Another interesting thing about the steam engine is much of science in the 1800s was dedicated to figuring out how steam engines actually worked to improve their efficiency. That may be similar for AI, or it may not!
We made an AlphaGo like implementation for the card game Dominion. Certainly not the same number of cards but similar complexity. I have high confidence the same techniques would work for mtg. In fact possibly better as mtg doesn't lend to large search depths. Though possibly worse as there is more hidden information (though that depends on if the format has open deck lists and/or how much of the meta is provided to or trained by the nn)
And in fact, the first engines were developed without a robust understanding of the physics behind them. So, the original version of 'engineering' is more closely to the current practices surrounding AI than the modern reinterpretation the root comment demands.
(1712) Newcomen Engine
(1776) Watt Engine
(1807) Atomic theory of Gasses (Dalton)
(1807) Concept of Energy (Young)
(1824) Carnot Cycle
(1834) Ideal Gas Law (Clayperon)
(1845) Relationship between work and heat (Joule)
(1840-60s) Laws of Thermodynamics (Carnot, Clausius, Kelvin)
For over a century, there were a group of people working on building, maintaining, repairing, refining and improving engines, called 'engineers', who had a very incomplete picture of the physical laws surrounding them. I would assume there were many explosions and other accidents along the way (as there continue to be).
The investment in the science of thermodynamics and the chemistry of fuels was largely motivated by the value of the steam engine, and the attempts to improve efficiencies allowing miniaturization, enabling locomotives and the railroad boom, and eventually automobiles and powered flight.
I think the era from say 1950..2020 has been a relatively unique period in history where science has been ahead of praxis (though folks in medicine or other fields might not have had that luxury). Recent advancements in AI preceding strong theoretical foundations might be a reversion to the mean.
Seems like it'd be relatively easy to allow one to 'smooth' their income over multiple years. Imagine paying 100 income at 40% tax year 1 and 0 income year 2. A scheme where you could retcon things to be 50, 50, each at say 30% for a 10k refund (or at least credit) seems very doable.
I don't understand how inflation and risk wouldn't/aren't priced in. You have $1000. You can: put it in your mattress, put it in 'safe' treasury bonds at inflation +a few percent, or yolo it in NVIDIA. Yes if bonds are returning less than inflation you don't buy them and that makes financing more expensive but it's not somehow unfair vs the other things you could do with capital.
Seems like return is roughly proportional to risk(1-tax)investment so changing tax should affect everything proportionally (barring cheating/avoiding the system in some way).
There's no inherent right to anything, really. The statements in whatever declaration or philosophy are just arbitrary lines. Physical property rights are just as arbitrary as the divine right if kings (and incredibly closely related when that property is inherited!)
The argument really isn't based on rights, it's based on the rules of the game have been that people that make things get to decide what folks get to do with those things via licensing agreements, except for a very small set of carve outs that everyone knew about when they made the thing. The argument is consent. The counter argument is one/all of ai training falls under one of those carve outs, and/or it's undefined so it should default to whatever anyone wants, and/or we should pass laws that change the rules. Most of these are just as logical as if someone invented resurrection tomorrow, then murder would no longer be a crime.
The similarity between divine right of kings and inheritance is that an unearned is transferred via circumstances of birth.
Your statements seem to extend that further: If you rent an apartment, you the property is owned by an landlord (lord is literally in the title!) and passed down by their wishes. Similarly if you work for Walmart for life, the company is owned and passed down by the Waltons. In these cases the property rights extend beyond life and are transferred via circumstances of birth, while the rights of labor end.
Interesting that IP rights are ended by death (or death+n years) as well. This line of reasoning suggests maybe that should apply to all property.
Real world efficiency factors are in the 90s and basal rates aren't constant. The model you're proposing is too artificial to draw conclusions about fasting over a short timeframe.
5. Fixing a bug means you have to go through a re review of your marketing assets that haven't changed in 3+ years and there's a non zero chance each time your review could result in _your app being removed from the storefront_ and losing _days_ of revenue after you appease whatever whimsical issue wasn't an issue the hundreds of times you've submitted previously and wait for the next review slot.
> You can't just plug numbers into Coulomb's Law for this case, because Coulomb's Law by itself is not relativistically correct.
Sorry if this is a bit pedantic, but as someone trying to study this at the moment, I don't see this the same way and I'd like to validate my interpretation: You can just plug numbers into Coulomb's law, that part is correct. But then the problem of infinite velocities comes from interpreting the 'F' side of the equation, assuming Newton's law (F=ma), rather than using its relativistic counterpart.
Coulomb's law:
F = qq'/r^2
Lorentz force law:
F = q(E + mu x B)
For the 2 particle case, both of these say the same thing (substitute into the Lorentz eq E = q'/r^2, B = 0 and you get the same thing).
The promotion from non-relativistic to relativistic mechanics is a change of what 'F' means.
nonrelativistically: F = p' = m v' = m x'' = m a
relativistically: F = p' = \gamma m v' = \gamma m x'' = \gamma m a
where \gamma is the Lorentz factor.
Interpreted this way, infinite velocities are avoided.
But, as r->0 we still have an infinity problem - namely infinite energy! This necessitates a quantum mechanical correction to both the Coloumb and Lorentz laws.
TLDR: relativity is necessary when things start to move 'very fast', qm is necessary when things are 'very small'
You can plug arbitrary values in, but you can not expect to gain any valid predictions or reasonable physical insight from Coulomb's law as soon as you are no longer dealing with static point charges. That's because B and E are not independent quantities but actually closely intertwined components of the electromagnetic field strength Tensor F. As soon as you start dealing with motion, these components will mix, preserving only certain quantities like the tensor contraction E^2-B^2. So even if you construct a case where B=0 at time t=0, that will no longer be true once you had any acceleration of your charge carriers.
In the fundamental quantum field theory picture you don't even have forces and particles in the original sense anymore. The dynamics are then described by interaction between the em field and charged fermionic fields. Stuff like Coulomb's law (or any other force potential) only emerges as a macroscopic low energy approximation for specific field configurations.
In a classical view of 2 particles accelerating towards each other v x r will always be 0 so B will always be 0 even if the particles are accelerating towards each other. I believe all this holds under QFT [1].
Looking further a redefinition E is necessary when including the \beta factor [2]. So that was a mistake on my part - relativity does change the rhs of Coulomb's law.
Admittedly the problem as stated (two particles falling towards each other) constrains things in such a way that there is no off-axis contribution. Or to put it another way, 1d electromagnetism doesn't have magnetism.
It doesn't even hold in ordinary QM (because there are no point charges anymore, only charge densities) and it fails completely in QFT for interacting fields. What you linked is an intro example from many textbooks that shows how the tree level diagram in the nonrelativistic limit can indeed yield the Coulomb potential. At the tree level you will often see such "classical" behaviour. But if you consider higher order corrections, the picture changes rapidly. See the Uhling potential for a practical example, but for higher loops this gets analytically intractable very quickly. The world starts to work very differently once you reach these length scales.
Not if you want to get correct answers in problems that involve moving charges.
> relativity is necessary when things start to move 'very fast'
In electromagnetism, relativity is necessary whenever charges are in motion. Whether or not they are moving "ver fast" is irrelevant. Coulomb's Law is only valid when you have a charge at rest.
That said, the post I originally responded to obviously was talking about charges moving "very fast" since it claimed an electron falling towards a proton could exceed the speed of light.
Hi greysphere, you are definitely correct that one primary thing preventing velocity of the electron from exceeding than the speed of light is the presence of gamma in the relativistic force law, aka \partial_t (m_e \gamma v ) = q_e(E + v \times B), although the LHS doesn't quite equal \gamma m_e a, since \gamma also depends on v...
In general I think it's fine to use Coulomb's law as an approximation in this case because the proton is much heavier than the electron and so we can just stay in the proton's reference frame and let the electron fall in from infinity (and we're ignoring QM and just doing relativistic EM here). We could also switch to a tritium nucleus and make it a bit better of an approximation, or indeed add a whole bunch more neutrons and get lucky that they don't beta decay to make it an arbitrarily good one. It is true that if the proton starts moving that you will no longer have a pure Coulomb field with respect to the original reference frame, as after a Lorentz boost the E field gets squished into the transverse direction somewhat, and you'll gain a B field swirling around the proton...
Staying with the frozen proton approx, if we plug numbers in we get quite a bit of energy: set the proton radius r_p to 1E-15, and we get U = q_e^2 / ( 4 \pi \eps_0 r_p ) ~ 1.4 MeV, or a gamma of about 4, so yeah, it would be moving faster than c if we stayed with Newtonian mechanics. But there's another wrinkle: the 1.4 MeV of liberated potential energy won't all go into the electron's relativistic kinetic energy, because it is accelerating like crazy, especially in the final femtometers, and that acceleration (essentially Bremsstrahlung, although its not braking here) will generate an intense pulse of EM radiation as well - a decent fraction of the 1.4 MeV will go into that instead. You could perhaps estimate how much using the Larmor formula (in general calculating this radiation reaction force precisely becomes very complex, because the excitation of the EM wave modifies the acceleration, which modifies the excitation of the EM wave etc... And, now looking on Wikipedia, I'm not surprised to see that the first QM version of the calculation was done by Sommerfeld).
So yeah, the electron will zip through the proton, with much of the potential energy converted to an EM pulse that zips off to infinity, and so the electron is now bound to the proton, and will continue to zig zag back and forth, emitting more radiation until it comes to a rest inside the proton. So yeah, we do need QM after all.
Thanks for the explanation of some of the interactions I was missing! It's amazing the complexity of what's basically the simplest setup one could think of.
This is extremely unlikely unless the relative motion is very slow, or, to put it another way, the total center of mass energy is very close to the rest energy of electron + proton, so there is a significant probability amplitude for capture into a bound hydrogen atom.
The post I originally responded to was obviously not considering such a case since it claimed the electron could exceed the speed of light.
If the electron starts with zero energy at infinity (e.g. a parabolic orbit, a natural default assumption), and some of the potential energy is converted into free EM radiation due to acceleration of the electron as it is falling down the potential well, then it will become bound to the proton. My reading of phkahler's original statement is that the electron will wind up going faster than the speed of light (which is incorrect, due to gamma) due to falling down the potential well, and not due to having non-zero kinetic energy at infinity...
> If the electron starts with zero energy at infinity...it will become bound to the proton
Even if that's true (I'm not sure it always is--see below), that case is extremely rare. A much more common case is Bremsstrahlung, which you mentioned upthread--and as the Wikipedia article you referenced notes, the electron in this process starts out free and remains free after the radiation is emitted; it does not become bound to the proton.
> My reading of phkahler's original statement is that the electron will wind up going faster than the speed of light (which is incorrect, due to gamma) due to falling down the potential well, and not due to having non-zero kinetic energy at infinity...
That may have been the original intent, yes (and, as you note, it's wrong because it neglects the gamma factor). However, even in that case, what matters is not the electron's energy at infinity in the proton's rest frame, but its energy in the center of mass frame. If the electron is really falling in from far enough away that the relativistic gamma factor is relevant, which is what was implied by pkahler's original statement, then its energy in the center of mass frame (or more precisely the center of momentum frame, since in relativity you have to take momentum and energy into account) will be relativistic, i.e., large enough that it's by no means guaranteed that it will emit enough energy in radiation to become bound to the proton.
