry hole and one exit hole . Whats in between is a hollow.
Here's ALL the correct answers :
Straws have one hole, topographically speaking - but only because, in the field of topology, a hole has a very specific meaning and we're considering the straw to be an ideal mathematical surface (which it clearly isn't)
Then there's semantics... one can dig a hole in the ground but it is not (topographically speaking) a hole - however it IS still a hole according to the english language. How many of these non-topological holes a straw has is merely a question of scale... since the surface of a straw is not an ideal surface. So, the answer is likely to be between zero and trillions.
Then there's the functional answer. Having defined the object to be a straw - how many holes does the STRAW have? None... it is a perfect straw. If it had a hole it wouldn't work very well. This is a logical statement based upon types, equivalent to asking whether a bicycles inner tube has a hole in it ... the concept of the item itself establishes the baseline of form, and this ideal conceptual form is then compared to the item under test.
Then there's the material sciences answer. A straw has enough tiny (and, indeed, also properly topological) holes in it to lose water/gas molecules by osmosis, so again the answer is trillions. This IS still a topological answer, but one properly recognising that the straw is NOT some ideal mathematical surface as those weird beardy mathemagicians would have you believe.
Then there's a pragmatic materialists answer... there IS no straw, just a collection of atoms which are held in proximity but never touch. The concept of holes cannot be reconciled with this view.
Which brings us neatly to the Zen answer: Mu!
Clearly one needs to first :
- define a straw that we can all agree on.
- define a hole that we all can agree on.
- define a scale that we can all agree on.
Only then, can a proper answer be attempted.
To hold out that a hole is a strictly topographic feature and that we should imagine a straw to be an ideal surface - is a cartoonish simplification. Similarly, one could establish how many sheep can fit in a field by first considering all sheep to be perfect spheres...
... by doing so, we answer an *entirely different question* - and usually one which is more comfortable to work on.
But yes, I'd also default to claiming that a straw only has one hole... and, probably, later get arrested for brawling with pragmatists in the car park.
GaryChap minimum 10 minute writeup
GaryChap
Modern Sofokles
Stfu nerd
Kahn Devine no u
Rubik’s cube 21 lmao kid go back to roblox
The straw has 0 holes and 1 tunnel
Yeah that’s true
Not a hole. A fooking tasty tunnel
It's just a long donut
RealRupert topologically, there is no difference between a hole and a "tunnel" as you call it. If a circle with no depth drawn on a piece of paper is a "hole" then more accurately it is a hole with no depth. An open cylinder or "tunnel" is therefore a hole with depth L. It's less accurate to say a tunnel is not a hole than it is to say all tunnels are just holes with depth
Give this guy a Nobel
It also depends on how you define a hole.
No it depends on what is a hole
Which has different definitions in different languages
A hole is a hole, weather it goes all the way through the object of half way through its a hole.
If its only like 1mm or less it might not be a hole
Yeah, you could either define it as just an opening on the surface of an object, or the entire empty space inside the object.
My first thought was to define a hole. It must have some height, so any solid with a change in surface height downwards must be a hole. After that I struggled with all sorts of counter definitions. It was a really interesting exercise. Thanks.
We must first define what is a straw. Could the straw have a cross section structure inside to support the wall? Creating four paths for fluid to flow? Would it still be a straw? Does the word straw actually just define how an object is used? "a thin hollow tube of paper or plastic for sucking drink from a glass or bottle". This may be the common image of what we think a straw is. But how does this explain if I use a short section of a thin wall tube or pipe as a straw. My answer is there is no answer. A straw can have as many holes as anybody wants to design into it. I remember as a kid straws that had basically two in one twisted around each other. But to define a hole. Can a hole have a hole in it? Or would that just be one hole with variable dimension?
If you had an infinitely thin plane and there was an area which lacked material where you could go from one side of the plane to the other, wouldn't that be a hole?
By that logic (and dont get me wrong there is nothing wrong with that logic) holes as we usually think they are can not exist. Since you can allways travel on the edge of the "hole" and end up on otherside of that "hole" which is still on The same infinitely thin plane. This is why my reaction to this riddle was that this can not be answered before The question defines "a hole".
A hole is an exit point. A cup has one exit point, one hole, a leaky cup has two exits, so two holes. A straw? Two exits, so two holes.
@@macmcleod1188 you cant use impossible scenarios to prove a real scenario.
The reason why people "debate" about it, is because it is a debate about the meaning of language words, which is defined by the people, and not by experts. What is a "hole", anyway.
Mouth is an entry hole and the ass is an exit hole. Is it really 1 hole or two holes?
Clement Lo mind blown!
Riki but it has two openings, right?....and ppl just use "hole" to replace "opening", so saying there is two hole is not entirely incorrect
there's a topological definition for it which ought to be used in mathematics.
but in real life its not practical. e.g. if you dug a hole in your backyard, the topological definition would say that you haven't added a hole at all.
Gustavo
The question wasn't "how many holes does THIS straw have" but "how many holes does A straw have"
meaning, if in your definition of straw you consider it an object with a hole, then the answer to those question would be 1, not 0.
Does this mean that if i fold a piece of paper into a cylinder and tape it, I've just made a hole in it?
The question will then be can you make a hole in a pice of paper without poking a hole through it?
Clement Lo that's a great question. yes.
Tushar Sadhwani No you’ve made it into a hole
Taping the ends together changes the topology of object. You cannot change the number of holes in an object without fusing two separate ends together or tearing apart two ends that are connected.
Nice question, think about making a hole with modeling clay. Now you don't have the taping problem.
Interesting. I was looking at it geometrically, without the mathematic elements. I figured a straw was basically a hollow cylinder so it was pretty much a rod with a single hole inside. I came up with the same answer by intuition instead of math.
Personally, I used observation to arrive at the same conclusion.
I came up with the same answer based on how I could create a straw in cad. Create a solid cylinder and use the hole command to create 1 hole through the entire thing.
Yes, a rod with a hole in it!
Of course no other comments were read at the time either...
Non mathematically speaking it must have only one hole for engineers.
Because if you drill 16 Holes into a metal plate with a regular drill to put screws inside its still just 16 holes and not 32.
If you would tell 1000 handcrafters to drill 16 holes they would all drill only 16 holes, no matter how long or wide the object is they drill into.
I think this is the only explanation as to why its only one hole for the majority of people.
there are two correct answers to this problem, depending on your starting point. As illustrated if the starting point is a circle then the straw has 1 hole, but if the starting point is a parametrized continuous surface in R^3 which curves back on itself, then the answer is 0 holes.
The apparent paradox is due to the lack of initial definition.
But then what even does have a hole
@@itismethatguy That's the point being made.
i have the feeling maths are over complicated for no reason
@@itismethatguy exactly. Holes don't exist. Holes are consequences of the geometry of the surface itself....
My definition is that entrance = hole.
Morphing the shape of the straw like you did is the most intuitive way (for me) of looking at the problem. A good way to illustrate this is with the similar question of how many holes a tea cup with a closed loop for a handle has. Morphing the cup into a toroid gives a strong intuitive basis for working out similar problems in the future.
Does this mean that a hollow sphere with an opening at the top and the bottom mathematically has only one hole?
@@SimGamerTV from a topological viewpoint, yes, a hollow sphere with two holes top and bottom has one hole. Similarly a hollow sphere with on hole in its surface has zero holes. If you stretch it out, you will see it has the same topology as a disk, with the edges of that single "hole" now forming the circumference of the disk.
Yes, probably a better example than my doughnut analogy.
@@AlDunbar similarily if you stretch the two opening sphere you will get a disc with one opening the circumference edge and the other opening the hole in the middle.
So back to the straw (cylinder) , if you slit it lengthwise and roll it out it will form a rectangle with no hole , just as if you started with an unclosed circle it would not have a hole till it was closed.
All I could see was a coffee mug.
Strange, I was seeing a Klein bottle split in half.
Now I see a furry red rabbit.
PaintingJo You were seeing a Möbius strip?
Nice one 👍
;P
Love this channel. As a patent lawyer, I actually have to consider questions quite similar to this on a routine basis. "Is this two holes? Or one long hole? Or if I call this a 'straw' then is it implied there is a hole, and if I say there is a hole, then am I saying there's two holes?" The process of drafting a good patent claim is bit like doing math in words.
What if you define a straw as an area rolled up into a cylinder?
As a hole is a perforation, and straws are made not by punching holes in matter, but by wrapping sheets or extrusion, they don't really have "holes" in them.
They do... a through hole. You just created what is commonly referred to as a "tube".
@@rhodesj1893 But if it's a tube then it's debatably not a hole, for the reason mentioned above. there's a reason those two things are different words.
@@Person01234 By rolling a sheet of paper into a tube, you break the rules of homeomorphism. A sheet of paper has no hole. You can‘t flatten a strawhat and make the hole vanish while following the rules of homeomorphism.
I think much disagreement comes from how hole is defined in regular language and how it is defined in mathematics. In real life you can dig a hole in the dirt, but a mathematician would say it is not a hole, but an insignificant dent. Likewise the interpretation of the word hole can lead to disagreement in this conundrum.
But the straw has 1 mathematical hole, that is for sure.
Turns out "hole" is not defined mathematically, and by some definitions a real drinking straw that exists in the real world would have 2 holes, and depending on how you idealize the drinking straw it can have 1 or 3 holes.
I feel like a similar thing happens when using the word "theory." Scientifically for something to be a theory there are defined standards that have to be met. Problem is when most of us (and I'm guilty too) say theory, at best what we're describing is a hypothesis. In everyday speech people have "theories" about everything... No, no we don't, we've mostly got ideas and an occasional hypothesis. So then when an article is published regarding say gravity, and it's referred to as a theory, people misinterpret. Establishing definitions is paramount before a dialogue can take place.
Depends on your reference surface. If you consider only the surface of the dirt in an arbitrary circle around the point of interest, what you end up with is what one may consider a "hole" mathematically speaking. After all, you can technically go through surfaces as if the yaren't there. A surface is just a set of points. It has no specific physicality.
@Z-Statistic Good point. These foold need to learn some non-Euclidean Topology
I think what made me decide on one hole is that the wall thickness of the straw is measurable. even if its just a few thousandths that makes it a side/face that you would use to calculate the surface area. so basically you have a cylinder with a hole through it, even if the hole is near the size of the outside diameter and the straw was manufactured by extrusion.
I think a more casual-friendly way to explain it is to ask: "how many holes does a donut have?" You can deform a torus into a straw.
Derek Neal but couldn't it be zero as well? Extrude a long rectangle around a circular path and attach it to itself?
The fact that you attach ends together changes the topology, so no.
No, cutting is not allowed
REMEMBER, YOU MUSTN'T TEAR OR CREASE IT.
there are different types of holes and you must consider the second hole the torus surrounds so they are no topologically equivalent i.e T^2 is isomorphic to S^1 x S^1 not S^1 X R like the straw is here in the video.
Depends on how you define a hole. It’s not only a mathematical problem, but also a linguistic and psychological-conceptual problem.
I agree. It would have been nice to see an application of its mathematical use. Otherwise I’m left thinking the mathematician has just defined it their way without respecting another perspective.
I do however accept that there is just one hole, mostly because I would consider that if the tube was bent into a continuous circle there would be only one hole.
I just saw the donut comment 🤣 I guess that makes two holes
If we're talking about real world than It's exclusively mathematical problem.
I've never done something in that field but here is my explanation so far:
Assuming that you take a piece of paper without holes. You have an area with 0 holes. If you create a hole in there, you have a plane with a hole but notice that the amount of borders that exist has increased by 1. Instead of having just 1 border, you end up with 2.
This can be translated to any surface I assume.
Second, I imagined a cup. Nobody would ever say that a cup has a hole.
It's just a shaped surface. Now, if you remove the bottom of the cup, you will have a cup with a hole on one side which is pretty much a straw.
Therefor a straw has only 1 hole.
If you punch a whole through thin piece of dry wall, that's 1 hole. It has the entry and exit but is considered 1 hole in the wall. Same as if you ram an iron rod through many pieces of dry wall, creating a long straw shape. Still 1 hole.
But what if you dig a cave-like hole in the side of a mountain. It has no exit. 1 hole. You start another hole on the other side of the mountain. That's 2 separate holes. You then connect the 2 tunnels in the middle, is there still 2 holes or did you just reduce the holes from 2 to 1?
Anyways it all depends how you're defining the word hole to begin with.
johnny_schwifty.soundcloud as soon as they connect then you’re back to having one hole as you can’t define where one hole is and whether the other is, separate to it, ergo it’s only got one hole
i would cal the first and second a "PIT" once joined it become a "HOLE"
no a pathway or tunnel.
johnny_schwifty.soundcloud what about ur mouth and ur ass. They're both connected with a long tunnel of an entry and an exit and people considered them two different holes
Johnny - You have TWO holes until they meet. Note that "hole" is simply a word, while the math itself doesn't change. If you apply your logic about the iron rod and the drywall to it. Think of this. When the "Chunnel" was being built, they bored from both ends. There were two distinct holes. You couldn't go from one side to the other without exiting one hole and entering the other. Once the two holes met, they became one hole.
Here's another way of thinking about it. You take an ice cube in each hand, allow them to melt a bit, then you hold them touching each other and allow them to freeze together. How many ice cubes do you now have?
Yes but this isnt even about math, its about how you define the word straw and hole
Pretty sure it’s about math.
Precise definition is done with math. But yeah I get ur point.
PewDiePie 3 yeah, for me it is not a circle with depth, it’s a bended rectangle.
PewDiePie 3 no this is about a part of math, the part of math that is about shapes, and wich you can use to prove things.
PewDiePie 3 is right, this video is not really about a clever insight in math, but about how the mathematical definition of "hole" differs from the everyday (pluriform) use of the word "hole" in English.
Sure, the topological "hole" is specifically defined so that it serves a useful and meaningful mathematical purpose, but this video doesn't show us anything of that purpose. For the casual viewer, the way mathematics chose to define "hole" seems just arbitrary.
well so basically it depends on the definition of a hole. the topological definition would give the answer 1. if you define a hole intuitively, not mathematically, as any entrance into the object's 'core', then it has 2 holes.
No, because then when you drill a hole in a piece of wood or metal, you would have drilled two holes?
@@jiminauburn5073 So if you were to create a hole in a tree, would you say that has 2 holes?
@@trisk4806 I agree with you. I was disputing the OP, saying that you would not have two holes if you drilled a hole in a piece of wood.
Oh boy I win yesssss!!! I’m gonna buy mocha frape now and explain hole theory to Macdonald cashier let’s see how it goes
Youre a champ 👍
MmhH... .
@@OphiuchiChannel lol
How it went?
2 years ago lmfao I doubt we'll ever know
This is how I have explained the 1 hole answer: imagine a sliver of wood as thin as a piece of paper with a single hole punched in it, now make the wood thicker, still only one hole. No matter how you change the shape of the surrounding wood, it will just be one hole, so if you had a very thick piece of wood, and then shaved off the excess and just leave a thin bit around the hole, you have a straw!
You only have 1 hole in a 2-dimensional space. Since we’re talking about 3 dimensions, it has two holes.
2:15 It basically takes 15 seconds to go from "Lets keep the party rolling and make math exciting for everyone" to "dafuq he just say"
Steven Warren all he said was the unit circle x length.....
Steven Warren 'short' he said
came here because of txt debate at weverse
Same I'm team one hole
@@alltheboysloveleah team one hole rules
I am here because of the poll
It is clearly infinite holes stacked on top of each other
Depends of ,,hole" word definition.
in bed: ah yes babe, stick it in da hole
the invention64: ?????? ahhhhh, you mean "infinity" holes...
My answer was 0 holes..
But 1 hole makes sense now
It's an intriguing one by the way that if you were to make a straw with 3 ends, you would say it had 3 holes since there were 3 places a substance could come out of the containment of the straw. If you then remove 1 of the holes, for example return it back into the original straw, surely it would now have 2 holes.
Just like if I asked how many holes are in a regular t-shirt. You would say 4: the 2 sleeves, the collar and the base. If I sew up the sleeves, you would say it had 2 holes: the collar and the base. But it's still topologically the same shape as a straw.
However, the straw having 1 hole totally makes sense; it is all the same space all the way through. So does that mean that a t-shirt really just has 1 massive hole? It's all the same space. Or does it mean that a straw has 2 holes? I think it always depends on how you define the terms in the question.
Just like you can't assume an angle in a triangle is a right angle because it looks like it, you also need to set the parameters of the question. And therefore the answer is there isn't really a correct answer
You are interchanging hole with opening or orifice... and they are not the same thing. A Door is not a Hole in your house... Neither is a window. Your sewage drain is a hole in the floor to the city sewage or your septic tank... sure. Your Radiator has an inlet, outlet, petcock drain, and burp bleed-off tube.... but only ever has a "hole" if it is leaking. Words need to be used appropriately and correctly.
1 hole is probably the most practical answer.
The material used to make the straw, which effectively is the entirety of the straw - has 0 holes, but that material was formed specifically to create an aperture, which now meets the definition of "hole"
The less compelling answer could be 2 unique openings, where the materials seems to open up And no longer restrict the contents of the straw, so 2 holes
You could make a straw (albeit an impractical one) by taking a block of wood and drilling a hole through it. One hole!
At first, you should show the exact definition of HOLE in mathematical term.
Yes because it is through something
Notice how the video is 4.20 long
Illuminati: Stay right where you are
Yeet
Notice how SHUT UP
So what?
And: no→ 4:20.
How many holes are there on an 18 hole golf course? How much dirt is in a 1m x 2m x 3m hole? Are any of the holes that the movie "Holes" is named for actually holes? Could there be a hole in the definition of hole, rather than a hole in people's logic? Topologically speaking I should be able to eat as many donut holes as I want and never gain weight!
I love this comment so much
You wouldn't gain any topological weight, that's certain.
Michael Geiss the answer to that question is the fact that there are different types of holes. It depends on the context.
Evan Smith Thanks! That was the exact point of my intentionally humorous questions.
Michael Geiss woah! Lmao
3 holes, actually. I refuse to elaborate for I am fundamentally and undeniably correct
2 holes, one hollow as the straw is a tube
@@liamg1706 No actually it’s 3 holes. You’re just too blind to see it
@@hydropage2855 there are 2 holes either end of cylindrical hollow tube. That is of what a straw is. You are too simple in the brain to realise that.
@@liamg1706 How can you not see there’s a third one right there? It’s literally right there in plain sight and you can’t see it. Are you messing with me?
@@hydropage2855 for a 3rd to exist it would have to be seperate from the other 2 which in this case there is no seperate hole just one either end of the hollow tube
"When science is in the news, scientists are consulted." ...unless it is anthropogenic climate change.
and unfortunately a pandemic...
What do you mean?
@@spaghettiking653 Who are you asking?
@@jeffc5974 You - are scientists not consulted on anthropogenic climate change? Surely that's the field where research is most cited, right?
@@spaghettiking653 It was a bit of an exaggeration, but non-experts are brought on news shows way more than experts, and when experts are brought on, it is much more likely there will also be a non-expert to contradict the expert.
Video starts at 2:10
Thanks
Thanks
thanks
Thanks
Yeah thanks mate
Great videos, thanks Presh! Another intuitive way to look at this is as follows. Imagine that you have a small metal cylinder 2cm diameter and 3cm long. You place it standing upright in a bench drill and drill a 5mm hole in the center of the round face through to the other face. (You now effectively have a "straw".) How many holes did you drill in the cylinder? Just one! This logical answer is independent of the dimensions (and material) of the original cylinder.
Or you have one piece of paper with no holes. You roll it upon itself and secure it with adhesive. Still a piece of paper with no holes, just rolled to form a straw.
If you drill the hole almost halfway through the cylinder, and drill a second hole from the other end, you have two holes. Now if you complete the drill through, you have now only one hole.
So by drilling a 'third' hole, you've subtracted a hole?
Before I watch the video I'm going to say no holes. The mathematical definition of a hole is very precise. For polyhedra the definition is Euler's Formula for Polyhedra. I started looking a little closer at topographic analysis, and even then by strict definition there are no holes. It's basically a plane that has been curved (revolved) along an axis. The plane is continuous, so there are no holes geometrically speaking.
I think the confusion comes from differences in basic language and in topology.
Let me give an example, if we take a balloon and ask any average person, now many holes does this balloon have they will say one.
If you ask someone that deals with topology, they may say one, as it's a common excepted answer. However topologically a balloon has 0 holes unless we poke one in it to complete the hole.
In topology any object with 0 holes can be transformed into any other object with 0 holes. (Paper, Balloon, Cup, Fork, etc.)
The same is true of an object with 1 hole. (Donut, Coffee Cup, Straw, Ring, etc.)
So it really comes down to whether we are speaking in basic language, or topology.
So both 1 and 2 are correct, we just need to agree on which system is being used.
All three answers are correct when given the right definition of hole. If a hole has to be intentionally added to a complete object, then zero is also an exceptionable answer.
For example, if someone said, "This straw doesn't work. It has a hole in it". That implied that in language, the word straw is a complete object and any descriptor is in addition to that object.
Just thought I'd help complete your point for all three answers.
Derek Gooding
I think the implication of that statement is that the straw has an [extraneous] hole, therefore it doesn’t work. Not that the straw had no holes prior and now that it does have one, ceases to work. So in that sense the meaning of straw already implies a hole to begin with, otherwise it would just be a solid stick or a stick with a deep depression (ie a long and thin cup).
If I'm understanding you correctly, this is in line with my way of thinking. I consider it a cylinder if the center of the straw is not "missing". Therefore, my answer is that a straw has no holes until one occurs through the side-wall. By name, a "straw" starts as a whole, not holey.... ;)
netrogue1
I don’t think we’re saying the same thing entirely. We both agree that by definition a straw comes with a hole. That means a complete and functional straw is an object that inherently embodies a hole. For me that means the identity of the whole object contains a hole. That hole is what makes it a straw. So for us to call it a straw, there must be one identifiable hole.
So when someone states there is a hole in their straw, they are imo implying that this hole is extra to the one that makes the straw a straw. They need not describe the extraneous hole as a second hole since that meaning is implied.
1 hole, it's called a through hole as it has 2 openings as aposed to a blind hole that has only 1.
A "blind hole", as you put it, is not, topologically speaking, a hole, at all...
Gerry Iles That is, until you realize that objects made of atoms dont give a crap about the silly rules of topology. Good luck at stretching a blind hole in real life.
+Mahikan Nakiham objects do give lots of crap about topology. solid state physics, biology, quantum field theory, and data analysis etc. there's a reason Nobel Prize was given for it.
+Mahikan Nakiham they do. how many years of school did you skip. all?
So does a long tunnel with an opening on the other side have one or two holes?
7PM:gotta go sleep early today
3AM:
Your content is very interesting. Thank you for posting.
I initially thought a straw would have infinite holes. Why? - A straw can be thought of as infinite number of 2-D circles stacked together - each circle having 1 hole. :)
One I saw a chair with a mustache on it and then a dancing water bottle went up to the to me to you and said hey, why don't we see some picture frames fall out to the ceiling tonight
a huge chunk from the center is missing, that is the definition of a 🕳
Cash cab..... With
This is actually pretty close to what he did. The difference is that the correct way is not to add the circles (and it's holes), but to multiply the circle. Also the multiplication is not by infinity, but by the straw's length :)
@@whitewhitewhite2446 I'm pretty sure there never was anything in the centre, nor is there supposed to be, so what is missing?
It's black and blue.
Or white and gold.
We should understand the difference between hole and opening. Hole is one but straw has two opening.
I think this is the perfect response
A hole was always equivalent to a tunnel for me, so this "debate" is really confusing...
What is an opening that isn't a hole?
@@graygraygray4454 a plate
I thought of relating to doorways. Doorways are basically holes into another room. If you 2 doors in one room, regardless of the size or shape of the room, each doorway is a separate "hole" into that room; an entry point. The room inside is just the space between the entry points.
DragoNate You've got a very flawed concept of this.
How is it flawed? I'm literally just sharing what it made me think of...
Its flawed because that's nothing like how actual holes work. And using your flawed logic the answer would be 2, not 1.
Doors open into 3d spaces, and aren't passages through planes...so that analogy is totally flawed when talking about topology.
Opening
Exactly. A straw is 2 holes with a tunnel in between. Like a hallway with one doorway at each end.
For real I watched this because of txt debate
LMAO REALLY WAIT IS IT ON UA-cam I WANNA WATCH THEM DEBATE ABOUT THIS
@@lizzy6514 they debate it on weverse!! They commented on moa post and making a whole debate there 😂
@@nurinsyirah6398 Ohhh LMAO THANKS
How many holes can you count in the word "hole" ?
johnny_schwifty.soundcloud 2
Two
Dekross HOLE INCEPTION
johnny_schwifty.soundcloud three. There is a "hole" in "e" also.
+UltraBall333 There's a hole in the "o" and a hole in the "e". Where did you get the other hole?
I think a more suitable approach for people who don't know much about mathematics and who think that it's two holes would be to ask them: "How short would a straw have to be in order to have just one hole?" This way you could lead their claim about two holes ad absurdum.
panulli4 Of course they could just say infinitely.
Best answer
Panulli4, I think your question is absurd because in y6our context, there's no such thing. To anyone who thinks it is two holes, if it were short enough to have just one hole, it is no longer s straw. The circle in the explanation is a two dimensional object, and I defy you to suck up a drink with it.
James, just like everyone else, you are living in Fantasyland and not in the real world. Haven't you ever seen a door that says "exit only"? Not every door has an entrance. Did you ever hear of P.T. Barnum? He had one of these extraordinary doors in his museum in New York City. It was designated by a sign saying "To the Egress". Look it up, it's a fascinating story. It might even give you a perspective on real life.
As soon as the straw is shorter than it's diameter it has one hole. When the length of the straw is longer than the diameter there are two holes. Where is the ad absurdum?
It's like a long streched Torus, it has 1 hole.
And then a DVD is like a flattened torus, and most people will say it has 1 hole
@@Mike-739 Good analogy. Defo one hole.
Yuj
But is it more like a sealed tube that has both ends cut off? If you take a long thin ketchup sachet and cut opposite ends off will most people say it has one hole or 2?
@@Mike-739 most people will say a Wiffle ball has as many openings as counted
Using the formula you provide, S X ("0",L), the 2-dimensional circle has "0" holes, since the L=0, and S X "0" = "0". You only introduce a "hole" when "L" becomes a positive number.
I am guessing 1. But really, the answer is: "It depends on how you define hole".
And no, we don't need profesionall mathematicans to explain this. Because you don't have to use the mathematical definition for "hole".
it depends how you define straw.
IMO, it depends on how the straw in manufactured (ignoring classical topology because this is a straw, not a hypothetical shell in Euclidean space). The most common way to mass produce a straw is to create one long cylinder and then cut at regular intervals. For this explanation, I'll define a hole as an opening created in a closed shell. Imagine an infinitely long straw. At that point, you would be forced to say there are no holes, as the surface is completely self-enclosed. If I cut it in half, making it only infinite in one direction, it would have one hole. In the same way, if I were to cut it twice, it would have two separately created holes. A less common method of manufacturing straws is folding a rectangular strip into a cylinder. In this case, the straw has no holes, as it is an undamaged rectangle morphed into the third dimension. For there to be only one hole, the straw would
a) have to be made by punching a long hole in a cylinder or
b) never be created, existing just because it does.
In the second case, we have traditional topology. All answers are equally right, depending on how you view this straw puzzle.
My first thought was that the answer depends on the definition of what we actually call a "hole".
Starting from the one-dimension space a "hole" could be defined as a discontinued object, a gap of a line.
In the 2D space, a hole can be easier identified, since we're more familiar with it. Well, a hole in the 2D space could be defined, as before, as a lack of space INSIDE a 2D object. For instance, think o a piece of paper with a hole in the middle. You wouldn't call it a "hole" if a piece of this paper was missing from the edges, right?
Staying in the same line, a hole in a 3D object would be a lack of material INSIDE a solid 3D object. Otherwise, a hole could be a called a bubble in the cake, or INSIDE a piece of cheese.
So from this point of view, a straw could have a hole if there was a discontinuity in its material or a "bubble" inside it. Therefore I assume that a usable straw has no holes or else you wouldn't be able to use it.
Is that your name or you've just typed math symbols there 🤔
oof it's and old comment not sure if you're alive
Yo
0 holes is also a good answer. Think of a straw that starts out as a sheet with 0 holes. Then you wrap a sheet into a cylinder and attach one end to the other. The sheet still has no holes, but now they inscribe a space inside it.
2 holes is definitely wrong any way you construct it.
"attach one end to the other" by doing that you created a hole topologically speaking
topology is really weird, and in there, if you connect something you're changing the object basically. If you connect a cylinder, you're making something different, which is an object with 1 hole
Why would the properties of a straw formed by joining two sides of a rectangle be any different from the properties of a straw formed by the topological product of a circle and an interval? Contrary to what your math teacher may have told you, it's the end result that matters, not how you got there. It's kinda like thinking the result of 2² is a square number, but the result of 2+2 isn't.
"Since S¹ (unit circle) has one hole..." A circle has a hole? I beg to differ.
A circle IS a hole technically speaking
No begging
Well you would most likely say a _donut_ has 1 hole, and technically speaking, a straw is almost just an elongated donut
@@Mike-739 What about a bent straw
@@NotABirdd think of a flexible donut which you can bend just like bent straw
I think we need a better definition of a hole!
A-hole
noun
1. a contributor to Buzzfeed
Lugh Summerson bwahahaha! Well done!
A hole is nothing surrounded by something.
Kool Boi like you head?
Jk just a joke
This comment is what more people should have said.
Even if it's not very clear in this video, "this object has n holes" is a perfectly defined topological proposition. Search for "homotopy between curves".
2016: Actually smart people
2017: *plays with fidget spinner*
2018: How many holes are in a straw?
2018: *chewing Tide Pods*
2018: Stephen Hawking dies
2019: *humanity ends*
2019: end game
this puts a smile on my face
2020: "I'll do it by myself" 🙂
I would say it depends on how the straw was made. Most plastic straws are a product of a long cylinder of plastic getting a hole punched in it and being cut and results in 1 hole. If a straw was made from a piece of plastic or paper that was rolled/folded and then sealed along the length, I'd say that it has 0 holes as it is not a circle/tube/cylinder, but a rectangular surface that has been rolled.
clever, but i don't agree.
The math solution was more math than I expected lol. Once you said topology I thought you were gonna show a straw is topologically equivalent to a donut, which people unquestionably believe has only one hole.
I have a follow-up question: if you drill a hole into the straw in the middle, how many holes does the object have now?
I'd say it is 3 then but not sure...
2. 1 through hole and 1 stopped hole. however if the new hole is drilled through then you have 2 through holes.
Topologically speaking, there is only one type of hole, which is a through hole that goes all the way from one side of an object to the other. In that case, as the video demonstrated, a straw has only one hole.
Many commenters claim that if you use the everyday definition of a hole, then there are two holes. We talk about things like holes in the ground even though the hole does not go all the way through the Earth, making it not fall under the topographical definition of a hole.
However, even under the colloquial definition of a hole that we use more regularly, there is still only one hole in a straw. This is because there are two types of holes. There are through holes, which go all the way through the object, and there are blind holes, which do not go all the way through. Holes in the ground are an example of blind holes. A straw does not have two blind holes, because the hole never stops. It goes all the way through the straw, making it a through hole. Straws would be completely pointless if they had two separate blind holes, because then the beverage would never make it from your drink to your mouth.
Side question for people who still think there are two holes:
At what point when you are sucking the drink through the straw does the drink switch from one hole to the other?
Colloquial basically means ordinary or familiar conversation. In other words, conversation that people use when they are just talking to each other in a casual manner. In a casual conversation, most people would say a straw has two holes, therefore, *by definition of the word colloquial*, a straw has two holes, in a colloquial context. In other words, many people say it has two holes, therefore, for those people, it does have two holes. Just like a large hill could be called a mountain because the locals call it a mountain. Or, a tomato is a vegetable because plenty of people call it a vegetable, or because it's used like one in cooking. Or that, for many people, Pluto is still a planet, because they call it a planet.
What if by just hole. You mean entrance? So.... Two entrances to one hole.... Huh
What about a hole that doesn't go through all the way? For example, if either I puncture a side of a cube without going all the way, or I take away one whole side of a cube, does it count as hole?
I could argue that a straw is just a really thin cylinder that is missing both sides. If it's just missing one side, does that count as a hole?
Epic Deception
A hole isnt always an entrance
to me, people trying to say its 2 holes are like flat earthers, who dont think and only use what they see at face value. its obviously 1 long hole when you actually think about it.
Take a piece of PRINTER paper. Stab it with a pencil. I think we can all agree it has one hole. Shape wise, the only difference between that paper and a straw is the straw is thinner, longer, and circular. Straws have one hole.
Joseph Stalin but what if you got that undamaged piece of paper and rolled it up into a straw... it originally had no holes and it remains undamaged so is there a hole?
Joseph Stalin if you do that at school, you'll probably be in a hole lot of trouble for wasting stationery.
gorillaau I have done it 3 times arguing this point. I use my own paper, and even if I didn't it wouldn't be a big deal.
Joseph Stalin Yes, as far as topology goes, the piece of paper with a hole in it is the same as a straw.
I was kidding about the paper waste earlier.
Nice one. I guess you could've mentioned that the (physical) straw is also topologically equivalent to a "donut" (torus). And also show some object with two actual holes.
xnick an object with actual two holes in it like a soccer ball ⚽️ it topologically equivalent to a doughnut as well you know...
I don't see how, Alan. Could you clarify your observation? For me, an object with two holes could be reshaped into the form of the number eight, "8", and anything with a single hole into the form of the number zero, "0". How can you continuously transform the soccer ball into any of those?
Your nose has two holes. LoL
actually it's not equivalent to a donut, though they both have 1 hole. A donut (torus) is equivalent to the product of 2 circles.
actually nevermind a torus has 2 holes, technically. A 'hole' in mathematics is what you'd call an equivalence of loops. The 2 holes in the torus comes from the two circles being producted.
Before watching the video, my opinion is that the answer is pretty clearly 1. If you drilled through any other 3D object from one surface to another, it would be one hole. It just so happens that this hole takes up like 99% of the volume and runs lengthwise through the long axis of the object.
Now, to see if Presh can make any compelling argument to *consider* other possible answers...
At the end of the video, I can see a small argument in favor of 0 (with the definition of "hole" being something that was not intended to be a part of the design). I can't see any in favor of 2 ("hole 1" and "hole 2" are clearly connected to each other and in fact it's impossible to specify the boundary between the two of them).
If you take the convex hull of a straw, there are two compact regions where the material of the straw is significantly distant from that surface. Two gaps in the surface.
Can't you say that a straw is just a plane that is folded in such a way that its long sides meet. This way the "hole" we see in the straw is just a byproduct so there isn't an actual hole. That's why i'd say a straw has 0 holes as it's the middle section is not part of the actual straw.
+Jose Hoyos
chinareds54 asked how people could argue for 2 holes. I gave an example of a way to get the number 2.
If you want to get into the physics of it, the straw, like almost all matter, is mostly empty space. When you talk about a "solid object", you're talking about either an abstract approximation, or a statistical feature of a large collection of subatomic particles. Depending on how you choose to model it, a straw can be a curved 2-dimensional surface, or a solid cylinder with a cylindrical tunnel passing through it leaving only fairly thin walls, or something with a complicated surface that's approximately a thin-walled, open-ended hollow cylinder, or...
+TTeaMeister Inspector Tea
You could say that, but that "long sides meet" means the topological properties of the shape change. In particular, if you run some elastic through a straw then tie the ends together so that it forms a slack loop, you can't get the elastic away from the straw without either breaking the loop, or breaking the straw, while with the plane folded so that the sides don't quite meet, you can slip the elastic out through the gap.
It's not like a hollow object which actually partitions space - but it does divide loops into different categories - those that are entangled with the straw and those that aren't.
If you polled topologists, I would expect you get different answers depending on whether they think a drinking straw is a cylinder with no end caps or a long torus. Those shapes have different topologies and have different numbers of "holes".
After watching this video I understand why "the media" avoid asking for math experts opinion.
My thoughts are along the lines of: if you start with a sphere, you need to cut two circular holes in it (then squish the middle portion) to get it to be a straw shape. The only way 1 hole makes sense is if a sphere has -1 holes, which is clearly wrong. Therefore, a straw has 2 holes.
Why would you start with a sphere though?
That was exactly my reasoning. Or start with the straw, blow it up in the middle to become a ball, after which you can argue it has 2 holes.
The straw has 1 hole, a glory hole
🤢
a--hole
**Winds up arms*
*GLORIOUS*
69696 subscribers with no videos challenge wish u luck with the challenge
I kinda see u everywhere
one??
P.S.- I haven't watched this video before commenting
I haven't watched- prob. won't.
BTW, I agree. 1.
Barbara Pierce 👍👍
WOW YOURE GENIUS!
Amoon RA 😁😁
Well its not 2 for a fact, and I would say 1 because of the definition.
YAY you said 1 also! And for the same way I thought!
Robeon Mew umm, replying to yourself?
+Robeon Mew you good?
did you watch the video? he said giess then continue. I'm talking to the video
01 - We can close one of the two holes and leave the other open
: so there are two holes
02 - If the straw is conical : we will say that one hole is larger than the other : so there are two holes
03 - What if the straw is Y-shaped : will we say that it has 2 or 3 holes (knowing that we only added one hole) : so the original one has two holes
wrong, wrong, and wrong again!!
So weird, the guys I work with and I were talking about this the other day! Now I know what to tell them.
Thanks!
lincoln
When a solid stick has a long longitudnal hole from one end to other then it becomes a straw. So a straw does not has holes it is the stick which has a hole
nicely put.
That's why you never get answers but only headaches from philosophical arguments ;-)
my gut reaction was one hole
I literally just thought of the straw as a donut and went “oh that’s easy, there’s one!”
Another argument for 0 holes is that you don't dig into the straw, you bend it around the air
which forms a hole?
It has a hole with two openings
Ancuta Drimbu but a hole always have 2 or more opening
Lancelot V
Dig a hole. Then tell me if you arrive at the other side of the planet.
Ancuta Drimbu, correct answer
# Bob Silver: According to Quantum mechanics, nothing is the world is tangible. So, there is no actual atom. Atom is not a solid thing. Atom consists of particles which are actually clouds/cyclones of energy.
a cave
Life biggest questions
1998: When will we fly?
1999: Probably 2019!
19 years later
2018: How many hokes are in a straw?
2019: ....
yeah except we had planes in 1998
What are hokes btw?
Three.
I wanted to piss everyone off, so I poked three holes in every straw at the McDonald's fountain machine.
txt brought me here
Me too! 🤣🤣🤣🤣🤣
Me too 🤣🤣
LMFAOOOOOOOOOOO
cooks
What if you bend the straw in the middle and put the "1" hole side by side?..
Does it become 2 holes?
Yes
I stand with 2dimensional holes
It all depends on your perspective(s) and what is the definition of a word or concept to you. What is a hole? (in your own point of view) The "one-hole thing" is based on a mathematical (dunno what branch) perspective, as he'd said earlier.
To my mind it has no holes and two openings, it is a hollow tube. A hole has a bottom which defines the term hole, as in dig a hole. If you dig a hole deep enough, or long enough you get a tunnel which is a tube. If you make a hole then that has no bottom, unless in your jeans or underwear, but the that is then not a straw.
you're describing a blind hole. there are blind holes and through holes. a straw has one through hole, as does a donut, as does a piece of paper with a hole in it, etc.
I think it is wrong say that there is a right answer to this question. There are different ways to interpret a straw and a hole mathematically, and a reasonable answer would acknowledge this and discuss the various interpretations.
Eli Damon You're wrong.
Eli Damon There are different ways to interpret a straw and a hole. There however is only one mathematical way to interpret a straw and a hole. Math does not deal with language and thus the only way to interpret a straw is as a topological shape. A hole actually does have a mathematical definition and thus is interpreted as such: "A hole in a mathematical object is a topological structure which prevents the object from being continuously shrunk to a point."
mathworld.wolfram.com/Hole.html
Let me tell you, atoms are mostly nothing, so there are indefinitely many holes
Jk
Lol gottem
AlexATG Topologically, no hole (nor bubbles) as the space is not bound (by a one dimensional line or two dimensional surface).
The idea that atoms are mostly empty is wrong actually
@Tien Dang they are mostly empty space
Who else is here bcs of txt's argument?
Me!!
I'm here because of the poll
Taking forward the example in this video, instead of stretching the 2 dimensional circle-with-1-hole to form a straw-length, we could consider the length of this straw being composed of an infinite number of such 2D circles stacked together. The straw then has an infinite number of holes! Now, since the group of the 2D circles result in a single straw, the group of those infinite holes collectively become 1 single hole.
On the other hand, if a paper sheet were to be rolled into a cylinder/straw, it could be said that there are no holes as there wasn't any to begin with, nor has the paper been punctured. Yes, there would be inner and outer 'space' within and around the straw.