Amen ;)

The difference between man and the lower animals is perfectly "natural" as fact. Religious fantasies about "souls" as the supposed difference are irrelevant.

We are coming into alignment.

I thought most of the resistance would be religious, but you were the most vocal, surprising me.

Of course we have evolved to a better, more advanced state. It is not biological evolution.

Evolve:

to come forth gradually into being; develop; undergo evolution: The whole idea evolved from a casual remark.

to gradually change one's opinions or beliefs: candidates who are still evolving on the issue; an evolved feminist mom.

Biology. to develop by a process of evolution to a different adaptive state or condition: The human species evolved from an ancestor that was probably arboreal.

"The two great values to be gained from social existence are: knowledge and trade. Man is the only species that can transmit and expand his store of knowledge from generation to generation; the knowledge potentially available to man is greater than any one man could begin to acquire in his own life-span; every man gains an incalculable benefit from the knowledge discovered by others. The second great benefit is the division of labor: it enables a man to devote his effort to a particular field of work and to trade with others who specialize in other fields. This form of cooperation allows all men who take part in it to achieve a greater knowledge, skill and productive return on their effort than they could achieve if each had to produce everything he needs, on a desert island or on a self-sustaining farm." -- "The Objectivist Ethics"

The memory you are talking about and concepts go together. You need memory superior to what lower animals seem to have, but conceptual thought allows you to organize what you remember just like it organizes any experiences integrated into concepts. Otherwise you have no way to retain the multitude of particulars and their relations. Remember the "crow epistemology".

First, I disagree with the assertion that man has evolved with accumulation of knowledge. If we took a baby from today and placed them 4,000 BC, or took a baby from 4,000 C and placed them today, they each would grow up in accordance with their environment, although the chance a baby today had bad eyes is pretty high.

I agree, the concept of rational thought is broader than memory, but it can not happen without episodic memory. This is the first step, and animal thought has not achieved it, at least as analyzed by experts (to my knowledge).

This is better than mu original post!

Man certainly has evolved through accumulation of knowledge. We are much different and more advanced in modern society than centuries ago, let alone millennia. But it is a more general evolving by choice, not Darwinian evolution in particular modifying biological nature.

The process of thinking rationally with concepts is much broader than memory. In particular it requires the capacity to conceptualize your own experiences.

This excursion into automatic functions does not address the impossibility of human life without any concepts at all, and the location and operation of neurological functions in the brain and nervous system for regulating bodily functions are not relevant to the fundamental distinction between man and the lower animals. But such functions do not include finding food and putting it in your mouth, and if you can't or don't take the effort to do that you will in fact die if someone else does not feed you.

This statement is false: Blarman: "Any infinite progression of diminishing inverses (fractions) approaches a finite limit and can be solved for using integrals... Because the individual terms as they extend out toward infinity add less and less to the real answer, reaching a point at which the answer does not meaningfully change."

The terms of a series diminishing to zero is a necessary but not sufficient condition for convergence of a monotone series. The series

1/2+1/2+1/4+1/4+1/4+1/4+1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8+...
= sum(n=1,N){2n(1/2n)}
= sum(n=1,N){1}
= N

diverges as N increases even though 1/2n->0.

The harmonic series

sum{1/n} = 1 + 1/2 + 1/3 +...+ 1/N + ...

diverges as log(N+1) as can be seen by bounding it below with integral{dx/x}. No calculus text says otherwise, contrary to the instruction "I'll leave the reader to consult a text on calculus for the answers".

More generally, the series sum{1/n^r} converges if and only if r>1; for the harmonic series r=1. Most series are more complicated than the simple term 1/n^r.

The series of inverse composites (non-primes)

sum{1/c} = 1/4 + 1/6 + 1/8 + 1/9 + 1/10 + ...

is greater than 1/2 of the harmonic series and therefore diverges:

sum{1/c} > sum{1/2k} = 1/2 sum{1/k}.

Whatever Blarman or his son did to deduce that it converges to 9/4 was wrong.

The divergence of the harmonic series is also seen, without calculus, to diverge by bounding the sequence of partial sums in the form

1+1/2 + (1/3+1/4) + (1/5+...+1/8) +... + [1/(2^(n-1)+1) +... +1/2^n]
> 1/2 + (1/4+1/4) + (1/8+1/8+1/8+1/8) + ... + 2^(n-1)/2^n
= 1/2 + 2(1/4) + 4(1/8) + ... + 2^(n-1)/2^n
= n/2

which is unbounded.

Integrals are not "extrapolation of limits" and the "purpose of limits" is much broader than assessing series. The limiting value of "any infinite progression" cannot generally be "solved by using integrals" (though there are correspondences with the finite difference calculus).

The "integral test" for series from calculus is based on integrals as upper and lower bounds of series (as Riemann sums) that determine convergence of the series, not the value of the series when it does converge. An example is the use of integral(dx/x) to show that the harmonic series diverges logarithmically and the more general criteria for 1/n^r.

Blarman's sum 1/n^(n-1) is evaluated by reformulating it as the telescoping series

sum 1/n^(n-1) = sum{1/(n-1) - 1/n}
= (1-1/2) + (1/2-1/3) + (1/3-1/4) ...

All the terms cancel except the first and last:

sum 1/n^(n-1) = 1 - 1/N
-> 1

There is no such easy way to compute limits of most series, and directly replacing them with integrals does not generally give the sum.

For an alternating series -- one in which the terms successively alternate in sign -- then the series converges if the terms absolutely converge to zero -- for similar reasons of partial cancellation between successive terms. But that is not true in general, including for the harmonic series and the series of reciprocal composite numbers, and turning to a calculus book does not provide the values of limits, where they exist, based on integrals.

Agree that it is a fascinating subject!

I recall reading somewhere that in the study of Einstein's brain, and then others (musicians I think), they found the number of connections between the hemispheres was significantly higher.

I find this subject fascinating. When I started my career, I did work with Neural Networks to manage non-linear control problems. In studying them, I read a lot of brain/mind literature, and found a few interesting behaviors in them.

There is a behavior called "grandmothering", where a neural network essentially memorizes the training set. In this case, it memorizes, but completely fails to generalize. It generally happens when there are far too many neurons for the problem (as represented by the training set).
Reorganizing in sub-nets works very well, particularly to make the data exchanged (via synapses) "canonical". The cochlea is a good example of this. The data from the cochlea to the brain is already heavily processed, long before any speech processing occurs.

The "grandmothering" behavior, makes me wonder if the large numbers of neurons and synapses in elephants and fin whales do not engender higher thought. It is an analogy, nothing more.

"Seems it is really the number of neurons, which doesn't correlate that well to brain size."

I agree. To be precise, neural pathways are the methods by which the brain facilitates the processing of information. The more pathways, the more ways there are to process the information and the more information which can be processed at a time. So brain density is the ability of the brain to process more and more complex information. At a bare minimum, in order to hold that animals and humans have similar cognitive capacities (regardless of whether or not they are actually used), one must show that there are similar neural densities. (I found one such article here: https://www.frontiersin.org/articles/... which shows that the neural densities of humans is much higher than other animals.

It seems that human brains are also unique in their concentration and specialization of brain matter to the portion of the brain used for higher functions - especially that normally associated with critical thinking. Without this critical specialization, the equalitative comparison of animal brains to those of humans leaves me decidedly unsatisfied.

Seems it is really the number of neurons, which doesn't correlate that well to brain size.

I discount Alzheimers, Autism and other maladies as part of the argument. Clearly a human or animal can have a large brain that is broken.

"It's not the size that counts! It's how you use it!"

- Robin Hood - Men in Tights

Levity aside, simple size holds little if any correlation to intelligence either in the animal world or the human one. Indeed, studies of Alzheimer's patients show a degradation in the brain - a breaking down of previously functioning neural pathways. The patients lose brain density but not overall size. A far better argument than simple size is found in brain density - which is astronomically greater in humans than in other animals.

Any infinite progression of diminishing inverses (fractions) approaches a finite limit and can be solved for using integrals. Here is the problem:

What is the sum of 1/4 + 1/6 + 1/8 + 1/9 + 1/10 + 1/12 + 1/14 + 1/15 + 1/16 + 1/18 ...

Because the individual terms as they extend out toward infinity add less and less to the real answer, reaching a point at which the answer does not meaningfully change. That is the purpose of limits and their extrapolation using integrals. A similar problem is:

What is the sum of 1/n^(n-1) where n = 1 -> infinity?

I'll leave the reader to consult a text on calculus for the answers.


I would also point out that the brain functions that maintain life are relegated to a separate part of the brain entirely and do not require ongoing conscious thought to maintain. Indeed, a person may be rendered unconscious by trauma (or even basic sleep) and they do not die nor do their bodily functions shut down, but their cognitive faculties certainly do. The employment of the cognitive faculties - Poirot's "little grey cells" - requires more than either simple animal intelligence or the rote of everyday life. Cognition is the building of new pathways in the brain and requires significant energy and effort towards a specific purpose. It is neither random nor the product of happenstance. The mechanisms of construction are energy-consuming rather than energy-liberating and no known natural process is anything but energy-liberating.

I agree, evolution is not invention. Clearly.

Man has not evolved through accumulation of knowledge. This is not evolution. I'm arguing the capacity for episodic memory and communication led to the accumulation of knowledge. Then the accumulation of knowledge changed the formula for success to learning from this information, rather than other instinctual survival traits.
How we achieved episodic memory, and to what degree other animals have it (my last reading was that this evidence has not precipitated) is not known to me.

Should've been "a little evolution". By that I mean that we have larger brain capacity and a thought process (physical pathways for example) that we have evolved allowing us to reason.
I reject the concept that this is unique in humans, beyond the fact that we got here first.

What is "little evolution"?

Evolution isn't invention. Man has "evolved" through his thinking and accumulation of knowledge to make better use of his intellectual capacity, but that isn't is the same as Darwinian evolution through better adaptation from mutation.

Humans do not typically live up to their full capacity for abstract conceptual thought (as described in Ayn Rand's discussion of what she called the "anti-conceptual mentality"), but we cannot degenerate to literally the non-conceptual thought of the lower animals either (despite the appearances of certain examples). Certain low level concepts are nearly automatic. To stop using concepts at all you would have to literally shut your brain down and would not survive unless someone took care of you as in a coma.

The limit of the sum of the inverse composites (non-primes) is unbounded, i.e., does not converge, but your son did not degenerate to the intellectual level of the lower animals -- which could not understand the problem at all.

Ok, that is what I meant with the note about evolution. It affects brain capacity, but also the features of the brain. Necessity is the mother of invention.

I accept that little evolution for larger brain capacity like we have sets us apart.

The human brain evolved to be much more functionally complex, giving us the intellectual capacity for rational, conceptual thought that the lower animals do not have. It is not just a matter of brain size (larger animals like elephants and whales have larger brains). You can't train a non-human animal with a bigger brain to think conceptually. There are other differences between man and the lower animals, but that is the fundamental distinction.

The real question to me is simply can humans rise to their capacity, because they certainly can degenerate to the lower levels of the animals.

But you show me a dog or cat who can figure out the sum of a an infinite inverse progression of non-prime numbers is 9/4's like my son did in about 15 minutes and you can argue to me that animals and humans are on the same cognitive plane. IE I'm not buying it.

Note, I did not suggest careful training alone was adequate.

We seem to have a difference in our assertions.
I'll restate mine try to get to the difference:

I assert that animals merely lack the capacity we have evolved to, but are otherwise the same, and that our ability to reason is the result of capacity and training.
Are you asserting that our ability to reason is more than capacity and training, perhaps an evolved survival trait?