butt*

Always probe multiple spots before taking it off. The probe you leave in the meat while it smokes won’t necessarily give you the right info about the meat as a whole. Usually when this probe hits 200 I’ll start poking around the rest of the butt with my probe, and often times I find that it’s much lower, like 193. So then you know to keep it on a bit longer.

Also I personally think it’s better to pull around 202 rather than 197. But others may disagree on that.

I’m sorry, I truly didn’t mean that to sound rude. But in retrospect it came off that way. I apologize about that.

That said, you are definitely mistaken here. This is all standard dimensional analysis. Indeed, the first source you list literally says exactly what I wrote in the very first sentence: “there are dimensionless quantities and dimensionful ones like c and h”. I.e velocity and action are dimensionful.

You may be thinking that the comment on page 6 means that natural units makes velocity dimensionless. But we need to interpret the authors’ statement correctly. The first key thing we need to notice is that a ratio whose numerator and denominator have the same dimensionality (e.g. a ratio of velocities) is always dimensionless, because the units cancel. As an example, no matter what units we pick, a velocity ratio v/c (where c is the speed of light) is always dimensionless. However, in natural units it just happens to be the case that v = v/c for all velocities v. But we have to be careful about interpreting the "equation" v = v/c. Both sides have the same *numerical value*, but not the same *dimensionality*. It is only the right side, v/c, that is dimensionless; the lefthand side -- which is just a velocity, not a ratio of velocities -- is still dimensionful. (The first reference you linked says precisely this on page 6).

This is also why angles are dimensionless. They are equivalent to ratios of lengths.

This is also why the fine structure constant is dimensionless. It’s given by

alpha = e^ 2/(4\pi\epsilon_0\hbar c )

If you do the dimensional analysis, most of the units in the denominator cancel, leaving you with a dimensionality of [Q]^2, I.e. charge squared. That’s the same dimension as the numerator so we are left with a pure number, I.e a dimensionless quantity.

Consistent with these examples, most physical dimensionless quantities are described as dimensionless precisely because they are *defined* as a ratio whose numerator and denominator have the same dimensionality.

For more discussion, see, e.g., this discussion on stackexchange.

https://physics.stackexchange.com/questions/224232/why-is-the-action-dimensionless-in-natural-units#:\~:text=Since%20the%20action%20is%20the,it%20has%20mass%20dimension%20zero.

As the first reply to this question says, in natural units with hbar = 1, it is not action that is dimensionless, but rather ratios of the form S/hbar (where S denotes action). Action, S, is still dimensionful. But it just happens that in natural units *the numerical value* of the ratio S/hbar is the same as the numerical value of action itself, S.

I hope this helps to clear this up.

Err…this is not a subjective issue, so there isn’t really room for disagreement. And all of your statements in this comment are false. You are confusing a convenient choice of units (such as units of time and distance that result in c=1) with the property of being dimensionless. They are not the same thing.

With some Googling you could easily find a good resource for leaning about what it means for a quantity to be dimensionless versus dimensionful. That would be more productive than trying to debate the issue before knowing the basic definitions. Then it will become clearer why velocity and most other physical quantities are dimensionful, whereas angle is not.

Velocity is not dimensionless. You can normalize c=1, but that doesn’t make it dimensionless. Angle is dimensionless because it is equivalent to a ratio of lengths, and in that ratio the operative unit of length cancels out (i.e. the numerical value of this ratio doesn’t depend on what unit of length you choose).

Perhaps it was just a really bad churro

“This retort is full of misunderstandings.”

[proceeds to write paragraphs of gibberish]

This happens to me all the time when I eat markers and crayons

Also if it’s gonna be 6-8 eps every 2 years that’s just too slow to revive the massive popularity GOT reached in its prime

So does she

I’m told that an affinity for corndogs is the third core element of attractiveness

I hope not. Then you’ve gotta worry that some horny teenagers will bust into the truck and suck on him. Of course, some might say that kind of thing is “just a natural part of growing up” or “we all did that stuff,” and I suppose there’s some truth to that. But there’s still a part of me that thinks it’s just not good behavior.

One little nitpick. Your statement that log(y) doesn’t make sense if y is a function is not correct. So long as the image of y is a set of positive numbers, this is just a simple composition of functions.

He’s big-timing us while complaining about a big-timer!

This is top-notch badmath. The secondhand embarrassment is intoxicating.

Actually this happened because someone forgot to turn on airplane mode on their phone

Well, the researchers of Reddit are quite confident

Hopefully he wasn’t seriously injured

Have you considered simply making more money?

You could buy a lot of butterscotch with that much money.

Yes, but here dx is applied to only one of two terms in a sum, which is nonsense.

They’re generally price regulated.

8 mile is good, but I’ve always felt the main character should’ve been played by Tom Selleck.

I once made the mistake of mixing my politics with my corndogs. Never again.

Man, the grilling and smoking subs are so filled with douchebags.