If it takes multiple action-potentials to cause one action-potential in another neuron, why don't brain signals dissipate almost immediately I just got into neuroscience like a couple of months ago, but I can't, for the life of me, figure this out. Wouldn't it take a humongous amount of action-potentials in, for example, the thalamus for a small number of neurons to fire at the opposite end of the brain in the frontal cortex? Also, usually, signals travel from the cortex back to the thalamus, so is it possible for signals to get boosted in some way? It just seems there wouldn't be enough action-potentials for there to be any circuitry in the brain. 

Edit: My thought process is very mathematical, and I didn't think about temporal summation when thinking about this, but let's say, for example, that it takes 4 APs to fire a single neuron. That would mean that y = x/4, with y being the amount of output APs and x being the amount of input APs. Let's say that 100 million neurons need to fire to reach the end of the frontal cortex. That would mean you'd need 400 million input APs in total to reach the end of the frontal cortex. That seems like a lot, but while typing this, I feel like my grasp of some of the more basic aspects of neuroscience isn't really that great. I'm self-teaching so maybe that has something to do with it.
This answer is a bit below my normal referencing standards, but hopefully helps you with some things you're missing and motivates further reading...


Thalamus (at least parts of it) projects directly to frontal cortex (and everywhere in neocortex). Just one synapse from thalamic cell to cortical cell. Neurons send long projections (axons) from region to region. So, with your assumption of 4 presynaptic neurons per cell (which is probably on the low side, but see 2 and 3 below) that would mean just 4 cells in thalamus, rather than 400 million.
In the CNS, especially in the brain and even more especially in neocortex, connections are one-to-many (divergence) and also many-to-one (convergence). When one cell fires, it influences many other downstream cells (for order of magnitude you can assume "thousands"). The strengths vary: some cells get larger inputs than others from the same cell.
Most connectivity is local, and the entire brain is constantly active. For typical neocortical cells, you might see a minimum firing frequency of around 1 Hz in normal in vivo conditions. There are billions of cells each connected to thousands of others, so any one cell is receiving many many inputs at any one time. Other inputs arrive on this background of activity.


I'd recommend starting with a basic neuroscience textbook; Purves' Neuroscience is a good one as is Kandel's Principles of Neural Science. If you're coming from a more computational background, Dayan and Abbott's Theoretical Neuroscience is also a good book, but I'd suggest pairing it with something more rooted in biology as well.