How much clamping pressure would it take to hold up the weight of a human? I don't know anything about physics. This question comes from an argument I had with a friend. Basically my question is this: Is it possible for a human to hold themselves up only by clamping their hands down on a flat wall overhead. The wall is completly flat and their arms are at full extension. I want to know how much pressure the person would have to exert to accomplish this and if it is humanly possible. 

 A: Interesting experiment. Let's have a look.
In order for you to hold yourself up, there must be a force pulling upwards. Your weight $w=mg$ pulls down as always ($m$ is your mass in kilograms and $g=9.8\;\mathrm{m/s^2}$ the gravitational acceleration here at Earth), and in this scenario I can only identify one force pulling up: friction. Static friction $f_s$, to be precise. In fact, this force is acting at each hand, so you have it twice. The force balance (Newton's 1st law) will look like this:
$$\sum F=0\quad \Leftrightarrow \quad 2f_s-w=0\quad \Leftrightarrow \quad 2f_s-mg=0$$
Static friction can be modelled as
$$f_s\leq \mu_s n\quad ,$$
where $n$ is the normal force caused by your perpendicular pressure onto the surface and $\mu_s$ the friction coefficient that depends on roughness and alike. According to this model, static friction is always less than the product $\mu_s n$, which constitutes the maximum value it can take. Let's replace $\leq$ with a $=$ so that we are just at the max limit; the $n$ will then be the minimum necessary normal force that you must apply to still have enough friction:
$$f_s = \mu_s n$$
We can now plug this in and isolate the normal force we must exert:
$$2\mu_s n-mg=0 \quad \Leftrightarrow \quad n=\frac{mg}{2\mu_s}$$
So here we are at a final expression for the force $n$ you must apply with each hand.


*

*The heavier you are (the bigger your mass $m$), the more force you must apply - of course. 

*Conversely, if the surface is rougher (has a higher friction coefficient $\mu_s$), then you need less force (try to wipe the wall in soap first, and you'll see the effect of a reduced roughness and $\mu_s$).


Compare this with the derivation in this link where they do pretty much the same considerations to calculate the force needed to do parkour wall climbing, except for having a slightly more complicated scenario with angles that must be taken into account.
With this expression we can basically calculate the necessary force and compare with what is humanly possible. We just need to know the value of $\mu_s$. I looked it up and found this article about friction on a rough climbing wall where they measured $\mu_s\approx0.7$ (I rounded up a bit). This is for a hand against a quite rough wood-like surface. Let's go with that for now and calculate this for an adult at $m=80\;\mathrm{kg}$:
$$n=\frac{mg}{2\mu_s}=\frac{80\;\mathrm{kg}\cdot 9.8\;\mathrm{m/s^2}}{2\cdot0.7}=560 \;\mathrm N$$
So, this would be an estimate for the necessary force exerted per hand. Is that possible by the human body? We'll have to find some measurements and studies to compare with to figure that out.
I found this NASA study that tests strengths of either hand in different positions and setups. It shows something around $500-700\;\mathrm{N}$ for an average male when pushing to each side and up to above $1200\;\mathrm N$ when having your back against a wall and pushing with both hands forward. Neither scenario fits our scenario perfectly, so you'll have to go Google for some better values - or test it yourself with a newton-meter pressure-plate or alike to get a better feeling of it.
(Maybe try to simply measure it with a household scale? Grab it in your hands and press from either side with stretched arms. The reading of the scale is given in kilograms, so multiply with $g$ and you have it in Newton. It might give a fairly reliable value for the force you can exert in this stretched positioning manner.)
Also, keep in mind that $\mu_s$ might be much smaller than the one used above if your wall is more smooth or slippery. The value used above is fairly rough I would say, but more Googling might help you out here as well.
I hope this helps.
