“Because the telegraph analogy is actually a pretty decent analogy.”
No it isn’t. Constructing analogies is for poets and fiction writers. Science does not construct analogies. The force on an accelerating mass isn’t analogous to F=ma, it IS F=ma. If what you said is true, that neurons are like telegraph stations and their dendrites the wires then it could not be true that neurons can communicate without a direct connection or “wire” between them. Neurons can communicate without any synaptic connection between them (See: “Neurons Talk Without Synapses”). Therefore the analogy is false.
“What makes you think a sufficiently large number of organized telegraph lines won’t act like a brain?”
Because that is an example of magical thinking. It is not based on a functional understanding of the phenomenon. “If I just pour more of chemical A into solution B I will get a bigger and better reaction.” We are strongly attracted to thinking like that. It’s probably why it took us thousands of years to really get how to do science properly.
No it isn’t. Constructing analogies is for poets and fiction writers. Science does not construct analogies. The force on an accelerating mass isn’t analogous to F=ma, it IS F=ma. If what you said is true, that neurons are like telegraph stations and their dendrites the wires then it could not be true that neurons can communicate without a direct connection or “wire” between them. Neurons can communicate without any synaptic connection between them (See: “Neurons Talk Without Synapses”). Therefore the analogy is false.
Science uses analogies all the time. For example, prior to the modern quantum mechanical model of the atom one had a variety of other models which were essentially analogies. The fact that analogies break down in some respects shouldn’t be surprising: they are analogies not exact copies.
It might be useful to give as an example an analogy that is closely connected to my own thesis work of counting Artin representations. It turns out that this is closely connected to the behavior of the units (that is elements that have inverses) in certain rings). For example, we can make the ring denoted as Z[2^(1/2)], which is formed by taking 1 and the square root of 2 and then taking all possible finite sums, differences and products of elements. Rings of this sort, where one takes all combinations of 1 with the square root of an integer are have been studied since the late 1700s. Now, it turns out that there are some not so obvious units in Z[2^(1/2)]. I claim that in this ring, 1+2^(1/2) is a unit.
It turns out that if instead one takes a ring in the following way: Take 1, and take 1/p for some prime p, and the form all products, sums and differences, one gets a ring that behaves in many ways similarly to the quadratic fields, but is much easier to analyze. The analogy breaks down pretty badly in some aspects, but in most ways is pretty good to the point where large classes of results in one setting translate into almost identical results in the other setting (although the proofs are often different and require much more machinery in the quadratic case) . So here we have in math, often seen as one of the most rigorous of disciplines, an analogy that is not just occurring at a pedagogical level but is actively helpful for research.
t is not based on a functional understanding of the phenomenon. “If I just pour more of chemical A into solution B I will get a bigger and better reaction.” We are strongly attracted to thinking like that. It’s probably why it took us thousands of years to really get how to do science properly.
You appear to be ignoring the bit where I noted “organized”. But actually, even without that your statement is wrong. Often we do get critical masses where behavior becomes different on a large scale. Indeed, the term “critical mass” occurs precisely because this occurs with enriched uranium or with plutonium. And there are many other examples. For example, shove enough hydrogen together and you get a star.
“Because the telegraph analogy is actually a pretty decent analogy.”
No it isn’t. Constructing analogies is for poets and fiction writers. Science does not construct analogies. The force on an accelerating mass isn’t analogous to F=ma, it IS F=ma. If what you said is true, that neurons are like telegraph stations and their dendrites the wires then it could not be true that neurons can communicate without a direct connection or “wire” between them. Neurons can communicate without any synaptic connection between them (See: “Neurons Talk Without Synapses”). Therefore the analogy is false.
“What makes you think a sufficiently large number of organized telegraph lines won’t act like a brain?”
Because that is an example of magical thinking. It is not based on a functional understanding of the phenomenon. “If I just pour more of chemical A into solution B I will get a bigger and better reaction.” We are strongly attracted to thinking like that. It’s probably why it took us thousands of years to really get how to do science properly.
Science uses analogies all the time. For example, prior to the modern quantum mechanical model of the atom one had a variety of other models which were essentially analogies. The fact that analogies break down in some respects shouldn’t be surprising: they are analogies not exact copies.
It might be useful to give as an example an analogy that is closely connected to my own thesis work of counting Artin representations. It turns out that this is closely connected to the behavior of the units (that is elements that have inverses) in certain rings). For example, we can make the ring denoted as Z[2^(1/2)], which is formed by taking 1 and the square root of 2 and then taking all possible finite sums, differences and products of elements. Rings of this sort, where one takes all combinations of 1 with the square root of an integer are have been studied since the late 1700s. Now, it turns out that there are some not so obvious units in Z[2^(1/2)]. I claim that in this ring, 1+2^(1/2) is a unit.
It turns out that if instead one takes a ring in the following way: Take 1, and take 1/p for some prime p, and the form all products, sums and differences, one gets a ring that behaves in many ways similarly to the quadratic fields, but is much easier to analyze. The analogy breaks down pretty badly in some aspects, but in most ways is pretty good to the point where large classes of results in one setting translate into almost identical results in the other setting (although the proofs are often different and require much more machinery in the quadratic case) . So here we have in math, often seen as one of the most rigorous of disciplines, an analogy that is not just occurring at a pedagogical level but is actively helpful for research.
You appear to be ignoring the bit where I noted “organized”. But actually, even without that your statement is wrong. Often we do get critical masses where behavior becomes different on a large scale. Indeed, the term “critical mass” occurs precisely because this occurs with enriched uranium or with plutonium. And there are many other examples. For example, shove enough hydrogen together and you get a star.