Pythagorean Cup: the 2,500-Year-Old Practical Joke

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Typically attributed to 6th Century B.C. Greek mathematician and philosopher Pythagoras of Samos, the Pythagorean or "Greedy" Cup works like a normal cup when filled up to an inscribed line, but drains its contents when overfilled - teaching the user a lesson about overindulgence.
The cup works via the principle of the siphon, a channel that allows fluid to be transferred from a higher elevation to a lower one while passing through an even higher point. While siphons have been used for thousands of years, the physics of their operation are more complex and mysterious than they might appear, and have been the subject of much experimentation and scientific debate - even up to the present day.
SOURCES:
www.ncbi.nlm.nih.gov/pmc/arti...
web.archive.org/web/201307290...
www.phys.uhh.hawaii.edu/docum...
hawaii.edu/news/article.php?aI...
commons.wikimedia.org/w/index...
www.ncbi.nlm.nih.gov/pmc/arti...
www.sifouniospottery.com/pyth...
www.ancient-origins.net/news-...
davidson.weizmann.ac.il/en/on...
www.romanaqueducts.info/siphon...
eprints.qut.edu.au/41923/1/Th...
iopscience.iop.org/article/10...

[@TheChipmunk2008]

SOMEONE GET THIS MAN MORE SUBSCRIBERS

[@aerodesic1]

Agreed!

[@surferdude4487]

It blows my mind that a siphon can be used over heights beyond the vaporization pressure for a fluid more or less for the same reason that water can go below freezing without freezing.

[@deucedeuce1572]

It can? I thought there was a theoretical maximum that water can go up a tube (that's also tested) before is starts to boil and make any farther increase in height impossible. (I didn't watch the rest of this video to see if he mentions that... but I just read your comment and was wondering about that).

[@surferdude4487]

@deucedeuce1572 At sea level water can only rise about 30 feet by suction before it becomes a vapour. Just like at 0 C or 32 F, pure water freezes. Both are phase transitions. If something prevents the transition, water can seem to do things that defy the laws of physics. We already know about super-cooled water. This happens when water is below freezing but there are no nucleation sites for crystalization to begin, so the water freezes when it comes into contact with a surface or it is agitated. apparently, this super siphon works the same way. If there is nowhere for vaporization to begin, the water can remains a liquid at much lower tempertures. This is a good video. It's worth your time to watch the whole thing.

[@thierrystoll1487]

A practical application of the pythagorean cup is the dosing system of liquid detergent or softener in a washing machine. The detergent stays in the cup until water is overfilling the cup.

[@greenaum]

A better example of a toilet syphon is the one in the tank. Normally the water level in the cistern tank isn't enough to spill over the top of the syphon, but using the flush handle lifts some water so that it does. Once the water starts falling down the tube, towards the toilet bowl, it keeps flowing til the tank is empty. Once it's empty, air gets in, and you need to use the handle once more for another flush. Also the automatic flushers some urinals have, use a similar method. Here an elevated tank fills slowly, until it reaches the critical height and starts the syphon flowing, again until the tank is empty. So you get self-flushing urinals every so-many minutes or hours, depending on how busy the toilets are.

[@Nachiebree]

I thought the tanks worked differently? There's a rubber flap with a mass of trapped air inside, making it lighter than the water it's in. Flushing pulls up on it, causing it to float and allow the water to start draining out, and then once the water is all out of the tank the flapper can no longer float and finally falls down to seal again. Now, it isn't going to float once the tank fills with water again because now the water is all on top of it, pushing down on it with air underneath.

[@greenaum]

@@Nachiebree The mechanism that drains a toilet tank? Nah it's just a syphon, a tube, bent double, with air that gets trapped in the top part once all the water has left the tank, and the tube's large entrance is open to air that's now at the bottom of the tank. That breaks the syphon and stops the flushing, there's no flap or moving parts. Maybe you're confusing it partly with the float that refills the tank? I could be wrong if they've changed the design in recent years but last time I looked it was like I describe.

[@glennjames7107]

Not in North America, all common toilets utilize a flap or some other type of valve to "dump" the water from the tank, into the bowl. The flap is what releases the water from the tank when you pull the handle. There are several different high efficiency designs that operate differently, but they only make up a small percentage of the total toilets here.

[@greenaum]

@@glennjames7107 Oh OK, you learn something new every day!

[@Skorpychan]

If that was a siphon, then it wouldn't jam partway open to just a trickle flowing through the system. Which some designs are prone to, unless you reach in and push the flap back down or simply smack the cistern hard enough to jiggle the plunger.

[@bassett_green]

I wasn't expecting a science lesson from you, but this was great!

[@wayneyadams]

I would argue that it was not designed as a practical joke but as a teaching tool, there's a big difference.

[@caittails]

I don’t know, I’d argue that two things can be true at the same time.

[@asadabdulqaabir4006]

It´s not unheard that philosophers could be extremely wise and total arseholes at the same time.

[@wayneyadams]

@@asadabdulqaabir4006 What does that have to do with something being a joke or a teaching tool?

[@frankentronics]

I'm really impressed with your channel.

[@hrvstmn31]

This made me remember the videos Big Clive and mrmattandmrchay on something called an auto syphon. Syphons are weird, I'm Just gonna blame it on Bernoulli's principle, everything almost always comes back to Bernoulli's principle.

[@PinkDinoStorm]

You should have so many more views/subs man please keep making videos! :)

[@jfu5222]

Thank you, from your newest subscriber. Your channel is right up my alley!

[@holeshothunter5544]

Amusing that the Burger Calif-a in Dubai has no siphons. it's drained daily into a fleet of red tanker trucks. There is no sewer system for that huge shiny pig to be hooked up to. Big Joke, eh?

[@leepalmer3634]

I always learn something in your videos, even when I thought I had a grip on the subject. I love it

[@miinyoo]

Lol Galileo's shades on backwards.

[@iainwalker8701]

Commenting just to help give you a boost and hopefully new subscribers like me. Really fascinating content.

[@26betsam]

Excellent science lesson. Thank you.

[@donaldhoot7741]

Nature is MOSTLY a vacuum when you discount the tiny pieces of dust we float around on. Vacuum on! Great video!

[@RWBHere]

Thanks for these videos. You've earned another subscriber. 🙂

[@Allan_aka_RocKITEman]

Great video...👍

[@RedRiverMud]

Great video!

[@Yoel_Mizrachi]

Nowadays we usually wonder how no one tested Aristotle theory that light objects fall slower to the ground compared to heavy objects. Not till Galileo Galilei test it everyone naturally assume it was true. It is entertaining to see we too keep believing theories untested

[@oldspicey6001]

Amazing content

[@wayneyadams]

8:50 Pressure is one of those physical quantities that has bzillions of units depending on the field you in which you are working. Here are the ones I remember, and I have probably left some out. Torr, Pascal, barye, Bars, Millibars, mm of Mercury, inches of Mercury, PSI (pounds per square inch), Atmospheres. I think that is all of them.

[@lloydevans2900]

Technically you can subtract one of those, because the units of Torr and millimetres of mercury (often shorthanded to mmHg) are actually just two different terms to describe the same thing: If you have a pressure quoted in Torr, the same pressure in mmHg will be exactly the same number.

[@wayneyadams]

@@lloydevans2900 Actually, they are not the same. The torr is defined as 1/760th of an atmosphere. This is equal to 133.322 Pa (Pascals), while mm of mercury is the height of a column of Mercury that can be supported by the pressure acting on its base. There is a difference of 0.000015 % so for all practical purposes we assume them to be equal. They are used in different situations. The torr is typically, but not always used in low pressure work to measure vacuum pressure, while mm of mercury is used for atmospheric pressure studies. That is my point, different fields of study use different units to measure pressure resulting in pressure having the most diverse set of units of just about any physical quantity we measure. When in doubt, ask a Chemist (BS)/Physicist (MS) we deliver the best of two worlds. LOL

[@lloydevans2900]

@@wayneyadamsOk, and what is the height of a column of mercury supported by 1 atmosphere of pressure acting against a vacuum? 760 millimetres. So if 1 torr = 1/760 of 1 atmosphere, then 1 torr also = 1 mmHg, at sea level and with the mercury itself at a temperature of 0 degrees C. Yes, I know that the SI units authorities did some redefinitions of what an atmosphere of pressure officially is, which led to there being some tiny difference. But this is usually irrelevant unless you need to measure pressures to beyond 5 significant figures - which would be well within the established error bars of most measuring equipment you are likely to use. Oh, and by the way, I am a chemist, with both a degree and Ph.D in the subject. Anyway, just because different units are typically used for different situations does not in any way mean that they have to be. Especially for torr being used for partial vacuum pressures and mmHg being used for atmospheric pressure studies: Since these two units are essentially the same (the miniscule difference between them being insignificantly small), there is no good reason why you could not use either torr or mmHg for either of these situations. What you described here sounds more like a mixture of convention and tradition than any hard and fast rules. It's like how we use miles per hour as speed units in the UK, whereas most of mainland Europe uses kilometres per hour - there is no good reason why that has to be the case either. It boils down to "we have always done it this way up until now, therefore we will continue to do it this way". Unless there is literally no other possible way to do it, such conventions and/or traditions are a matter of politics, not science.

[@wayneyadams]

@@lloydevans2900 If you are really a Chemist with a PhD then you know that the two units are not the same as you stated in your rebuttal which is the point of my response. Regardless of the precision they are not the same units, and no amount of argument will make them so. As to your last point, you are the one who is touting tradition when you argue the two units are identical since that was the old, traditional way they were defined. You have also wandered off into the weeds in this post which was originally about the large number of units used for pressure, each depending on the field of study. Also whether the units are identical or not does not have bearing on what I said, because we are really measuring the same physical quantity just using different units to do so. It's like I joke about when boiling water. Water boils at 100 degrees in my lab flask, and 212 degrees in my cooking pot at home.

[@lloydevans2900]

@@wayneyadamsI'm sorry, regardless of the precision? You're going to disregard the aspect that actually makes the difference here? The level of precision required could not be more relevant, and we both know why: Are the units of torr and mmHg absolutely identical in every possible way and for every possible situation where they could be used? No. Are there situations where the negligible difference between them matters? Yes - but those are a vanishingly small minority. In every other situation, does the difference really matter? No. For the vast majority of real situations, torr and mmHg can be considered to be the same: They can be used the same way, and the only real difference is which unit label you write (or type) after the number when you make and record a measurement. Other than that, a difference which makes no difference effectively is no difference, is therefore irrelevant and can be ignored. The level of precision required should not be ignored, because it does matter and does make practical and real differences. For example, if you're doing some GCSE level geometry homework, you don't need a laser theodolite - a cheap plastic protractor is probably accurate enough. However, if you're in the business of making highly accurate Ordnance Survey maps, most likely using triangulation stations (aka trig points), the reverse is true. If you want a chemistry lab related example, consider any of the reactions we can do, where reagent A reacts with reagent B to make product C, but reagent B needs to be present in excess, relative to what a 1:1 stoichiometric ratio would be. Say for example you need a 10% excess: Would using a few percent more make any real or significant difference to whether the reaction works as intended, or any of the other variables, such as temperature, time taken, percentage yield and so on? Probably not. The quantity of reagent A used would define the upper limit on the maximum possible yield of the reaction, assuming it goes to completion and the yield is quantitative. So the quantity of reagent A used would ideally be measured to the highest accuracy possible, using the most accurate balance available. But the quantity of reagent B used would not need to be measured to the same degree of accuracy: Provided that at least a 10% excess is used, going over that amount by a few percent more is unlikely to make any real difference. Finally, no I am not "touting tradition" in the slightest. I am completely aware of what the difference is and why that difference exists. But I am also completely aware that for the vast majority of situations, that difference is negligible, insignificant, irrelevant, makes no real difference to anyone or anything and can therefore be ignored. But anyway, even if I was somehow "touting tradition", this would in no way erase or cancel out the fact that this is precisely what you were doing. Appealing to whataboutery is rarely ever a good faith argument and as such is entirely unconvincing. Can you show me where it is written that thou shalt never use mmHg when describing partial vacuum pressures? Can you show me where it is written that thou shalt never use torr when describing atmospheric pressure differentials? Preferably with some genuinely technical or experimental reasons for this - though I won't hold you to that last part because I don't see how there could be any.

[@BerndUlmann]

Brilliant!!

[@rayfisher2160]

At 17:33 you said that a vacuum can make extremely pure water - can I clean up my well water with a vacuum system?

[@Coconut-219]

As a few comments have pointed out already, liquids and gasses are both 'fluids' which can be subject to pressure (although liquid is not 'compressible' it can itself still be subjected to physical pressure) - I'm sure this has already been thought about to death by actual scientists so it can't be this simple, but my educated guess would be the fluid going down the descending leg has it's inertia and acceleration due to gravity which still creates a "lower pressure" sucking fluid up the ascending leg, even without the need for atmospheric pressure because the fluid itself is a medium capable of creating a pseudo-vacuum effect, something about the way traveling through a constricted tube affects the flow and it's tendency to not want to create voids? (Otherwise in these vacuum experiments there would be nothing stopping the fluid from simply running down the ascending and descending legs and leaving the tube empty).

[@TimSmyth23]

Is water not compressible, which is why oils are used in car brake circuits?

[@lloydevans2900]

@@TimSmyth23The reason why hydraulic brake circuits don't use water is much simpler than that: You probably want your brakes to continue working in winter when the ambient outside temperature drops below freezing point. Now you could argue that this would be easy to prevent by mixing some antifreeze with the water (ethylene glycol, propylene glycol, glycerine, alcohol, glucose syrup or honey all work for that purpose), and that would be true, but hydraulic brake systems also suffer from the opposite problem: With heavy brake use, the fluid gets rather hot, and you don't want it to start boiling in the circuits, because that could cause all manner of problems. So the brake fluid not only must not freeze, but it also must not boil - this is the other reason why you don't just use water. Some synthetic brake fluids are silicone oils, since these have extremely wide liquid ranges (very low freezing points as well as very high boiling points), and are chemically rather inert - they don't decompose or react with anything under the conditions they are subjected to during use. This gives them the longest service life of any synthetic brake fluids - they are more expensive to buy (in terms of price per unit volume) but can result in long term savings since they don't need replacing anywhere near as often. There are alternatives to silicone oils though, the most common being polyethylene glycols - many different varieties exist, and brake fluids are often a mixture of several varieties. They are much cheaper to make, but are not as chemically inert as silicone oils: For a start, they are extremely hygroscopic, so will absorb water vapour from the atmosphere if not kept in an airtight container of some kind. This can be a problem if the brake fluid reservoir in a car is not sealed - when the fluid absorbs water, this lowers the boiling point and can cause some chemical decomposition of the fluid over time, degrading the physical properties and eventually requiring replacement. If you want to know whether a sample of brake fluid is of the silicone oil type or polyethylene glycol type, there is a very simple test you can do: Just add a few drops of the fluid to a glass of water - if it does not mix with the water and forms an oily layer floating on top of the water, it is most likely a silicone oil. However, if it completely mixes with the water, it is most likely some type of polyethylene glycol, since these are all water-soluble.

[@NSBarnett]

Very nice!

[@craigsawyer6453]

So, why don't we put a Pythagorean "valve" at the lowest point in all homes to evacuate any heavy non breathable gasses that might otherwise kill people?

[@RWBHere]

05:00 You d mention that the cistern also contains a second syphon which controls the amount of water which is flushed.

[@jdwilsun]

Wow thank you! Amazing!!!!!!!!!!!!!

[@rayfisher2160]

Thank you for not covering up the Artwork .

[@edhodapp6465]

My high school physics teacher made something similar, but used the cup handle for the siphon. He called it a, “greedy cup.” I have one of them. One of my prized possessions.

[@jp-um2fr]

In the UK due to its name the term 'ball cock' is now passed over to toilet valve or something else. It also means of course that all male chickens are called - male chickens.

[@KenMabie]

Pick up lines that don't work "Aye girl I'm gonna fill your vacuum"

[@j7ndominica051]

Could the cup drain when tilted and the level was temporarily increased on one side of it? A siphon could be used to draw clear liquid from a container through a tube without disturbing sediment or a stratum of higher density on the bottom of it.

[@greenaum]

It's definitely intended as a practical joke, if it were meant for filtering, the tube wouldn't spill out of the bottom. The Babylonians drank beer through a straw, because sediment would sink to the bottom of whatever jug-thing they were drinking from. But that sucked from the top, not bottom. Besides, you wouldn't drink beer from such a nice, and small, vessel as this cup. From looking, seems like tilting the cup far enough to start the syphon going with a lower level of fluid would end up spilling over the side anyway.

[@j7ndominica051]

I didn't mean to suggest that the Pythagorean cup should be used for practical applications. The video expanded to discuss how syphons function in general. My mother used to cook a fruit "extract," and syphon off clear liquid into bottles using a rubber hose without a sieve. I don't remember exactly why it was done. I suspected that the cup might drain even if the user filled it to the limit without overstepping it.

[@johnwax9759]

Would cups like that be available for sale? Great gift!

[@PeterEdin]

So that's how the fabric conditioner compartment works on my washing machine. 😮😊

[@dieseldragon6756]

Yep! Kicked into action by the water jet above the softener compartment triggering the siphon! 😇 You can experiment with this if you like: Remove the powder drawer - It's normally held in by a single clip on most British machines - Fill the softener compartment to the max line with coloured fluid, then _slowly_ pour clear water into the compartment until the siphon kicks in. 🌊 Using coloured fluid will allow you to see how the softener and the water mix during this stage, and whether the fluid goes in as-is or if the water dilutes this in the process. 😇

[@PeterEdin]

@@dieseldragon6756 Done that 😃

[@xixi560]

"I won't ask why" 🤣🤣

[@jakepatterson2798]

Turn up your volume at 20:50

[@Merlin3189]

Yes, science makes predictions, but they are quantitative. Both "theories" are perfectly correct if you calculate quantitative predictions.

[@funkmon]

The first known use of "hoser" was in SCTV. It is a made up term by Rock Moranis and Dave Thomas for fun to emphasize or poke fun at slightly different American and Canadian slang. There is no etymology beyond this. Any proposed etymology is entirely made up. The word is exclusively used in imitation of the two characters, unless evidence has changed since I last looked into it.

[@rogerszmodis]

For omnipotent beings who should have no problems whatsoever gods sure get triggered easily. They’re like tumblr users with lightning power.

[@davidliddelow5704]

I’m real confused here. I don’t see how siphons are not explainable with regular fluid pressure theory.

[@davidliddelow5704]

The weight of a fluid creates a pressure gradient. The deeper you are the higher the pressure. If you raise water in a tube you therefore can create a negative pressure gradient. If you take two tubes of water from two bodies of water of different height you will have different gradients. If the tubes are merged, there will be a pressure difference which will cause the water to flow.

[@davidliddelow5704]

Atmospheric pressure does matter but since air is light the pressure gradient is small and air pressure is effectively uniform at the scale siphons are built at.

[@davidliddelow5704]

You can’t trick a siphon by making one tube thicker than the other because tube thickness does not affect the pressure gradient. Tube thickness does affect flow rate because flow rate is equal to pressure times the cross sectional area of the tube. Thinner tubes also impart friction on the fluid which manifests as a pressure drop across the length of the pipe and hence a lower flow rate. All this is again, basic pressure theory.

[@SofaKingShit]

I prefer fart cushions. Stained robes suck.

[@ElectraFlarefire]

Only american(And it seems Canadian) toilets do the syphon thing! (Maybe other countries?) But Aussie dunnies don't work that way, if you fill them slowly, they just maintain that same level. You need the big RUSH of water of a flush to get everything through. :)

[@dieseldragon6756]

Do Aussie ones have a large bowl, no obvious cistern and a simple lever valve on the top of them? 😇 If so, filling the bowl slowly causes the water to run slowly through the U-bend, avoiding the siphon effect coming into play. If you pay careful attention to _where_ the water from the valve enters the bowl (You'll note it jets _up_ into the U-bend, and causes the water and waste above to be siphoned into the drain) you'll see how this American type differs from - But also works in largely the same way as - The European type. 😇

[@ElectraFlarefire]

@@dieseldragon6756 Norman high speed flush cistern. A common style of toilet has the pipe out the back(Just high enough to provide the airlock) with no downwards loop, and they work fine. Even with no plumbing attached(had one in the back yard ). As well as the waste pipe of the downwards ones being 90mm+ in size, so there is no way a flush from a 40mm cistern pipe can fill it enough to start a syphon. And finally, the water level never changes through the whole cycle, there is no 'fill, drain and fill'.

[@dieseldragon6756]

@@ElectraFlarefire Sounds a lot like the toilets we have in the UK, then. The action of the flush doesn't really siphon the whole lot away, but pushes the waste around the U-bend and into the drain. 💩 The U-bend is a hydraulic lock, and mainly there as a means for keeping nasty drain smells from filling the bathroom. (It's also why dunnies used to be sited in the garden where possible, rather than in the house) 😇

[@wayneyadams]

Decades ago I worked in the Chemistry Stockroom at the University of Miami as part of my financial aid (yes, in those day we were not spoiled snot nosed elitists who expected the government to pay our debts). We had this one girl who was trying to siphon ethanol (it was not denatured) from a five-gallon container into one-gallon jugs. The container was on the floor and the jugs were on the shelf above it. We watched in amusement as she struggled to get the siphon to work. Eventually someone (not me) took pity on her and explained what she was doing wrong. A good time was had by all, except the girl, of course.

[@apo_chromatic]

I don’t think you understand the degree to which the price of a college education has increased over time. Since 1975 the cost has nearly quintupled for a public, 4 year university, even after adjusting for inflation. The majority of the people you describe here do, in fact, work throughout their time in college. This point of view is so out of touch that you might as well hand someone a quarter and tell them to go to the movies.

[@maxpayne2574]

Yes long gone are the days when a person could work and save through high school and for a year after then pay for collage while working a part time job. Great analogy here's a nickel go buy a news paper. @@apo_chromatic

[@getmeagator]

Air AND water are both fluids. Stop referring to the liquid in the bottles as "the fluid." There are TWO fluids in this experiment.

[@urlocalhistorybuff316]

Dude, you don’t need to be a jerk

[@getmeagator]

@@urlocalhistorybuff316 or perhaps you could consider NOT calling people names. Am I the A-hole for posting facts?

[@urlocalhistorybuff316]

@@getmeagator erm actually ☝️🤓👉

[@richardmillhousenixon]

​@@getmeagatorFor posting them in the condescending way you did? Yes, you are the asshole.

[@oldspicey6001]

Bro this was not the way to act today

[@dieseldragon6756]

As I was watching this, the first _General Purpose_ siphon that came to mind was of course that in the standard European design of lavatory. Funnily enough; If you think carefully about the physics at work in an _American_ lavatory (The type with a large bowl and no obvious¹ cistern) the latter type achieves its work with only one siphon and a lot less complexity/points of failure compared to the European type! 🚽✅🙃 But if I was asked to speculate about what makes a siphon work, I'd agree with the _pressure equilibrium_ explanation, with attention paid to the fact that siphons might exploit *both* air pressure _and_ cohesion in varying degrees according to the circumstance at hand, resulting in one increasing in magnitude to compensate for any shortfall in the other. ⚖ (Possible test: Will a siphon still function in a vacuum if the liquid in the siphon has an extremely low cohesion factor? 🧪) (¹ - The American design _does_ in fact have a cistern, but it's much less obvious than the one on a European toilet. In this case the bowel _doubles-up_ as the cistern - The jet of water released into the U-bend by the valve kicks-off the siphoning effect, causing the water to push the waste away in front of it - And this is done to reduce space, part cost and complexity, and can be advantageous in areas with low water head pressure. 😇)

[@klausbrinck2137]

The siphon in a Lavatory is passive/coincidental, that means it does something, but not as a siphon, instead it just keeps the sewage-stunk out of the bathroom. Just like the "S"-bend in the toilet-bowl does. The S-bend has 2 functions, and thw 1st one of them is to siphon. The Lavatory-siphon fullfills solely the 2nd function, and not the siphoning-function.