As someone who uses both treadmills and jogs, I have no idea about the physics, but I suspect the constant interaction with the world in jogging - you're always making little turns, adjusting to the shape of the pavement, speeding up or down, etc. - makes it more of a general workout for the body even holding overall speed constant.
The OP as a whole makes me think of the argument that all language is analogy, varying from weak to strong, apt to inapt.
Thermodynamics without reference to the underlying statistical mechanics (the description of ensembles of particles or other objects that are in thermal equilibrium) is absolutely possible. The two approaches produce logically independent definitions of temperature and other quantities which coincide for systems in thermodynamic equilibrium.
Enrico Fermi's little book about thermodynamics is mostly written this way, and is really clear. For Stat mech, maybe the Feynman lectures?
IMO temperature is a fairly subtle thing, don't know that shorthand discussion in comment boxes of fundamentals will work well-- afraid that most of what I'd write would be either jargon or long-winded.
2: This could have unfortunate consequences for unfogged.
It never before occurred to me to consider topography and set theory as alternatives to each other, kinda like brain surgeon vs. fry cook.
Both work with things that are high in fat.
My J&O friend says Everything in life is made out if energy. Ever wonder why your heart has an electrical current? 🔌 Because it's full of energy. In essence, you are a big, flowing ball of energy. In a Reiki session, I connect with the universal life energy that is present in all things and let it flow to you. Your body is divinely wise and will take exactly what it needs. The beauty in Reiki is that you are taking part in your own healing process and Remember, Reiki is energy. Energy is not bound by time, space, or distance. Your body will still draw the healing energy to you, regardless of where you are or how far away you are! Hope this helps!
6: I'm thinking that "topography" was meant to be "topology."
I keep looking up set theory, going 'huh', and then forgetting set theory.
I find your lack of faith pants Reiki disturbing.
5,8: "topography and set theory" was meant to be shorthand for "areas of maths with which I am completely unfamiliar" so there's every chance that I got the name wrong.
OP, 7: On reflection, I think that my question may boil down to "does energy really exist or not?"
3: I'm going to download the Fermi book, much appreciated.
The Man Who Mistook His Wife for A Vector Field.
"does energy really exist or not?"
Energy is a wave and a particle, so it exists twice and doesn't exist three times.
Weirdly enough, my son had the same question about gravity that I had when the whole "everything falls at the same speed but for air resistance" thing came up. Sure the gravity of the earth is the same, but if something is really big it will be pulling on the earth more than a tiny thing so shouldn't it go some small amount faster. I think the answer is that being bigger the thing is harder to move so it still moves at the same speed, but I figure I'll let his teacher deal with.
You're both right, but the effect is mostly negligible. We only notice our gravitational attraction to earth because one of the two objects involved happens to weigh 6 x 10^24 kg
Related: I've been eating the unclaimed Halloween candy from like three houses.
Now looking up the equation for gravitational attraction between two objects, I think I was spectacularly wrong about why (although hopefully I got the mass of the earth right, and didn't confuse it with the number of particles in a mole or whatever). I'd like to revise my answer to: the F involved is proportional to m of the object being attracted to earth, and the acceleration is F/m. Hopefully.
There are thermodynamic definitions of temperature independent of any model of atoms bumping into each other, but like a lot of things in macroscopic thermodynamics, they are either not very intuitive or else seem circular.
Some treatments of thermodynamics start by simply postulating temperature as "that property of objects which becomes equal when 2 objects are placed in thermal contact" or "an intrinsic property of matter that quantifies the ability of one body to transfer thermal energy (heat) to another body".
"that property of objects which becomes equal when 2 objects are placed in thermal contact"
Let me guess. They define 'thermal contact' as "contact that lets objects become the same temperature".
20: That's why the textbooks inevitably start talking about steam engines. The best way to avoid hopelessly circular definitions is to relate everything to the amount of work that can (theoretically) be extracted from a temperature difference between 2 bodies.
Steam engines look fun. I see that you can buy little tiny ones for the home. You stoke them with very small pieces of coal.
If you accelerate a steam engine to the speed of light for one hour, at the end of the hour you'll be too dead to refill the hopper unless you also were accelerated to the speed of light.
The problem with accelerating a steam engine to the speed of light is finding someone who can shovel coal fast enough.
You put the steam engine on a spaceship with hyperdrive.
I'd like to go on the record stating that even the dryest and most formalistic aspects of thermodynamics are more pleasant to talk about than the 2016 primary.
Who's up for some Carnot cycles?
Once as a child about the age of Child Seeds I had a high fever, 102 or something, and started to get very worried because shouldn't that mean my blood had passed the boiling point? But eventually I realized I was just being delusional and Fahrenheit and Celsius are not the same. This was good discernment practice for a few years after that when in a feverish stupor I was convinced I had a tail, which spoiler alert I did not.
14, 18: Yeah, Seeds has it right. Another way to put it is that gravitational mass* and inertial mass† are always exactly the same. So when you have a heavy object and a light object, the earth's gravity exerts more force on the heavy object, but it needs more force to accelerate the heavy object by the same amount, so the gravitational acceleration of the two objects comes out to be same.
_______
*Which is a measure of how much force a gravitational field is going to exert on an object -- if you have a 1kg mass in the earth's gravitational field, and a 2kg mass in the earth's gravitational field, the force on the second mass is twice as big as the force on the first mass.
† which is a measure of how much force it takes to accelerate an object a given amount -- if you have those same 1kg and 2kg masses, you need twice as much force to accelerate the second mass by 1 meter per second squared as you do to accelerate the first mass by the same amount.
Just think, if you'd been using the Celsius scale you would have died! Thank goodness the US refused to go metric.
28: I guess my question was more thinking of two sets of gravity, the earth's gravitational force on the object and the object's gravitational force on the earth. Maybe that second thing doesn't exist but nobody has ever explained to me why.
27: Spoiler alert also for "A Day's Wait".
They're the same! Equal and opposite, like Newton said. When you hold up a 1kg dumbbell there's a 9.8 newton force pulling the dumbbell down toward the center of the earth, and a 9.8 newton force pulling the earth up toward the center of the dumbbell. You just don't notice the earth accelerating toward the dumbbell much because it's really heavy, and 9.8 newtons turns into a very small acceleration when applied to the mass of the earth.
I guess that makes sense. But what if you had a planet with mass X and a planet with mass X/2 coming together. And then you had a planet with mass X and a planet with mass X/4 coming together.
Assume one planet has everybody black on their left side and white on their left side, one planet has the reverse, and one planet has everybody dressed like 1920s mobsters from Chicago.
The one I remember as a kid, wandering around the playground in second or third grade thinking my thoughts, was: so God is all-powerful. What does it mean to be all-powerful? Then you can do whatever you want to do voluntarily, but you could also do everything without thinking about it, but you can also do the opposite of all those things simultaneously, both the voluntary and involuntary -- I didn't understand the relationship between power and will. I learned in college, if memory serves, that Aquinas says of God that he is "all actual and no potential;" but in my juvenile mind it was all potential too, and therefore a lot of self-cancellation, and then I couldn't derive the transcendental law that would select either one thing or its opposite and result in the world we live in. This was all in theory because I was raised by atheists, and the idea of God, introduced to me as a fiction, was a completey fascinating puzzle.
I also remember, more dimly, that the other kids found me kind of puzzling.
I bet Aquinas had the same problem.
35 reminds me of a conversation I overheard a few years ago. I was in a park and a group of kids around 8-10 years old nearby were having a quite elaborate discussion about whether God and Mother Nature were the same thing or different, and, if they were different, then in what way.
There is this painting of him boring Averroes into a coma. I totally bored more people than that at a time.
33:
Attraction between X and 0.5X is F = 0.5GX^2 / R^2
Attraction between X and 0.25X is F = 0.25GX^2 / R^2
Acceleration of mass 0.5X towards mass X is a = (0.5GX^2 / R^2) / 0.5X = GX / R^2
Acceleration of mass 0.25X towards mass X is a = (0.25GX^2 / R^2) / 0.25X = GX / R^2
So both of the lighter planets would accelerate towards Planet X at the same rate. However...
Acceleration of mass X towards mass 0.5X is a = (0.5GX^2 / R^2) / X = 0.5GX / R^2
Acceleration of mass X towards mass 0.25X is a = (0.25GX^2 / R^2) / X = 0.25GX / R^2
So mass X accelerates towards mass 0.5X twice as fast as it does towards mass 0.25X. The same is true of two objects on earth, one twice as heavy as the other - but as per LB's 32, because of the relative difference in masses, nobody cares about the force exerted on the earth by a homeless person's defecation as it falls from a tall building onto somebody's step. But looking at the answers above, we see that with planets of similar masses, the acceleration of both planets is important - Planet X falls towards the smaller planets with either a half or a quarter of the acceleration with which they are also falling towards Planet X, which will have a significant effect on the relative velocity when they meet.
39 was me. Sorry that it's not very easy to follow.
I was told there wasn't going to be math on this blog.
That makes sense. Unless R^2 is the coefficient of determination like it is for normal people.
Basically, I was picturing it like two people on wheeled carts pulling on a rope from two different ends and that's not the right analogy.
The right analogy is an elevator being pulled through space by a rope attached to giant elephants standing on turtles.
I'm pretty sure 39 is right, and is sufficient to answer the question. If we actually wanted to figure this out how much faster it'd appear to be accelerating the other object, we'd probably have to do some integrals over time (since the positions of the two centers of gravity affect each other, constantly changing the distance between them) and we'd want to compute the acceleration of the second body in a non-inertial frame of reference centered on the moving first body (assuming an earthbound observer). Tricky. Or maybe I'm overthinking it, not having done this in years.
If we assume that Planet X is earth then it's all purely academic anyhow, as either of the other planets will be sufficient to wipe out all life when it arrives. Unless the earthbound observer is Bruce Willis and a ragtag team of rapidly reskilled former coal miners, I suppose. Also, this kind of problem is probably why Newton invented calculus, before getting distracted by capturing coin forgers.
To the question of "is energy real?", I think the answer is actually no. It's a useful concept, but not a real phenomenon. All conceptions of energy, even something as intuitively tangible as temperature, are actually measured in incredibly indirect ways. For example, temperature is usually measured by bringing a liquid into thermal equilibrium with your sample and then relying on the fact that its volume happens to be proportional to the temperature.
Or the earthbound observer is a hyperintelligent AI - in which case it probably welcomes the planet and its mineral resources, which can be extruded into wire for the production of stationery.
Similarly, the fact that heat is a thing and cold is not a thing is also semantic. We insist on it because we know temperature is motion, and we semantically feel that motion is a thing and "less motion" is not a thing. When you break in pool, you say that the moving cue ball caused the other balls to move, not that the unmoving racked balls caused the cue ball to move less.
How about, coming at this from a surely philosophically unsound way: energy is the metric used in various conservation laws. Conservation laws are the results of various symmetries over time, space, etc (Noether). Those symmetries are, if not real, closer to the truth.
Anyway, playing around with what I said before, we want to consider the distance between the two bodies; if we consider the body we're on fixed, we'd assign the acceleration entirely to the other one. Let f(t) be the distance between the two bodies; playing around with the equations, it must satisfy the gratifyingly obvious equation f''(t) = -G(m1-m2)/f(t)^2 (the sign is an artifact of how I got there and can be ignored). Alas, I'm not very good at diffeqs.
I have a vague feeling that that semantic distinction is a consequence of being on a [0, inf) scale, i.e. because it's bounded at one side and unbounded at the other.
49 (especially): I think this is probably where 7 year old me got stuck, and where much-older me continues to get stuck. We've evolved to intuitively understand things in a highly specific context. (Things that we can directly observe with our sense organs, or imagine observing - did a particular person read an email regarding contact with Russia, Y/N?)
For everything outside of that, we need to use models, which we can analogise to more- or less-intuitively attractive Just So stories. The concept of "truth" in the sense of "did a person read an email" isn't so useful here - the model may or may not correspond to an intuitively sensible experience, but better questions might be "does this fit the data?" or "can we use this to make predictions?". To put it another way, the concept of energy is unlikely to be anything that I can truely understand, other than through a mathematical model, or by imposing the idea of it on bathwater or a train or whatever - so is it really relevant whether it truly "exists" or not?
53.last: Not really, as far as I'm concerned. It's totally okay to act like it's a thing that exists much in the same way you act like cows and clouds and me and you are things that exist. All thinking is modeling, to various degrees.
'"I am"... I said,
To no one there.
And no one heard at all,
Not even the chair.'
Thanks for introducing me to Noether's theorem. I'd never seen it before.
I agree with 53 and 54. We're modeling like crazy based on algorithms we evolved to deal with observable phenomena. Quantum mechanics drives people crazy because its behavior doesn't fit any of our pre-existing modeling algorithms, hence it doesn't "make sense".
33: I thought, "ooh, you know, that's probably close to the Pluto/Charon condition". But it turns out that Pluto is ten times as massive as Charon, so it's not as cool as your X and X/2 condition.
(From the discussion after Pluto's demotion and on the recent New Horizons mission, I thought that they'd be closer, particularly given the "double dwarf planet" loose talk. But 1/2 the diameter is 1/8 of the mass...)
47. We're all just vibrations, man.
Conservation of energy for the motion of the solar system is pretty precisely measurable-- energy has a definition as specific as that of momentum.
Millikelvin refrigerators are pretty common. Microkelvin refrigeration is possible, but only for much smaller volumes of helium. NIST publishes standards for precision of radiometric measurement of higher temperature. Very close, I don't know how to many significant digits, conformance of observed spectra to Planck's law is another consequence of a definite definition of temperature.
Millikelvin refrigerators are pretty common.
All the beer bottles shatter when I use one.
59: I was going to bring up the issue of quantisation of energy (absorption and emission spectra etc) but decided that I'd already got myself in enough hot water. As it were.
A previous time where the boundary between empirical observation and speculative math came up here, Quine's essay on the topic, Two Dogmas of Empiricism, got mentioned.
Someone, I think McG, mentioned that it's now seen as dated, but I didn't retain pointers to further reading, if any got mentioned.
Also worth mentioning that any mathematical formalism that tried to be based around "coldness" would probably just end up being heat-based, but with more complexity thrown on top. Like epicycles. You could do it, but with what we know why would you? (For the lolz, obviously.)
Someone, I think McG,
I like to imagine that McG would like unfogged if he read it.
52: I have a vague feeling that that semantic distinction is a consequence of being on a [0, inf) scale, i.e. because it's bounded at one side and unbounded at the other.
In geophysics for certain problems it is easier to think about/work with "slowness" (it is just the inverse of velocity). And a potentially useful concept for other simple motion problems but it does suffer from just that--at rest value is ∞.
I guess the tail thing was really disappointing?
Not that anyone needs more to read, but Jennifer Coopersmith wrote a tolerably accessible book on this: Energy, The Subtle Concept. It's a pretty comprehensive history of various attempts to define what energy is, and it sheds some light on the legitimacy of anthropocentric-mechanistic definitions. Apparently she also has a blog where she's posted a short summary as well ("What is energy?").
Bruce Willis and a ragtag team of rapidly reskilled former coal miners
Please. They were oil drillers.
"In a world where shutting the fuck up can't happen...."
It's just so loud with only one kid.
I have no idea how people with 2+ kids find space to think.
OT: It's getting impossible to pick your nose in public anymore.
I'm beginning to have doubts about your J&O friend. Is she good at meaningful silences?
76: I haven't seen her in person in ages, but she was a music major of some sort, so I suspect she can be quiet when she needs to.