That's inductive reasoning.

You see the transducer, the light blue.

There's water in between the skull and the transducer.

And you often hear another type of reasoning, inductive reasoning.

On the right hand side, you see an ultrasonic transducer.

We attach a transducer, in this case, to the brain, but if it will be a different organ, it will be a different transducer attached to the patient.

Francis Bacon and then, later, Isaac Newton, had proposed an inductive scientific method.

Well, this is more of what I had just talked about, inductive reasoning.

So the ultrasonic transducer emits basically an ultrasonic beam that focuses inside the phantom.

So it consists of two parts, what we call an encoder and a transducer.

So, when we did this for responses from the standard method and from our encoder and transducer.

And you can put a t n here and use an inductive argument to figure out a general formula.

But the key one really is the encoder alone, because we can team up the encoder with the different transducer.

And now we're going to use our inductive hypothesis that T(n) â 4n to get an upper bound on this quantity.

So on the left is the encoder alone, and on the right is from an actual blind retina, so the encoder and the transducer.

They wrote books and articles promoting inductive method in all the sciences that were widely read by natural philosophers, university students and members of the public.

For inductive step, we know from the structure of the algorithm that the time it takes to handle an input of size n is on average going to be

And then the transducer then makes the output cells send the code on up to the brain, and the result is a retinal prosthetic that can produce normal retinal output.

You can see, in her case, she's wearing her transducer arrays, one of the front of her chest, one on the back, and then the second pair side to side over the liver.

The top one is from a normal animal, the middle one is from a blind animal that's been treated with this encoder transducer device, and the bottom one is from a blind animal treated with a standard prosthetic.

We're just jutting into some region inside or outside, but it doesn't change the total number of regions (n 1) (m 1) these ones cancel, and we get n m r, which by our inductive hypothesis we said is 2.

The whole notion, then, is one that at the interface there are physical properties in that transducer in this case it's pressure and touches that allow you to present things to the user that you could never present before.

We really don't want this to be n here because our inductive step is going to assume this true for everything smaller than n and not equal to n but the reality is this is actually a tiny little bit less than n.

So as you can see, the firing patterns from the blind animal treated with the encoder transducer really do very closely match the normal firing patterns and it's not perfect, but it's pretty good and the blind animal treated with the standard prosthetic, the responses really don't.