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From what I can tell, if this work is actually correct it is an extraordinary accomplishment: we can both read and perceptibly write information in the brain, and transmit it between individuals directly. I mean, sure we can do that already by talking or waving hands or any number of other methods, but this means that perception-coding is effectively a solved problem.
I have not read the entirety of the detailed paper, so I cannot be sure that my critique is bulletproof, but based on my cursory reading, the following critique:

Unfortunately, because the information transmitted is a single bit, I'm concerned that there are all kinds of ways this sort of system could amount to "are they using this very, very general part of their brain or not?" transmission. On the receivers side the decoding could be accomplished not by "feeling the thoughts" in the sense we would expect (i.e. the thoughts of another person inside your head), but rather by having that single bit of information felt by the electric stimulation of the skin of the scalp, etc.

Granted, they do say they introduced noise into the signal -- but again, if the information is just one bit, and you're aware of exactly the information's timing, etc, it makes decoding it a lot easier. (No "When does the signal start?" problem)

I am long-term BCI/CBI Bullish, but I'm concerned this is less of a "new age" moment, and more of a "clever headline" moment

I believe some research out of Duke had already done similar things with chimps, but bringing it to humans is major. Each of these studies becomes a proof of concept for what "should" be true of the brain, but theories fall flat all the time. Each lays a brick in the foundation for building a true BCI.

I'm most excited that this was done with only an 8-channel OpenBCI headset, 16-bit, for the "Receiver". The "Senders" had a much stronger/better headset, but seeing open hardware show up in this is awesomely inspiring!

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One thing you have to be careful in EEG studies that transmit single bits is that EEG is very suspectible to muscle artifacts.

From:

https://www.ncbi.nlm.nih.gov/books/NBK390358/

Physiological artifacts may include cardiac, pulse, respiratory, sweat, glossokinetic, eye movement (blink, lateral rectus spikes from lateral eye movement), and muscle and movement artifacts.

You may not actually reading the brain of the sender, but rather that the sender moves their eyes or their jaws or gets excited and increases their heart rate when transmitting the information.

This 100%. There's just too much electromagnetic interference. EEG picks up facial movements most of the time, and greatly attenuated large-scale neuron oscillations at best. That's why neuroscientists studying brain functionality put electrodes in rodents rather than put EEG devices on them. This gives them way higher-fidelity data.
Follow up -- whatever people think of Elon Musk, he isn't wrong about this. If humans ever reach a BCI future, it will have to be in vivo. The first step is making intracranial BCIs safe, the next step is to make them useful. They have much more promise than external BCIs, but until they're safe, people will continue to doubt them.
Could it be a bullshit article to prove the point that they can end up in Nature?

Just asking because some part looked really dubious, but I have no expertise at all in this area so maybe it's fair.

They are not publishing in The Nature.

Nature Scientific Reports is open access mega journal with low selectivity for articles. Mega journal publishing model is to accept articles if they are technically sound and ignoring scientific importance.

Nature Scientific Reports is open access mega journal with low selectivity for articles. Mega journal publishing model is to accept articles if they are technically sound and ignoring scientific importance

> Our results point the way to future brain-to-brain interfaces that enable cooperative problem solving by humans using a “social network” of connected brains.

When you read the procedure, it's underwhelming. Using EEG to extract one bit of information is relatively easy. Using TMS to transfer one bit of information is relatively easy. Connecting the two is trivial. Might be demanding for a undergraduate project in medical physics but that's it.

My read also. This is a parlor trick at best.
Can this system do anything better than normal communication? (Which is also a brain network, obviously, and just as "direct")
It's more efficient.
I'm assuming you're joking; if not, can you explain?
Probably not, but that's not important because it's research, not a commercial product. The question to be asking to evaluate how exciting it is is "Could this do anything better than normal communication if it were developed further?" As others have pointed out, the answer to that may be a no.
This is equivalent to sitting three people back to back and they can only tap each other as a form of communication. Left hand for rotate left right hand for rotate right. The Eeg is not amazing we know they can be used to estimate intent and play games. Tms has a physical feeling to it and in this case a visual phosphene cue. You haven't introduced thoughts magnetically you've introduced a feeling.
Yes. This method will never scale up to meaningfully transmitting information between individuals. I'm not sure why this was deemed worth funding when it's a dead end and I'm sure the authors know that.

We are not going to get a useful BCI without sticking electrodes into people's brains in the next few decades.

This doesnt sound much different than having the subjects tap each other to communicate, just done with fancy head mounted equipment. It could be useful for completely paralyzed people to play games