It is immediately clear that Sardi et al.'s new Dendritic, non-synaptic paradigm of memory acquisition was inspired by the Codex Seraphinianus:


The paper is written in first person despite having six authors. The first-person "I" appears to be Prof. Ido Kanter, a reincarnation of Copernicus, who even remembers Copernicus' unrecorded thoughts.
It does not present any data, or any novel hypothesis... the paper is best understood as a paid advertisement for an earlier publication by the same group which did have a hypothesis and a lot of hand-wavy computer simulations, also some results from new types of experiment on
All becomes clear when we examine a press release for that earlier publication and discover that Prof. Kanter is a physicist. Stand back, neuroscientists! Here is a physicist, to explain how you have been neurosciencing wrong all these past seven decades!
The press release is a small masterpiece of dumbing-down, combined with imprecision, hubris, profound ignorance of the "century-old assumption" that the author intends to topple, and a grim determination to be not even wrong.

Their number is approximately one Tera (trillion), similar to Tera-bits in midsize hard discs.Towards the end it climbs to new heights of bafflegab:
The new results call for a re-examination of neuronal functionalities beyond the traditional framework and, in particular, for an examination into the origin of degenerative diseases. Neurons which are incapable of differentiating between "left" and "right"—similar to distortions in the entire human body—might be a starting point for discovering the origin of these diseases.Neuroskeptic noted "the problem with dendritic learning as an exclusive mechanism of learning" (compared to the old pre-shift paradigm of post-synaptic modification learning)
...is that it leaves each neuron with only two or three ‘degrees’ of information capacity.
A neuron can have thousands of synapses and if they are all independent, that’s a lot of potential information storage. Whereas if plasticity is confined to the primary dendrites, this massively reduces the information capacity of each neuron.
[See also S. Clyde, two months ago]
From the Physicist perspective, this stark simplicity is Feature not Bug... an index of how Nature should work, if only a physicist had been in charge of the design. If Kanter were right, Evolution would have been negligent by missing the opportunity to store information ('memories") in the medium of synaptic changes...Clear out your desk, Evolution, you are fired.
[H/t Leonid Schneider]