Unless the author redefines the words used in the bit that you quoted from them, I addressed their argument just fine.

so you aren’t going to read the article then.

No Investigation, No Right to Speak.

Here follows some selections from the article that deal with exactly the issues you focus on.

I strongly advise reading the entire article, and the two it is in response to, and furthermore reading about what a Turing Machine actually is and what it can be used to analyze.

The debate on whether the brain is a computer or not seems to have died down given the recent success of computer science ideas in both neuroscience and machine learning. I have seen a few recent articles on this subject from scientists, who have made strong claims that the brain is in fact literally a computer, and not just a useful metaphor backed up with their reasons to believe so. One such article is this one by Dr. Blake Richards (and here is another one by Dr. Mark Humphries). I will mainly deal with the first one — a really good and extensive article. I would encourage readers to go through it slowly, and in detail for it provides a good look at how to think about what a computer is, and deals well with a lot of the weaker arguments brought against the ‘brain is a computer’ claim (like the ones here.) Dr. Richards addressed a good variety of objections that people might rise to the claim that “the brain is a computer” towards the end of his article. I will raise an argument here that I feel lies at the heart of this discussion, not addressed in the post and is often overlooked or dismissed as non-existent. The reason I think it is important to discuss this question (and/or objection) in detail is that I strongly believe it affects how we study the brain. Describing the brain like a computer allows for a useful computational picture that has been very successful in the fields of neuroscience and artificial intelligence (specifically the sub-area of machine learning over the recent past). However as an engineer interested in building intelligent systems, I think this view of the brain as a computer is beginning to hurt us in our ability to engineer systems that can efficiently emulate their capabilities over a wide range of tasks.

the bolded part above is ‘why the author has a problem with the computer metaphor’ since you seem so confused by that.

There are a few minor/major problems (depends on how you look at it) in the definitions used to get to the conclusion that the brain is in fact a computer. Using the definitions put forward in the blog post —

(1) an algorithm is anything a Turing machine can do, (2) computable functions are defined as those functions that we have algorithms for, (3) a computer is anything which physically implements algorithms in order to solve computable functions.

these are the definitions the author is using, not ones he made up but ones he got from one of the articles he is arguing against. note the similarities with the definitions on https://en.wikipedia.org/wiki/Algorithm :

One informal definition is “a set of rules that precisely defines a sequence of operations”,[11][need quotation to verify] which would include all computer programs (including programs that do not perform numeric calculations), and (for example) any prescribed bureaucratic procedure[12] or cook-book recipe.[13] In general, a program is an algorithm only if it stops eventually[14]—even though infinite loops may sometimes prove desirable. Boolos, Jeffrey & 1974, 1999 define an algorithm to be a set of instructions for determining an output, given explicitly, in a form that can be followed by either a computing machine, or a human who could only carry out specific elementary operations on symbols.[15]

note the triviality criticism of the informal definition that this author previously addressed, and the ‘human who could only carry out specific elementary operation on symbols’ is a reference to Turing Machines and the Chinese Room thought experiment, both of which i recommend reading about.

The concept of algorithm is also used to define the notion of decidability—a notion that is central for explaining how formal systems come into being starting from a small set of axioms and rules. In logic, the time that an algorithm requires to complete cannot be measured, as it is not apparently related to the customary physical dimension. From such uncertainties, that characterize ongoing work, stems the unavailability of a definition of algorithm that suits both concrete (in some sense) and abstract usage of the term.

this is still a matter under academic discussion, there are not widely agreed on definitions of these terms that suit all uses in all fields.

Most algorithms are intended to be implemented as computer programs. However, algorithms are also implemented by other means, such as in a biological neural network (for example, the human brain implementing arithmetic or an insect looking for food), in an electrical circuit, or in a mechanical device.

algorithms can be implemented by humans, intentionally or not, the hardware is irrelevant to the discussion of Turing machines since they are an idealized abstraction of computing.

enough wikipedia now back to the article

Number (3) is the one we will focus on for it is vitally important. To complete those definitions, I will go ahead an introduce from the same blog post, an intuitive definition of algorithm — “ an algorithm is a finite set of instructions that can be followed mechanically, with no insight required, in order to give some specific output (e.g. an answer to yes/no integer roots) for a specific input (e.g. a specific polynomial like 6x³yz⁴ + 4y²z + z — 9).” And the more technical definition of algorithm in (1) as “ An algorithm is anything that a Turing machine can do.” This equivalence of course arises since attempts to achieve the intuitive definition about following instructions mechanically can always be reduced to a Turing machine. The author of the post recognizes that under this definition, any physical system can be said to be ‘computing’ it’s time evolution function and the meaning of the word loses it’s importance /significance. In order to avoid that, he subscribes to Wittgenstein and suggests that since when we think about modern day computers, we are thinking about machines like our laptops, desktops, phones which achieve extremely powerful and useful computation, we should hence restrict the word computers to these type of systems (hint: the problem is right here!!). Since our brains also achieve the same, we find that our brains are (uber) computers as well (I might be simplifying/shortening the argument, but I believe I have captured it’s essence and will once again recommend reading the complete article here.) Furthermore, he points out that our modern day computers and brains, have the capability of being Turing complete, but are not of course due to physical constraints on memory, time and energy expenditure. And if we do not have a problem with calling our non-Turing complete, von Neumann architecture machines as computers, then we should not let the physical constraints that prevent the brain from being Turing complete stop us from calling it a computer as well. I agree that we should not restrict ourselves to only referring to Turing complete systems as computers, for that is far too restrictive. The term ‘computer’ does have a popular usage and meaning in everyday life that is independent on whether or not the system is Turing complete. It makes a lot more sense to instead refer to those computers that are in fact Turing complete as ‘Turing complete computers’.

this explains the author’s reasoning for their definitions further, he is not making these up, these are the common definitions in use in the discourse.