Math Questions (as in "please do this math for me...")

[ceptimus]

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That's sort of what I mean

Adam

The pupil of your eye is already tiny in comparison to the desk, before you begin to shrink. It can only get a few millimetres smaller, no matter how small you get. I don't think this makes any difference anyway. As long as the image on the film or retina is in focus, it doesn't matter how big the lens is. When you stop down the aperture on a camera, the depth of field changes and you need a longer exposure, but the resulting picture, other than depth of field effects, is exactly the same.

You wouldn't get the depth of field changing effect when you shrink the whole camera, as the film would shrink in proportion to the aperture.

We really should draw out the light paths to an image on the film or retina - that would be tricky using ASCII art!

 

[c0rbin]

Thanks, Phil.

Also, Crossbow, I agree that a mile is a mile and that a ton of feathers weighs the same as a tone of lead. I was looking for perception (ie 10 feet would seem like 2 miles).

Your input helps a bunch though, thanks!

 

[slimshady2357]

The pupil of your eye is already tiny in comparison to the desk, before you begin to shrink. It can only get a few millimetres smaller, no matter how small you get. I don't think this makes any difference anyway.

Well, your pupil is going to shrink a lot! It would be only 1/1800th the size it was to start with (for me), this is a significant shrinkage!

Are you saying that if I start with a lens 1800 feet across and go to a lens 1 foot across this effect will be not noticable? I don't think I can agree with that.

As long as the image on the film or retina is in focus, it doesn't matter how big the lens is. When you stop down the aperture on a camera, the depth of field changes and you need a longer exposure, but the resulting picture, other than depth of field effects, is exactly the same.

I think I see what you're saying... Are you saying that the adjustments that your eye would make to get the picture back into focus would 'widen' the lens a little and compensate for the loss in size, resulting in the same amount of objects being in your visual field?

You wouldn't get the depth of field changing effect when you shrink the whole camera, as the film would shrink in proportion to the aperture.

Hmmmm, I'm not sure depth of field is the term I would use, but I think we're on the same page none-the-less. Are you saying this effect would translate into humans? I guess it would....

We really should draw out the light paths to an image on the film or retina - that would be tricky using ASCII art! [/B]

Now that would be quite the talent!

Thanks for your input ceptimus, I'm going to think about it some more.

Adam

 

[Deetee]

I'm with ceptimus on this one.......

Also I am reminded of the paradox of Poincare -

Imagine if overnight the universe, and everything in it, doubled in size.

How would you know?

 

[Crossbow]

Thanks, Phil.

Also, Crossbow, I agree that a mile is a mile and that a ton of feathers weighs the same as a tone of lead. I was looking for perception (ie 10 feet would seem like 2 miles).

Your input helps a bunch though, thanks!

Anytime!

 

[phildonnia]

I'm with ceptimus on this one.......

Also I am reminded of the paradox of Poincare -

Imagine if overnight the universe, and everything in it, doubled in size.

How would you know?

Well, for starters, everything would octuple in mass, which would cause a lot of stuff to implode from its gravity, buildings would be crushed, people would be unable to move, there'd be earthquakes, stars would burn much hotter, neutron stars would go black hole...

Other than that, you wouldn't notice a thing.

 

[ceptimus]

Maybe time would have to be stretched out too, in which case the 'speed' of light would stay the same - distance doubles, but so does time. Interesting...

Density of the fundamental particles (whatever that means) would decrease by a factor of 4? The planck length would double. I think if you scaled the time and fundamental constants appropriately, you could not be aware of the size change. For all we know, the universe might actually be doing exactly this, right now.

 

[phildonnia]

... I think if you scaled the time and fundamental constants appropriately, you could not be aware of the size change. For all we know, the universe might actually be doing exactly this, right now.

If the fundamental constants all changed appropriately, and the universe were actually doing this right now, then those fundamental constants, along with the "true" notion of "size" would never have been discovered. We'd have discovered similar constants, that actually were constant, that were based on our erroneous perception of "size".

The idea of "True size", as distinguished from that which we base the fundamental constants on, would be basically unobservable, and might as well not exist.

The question would be right up there with "If the ether flow changed direction, would anyone notice?".

 

[ceptimus]

Some constants are just dimensionless constants, and would have to remain the same, but others like G, the gravitational constant, are measured in terms of lengths, masses and time (all other units can be derived from these three).

So if you mess with the lengths time and the masses, the constants do automatically change, but the people in the universe, meausring them get the same answer as before.

One of the fundamentals you could change would be the rest mass of a proton. All mass is eventually measured, relative to this fundamental.

Similarly if you stretch time so that (to an outside observer) a second is longer, but it is still measured as a second by the observers within.

I agree, it is a super-ultimate unanswerable question.

 

[BillyJoe]

I still think you are all wrong.....

Let me make this clear by using an exaggerated example.

We are in outer space so as to eliminate visual clues. Here you
are floating in space. You cannot see any part of your body - again to eliminate visual clues. All you can see is a 10cm X 10cm sheet of paper. Nothing else changes except that suddenly you are dramatically reduced in size by a facor of, say, 10.

Now, are you really telling me you won't notice any difference?

Isn't it the same as the sheet of paper suddenly increasing its dimensions by a factor of 10 so that now it measures 100cm X 100cm.

You think you won't notice that??

I'll give you all a clue now...
If the distance between you and that sheet of paper increased by a factor of 10 as well as the paper increasing its dimensions by a factor of ten, then, no you won't notice that there has been any change.

Does anyone not understand this???

BillyJoe.

 

[BTox]

I still think you are all wrong.....

Let me make this clear by using an exaggerated example.

We are in outer space so as to eliminate visual clues. Here you
are floating in space. You cannot see any part of your body - again to eliminate visual clues. All you can see is a 10cm X 10cm sheet of paper. Nothing else changes except that suddenly you are dramatically reduced in size by a facor of, say, 10.

Now, are you really telling me you won't notice any difference?

Isn't it the same as the sheet of paper suddenly increasing its dimensions by a factor of 10 so that now it measures 100cm X 100cm.

You think you won't notice that??

I'll give you all a clue now...
If the distance between you and that sheet of paper increased by a factor of 10 as well as the paper increasing its dimensions by a factor of ten, then, no you won't notice that there has been any change.

Does anyone not understand this???

BillyJoe.

M ake s p erf ect se nse to m e. I j sut shr unk my self t o 1/100 zise and h ving h e;ll o f t ime t yping by j umpin g on k eyys.

 

[Brian]

Would being shrunk to that size create a "new" horizon for the shrunken person?

 

[BillyJoe]

Would being shrunk to that size create a "new" horizon for the shrunken person?

No, he would have to be shrunken down a lot further than that to become a black hole.
I don't know the maths though.

BillyJoe.

 

[jj]

You asked a question of perception, not of mathematics.

You can assume scaling in the human, I suppose, but I think physics would create some problems there.

 

[Walter Wayne]

...because I wouldn't know where to begin.


How many miles would 10 feet seem to be to a person shrunk to 1/25 inches tall?

How mank kilometers would 10 meters seem to a person shrunk to 0.1 mm tall?

The question says shrunk to x tall. In which case one would definitely notice a difference in size perception. Even without changing pupil size, if you just rest your head on the ground things look bigger.

If you put a dot 10 feet away it takes 3 or 4 strides to get there. Shrink by a factor of 1000, and the angle of perspective on that dot will be the same as if it had been moved away by a factor of a 1000, and you would require 3000 to 4000 strides to get there.

If you bring in things other than distance perception, things don't scale well. With just size perception taken into account, almost everything is trigonometry, and that does scale.

Walt

 

[Deetee]

Well, for starters, everything would octuple in mass, which would cause a lot of stuff to implode from its gravity, buildings would be crushed, people would be unable to move, there'd be earthquakes, stars would burn much hotter, neutron stars would go black hole...

Other than that, you wouldn't notice a thing.

Why does mass increase? Atoms would also double in size (impossible on a quantum level I imagine, but for this scenario I assume they do so).

Gravity will then be 1/4 strength (size of objects will double but mass remains constant)

A wind up watch will run at the same rate, but a penduluim clock will go slower.

 

[c0rbin]

You asked a question of perception, not of mathematics.

You can assume scaling in the human, I suppose, but I think physics would create some problems there.

I am going to assume that I am the "I" mentioned above.

I think it is a question of math and perception. If I shrink by a factor of 100, I percieve things as being scaled up by a factor of 100.

If I am following the thread correctly.

BTW, thanks, Walter.

 

[69dodge]

Originally posted by BillyJoe
We are in outer space so as to eliminate visual clues. Here you
are floating in space. You cannot see any part of your body - again to eliminate visual clues. All you can see is a 10cm X 10cm sheet of paper. Nothing else changes except that suddenly you are dramatically reduced in size by a facor of, say, 10.

Now, are you really telling me you won't notice any difference?

Yes.

Isn't it the same as the sheet of paper suddenly increasing its dimensions by a factor of 10 so that now it measures 100cm X 100cm.

No.

You think you won't notice that??

I would notice that.

If the distance between you and that sheet of paper increased by a factor of 10 as well as the paper increasing its dimensions by a factor of ten, then, no you won't notice that there has been any change.

I agree. It's this case that is similar to the case where the person is shrunk.

 

[69dodge]

Originally posted by ceptimus
Why should a person's perception of a mile change, just because (s)he has been shrunk?

Because people measure the size of things relative to their own size.

If you measure distance by counting strides then fair enough, but if the person is travelling in a car, or just looking out of a window, wouldn't a mile still seem like a mile?

It would if you eliminated enough cues. But, then, going ten miles in a giant, fast car on a giant road in a giant world would also seem like going a mile.

I don't think that the angle an object subtends at the eye really captures the intuitive notion of "how big it seems" very well. Does a nearby model train seem the same size as a far-away real train if they both occupy the same fraction of the visual field? Most people would say, "no," I think. If enough cues were missing so that they couldn't tell how far the train was, they'd call the situation an optical illusion, and not consider it representative of the normal state of affairs.

 

[ceptimus]

Because people measure the size of things relative to their own size.

I don't think we do. I think (visually) we gauge the size of things, relative to each other.

It would if you eliminated enough cues. But, then, going ten miles in a giant, fast car on a giant road in a giant world would also seem like going a mile.

I agree with that, but the question asked here would be more like going ONE mile in a giant, ordinary speed car, in an ordinary size world. If you couldn't see the car itself, and could only see out of the window, then you still could tell that the car was bigger, because you'd be higher, but if you eliminate that height difference, as in the hydraulic chair example, I think you would not know you were in a larger car.

I don't think that the angle an object subtends at the eye really captures the intuitive notion of "how big it seems" very well. Does a nearby model train seem the same size as a far-away real train if they both occupy the same fraction of the visual field? Most people would say, "no," I think. If enough cues were missing so that they couldn't tell how far the train was, they'd call the situation an optical illusion, and not consider it representative of the normal state of affairs.

I agree that it would not be a normal state of affairs; as soon as you move your head, you would know. However, if a model is detailed enough and far enough away (say more than ten feet) so that you don't have to focus your eye differently and you close one eye to remove stereoscopic vision and you don't move your head, then you can be fooled easily. There is a museum exhibit where you look at a full size car, walk further round the exhibit, where you can only see the car through a peep hole, then walk still further and can see that the car you saw through the peep hole, which you assumed to be the same one, is a actually about a 1/10 scale model, close to the peep hole.