Are his bumper stickers still available? Could be a rush on . . .
Yes, right here, right now, you can obtain image files in a variety of resolutions and/or the master PostScript source code for The One, The Original, The Prophetic (July 1990), The Authentic “Evil Empires: One down, one to go…” bumper sticker, anticipating the obsolescence of railroad era continental-scale empires in the information age.
A caveat.
I had the change to perform a similar experiment at work testing very sensitive accelerometers. Believe it or not, the biggest source of errors was the bending of the floor due to the test masses!
A better setup would be to suspend the spheres exactly like the tuna cans, and test two configurations rotated by 90 degrees.
For the accelerometers the problem was the tiny tilting of the sensitive axis in the gravity field. In this case you're probably right that this doesn't matter -
but in general it is difficult to rule out every second-order effect when the forces at play are so small with respect to g.
OK, that I guess that kinda-sorta makes sense if the accelerometers were rigidly mounted to the floor. Was that the case? Because if so then what you would have would basically be a seismometer, and floor bending from the test masses would, it seems to me, be the least of your worries.
Yes, the accelerometers were mounted on an optical bench and of course we could detect any minor earthquake (sensitivity was around 1e-10 ms^-2).
The bending of the floor due to the presence of people in the room was noticeble indeed.
I assume if your weights are resting on the floor, and the pivot point of the swing arm is resting on the floor, then the floor deflecting may cause the arm to swing even in the absence of an attraction to the weights.
That's true, but the details of the placement of the ladder doesn't matter at all. The only thing that matters is that the ladder doesn't move or wobble around during the experiment.
I've come back to this idea of "differences" from many angles...
From images: information _is _ the differences between pixels
From opinions: my opinion alone is worthless, but a difference of opinions? now we've got something
From relationships, graphs, networks: edges are _differences_ between nodes. the edges are everything. nodes alone... are meaningless
From music: this one is a little easier to take at face value, you can't have a sound without a change (difference) over time. the speaker cone can only wobble...
Not sure about the absoluteness or correctness of this intuition, please criticize
For images, you need a reference pixel to get the color right. You can apply differences from there but you’re effectively working with absolutes because of that so it’s a meaningless distinction.
Any time an absolute reference point is assumed, all downstream calculations are effectively absolutes
I have a blue/black (or possibly white/gold) dress that says it's relative.
You can also ask a UI designer about "absolute" colors. One color needs to be different depending on the context it's in order to LOOK the same (it's size/thickness, background, what it's next to).
Suppose you have a reference pixel but don’t know its value. You don’t get the color right but there is plenty of other information there, right? Which pixel also probably limits the range of values since your highest and lowest values are probably within a certain range.
Or said another way, forces carry the structure of G-torsors! The terminology is way too pompous for such a simple concept, though. John Baez has a really clean writeup on them, accessible to anyone interested: https://math.ucr.edu/home/baez/torsors.html.
Heck, even differences are usually non-physical; it's their ratio that matters. I.e. choosing feet or meters doesn't change the physics; the same goes for energy. So we have two free parameters: choice of origin and choice of units.
Baez only hints at this near the end of the above article, but we can actually fuse translations and scalings into a single group of elements that are combined translation + scale operations, an affine group. It turns out that this combined group is just a certain combination (semidirect product[0]) of the translation and scaling groups, as one would hope.
And once we are thinking about affine groups, it's natural to consider more complicated ones. Most famous is probably the Poincaré group[1]. That is, points in space are physically described by G-torsors over the Poincaré group!
Excellent comment. The only thing I can add is the obligatory "why stop there?", Poincaré true to form gives a beautiful description of the symmetries of flat spacetime, but we know that spacetime is only locally flat, the measurement symmetries at large scale are carried by the (unfortunately named) Killing fields[0].
there most certainly are absolutes. theres an absolute maximum amount of distance a massive object can travel through spacetime. theres an absolute maximum amount of mass/energy that can exist within a volume of space before an event horizon forms. universal constants which have dimensions are more or less measurable absolutes. differences maybe more apparent but that doesnt mean absolutes dont exist.
An absolute on the upper bound of velocity that a massless object can travel through space at maybe?
Although - I had it explained to me that the fabric of space was entering a black hole faster than light could travel, which is why light couldn't escape.
Which made me wonder - is light (the massless object) travelling, or is it space travelling and carrying things at different velocities.
Heh, i wonder what the mean free space between blackholes is?
Now, given that in quadrillions of quadrillions of years all black holes will evaporate and potentially even protons decay there could be a time in the universe where everything is mass less radiation.
I agree OP misspoke, but are we sure the time axis has no upper bound? Or that it doesn’t loop back round on itself? Or that it even exists meaningfully as an axis?
I’m on my second attempt at this. The first worked but it was unwieldy and kind of unsatisfying. I’m going to make a second attempt using a bearing of ferrofluid, which has a damping effect, and use field alignment with the earths magnetic field as the source of torque. It’s really fun and at times frustrating trying to eek out effects of nanonewtons of force, highly recommended.
A cursory search on my phone gave a picture of the device and the biography of the person, but not a detailed explanation of how the device works or how to replicate it.
i'm still amused there's no real explanation of how it works. Like, can i do this with three X 9-DOF sensors in a box? you don't need light or film, you can use a TCO for accuracy in timing... I don't know why it keeps saying 3 pendulums, but a pair, but a "virtual third pendulum".
I learned about it at university. The idea is to measure the difference between periods of the short and the long pendulums. In particular, how many swings it takes for their swings to match (both pendulums arriving at the apex at the same time).
oh, and if it takes a different amount of time, something interfered, I'll have to try and make a simulation using the formulas on that page, then i can see if it can be copied with 6|9DOF, MEMS vibrate and i think you can control how fast, or at least track how fast over a period of time. i think you'd need 3, but i haven't messed with the expensive bosch sensors in a while.
Not even that, the period of a pendulum is 2pisqrt(L/g), so the interference will likely affect _both_ pendulums similarly.
The cool thing is that two pendulums can be modeled as simple sine waves (and you can do Fourier series to account for non-linearity of real pendulums), so the sum of them is _also_ a sine wave. And if you get its period, you can easily compute the `g` (since the ratio of lengths of pendulums is known to a good precision).
Detecting the period is also easy, you can have two electric contacts at the apex of the swing, and the circuit gets completed when both pendulums arrive at the same exact time to touch both contacts.
I did this one in the senior lab as an undergrad studying physics at New Mexico Tech.
I got to use a whole gymnasium for a weekend and used a laser beam projected across the gym to read out the torsion balance. Pretty cool that you can measure the gravitational constant [1] so easily, if approximately.
I ran out of time to finish reading the article. He explained the importance of using a camera to observe the results due to the ways a human presence would interfere with the experiment.
When he talks about how Archimedes might have reproduced his device using technologies of the time, did he address what historic alternative might take the place of the camera?
transparent glass was not really a thing in ancient Greece. That said with careful design you could make it work with just small openings into the room which are covered except for occasional observation.
"your bailiff comes,
shows me his writ - I, standing thus, d'ye mark me,
in the sun's stream, measuring my distance, guide
my focus to a point upon his writ,
and off it goes in fumo!"
You can rule out electric forces by just grounding the masses to have them at equal potential, at least as long as your test masses are conductive. Magnetic forces seems harder, use a non-magnetic material does not really help, how would you know that it is not ever so slightly magnetic, maybe even just due to contamination? Maybe try different materials and find that the effect scales with mass but seems independent of the material, that could increase confidence as it seems unlikely that different test masses made of different materials would exhibit the same tiny magnetic forces. Also I would first do a calculation, I have no idea how the gravitational forces compares to say paramagnetic effects you might encounter, for all I know they could be of similar size or orders of magnitude apart.
How about deliberately putting a strong magnet close to the rotating test masses, then repeating the experiment with the magnet on the other side and verifying that it doesn't make a difference?
Of course, that might be the easiest way. Given that you can get tiny magnets that are pretty strong but only a millimeters or so in size and therefore also light, you could just stick them to your different test masses in various configurations and see if it makes any difference while leaving the mass distribution pretty much unchanged.
The metal masses over a styrofoam bar look as a serius problem because they may collect static electricity. Perhaps a thin coorer wire that connect them to the aluminium foil in the water may solve that.
Fun fact. Charles Mason and Jeremiah Dixon, using theodolites, plumb bobs, and spirit levels, were able to detect variations in gravity from the local environment in 1767. Upon completing the resurvey on the way back to Philadelphia, they noticed a systematic error and concluded it was because of gravitational deflection due to the Allegheny mountains (with the help of Maskelyne, Cavendish and the Royal Society).
Sometimes I think about that and it just blows me away.
I miss John, this has much of the charm of the old "Amateur Scientist" columns from Scientific American. I remind myself from time to time that so much great work has been done by scientists with simple hand tools and a thoughtful experiment.
> The reason lies in the extraordinary weakness of the gravitational force.
I recall reading Brian Greene giving the example of sitting in a chair. The molecules of the chair are stronger than gravity. You're not crashing through to the floor.
John Walker, the author of this and host of Fourmilab, passed away last year: https://news.ycombinator.com/item?id=39297185
Are his bumper stickers still available? Could be a rush on . . .
https://www.fourmilab.ch/evilempire/When did the "one down" go away? It just morphed into a different thing, but it's still kicking, and winning in certain areas
Kelvin is an odd childhood nickname for a JWW, maybe a reference to Lord Kelvin, or, a referent of Kelvin R. Throop?
https://www.fourmilab.ch/autofile/www/section2_46_1.html
https://www.keanw.com/2007/01/protecting_inte.html
A caveat. I had the change to perform a similar experiment at work testing very sensitive accelerometers. Believe it or not, the biggest source of errors was the bending of the floor due to the test masses! A better setup would be to suspend the spheres exactly like the tuna cans, and test two configurations rotated by 90 degrees.
Huh? Why would the bending of the floor matter?
For the accelerometers the problem was the tiny tilting of the sensitive axis in the gravity field. In this case you're probably right that this doesn't matter - but in general it is difficult to rule out every second-order effect when the forces at play are so small with respect to g.
OK, that I guess that kinda-sorta makes sense if the accelerometers were rigidly mounted to the floor. Was that the case? Because if so then what you would have would basically be a seismometer, and floor bending from the test masses would, it seems to me, be the least of your worries.
Yes, the accelerometers were mounted on an optical bench and of course we could detect any minor earthquake (sensitivity was around 1e-10 ms^-2). The bending of the floor due to the presence of people in the room was noticeble indeed.
That makes sense. Thanks!
I assume if your weights are resting on the floor, and the pivot point of the swing arm is resting on the floor, then the floor deflecting may cause the arm to swing even in the absence of an attraction to the weights.
> the pivot point of the swing arm is resting on the floor
But it isn't. It's suspended from a support by a thin filament. That's the whole point of the experiment.
It’s suspended from an aluminum ladder standing on the floor.
That's true, but the details of the placement of the ladder doesn't matter at all. The only thing that matters is that the ladder doesn't move or wobble around during the experiment.
> This is the consequence of all the forces of physics being gauge invariant: absolute values don't exist—only differences matter
there's something about this quote that i really like, going to have to use it out of context on people
I've come back to this idea of "differences" from many angles...
From images: information _is _ the differences between pixels
From opinions: my opinion alone is worthless, but a difference of opinions? now we've got something
From relationships, graphs, networks: edges are _differences_ between nodes. the edges are everything. nodes alone... are meaningless
From music: this one is a little easier to take at face value, you can't have a sound without a change (difference) over time. the speaker cone can only wobble...
Not sure about the absoluteness or correctness of this intuition, please criticize
For images, you need a reference pixel to get the color right. You can apply differences from there but you’re effectively working with absolutes because of that so it’s a meaningless distinction.
Any time an absolute reference point is assumed, all downstream calculations are effectively absolutes
I have a blue/black (or possibly white/gold) dress that says it's relative.
You can also ask a UI designer about "absolute" colors. One color needs to be different depending on the context it's in order to LOOK the same (it's size/thickness, background, what it's next to).
The blue black dress thing is how people perceive it, but the values for pixels are absolute. The pixel values aren’t changing from viewer to viewer.
If OP had said “perceived color”, I would agree. But we’re talking at pixel level here.
Is this strictly true?
Suppose you have a reference pixel but don’t know its value. You don’t get the color right but there is plenty of other information there, right? Which pixel also probably limits the range of values since your highest and lowest values are probably within a certain range.
For music, a note is just a frequency. It is the difference between the notes that makes music, not the notes themselves
"Information: any difference that makes a difference" - Gregory Bateson
Or said another way, forces carry the structure of G-torsors! The terminology is way too pompous for such a simple concept, though. John Baez has a really clean writeup on them, accessible to anyone interested: https://math.ucr.edu/home/baez/torsors.html.
Heck, even differences are usually non-physical; it's their ratio that matters. I.e. choosing feet or meters doesn't change the physics; the same goes for energy. So we have two free parameters: choice of origin and choice of units.
Baez only hints at this near the end of the above article, but we can actually fuse translations and scalings into a single group of elements that are combined translation + scale operations, an affine group. It turns out that this combined group is just a certain combination (semidirect product[0]) of the translation and scaling groups, as one would hope.
And once we are thinking about affine groups, it's natural to consider more complicated ones. Most famous is probably the Poincaré group[1]. That is, points in space are physically described by G-torsors over the Poincaré group!
[0]:https://ncatlab.org/nlab/show/semidirect+product+group
[1]:https://en.wikipedia.org/wiki/Poincar%C3%A9_group
Excellent comment. The only thing I can add is the obligatory "why stop there?", Poincaré true to form gives a beautiful description of the symmetries of flat spacetime, but we know that spacetime is only locally flat, the measurement symmetries at large scale are carried by the (unfortunately named) Killing fields[0].
[0] https://en.wikipedia.org/wiki/Killing_vector_field
there most certainly are absolutes. theres an absolute maximum amount of distance a massive object can travel through spacetime. theres an absolute maximum amount of mass/energy that can exist within a volume of space before an event horizon forms. universal constants which have dimensions are more or less measurable absolutes. differences maybe more apparent but that doesnt mean absolutes dont exist.
An absolute on the upper bound of velocity that a massless object can travel through space at maybe?
Although - I had it explained to me that the fabric of space was entering a black hole faster than light could travel, which is why light couldn't escape.
Which made me wonder - is light (the massless object) travelling, or is it space travelling and carrying things at different velocities.
> theres an absolute maximum amount of distance a massive object can travel through spacetime
Wut. No there's not? Specifically for spacetime it's obvious to see that's not correct because the time axis has no upper bound.
Heh, i wonder what the mean free space between blackholes is?
Now, given that in quadrillions of quadrillions of years all black holes will evaporate and potentially even protons decay there could be a time in the universe where everything is mass less radiation.
I agree OP misspoke, but are we sure the time axis has no upper bound? Or that it doesn’t loop back round on itself? Or that it even exists meaningfully as an axis?
It's all relative!
sounds like Robert California
I’m on my second attempt at this. The first worked but it was unwieldy and kind of unsatisfying. I’m going to make a second attempt using a bearing of ferrofluid, which has a damping effect, and use field alignment with the earths magnetic field as the source of torque. It’s really fun and at times frustrating trying to eek out effects of nanonewtons of force, highly recommended.
Another interesting way to see the effects of gravity can be done with pendulums, using a Vening Meinesz apparatus.
It's not as spectacular as seeing a torsion bar move, but it's more sensitive.
A cursory search on my phone gave a picture of the device and the biography of the person, but not a detailed explanation of how the device works or how to replicate it.
I can't find a complete explanation, but there are some technical details in https://deepearthscience.blogspot.com/2016/06/the-gravimeter...
https://nextcloud.projectftm.com/index.php/s/gravitycompare that is really impressive, the 100 year old data compared to recent data.
i'm still amused there's no real explanation of how it works. Like, can i do this with three X 9-DOF sensors in a box? you don't need light or film, you can use a TCO for accuracy in timing... I don't know why it keeps saying 3 pendulums, but a pair, but a "virtual third pendulum".
but what this is, is an analog computer, right?
I learned about it at university. The idea is to measure the difference between periods of the short and the long pendulums. In particular, how many swings it takes for their swings to match (both pendulums arriving at the apex at the same time).
oh, and if it takes a different amount of time, something interfered, I'll have to try and make a simulation using the formulas on that page, then i can see if it can be copied with 6|9DOF, MEMS vibrate and i think you can control how fast, or at least track how fast over a period of time. i think you'd need 3, but i haven't messed with the expensive bosch sensors in a while.
Not even that, the period of a pendulum is 2pisqrt(L/g), so the interference will likely affect _both_ pendulums similarly.
The cool thing is that two pendulums can be modeled as simple sine waves (and you can do Fourier series to account for non-linearity of real pendulums), so the sum of them is _also_ a sine wave. And if you get its period, you can easily compute the `g` (since the ratio of lengths of pendulums is known to a good precision).
Detecting the period is also easy, you can have two electric contacts at the apex of the swing, and the circuit gets completed when both pendulums arrive at the same exact time to touch both contacts.
thank you!
I did this one in the senior lab as an undergrad studying physics at New Mexico Tech.
I got to use a whole gymnasium for a weekend and used a laser beam projected across the gym to read out the torsion balance. Pretty cool that you can measure the gravitational constant [1] so easily, if approximately.
[1] https://en.wikipedia.org/wiki/Gravitational_constant
Do you remember how accurately you were able to measure the gravitational constant?
I ran out of time to finish reading the article. He explained the importance of using a camera to observe the results due to the ways a human presence would interfere with the experiment.
When he talks about how Archimedes might have reproduced his device using technologies of the time, did he address what historic alternative might take the place of the camera?
Yes - a window.
transparent glass was not really a thing in ancient Greece. That said with careful design you could make it work with just small openings into the room which are covered except for occasional observation.
The greeks and egyptians had transparent glass, even glass magnifying lenses. https://en.wikipedia.org/wiki/Burning_glass
"your bailiff comes, shows me his writ - I, standing thus, d'ye mark me, in the sun's stream, measuring my distance, guide my focus to a point upon his writ, and off it goes in fumo!"
How do I rule out the masses being attracted by electromagnetism?
You can rule out electric forces by just grounding the masses to have them at equal potential, at least as long as your test masses are conductive. Magnetic forces seems harder, use a non-magnetic material does not really help, how would you know that it is not ever so slightly magnetic, maybe even just due to contamination? Maybe try different materials and find that the effect scales with mass but seems independent of the material, that could increase confidence as it seems unlikely that different test masses made of different materials would exhibit the same tiny magnetic forces. Also I would first do a calculation, I have no idea how the gravitational forces compares to say paramagnetic effects you might encounter, for all I know they could be of similar size or orders of magnitude apart.
How about deliberately putting a strong magnet close to the rotating test masses, then repeating the experiment with the magnet on the other side and verifying that it doesn't make a difference?
Of course, that might be the easiest way. Given that you can get tiny magnets that are pretty strong but only a millimeters or so in size and therefore also light, you could just stick them to your different test masses in various configurations and see if it makes any difference while leaving the mass distribution pretty much unchanged.
The metal masses over a styrofoam bar look as a serius problem because they may collect static electricity. Perhaps a thin coorer wire that connect them to the aluminium foil in the water may solve that.
Fun fact. Charles Mason and Jeremiah Dixon, using theodolites, plumb bobs, and spirit levels, were able to detect variations in gravity from the local environment in 1767. Upon completing the resurvey on the way back to Philadelphia, they noticed a systematic error and concluded it was because of gravitational deflection due to the Allegheny mountains (with the help of Maskelyne, Cavendish and the Royal Society).
Sometimes I think about that and it just blows me away.
I miss John, this has much of the charm of the old "Amateur Scientist" columns from Scientific American. I remind myself from time to time that so much great work has been done by scientists with simple hand tools and a thoughtful experiment.
> The reason lies in the extraordinary weakness of the gravitational force.
I recall reading Brian Greene giving the example of sitting in a chair. The molecules of the chair are stronger than gravity. You're not crashing through to the floor.
Reminds me a bit of Greg Egans' Incandescence [1]
[1] : https://en.wikipedia.org/wiki/Incandescence_(novel)
The problem I have with the article is that gravity is not a force. Magnetic is a force, but gravity is not a force.
Since this is written in metric/si units, I will read it!
I saw this documentary, it was called 'Sliders'.
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