Alice has been shrunk! Will she notice?

Question

Situation:

Someone (let's call him Bob) is playing games with someone else (let's call her Alice). Bob used his shrink ray to reduce Alice in size by about 40% (for the purpose of this question, don't worry about how this was accomplished, or any of the potential physics issues).

He did this while Alice was sleeping, and then moved her.

So... Alice wakes up one morning in an unfamiliar bedroom, 60% of her former size (BTW, that's 60% height, not 60% mass). She is unaware of Bob's shrinking technology, but is predisposed to believe that Bob is pranking her by putting her in a room where everything is larger than normal. (Assume she believes that Bob has the means to accomplish this.)

Eventually, Bob is going to walk in and the jig will be up, but until then...

Caveats:

• Alice's body metabolism seems to be functioning normally.
• Alice's senses (sight, hearing, etc.) are not noticeably affected.
• Alice either doesn't speak, or her voice is not noticeably different.
• Alice doesn't figure it out from looking at herself.
• Alice doesn't get up off the bed before Bob arrives.
• The bedroom is clean and uncluttered (think 'magazine photo').
• There are no personal effects in evidence.
• There are no mirrors in the bedroom.
• There are light fixtures, but no visible bulbs, and no other electronics.
• There are several pieces of wood furniture (including the bed) and a chair or two.
• There are no visible clothes except what Alice is wearing.

...so Alice won't figure it out due to e.g. looking closely at something like a power plug (or smart phone) that would be difficult to fake, or noticing that the entire world (not just an immediate space that Bob might "fake") or just too many 'things' are "scaled up".

Question:

Will Alice figure out what has really happened before she sees Bob? Is it plausible that she doesn't? If she does figure it out, what gives it away? (Would the change in mass be blatantly obvious, if her muscles are also weaker?)

Details:

Alice is of sound body and mostly sound mind (above average naïvete), but for story reasons is not going to be poking around the room before Bob shows up... but this might not be for an hour (i.e. she has more than a few seconds). She will likely sit up, maybe stand, roll over, or curl up, but is not going to start doing calisthenics. She's also not going to take her clothes off. There is a window, but the view is not familiar, nor is there anything near enough to the window to make the shrinking obvious¹. She can closely inspect her clothes and the bed, and can look at other things in the room, but is inclined to believe the clothing could be a trick (coarser fabric, larger than normal thread and such).

(¹ At least, I don't think it would be obvious if all you can see is natural terrain, and that not very close by?)

Parting Thoughts:

Thank you everyone that answered! There are some good gems in here that I will use, however, I have ultimately decided to go with my original plan that she won't immediately figure it out (and have therefore accepted Halfthawed's answer. For my purposes, there are several reasons, including that the story circumstances are such that Alice will be less likely to notice the changes to her own body. I was looking more for some external (probably visual) hint that would give the game away, and no one (myself included) has been able to come up with one. (I'm also going to throw in something that looks "normal size" but isn't as an additional means of distracting Alice from the truth.)

Again, thank you all! This question went over much better than I was honestly expecting and the responses are of very high quality. Y'all deserve your upvotes!

Answer 1

No

Standard Bayesian analysis of the situation will suggest that Bob, rather than somehow violently breaking the vast majority of the laws of physics, has instead decide to play a practical joke by moving Alice while sleeping to a ludicrously accurate scaled-up room. There are objects which don't function well at larger sizes than they do at smaller sizes, so if Alice interacts with them they may cause questions, but since she's not getting out of bed to interact with it, she will assume the mundane explanation. In other words, when you hear hoofbeats, it's probably a horse and not a zebra,

Answer 2

Alice is an avid user of World-Builder. While the average person might not notice ...

The bed materials would be courser and stiffer than usual.

She will feel colder, especially in her extremities.

Her body mass will be distributed differently, e.g., her breasts would exhibit less sag, etc.

Her hair will be finer thus less stiff, and it will not fall as low as usual.

Breathing will be easier, even though her air passages are smaller, as she has to move a smaller volume of air.

She will feel both stronger and be more nimble. All movements will be noticeably fast.

Though most of these are not terribly noticeable on an individual basis, you brain is tuned for pattern recognition. You would likely get the feel that something is not right pretty quickly even though you may not be able to put your finger on it quickly.

Her world-building prowess will enable her to put the pieces together and realize this is no simple prank.

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Muscle strength various proportional to cross-sectional area, so less arm-weight probably does not correspond to whipping her arms around with super speed and strength. i.e, proportionally faster/stronger but only at the 40% level.

However, this reminds me of another subtle square/cube issue. Muscle cells are ultimately limited by the strength of their cell wells - in fact I've read before the limit is actually fairly close to the tear point.

The wall cross-sectional area will follow the square law, but I wonder about the motive force within a muscle cell. I am an engineer, not a biologist - my guess is that the motive force within a muscle cell follows the cube law. But, if it actually depends upon internal fibers, etc. it may follow the square law. In this case muscle strength may not vary as I and others previously assumed.

BTW, animals have cell membranes, not cell wells (like plants).

Answer 3

Will Alice figure out what has really happened before she sees Bob?

Gravity says she could, but she still won't work it out.

Stuff takes time to fall. We are adjusted by the experience of our entire lives (what age Alice might be I'm too much a gentleman to ask), so we have a very strong instinctive feel for the time it should take for things to e.g. fall from my hands to the floor when I'm standing.

If Alice holds something say one meter up and drops it to the floor she will expect it to take about 0.45 seconds (say half a second).

If Alice is shrunk by 40% then it will actually take about 0.28 seconds to fall.

So she's going to instinctively know that's not right - it's too big to dismiss easily.

Is it plausible that she doesn't ?

If she ignores this effect for a while she might become more adapted to it, but it's a big ask. I think she'll notice.

If she does figure it out, what gives it away ?

Timings of anything depending on gravity will be way off. Throw a ball up, takes too short a time to fall back. Drop something it seems to race at the floor faster than it should. Steam rising from a pot - it's going to seem like it's shooting out faster. Things like that.

But can she figure out she's smaller ?

She is unaware of Bob's shrinking technology, but is predisposed to believe that Bob is pranking her by putting her in a room where everything is larger than normal.

And the answer here is maybe.

Humans tend to let go of the initial idea they had slowly even when real evidence has long before demonstrated they're wrong. Alice starts out believing the room may be larger - well that's a darn sight more reasonable than a shrink-ray, so she'll take a heck of a long time to reach "shrink-ray", maybe never.

If Alice had a physics background, this might be easier, but a physicist would still balk at the shrink-ray option as it's, well, physically not plausible (impossible as far as we know).

Answer 4

Yes. Alice will feel lighter, or stronger, depending on how you look at it.

Perceived weight (that is, difficulty lifting something) corresponds to strength.

Presuming Bob's shrinking technology doesn't change the fundamental laws of physics, mini-Alice's atoms have to be the same size and mass as before, meaning she has fewer of them.

Mass scales with volume; that is, as the cube of the linear scale.

$$0.6*0.6*0.6=0.216$$

The strength of muscles scales with their cross-sectional area; that is, as the square of the linear scale.

$$0.6*0.6 = 0.36$$

If mini-Alice continued under the assumption that she hadn't been shrunk, she would find she could lift things that looked $0.36/0.216= 1.6666...$ times as heavy as before. If she could lift a 30 kg weight before being shrunk, she could lift a weight that looked like it was 50 kg (but really weighed just 10.8 kg) just as easily. If she could jump 1m in the air, she could jump a distance that looked like 167 cm to her (but was actually the same 1m as before).

This is the same reason that insects and spiders can lift heavier weights in proportion to their own sizes.

Answer 5

The snarky answer is that no she does not notice because Alice wakes up, realizes that this is not her room, then proceeds to roll over and get another hour of sleep. This is certainly Bob's doing and he'll explain himself later when he decides to crawl out of bed and draws upon his life-giving coffee.

And now for something less snarky:

When Alice wakes up, she is at 60% of her previous height. If I understand the fun-killing Square-Cube Law correctly, this should mean that she has about 21.6% of her previous mass.

Given the lack of power outlets and visible light bulbs in combination with Bob's nature, it would not be a stretch to Alice to assume that Bob has done something. In fact, the fact that it is not her room at all is the first clue that something is amiss.

As Alice wakes, the blankets are going to feel courser due to her smaller size. However, this also depends on what Bob is using for linens. Bedding with a higher thread count than normal may feel like a regular sheet to her smaller form. As her night clothes have (hopefully) shrunk with her, there is nothing there that gives the game away outright either.

The next clue is the different fit in the bed that Alice has, or the bed itself depending on what kind of bed it is. For a start, she now only has a bit over 1/5 of her previous weight. This means that the bed she is lying in will most likely not feel quite the same as her bed does. This bed will likely seem a lot firmer than she would recall given that her lack of mass would cause less distortion in the mattress.

Now the blankets are light, and maybe with the proportional change in strength, she might notice that the blanket seem lighter, but that will only be really noticeable with a heavier quilt-like blanket. But if Bob has used stock pillows, that is something interesting to note. Standard bed-type pillows only get wider as the bed size increases. Alice will no longer be in proportion to the pillows unless they were custom made for this prank. The pillows will need to be scaled down and recreated to hide this part.

As Alice will not really undertake physical exertion during this period, there is no immediate cause for her to find out that she may have gotten proportionately stronger at her modified height. Even then, she might just put it down to a good night's sleep unless she accidentally breaks something.

Wood grains could be a potential way to tell that something strange is going on. With 40% less height, the rings and grain of the wood around her would seem about 40% bigger. Depending on the composition of the nightstand beside the bed, the grain of its wood might look off, but not necessarily wrong. Wooden floors would fall under this vein as well.

The real question is how well Alice knows Bob in this case. While she is unaware of his Shrink-o-Mat, is she aware of any of his more fantastical inventions otherwise? She does know that he can be a bit of an elaborate prankster, so a scaled-up room is not out of the question and is a logical explanation. But so long as she knows nothing of his paranormal tech, then she would have no reason to suspect being shrunk if a simpler explanation works.

I would think that without considering the shrinking hypothesis in the first place, she would not really look for the cues that would point to it as opposed to dismissing them as Bob being a prankster and messing with her.

Answer 6

Sound and light will be very different. I would not like to say exactly how the differences will impact, but the optics in Alice's eyes will function differently; her smaller eyes will not gather as much light, and as wavelengths have not changed there may be some chromatic effects. (Edit: there is a difference between a child's eye and a scaled-down adult-s eye -- children have much larger eyes in proportion to their size)

Similarly her ears are now scaled wrongly for the frequencies she is used to hearing. What was a high-pitched note will be deeper, and she can now probably hear dog whistles but at the expense of loss of sensitivity in the normal human range.

Also, as noted by another, square-cube means she is radiating heat much faster and her face will feel very cold. With luck she will not freeze to death, as that would spoil the prank. (And yes, kids do freeze to death where adults don't -- which is why babies must be bundled up warmly).

Answer 7

Yes, through Deduction and Analysis of the Meta-Game

I will make a key assumption, as to how gifted Alice's reasoning abilities are. Can she deduce from root causes why she is in such a situation? I believe that the answer is yes, because Alice is only pretending to be naive on the surface, and is actually a genius in disguise.

From this knowledge, we have three possible conclusions to this question.

We can come to this conclusion by following the subsequent train of logic below:

1. Let's assume that although nothing physical seems to be out of place, Alice immediately notices that her surroundings have gotten larger.

2. The first conclusion that she can come to is that Bob has put her in a larger than life sized room.

3. We know this from the question explanation:

[Bob] is playing games with [Alice]

and

She is unaware of Bob's shrinking technology, but is predisposed to believe that Bob is pranking her by putting her in a room where everything is larger than normal.

4. We must, however, analyze, the reason as to why Bob and Alice are playing the game? Is there a reason as to why Bob must go so far as to make a physics-breaking shrink ray, rather than, as you said, making a room that is just ~66.66% larger than normal?

This is because Bob KNOWS that Alice is faking her Naivety, and must go through extraordinary lengths to trick Alice.

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Now that the situation has been clarified, we proceed to our final two (and one hypothetical) situations, a and b:

5.a) This is the most divergent step. It depends on whether Alice knows that Bob knows about her naivety ruse. It may be that the naivety was a ruse meant to be exposed, so that Bob will go to greater lengths to trick her. If Alice knows that Bob has seen through her naivety ruse, then she also knows that Bob knows using a larger-than-life room would naturally not trick her. She would thus know that Bob would not simply use a larger-than-life room.

6.a) If the room is not the problem, then there can only be one issue: herself. Thus, Alice can come to the conclusion that Bob has shrunk her, rather than made a room larger than herself.

5.b) Of course there exists the possibility that Bob knows that Alice's naivety is just a ruse, and he knows that she knows that he knows that she is acting naive. In that case, Bob can do it either way.

6.b) Bob presents himself in 'enlarged form' through some sort of holograph, convincing Alice of his 'Shrink Ray', although in fact, there was no shrink ray all along, the room is just large!, or alternatively, he can use the shrink ray. Both are possibilities, and Alice cannot know which he will do.

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5.c) Note that 5.a and 5.b all depend on mind games, and which will happen depends on who has outsmarted who. This state, 5.c, is a moot state, where Alice knows that Bob knows that her Naivety Ruse was all planned, as in that case both sides have a clear idea that both sides have all the information. In that case, they would not be playing this game, as both sides are clear that neither is naive enough to fall for simple tricks. They can just have a mind game in dialogue rather than going through the trouble of making shrink rays or larger-than-life rooms. Thus, we can rule out 5.c) and any subsequent 5.d), 5.e), ad infinitum, because they would simply not play the shrink ray or large room game.

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TL;DR: Alice is actually a smart cookie in disguise. Whether Alice can figure out that she has been shrunk depends on if she knows one piece of information: whether Bob knows that she knows he has seen through her ruse.

If she knows Bob has seen through only her naivety, but not that she expected him to see through it, then she can deduce that he would not pull a low-level prank like increasing the size of the room, and instead has shrunk her.

If she knows that Bob knows that she intended for her ruse to be blown, Bob wins, as the odds are against her, and she is lacking information.

Answer 8

Halfthawed's answer is right (I upvoted that; don't upvote this) - Alice will not work out she's been shrunk - but only because the question is so unreasonable. "Alice's body seems to be functioning normally" rules out any clues like mass/strength oddities and defeats the otherwise clueful points of Gary Walker; and not getting out of bed takes care of the rest. The room isn't likely big enough for the speed of sound of echoes to come into play; her sense of smell and taste might be affected (molecules are the wrong size) but she's not eating or interacting with much and the environment is unfamiliar anyway. If she's wearing perfume, she might find it odd now. Ambient sound might be the wrong pitch and if there is wind outside that might be a solid clue, but I think that's her best shot. I can't convince myself that light would be all that processed differently by her eyes because any effect I can think of involves her rods and cones, but they are "functioning normally." If she can observe ripples in water, they would definitely look a bit odd at her scale, but there isn't any here.

I suppose it depends on her relationship with Bob; but her first thought would probably be nightmare or delusion. I think she'd be frightened and start to doubt her sanity. By the same token, any normal person would immediately get of bed and start testing their perceptions against each other to see if they were sane or not. But the question rules that out. Now, why she thinks Bob has the resources to build a scaled-up room and why she thinks it's plausible that he would I don't know, but yes that's her next mental stop. Of course if she knows Bob is a god (which, after all, he is) or trickster, she has other avenues to explore, but again, they don't involving staying in bed, unless she's panicking from fear, which she might well be.

Her actions are so constrained by the OP that I don't think we can comment on her state of mind. I personally would start screaming "Bob, WTF!" and then fashion some sort of weapon because Bob's clearly a deranged god, and worse, a cad. She needs better friends.

Answer 9

The period of a pendulum varies with the square root of length. Her arms and legs are pendula and her head is an inverted pendulum. These pendula now have periods $\sqrt{0.6} = 0.77$-times as long as was previously the case. Steps are faster, arm swinging is faster, head lolling is faster. Her hair swings and bobs faster. That her usual learned control loops are mistimed for the new physics will be almost instantly noticed.