Thank you very much for sharing that paper! Its a really nicely written paper, I like their figures a lot.

I think you have slightly misunderstood the paper (either that or I am missing something). In the paper, I think they are abusing the word "spin". Every single place the paper says "spin", they don't actually mean spin (as in, the intrinsic spin angular momentum of light), they actually mean direction. So, when reading the paper try and read it through a mental translator where "left handed spin" translates to "left propagating".

The spin angular momentum of light is (for a plane wave in vacuum) controlled entirely by its polarization, either left handed circular polarization or right handed. Importantly, this polarization depends on the fact that their are 2 spatial dimensions that are orthogonal to the propegation direction, so that for example the electric field could be expressed as:  E = (1, i, 0) in an (x, y, z) basis and z the propegation direction. (Similarly (1, -i, 0) for the other polarization with the opposite spin).

In this paper they define what they call the "left handed" and "right handed" operators in the unnumbered equation immediately under equation (10). However, these operators are NOT left hand polarized and right hand polarized light waves. The operators differ, not by the relative phase of orthogonal electric field components, but by the relative phase of the electric and magnetic fields. This means they are "left travelling" and "right travelling" (IE propagating left or right) light waves. They have confusingly chosen to call these terms "spin", I think this is because the equation they have derived looks like a Dirac equation, and in the Dirac equation those terms are called spin. But they are not the actual spin angular momentum of the light, they are completely unrelated.

In short, they don't actually consider real spin at all, they just rename "direction" to "spin".

They say theyr are in full agreement with Stephen Barnet (option number (1) in my post), that Minkowski's momentum is the canonical one (to be used in Heisenberg uncertainty type situations) and Abraham's is the kinetic one (to be used in Newtonian recoil calculations).

If I told someone 'I bet stockfish could beat you at Chess' i think it is very unlikely they would demand that I provide the exact sequence of moves it would play. 

I think the key differences are that (1) the adversarial nature of chess is a given (a company merger could or should be collabroative). (2) People know it is possible to 'win' chess. Forcing a stalemate is not easy. In naughts and crosses, getting a draw is pretty easy, doesn't matter how smart the computer is, I can at least tie. For all I (or most people) know company mergers that become adversarial might look more like naughts and crosses than chess. 

So, I think what people actually want, is not so much a sketch of how they will loose. But more a sketch of the facts that (1) it is adversarial situation and (2) it is very likely someone will loose. (Not a tie). At that point you are already pretty worried (50% loss chance) even if you think your enemy is no stronger than you.

I was once in a situation much like yours considering the same question. 

Arguments I considered at the time (when considering if I should "dress up" more in search of a romantic partner):

• Do I actually know how to dress better?
• Would dressing up differently than normal make me feel like I was impersonating/deceiving, thereby feeling more insecure and countering any gains in dress with losses in confidence?
• Would this contribute to acquiring the wrong type of romantic partner? In the sense that, my interests, priorities etc might be strongly correlated with my poor dress sense, and that therefore changing the dress alone might disproportionately help with partners that are a bad match.

My very small data sample is that, I didn't change anything. Then, at a fancy dress party (where everyone was weirdly dressed and my costume had not been picked by me, but was part of a matching set with friends) I met  someone and things went great. I don't know what to take from this, maybe fancy dress parties (or other settings with "non normal clothes", like a wedding) are good for people in your situation. At the very least, if your clothing choice is proving to be a barrier then events like this provide you with a good opportunity, to either solve the problem, or possibly help diagnose if you could benefit from different everyday clothes.

Of course, there is a strong chance the fancy dress aspect was coincidence.

This was a fun post. I liked the way the "how many layers deep" idea was foreshadowed and built up to.

I see you are mostly on substack now, so you probably won't see this.

I was trying to think of a clean example of a many-layer deep interaction, and I think I have identified it in the way that my parents and their friends pay bills at a restaurant. (Obviously you are socially obligated to offer to pay, so you do. But they know that was a "forced move", which means that they can't take your offer to pay as a strong sign that you are genuinely happy to pay, so they don't accept the offer. But, you know that they know all that, so you can see that them rejecting your offer is also a somewhat forced move on their side, so you don't accept their rejection of your offer ... ).

Perhaps I am mudding the waters too much. I agree with your logic, and with your conclusions. I agree you are better off taking the option where you serve one less person to increase the total payoff.

What I was trying to say in the original post is that for most things there is the thing itself, and the measurement of the thing. For example maybe noisy thermometers are off from the actual temperature by some random variance. Things feel slightly more suspicious for utility, because the measure of the thing kind of is the thing itself, the split between the actual value and the measured value feels less defensible.

I don't think that is right.

If we ask 100 people which of two ice cream flavors they prefer, and get a 51/49 split, that does not at all imply that 99 people couldn't tell the difference and picked randomly, with the 100th person uniquely able to tell the difference. What we have is only similar to that on a population level. Its not that their is one person who can tell the difference perfectly and many who can't tell the difference at all, but instead many people who can all unreliably tell the difference a little bit.

You take a drug that reduces your chances of heart disease by 1%. You don't get heart disease. You will almost certainly never know if you would have got it without that drug. 

That is interesting. My guess would have been that you would learn fastest in jobs that are just a little above your current skill set. (Learn fastest does not equal 'most happy').

Although, your claim does seem to fit better with my lived experience.

While the argument itself is nonsense, I think it makes a lot of sense for people to say it.

Lets say they gave their real logic: "I can't imagine the LLM has any self awareness, so I don't see any reason to treat it kindly, especially when that inconveniences me". This is a reasonable position given the state of LLMs, but if the other person says "Wouldn't it be good to be kind just in case? A small inconvenience vs potentially causing suffering?" and suddenly the first person look like the bad guy.

They don't want to look like the bad guy, but they still think the policy is dumb, so they lay a "minefield". They bring up animal suffering or whatever so that there is a threat. "I think this policy is dumb, and if you accuse me of being evil as a result then I will accuse you of being evil back. Mutually assured destruction of status".

This dynamic seems like the kind of thing that becomes stronger the less well you know someone. So, like, random person on Twitter whose real name you don't know would bring this up, a close friend, family member or similar wouldn't do this.

In a vacuum, that logic seems good.

But, I know of several chain cooperatives that are very large, with lots of shops, etc. I live in the UK if that changes things at all compared to the USA. The ones I know are John Lewis, Waitrose, and Co-Op. (This is sort of double counting as John Lewis owns Waitrose).

So, all but one of the Co-Ops I know about are huge companies, although that comes with an obvious selection bias. (The only small one I know about is a random coffee shop I went to in Bristol that had a sign informing customers that they were helping to support a "radical, collectivist movement" (or something like that), they had 5 types of milk, none of them from animals. This sort of thing is very Bristol.)