Physics for Doofuses: Why Beds Exist

I promised to blog more about research, and I will.  Unfortunately, in the one week between my world tour and the start of the fall semester, I’ve been spending less time on quantum complexity research than on sleeping on a new mattress that I bought.  This has provided ample time to ponder the following question, which I’ve decided to add to the Shtetl-Optimized Physics for Doofuses series:

Why is a soft bed more comfortable than a hard one?

At first glance, this question seems too doofusy even for a series such as this, which makes its target audience clear.  The trouble is that, while perfectly reasonable-sounding answers immediately suggest themselves, several of those answers can be shown to be wrong.

Let’s start with the most common answer: a soft bed is more comfortable than a hard bed because it molds to your shape.   The inadequacy of this answer can be seen by the following thought experiment: lie on a soft bed, and let it mold to your body.  Then imagine that the bed retains exactly the same molded shape, but is replaced by ceramic.  No longer so comfortable!

Ah, you reply, but that’s because a ceramic bed doesn’t change its shape as you shift positions throughout the night.  But this reply is still inadequate—since even if you’re lying as still as possible, it still seems clear that a soft bed is more comfortable than a hard one.

So it seems any answer needs to start from the observation that, even when you’re lying still, you’re not really lying still: you’re breathing in and out, there are tiny vibrations, etc.  The real point of a soft bed is to create a gentler potential well, which absorbs the shocks that would otherwise be caused by those sorts of small movements.

(I was tempted to say the point is to damp the movements, but that can’t be right: trampolines are designed for minimal damping, yet sleeping on a trampoline could actually be pretty comfortable.  So the essential thing a bed needs to do is simply to make way in response to small movements and vibrations.  How hard the bed tries to spring back to its original shape is a secondary question—the answer to which presumably influences, for example, whether you prefer an innerspring or a memory-foam mattress.)

So then why aren’t beds even softer than they are?  Well, the limit of infinite softness would be a bed that immediately collapsed to nothing when you lay on it, dropping you to the floor.  But even before that limit, a bed that was too soft would give you too much freedom to shift into awkward positions and thereby cause yourself back problems.  This suggests an answer to a question raised by a colleague: is the purpose of a bed to approximate, as well as possible on the earth’s surface, the experience of sleeping in zero gravity?  Unless I’m mistaken, the answer is no.  Sleeping in space would be like sleeping on a bed that was too soft, with the same potential for back problems and so forth.

Given that lying in bed is normally the least active thing we do, I find it ironic that the only reasons we lie in bed in the first place (as opposed to, say, on steel beams) are dynamical: they involve the way the bed responds to continual vibrations and movements.

I’ll be grateful if knowledgeable physicists, physiologists, or sleepers can correct any errors in the above account.  Meantime, the next time your spouse, partner, roommate, parent, etc. accuses you of lounging in bed all afternoon like a comatose dog, you can reply that nothing could be further from the truth: rather, inspired by a post on Shtetl-Optimized, you’re struggling to reconcile your modern understanding of the physics and biology of lying in bed with the prescientific, phenomenal experience of lying in bed, and thereby make yourself into a more enlightened human being.

67 Responses to “Physics for Doofuses: Why Beds Exist”

1. Peter Turney Says:

Unless I’m mistaken, the answer is no. Sleeping in space would be like sleeping on a bed that was too soft, with the same potential for back problems and so forth.

“Dr. DANIEL BARRY (Retired NASA Astronaut): Oh, sleeping in space is fantastic. I mean, you just float, and it’s perfect, and it’s wonderful. It’s fabulous.”

2. NoJoy Says:

Great post. I look forward to the answers.

One niggle. The verb “lay” is transitive–it’s what a hen does to an egg or a person does to a book or their body. The verb “lie” is intransitive–it’s what a person, book, or body might do in a bed (or even a hen if it didn’t sleep standing up). The real fun comes in the conjugations: lie/lay/lain, lay/laid/laid.

3. Vipul Says:

I think the right explanation for why soft beds are comfortable is that the upward force applied (in response to gravity; in other words support) by such a bed would be “uniform” throughout the contact area between the bed and the body. So each part of the body undergoes very minimal upward force applied. This explains why sleeping on a needle for example would be the least comfortable.

I think it would be very hard to achieve this property with a hard bed by trying to mold it according to your body shape. The experiment you should think of is the following: make a small hole in the bed at an adversarially chosen place. If the bed now becomes somewhat more uncomfortable (i.e., pressure on rest of the body area in contact increases), then the bed has to be comfortable to start with.

4. Scott Says:

NoJoy: Cringe—thanks so much! I’ve corrected the error throughout. While I was sure that this post would make me look foolish, I didn’t know that at least part of the reason would be grammatical… 🙂

5. James Says:

I would imagine that the majority of back problems seen on a mattress are a combination of the downward force of gravity combined with either too much tension/too rigid a material on which you lay or not enough tension/rigidity. But, it is a combination where gravity is the main reason for too large a deficit or too great a surplus in the rigidity of a material.

A simple thought experiment: imagine being in gravity laying atop a material that is either too hard or too soft. Now imagine that gravity is taken away; if the material was too hard and the downward force pushing you against this material is alleviated you will no longer feel as if your back is taking the brunt of the pressure. If you are against something too soft, which is not accommodating enough in terms of support, the need for that support is also alleviated. If there is any force pushing away (as would normally exist in any material used for a bed, springs, memory foam, etc.) your body would naturally shift into the position it is most comfortable in.

The link above about the astronaut sleeping in space (along with other stories from the space program) should confirm that sleeping in null gravity is actually quite nice.

6. James Says:

Ah, grammar, my mortal enemy, my greatest weakness!

7. Scott Says:

Peter #1: Interesting, thanks! I’m curious: are these reports consistent, or have other astronauts reported not liking sleeping in space?

(Incidentally, as far as I remember, this is the first time in my adult life that I’ve been curious about a scientific question that plausibly requires a human space program to answer… 🙂 )

8. Scott Says:

For whatever it’s worth, some of the best sleep I’ve ever had has been in moving vehicles, and probably the optimal bed for me would be one that rocked back and forth as if it were on a ship. But maybe I’m unusual that way.

9. Scott Says:

Vipul #3: Yes, I thought about that! The desire for uniform pressure could be seen as the basic reason why you’d want a bed that “molds to your shape.” But as I said in the post, I still don’t think that can serve as a full answer, since a hard surface “pre-molded” to your shape still wouldn’t be particularly comfortable.

10. Bill Mill Says:

Scott, I don’t think it’s unusual to enjoy sleeping on a ship. David Foster Wallace, just for one example, mentions in “A Supposedly Fun Thing I’ll Never Do Again” that one of the few positives of the cruise ship he’s on is how nice sleeping on a ship is.

I too love sleeping on a boat. (In a car, not so much, but just because I’m tall and have difficulty finding a comfortable position, I theorize.)

11. Mary Says:

I think there’s a missing piece here — bones and soft tissue. If you lie on a hard surface, your skin and muscles and blood vessels and nerves will be compressed in between your hard bones and that hard surface — even if that hard surface is “molded to your body” (whatever that means, considering the body largely consists of little bags of water that take whatever shape you force on them.)

I feel like there should be a force diagram, the bones (and whatever’s stuck to them) pressing down on the soft tissue of your back with force F=m*g, and an equal and oposite normal force upward from the hard floor acting on the other side of the soft tissue. Squish! Ouch!

On the other hand, if you’re lying on a matress on the floor, it’s a more complicated force diagram. The matress can probably be modelled as a spring which is pushing upward with a force F=-k*x, where x is how much you’ve compressed it. It’s a crappy model, but let’s pretend your soft tissue is also a spring with a different spring constant “K”. It’s going to push up on your bones with an additional force F=-K*y (where “y” is how much you’ve compressed your soft tissue.)

I’m at work and even if I weren’t I’d probably be too lazy to carry this analysis all the way through, but I think the answer has got to be that the soft tissue doesn’t get as squished when there’s something squishable underneath it.

The model system I’m thinking of would be a soft spring (your soft tissue) supporting a mass above the floor, or a soft spring resting on a harder spring (the mattress) supporting the same mass above the floor. In the second case, wouldn’t you think the soft spring would compress less?

And that’s why I think we need cushions, for completely non-dynamical reasons.

12. gowers Says:

“… since even if you’re lying as still as possible, it still seems clear that a soft bed is more comfortable than a hard one.”

Not to me it doesn’t. There might be a problem with the texture of a hard bed, but I don’t find it obvious that if I lay very still on a wooden bed moulded very exactly to my shape and lined with some kind of cloth (thick enough to give a normal bed-like texture but thin enough not to provide any softness), then I would be able to tell the difference between that and a soft bed. Or rather I would, but only because I wouldn’t be able to get into position by just lying down and rolling about until I felt comfortable.

A thought experiment: suppose one were to lie in a bed made of a material that started out soft and gradually hardened. If one lay still, would one notice the hardening? It seems obvious to me that one wouldn’t.

13. Mary Says:

(Also, I have slept on a trampoline — we had one when I was a kid. A little uncomfortable since your middle ends up sinking lower than your head and feet and colder than sleeping on the ground… And the bounciness does tend to wake you up…)

14. sst Says:

> Why is a soft bed more comfortable than a hard one?

That is a strange question for a mathematician to pose being as how “assumptuous” it is. The answer is – it is comfortable to *you* because you are used to it. Where I come from a lot of people sleep on the floor and would be unable to even fall asleep on a soft bed.

15. Mike Cane Says:

I guess waterbeds would fall under the prior Comments about beds on a ship?

16. Scott Says:

sst: Where do you come from, and is there at least a mat on the floor? (If so, one could ask the analogous question: why is a mat more comfortable than, say, a hard wooden surface?)

Of course, it’s interesting that different cultures seem to have different preferences regarding the amount of softness of sleeping surfaces—something I’m reminded of the “hard” way (nyuk, nyuk) every time I go to Europe. I confess I have trouble understanding this phenomenon, since the notion that we only like sleeping on what we’re used to simply doesn’t jibe with my experience. For example, Tempur-Pedic mattresses are very different from anything I grew up with, but the first time I tried one I thought it was great.

17. sst Says:

@scott – India, and you’re right, degrees of softness vary with cultures, but now I can turn the question around – ‘why is a hard bed more comfortable than a soft one?’, and that’s a more appropriate question for many people, but to you it obviously sounds absurd. All I ask for is precision in the question posed 🙂

18. tdmg Says:

Two cents:

Like a couple of people above seem to say, I would personally find an infinitely adjustable hard surface (though I’m not exactly sure what that would mean, both malleable and resistant?) to be ideal sleeping surface.

19. Carl Says:

FWIW, I grew up in America but prefer to sleep Japanese style: a thin mat on top of tatami flooring. Also they have hardish pillows. They’re pretty good too, but take more adjusting to.

20. Raoul Ohio Says:

There is a huge industry competing to make beds that buyers find comfortable. Most of them have lots of internal structure, springs, and who knows what. Does anyone know any researchers in the bed world, that could spill some secrets about what works?

Personal sleeping preference is probably widely varied. I like firm beds. I can’t imagine sleeping on a boat. I love canoes and kayaks, but when on a boat you can stand up on, I can’t wait to get off, even in an LA marina, tied to the dock. This is probably something you get used to. Or, maybe not.

21. AK Says:

Fantastic discussion….off to bed now.

22. chazisop Says:

I believe it has nothing to do about hardness or softness, but about a “calm state of mind” , which we all know is necessary to be able to sleep. Just before sleep, the body needs input with no sudden changes or extreme values :

Most people can’t sleep with a bright light on, where some cannot sleep in total darkness, but I believe none can sleep with a blinking light above them.

Known sounds , repeatable or low frequency (this has to do with the mechanics of the brain) are preferred for sleeping (think of the ocean) . That’s because ears work a bit different than eyes.

So, making an analogue, touch should be at a local maximum or minimum, according to the person’s preferences, so that no sudden changes are perceived. Don’t you hate it when a spring has gone loose or you can’t find a “comfortable spot” ?

I also believe a great part to this conditions is experiences we had before we were born , as well as early childhood.

23. wolfgang Says:

Scott,

I would say the main purpose of a good bed is to maximize the area which supports your body weight.
The optimization has to be a dynamical process and cannot be static because people move and breathe etc.
(Therefore I do not accept your thought experiment, because replacing a comfortable bed with a hard surface *without changing the surface of your body* is close to impossible and therfore we do not know how this would feel.))

A hard surface is uncomfortable because the body is supported in a few points only which quickly causes discomfort.
The ‘ideal bed’ is dry sand at a beach or salt water, e.g in the Dead Sea or in an isolation tank.

Floating freely in space is not the ideal solution because human beings are not used to fall asleep during free fall (which is what ‘floating in space’ really is).

Finally, your argument about absorbing shocks and small, quick movements might apply in certain erotic situations, but does not really play a major role when people sleep imho,
but we shall not discuss these issues on this G-rated blog.

24. wolfgang Says:

by the way, another important feature is the heat capacity of the material, because we do not feel comfortable if our body heat dissipates too easily.
this is an impoprtant reason why steel plates do not make for comfortable beds.

25. Scott Says:

‘why is a hard bed more comfortable than a soft one?’, and that’s a more appropriate question for many people, but to you it obviously sounds absurd

No, it doesn’t! Indeed, if you reread the post, you’ll see that I discussed the question of “why not an infinitely soft bed?”, which is equivalent to your question at an appropriate hardness level (modulo the imprecision of the English language). The conclusion was that some finite softness value is optimal, and the very interesting question you raised is why that value seems to be different for different cultures.

26. wolfgang Says:

>> why that value seems to be different for different cultures.

i suspect it has to do with temperature and humidity.
a very comfy bed will isolate large parts of your body surface and this is not so good in a hot and humid atmosphere.

also, human beings are creatures of habit. once you get used to relatively hard mattresses then you wont change quickly ..

27. Scott Says:

Wolfgang:

I would say the main purpose of a good bed is to maximize the area which supports your body weight.
The optimization has to be a dynamical process and cannot be static because people move and breathe etc.

That’s consistent with what I understood.

Therefore I do not accept your thought experiment, because replacing a comfortable bed with a hard surface *without changing the surface of your body* is close to impossible and therfore we do not know how this would feel.

Wait, the whole point of a thought experiment is that we don’t need to have felt it to reason about how it would feel! (Cf. Einstein, freely falling elevators.) 🙂

The underlying question seems to be the following: does the definition of the concept of “softness” necessarily make reference to dynamics—i.e., to the response of the bed to small perturbations? If I understand correctly, you and I are saying the answer is yes, while Mary is saying the answer is no.

28. Scott Says:

The ‘ideal bed’ is dry sand at a beach or salt water, e.g in the Dead Sea or in an isolation tank.

I’ve never slept on loose sand (or in the Dead Sea). Has anyone here done so, and can they report on how it felt?

29. wolfgang Says:

>> the whole point of a thought experiment is that we don’t need to have felt it to reason

but while you can ‘think through to the end’ the consequences of Albert’s thought experiments (after all they are only about simple things like relativity, quantum theory etc.)

you cannot ‘think through to how something would feel’ in a complicated situation like somebody lying on a bed made of conrecte perfectly fitted to your body’s shape.

30. wolfgang Says:

>> I’ve never slept on loose sand (or in the Dead Sea).
but you have slept in salt water for the first 9 months of your life and i bet you liked it (even though you may not remember it) and slept like a baby.

31. Scott Says:

you cannot ‘think through to how something would feel’ in a complicated situation like somebody lying on a bed made of concrete perfectly fitted to your body’s shape.

Why the hell not? After all, the whole assertion is that it would feel the same as a soft bed (assuming the concrete somehow instantly re-adjusted itself as you moved around), and we know how that feels.

32. Scott Says:

but you have slept in salt water for the first 9 months of your life and i bet you liked it (even though you may not remember it) and slept like a baby.

True, but my preferences were different in some fundamental ways back then (for example, I didn’t breathe air, and I ate through my belly button, neither of which I’d enjoy much today).

33. wolfgang Says:

>> while Mary is saying the answer is no
i think Mary is making an important point about the dynamics i.e. how the ‘optimization’ takes place in a very simplified model.

and saying that it is only about maximizing the surface is probably to simplistic. It is about homogenizing the pressure etc.

34. wolfgang Says:

>> the whole assertion is that it would feel the same as a soft bed

but then all you do is repeat the assumption: you assume it would feel the same therefore you assert it has to be the same.
you did not reach your conclusion from ‘thinking through to the end’ what happens, from the concrete to the surface, through your nerve cells to your brain etc.

this is different from a ‘thought experiment’ in theoretical physics where one uses the known laws of physics to think through to the end a situation which cannot be done yet in real experiments.

35. wolfgang Says:

ok, here is a different thought experiment, one which we can think through to the end i think.
take an old fashioned bed with springs and some textile on top of it.
You lay down on it and quickly the system will reach some equilibrium (if you dont move too much).
Now we fix the springs somehow in place, so that they become completely stiff.
I assume that this will not make any difference to your comfort as long as you don’t move.

The reason we can ‘think through’ this particular thought experiment is that we dont have to worry about the interface between textile and your brain (which stays exactly the same). We only have to consider the simple springs, which we understand well.

36. PTA Says:

It’s just uniformity of support, and if you were *perfectly* still an arbitrarily hard surface molded exactly to your body would be perfectly comfortable. Hardness doesn’t play any role if there is no deformation.

37. Mary Says:

Scott’s right — I was saying the definition of soft doesn’t necessarily have to do with dynamics. A ‘soft’ spring compresses more under a given load in equilibrium than a hard spring. I was postulating that our “springy” soft tissue would get compressed less if you were to lie on a soft surface than if you lay on a hard one, in equilibrium.

This page conveniently has a force diagram and the equations of motion… Set m1=0 (for simplicity.) And on the right side of the y” equation, add an extra term +m2*g to represent gravity… Solve for the equilibrium positions by setting x”=y”=0. The answer we’re actually looking for is actually y-x, the amount by which the spring with constant k2 (your soft tissue) is actually compressed. By my calculation, that’s y-x = m2*g/k2, which is independent of k1.

In other words, it appears that in this toy model at least it doesn’t matter how soft what you’re lying on is, how much your soft tissue gets squished depends only on how soft it is and how much weight it’s bearing… (Also x = m2*g/k1, so how much the mattress gets compressed doesn’t depend on how soft you are either, which to me is at least a more intuitive answer…)

There’s still the issue of pressure points, though… If you’re supporting a large amount of your body mass on one corner of your pelvis, that’s still going to compress the soft tissue under that corner a heck of a lot more than if you are lying on a deformable surface, which can curve underneath you so that your legs and torso to stay in contact with the surface and their weight is spread out over a greater area instead of all being borne under the point of your hip.

But yes, as Scott said, if you had a hard surface that was molded properly, that would still relieve those pressure points for some unique static case, so I suppose the issue really is that we need to change positions during the night (or risk bedsores) and only a soft surface will take our weight evenly in a variety of different positions. So I guess it is a dynamics problem — sort of. But I’d still rather say it’s a statics problem and the issue is that a hard (but molded) surface is a statics problem with only one (comfortable) solution, while a deformable surface has many (comfortable) static solutions.

As for why some people like to sleep on hard surfaces and whether a surface can be “too soft”… I think soft surfaces resist your night-time movements, making it more difficult to roll over in your sleep or change positions. Those who are used to sleeping on soft surfaces might find that they can exert that extra effort in their sleep without waking themselves up, and they probably don’t need to move as often anyway in their sleep, since the pressure points are not as bad. But those who are used to sleeping on a hard surface might be adapted to shifting positions frequently (to relieve pressure points) and might not be used to exerting the greater effort required to shift on a soft mattress. Attempting to shift positions in their sleep might wake them up partially, preventing a good night’s rest, or they might simply move less in the night than would be ideal for them, and wake up sore because they slept on the same pressure points too long.

That wouldn’t apply to astronauts in space or any of us in the womb (because there aren’t any pressure points to relieve or significant resistance to shifting positions), but would apply to sleeping on soft sand or a water-bed (because although in those cases you don’t have a lot of pressure on any one point, you still have some, and it would take a lot of energy to move and relieve them).

If we’re adapted to a certain frequency of movement and a certain amount of effort required to move in our sleep, we probably find it hard to to sleep on a surface that requires either more frequent movements (soft sleeper shifting to hard) or more effort to move (hard sleeper shifting to soft.)

I’d also hypothesize that people who weigh more would prefer a soft mattress, since they are more vulnerable to high-pressure pressure points, and since it takes more effort to roll over anyway in that case so they are probably more static sleepers. Since people in India are on average less massive than people in the US, it might not be so surprising that they prefer sleeping on harder surfaces. (This fits with my personal experience of being pregnant over the last few months — the bigger I get, the bigger the stack of pillows under and around me gets. I feel for pregnant Indian women trying to sleep on a mat on a hard floor, even if they’re used to it!)

38. MattF Says:

Well, speaking as a physicist, I don’t think this is a physics problem. I think going-to-sleep is a highly non-linear process that’s triggered by a large number of small effects that vary by individual and by culture.

I’d like, at least, to have some understanding of the physiology of going-to-sleep before looking at the triggers– and I don’t think we’re even near that.

39. Scott Says:

MattF: If I can channel John Sidles for a minute, going to sleep is clearly an interdisciplinary challenge for the 21st century, which combines aspects of physics, biology, culture, and psychology (and of course, Kahler manifolds and quantum systems engineering as well… 🙂 )

40. Scott Says:

Mary, thanks so much for your thoughtful posts!

41. wolfgang Says:

>> soft surfaces resist your night-time movements, making it more difficult to roll over in your sleep or change positions.

great point!

I think Mary’s comment above really sums up the theory of beds very well.

42. PTA Says:

Mary: “I was saying the definition of soft doesn’t necessarily have to do with dynamics. A ’soft’ spring compresses more under a given load in equilibrium than a hard spring.”

“Softness” and “compression” make no sense without motion. You need at least two data points to define them, so there has to be a change in some dimension of the object whose compression or softness you want to define.

43. Ben Wieland Says:

The Indians I’ve talked with slept on stone for its heat capacity and didn’t mention the hardness.

44. John Sidles Says:

LOL … Scott, sleep is not an interdisciplinary challenge … it’s a multidisciplinary challenge … which is much the harder class of challenge! 🙂

Seriously, we not infrequently see in trauma conference patients suffering from truly dreadful injuries, that are brought on not by mattresses that are too soft, or too hard, but by sleeping without moving.

If a person lies down on any surface, and then (generally with pharmaceutical assistance) doesn’t move at all for (say) 30 hours, they will first experience venous pooling (in the extremities and points-of-contact), then ecchymosis (bruising), which eventually becomes so severe as induce outright skin necrosis (skin death) and/or compartment syndrome (muscle swelling within its fascial sheaths).

It’s a pretty lengthy struggle to rescue these patients … who typically have no idea of the risks they were running.

In the same vein, the surgeon Paul Brand has written a wonderfully interesting book titled The Gift of Pain, which is all about patients who are cursed by the lack of it.

In summary, a modest amount of discomfort during sleep, sufficient to induce movement, is a good thing … a necessary thing … even a vital thing. Apply metaphorical and/or allegorical filters as desired! 🙂

45. Christopher H Says:

One feature shared by tatami mats and soft mattresses is that they don’t subject you to shear forces (compression or stretching of your skin and surface tissues) while adjusting to support your weight. Hammocks and trampolines, by contrast, can adjust to support weight relatively evenly but in the process often pull at clothing and skin. I can recall small motions to lift parts of my body when adjusting to a hammock to relieve that strain.

I think that’s why mattresses have such internal complexity: like a car’s suspension, they’re trying to apply relatively uniform force to a changing irregular surface, without introducing extra forces in other directions which might mess up your sleep or handling.

My experience with chairs seems to indicate that a hard surface can be quite comfortable, at least for a while, if it’s supporting you in the right places. If I had to sleep on a hard surface, then I’d rather it be translation-invariant (ie. flat) and horizontal so that at it’s as neutral as possible to my movements and adds the minimum of shear force. There may still be some shear on a flat surface if parts of my body end up in some kind of bridge shape, but it’s not going to be a lot.

46. Christopher H Says:

For an amusing demonstration of the relevance of shear stress (and stability!) to sleep, watch the (fourth season?) episodes of Babylon 5 set aboard the Minbari “White Star”. The Minbari beds are hard slabs inclined to about 30 degrees, vividly uncomfortable for the humans.

Sadly, there was no detailed discussion of the features of Minbari biology (otherwise so close to human) which might make sure a bed desirable.

47. Sam Howley Says:

“since even if you’re lying as still as possible, it still seems clear that a soft bed is more comfortable than a hard one.”

I don’t think this is true. A ceramic bed perfectly moulded to the shape you currently want to lay in would be very comfortable for the couple of seconds before you decided to shift positions.

48. karthik Says:

Here’s the way I look at it: Our skin senses the pressure exerted by the bed on us. Imagine one were to apply a point force at the centre of the bed with a stick (say). A perfectly hard ceramic bed would exert the normal reaction force back at the stick. A perfectly soft bed would just allow the stick to sink right through. Softness values of the bed in between these two extremes will lead to some damping and the exertion of an intermediate pressure between these two extremes. The softer the bed, the more the damping, and therefore the more the point force to be applied for the bed to exert a certain pressure back. Now, I think there is an ‘optimal pressure’ on the skin for good sleep (within control limits/error \delta). So I would hypothesize that slim people (who exert less force per unit area at any point) would like a harder bed than bulky people in order that both experience the same pressure on their body ultimately. I think this theory would also nicely explain why different people prefer different hardness to a great extent (is somebody reading this funded to carry out the above weight correlation experiment?). Also, the undulations of the body are also accounted for because the pressure experienced is what matters, and a bed that provides optimal pressure within some \delta error (that occurs during undulations) is a good bed for that particular individual. Any feedback people?

p.s: I don’t buy the trampolines (with minimal damping) are perfectly good surfaces to sleep theory. Imagine doing a quick turn from lying on your back to lying on the side of your face. I imagine being jolted up and down so that in my dream I would be in an earthquake (Hat tip: inception).

49. I am rested. Says:

I am.

50. Greg Kuperberg Says:

Well, I have sometimes napped on a hard floor, and I’ve seen mattresses that are too soft, so I am a data point for some of these issues.

A hard surface feels bad only for one reason, pressure points, as everyone else has noted. You get sore exactly where your bones are prominent. Except for that problem, there is nothing particularly wrong with sleeping on a hard surface. It isn’t particularly marketable; people like the idea of touching soft surfaces, regardless of what works better.

If a mattress is too soft and not very thick, then the effective surface isn’t really soft. Instead, the mattress does a poor job of diffusing the pressure from the things that are under it, e.g., springs. An old mattress might also be non-uniformly soft, i.e., lumpy.

If a mattress is both soft and thick, then actually it’s easy to like it unless you’re not used to it. In the limit, two problems can arise. (1) Lacking a firm surface to work against, it can be difficult to reposition or even get up. (2) The bed can start to surround you and induce a sense of suffocation that then wakes you up.

There is a related issue, well known in astronaut medicine, which is different from what you might like or possibly even what might help you sleep. Namely, your muscles and bones don’t stay healthy unless they have something to do. This is possibly a reason to avoid a bed that is too soft, and certainly a reason not to stay in bed all day.

In fact, there is a standard Earth-based medical model for weightlessness: Forced bed-rest in a soft bed, elevated a few degrees at the foot. You might think that a human spaceflight program is the ideal method for studying the health effects of human spaceflight, but this is only sort-of true. It is actually an incredibly cumbersome research environment for any purpose, not only because the launch system is a white elephant, but also because the astronauts themselves have to be treated like royalty. So, much of the data is taken on the ground, once people decide on an approximation to weightlessness. You would get a better approximation if you also irradiated the subjects tied to their beds, but I think that this is considered unethical.

Of course, weightlessness also induces a sense of falling. I don’t know whether this feels good or bad in the long run, probably good I guess, but in the short run it feels bad. I read an account somewhere of an astronaut on a spacewalk (which admittedly is not the same as weightlessness inside the ship) who said that he couldn’t get over the sense that he was plunging into an abyss.

51. Quantum Tennis Referree Says:

@Gowers:

“A thought experiment: suppose one were to lie in a bed made of a material that started out soft and gradually hardened. If one lay still, would one notice the hardening? It seems obvious to me that one wouldn’t.”

I think one would notice. But you will have to grant that lying still includes letting the squishy cells that make up your tissue to move around. So even if you lie still on a hard surface, over time, cells will deform, move, and this will force you to notice that things are different.

So yes, it is indeed a dynamical problem. A soft bed is preferred because it too responds dynamically to the changing geometry of our squishy body.

An analogy: think of a hot air balloon landing on the ground with no hot air in it. Its slowly deflating stage can be compared to the short time when we first fall into a particular position in any bed. Its completely deflated stage in which it lies on the ground, can be compared to the stage when we are ready to switch positions.

Thus, sleeping on a bed is a game between our nervous system and various colonies of cells touching the surface of the bed. The NS wants to minimize painful impulses, and so it recruits various cellular colonies to contact the bed’s surface by shifting positions. The cell colonies on the other hand don’t like to be squished and so, when chosen, try to move away or become deformed, thus sending pain impulses. (Here, by pain I mean “discomfort.”)

In summary, I don’t think one can ignore this dynamical aspect from the analysis. And including it probably reveals the answer to Scott’s question immediately: softer beds lead less squishing and longer delays between shifting and less aggregate discomfort.

52. John Sidles Says:

As is commonplace in the TCS/QIS blogosphere, this thread has seen plenty of theorizing, relatively little experimenting, and *NO* practical engineering.

The limit of perfect softness, dryness, and thermal neutrality—three qualities conducive to skin comfort—can be approached quite closely by practical engineering … in service of a sobering objective: these devices are called “burn recovery beds” (Wikipedia has a nice article on them).

I tried one a few years back … the sensation of perfect, dry, thermally neutral support is eerie and definitely *NOT* comfortable. Perhaps that is why this near-perfect bed technology has never become popular for home use. Also, they are high-tech devices that require considerable maintenance.

Large medical meetings frequently include commercial exhibitors of burn recovery beds, and so (with advance planning) it is entirely feasible to experience this remarkable sensation oneself.

53. Joe Fitzsimons Says:

At the risk of even more theorizing, a very simple model of a bed would be to consider a 2D array of springs. For small perturbations these should obey something close to Hooke’s law: F=-kx, where x is the displacement and k is some constant. If the bed is very hard, then k must be large, and so when you lie on the bed you will not sink in sufficiently far to spread the pressure of the upward force over the maximal area (making it uncomfortable). It the bed is very soft, then the difference in force between two displacements x and x’ will be dF = -k(x-x’) and since k is very small there will be little difference, and hence little support (which presumably also makes it uncomfortable). And so an optimal solution should lie towards a hard mattress just soft enough for you to sink in enough that most of your body is making contact with it (maybe 1-2 inches).

On the question of zero-g: I have heard from a number of astronauts that it is very hard to sleep in space, not least because cosmic rays keep interacting with your eyeball giving you a light show when you close your eyes. Also,my understanding is that they are strapped into bed (to keep from drifting), which probably affects the comfort.

54. John Sidles Says:

Joe, if you reflect that a perfect bed necessarily insulates the sleeper from floor vibrations, and are motivated by this consideration to search YouTube for vibration isolation videos, you will find some remarkable examples, whose zero-spring mechatronic principles are broadly applied in both burn recovery beds and in quantum spin microscopes … and indeed, in QIP technologies of every kind.

After all, don’t a burn recovery bed and a good QIP device have the same broad engineering objective … namely, to provide near-perfect isolation from environmental perturbations … in service of noble objectives like a good night’s sleep and direct observation of atomic-scale healing processes (the latter being our QSE Group’s main interest).

Not to mention, what is proving to be, by a considerable margin, the toughest QIP challenge of all … factoring integers larger than 15! 🙂

55. Joe Fitzsimons Says:

John, I don’t see why a normal bed need isolate the user from floor vibrations (though I can see why this might be necessary for burns cases). My floor simply doesn’t vibrate enough for me to notice even if I lie directly on it.

56. Joe Fitzsimons Says:

Also, I kind of assumed we were talking about normal beds here: hard versus soft mattress, etc. So, I am certainly discounting designs which use sophisticated isolation systems.

57. John Sidles Says:

Not to take this topic too seriously, Joe (`cuz it’s mainly an excuse for fun), isn’t there a reciprocity principle here? Isn’t a bed a communication channel between the environment and the sleeper? Doesn’t quantum mechanics tell us that all communication channels are two-way?

More broadly, isn’t any apparatus similarly a two-way communication channel between a sample and an observer … whose dynamical roles are interchangeable?

From this quantum point-of-view, even beds—especially beds—reveal themselves to be very interesting devices indeed … well worthy of contemplation from every STEM perspective.

Thus perhaps our bodies are wiser than our minds … we rightly sleep uneasily in beds that isolate us too-perfectly from the world we live in.

As usual, apply metaphorical and/or allegorical filters as desired!  🙂

58. gowers Says:

FWIW my bed supposedly contains a top layer of soft springs and a lower layer of harder springs. The theory (which persuaded me to buy the fairly expensive bed) was that the lower springs would provide the large-scale support but the softness of the upper springs would cause the bed to mould itself to the shape of your body and apply a very even pressure, in whatever position you were lying. All I can say is that I have had the bed for many years and still find it more comfortable than any other bed I sleep in.

59. Raoul Ohio Says:

gowers; Interesting point. Is this arrangement nonstandard? If so, what is the name for such a bed?

60. Joe Fitzsimons Says:

I guess that combining smaller springs with different strengths you can approximate a more pleasing displacement dependent force. Certainly that mattress does sound comfortable.

I suspect the ideal case would be some kind of continuous material where the difficulty of compressing followed some more complex profile.

61. I was Says:

I have slept on the sand in space on another planet in a dream.

62. John Sidles Says:

Joe says: I suspect the ideal case would be some kind of continuous material where the difficulty of compressing followed some more complex profile.

Joe, pursuing this idea will lead you naturally to the most advanced frontiers of classical and quantum systems engineering, as follows.

A burn recovery bed supports the patient on an array of air-springs that are (in effect) adjustable to have near-zero spring constant … this class of mechanisms is informally called “zero springs” by engineers. A higher-precision (but still classical) zero-spring mechanism is used in the LaCoste-Romberg gravimenter, while GWR Instruments makes a superconducting version. Associated to zero-spring vibration isolation are well-understood quantum limit and thermodynamic limits that are approached in (land-based) experiments like LIGO and the (space-based) experiments like GRACE (both of which are very cool instantiations), in which measurement back-action effects begin to dominate the dynamics. Applied at the nanoscale, these same universal classical/quantum isolation principles are instantiated in spin biomicroscopy, which is pursued with a practical long-term view toward … the regenerative healing of the patients in those burn recovery beds.

Thus the in-depth contemplation of any one of these technologies (include beds) leads us to appreciate a natural cycle of macroscale/microscale & classical/quantum dynamics that amounts to a STEM instantiation of the Disney song “Hakuna Matata” … which is great fun to contemplate … while we lie abed! 🙂

63. Jan de Wit Says:

Something that popped into my mind on reading this, is that a not-too-soft bed makes it possible for side-sleepers to keep their spine straight. I think that if you sleep flat on your back, the hardness of the bed doesn’t matter as much.

64. Matt Zellman Says:

I find it interesting that this far down in the comments no one has suggested that the reason a molded hard surface is different from a (springy) soft surface is the difference in normal force exerted at each point. If you lie on your side in a bed, so that the differences in depression depth are most pronounced, this is clear. The force exerted on your shoulders and hips will be significantly more than the force exerted on your feet and neck. While the total force applied over your body area is obviously the same, the distribution of forces from a springy soft surface is not the same as the distribution of forces from a molded hard surface, even when you are not moving at all.

65. Sick Says:

All ye nerds are sick…:)

66. sebastian Says:

As Matt Zellman (64) said, when not moving, the main effect is the distribution of force applied to the body. For a bed with given potential well and with some assumptions on the internal forces within the body this can be computed. If this force distribution is wrong, discomfort and back problems can follow. A secondary effect noticed while making minute movements is the derivative of the potential near the equilibrium point.

This suggests that a comfortable should minimize internal skeletal forces. This could be achieved with a suitably shaped hard surface, though it might not be the shape an actual bed assumes when in use (hence back pain). This is also consistent with the rumours that sleep in space is comfortable.

Of course, in practice, most people shift positions while sleeping, and a rigid surface would need to be reconfigured. A soft bed does this to some extent.

To approximate such a reconfigurable surface better, it may be useful if parts of the mattress could be moved easily from place to place, ideally in ones sleep without waking. Thus from basic physical an biological principles, we have even deduced the existence of pillows.

67. Francis Says:

Peter Buckle, Avalino Fernandes (Universidad de Surrey, Guildford, GB), “Mattress evaluation—assessment of contact pressure, comfort and discomfort,” Applied Ergonomics 29: 35-39, February 1998. http://dx.doi.org/10.1016/S0003-6870(97)00023-9