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Intelligent life on earth is DNA/RNA based, not one or the other. If you take the mean rate your interpolation from now back the origin of such life with that particular mean rate of numerical growth in base pairs holds with error margins.

No evolutionary clock models used, instead a numerical model was used.

1) The rate of change not being constant is not significant as long as its variation is normally distributed about some mean. I expect that changes in environment are randomly distributed.

2) This is too small scale to have any impact on the trajectory of the numerical growth in number of base pairs.

We don't need to guess, life isn't special. The growth of complexity under favorable conditions is observable and occurs all over the place at the same rate, at scale.

Indeed the error range here is about 1.5 to 2 billion years. So from the paper we know that life began its growth in complexity about 6-9 billion years ago. This is strictly from numerical arguments. Evolution is just a random choice in the number of husbands per ceremony.

How do you think we determine the age of the universe? The age of rocks? Do you not accept carbon dating?

You could call this technique "complexity dating". First you show there is exponential growth (or decay) occuring naturally. The actual changes occur randomly but the mean rate is fixed. Then you plot on log scale and voila you have complexity dated life itself. The only argument you can make against is that the laws of physics are somehow not constant, but I think everything froze out by the time molecules were forming.

So in your cartoon, the bride can marry a random normally distributed number of husbands each time. We would determine the average rate of husband accretion. Then given the number of husbands at any time we could determine when the rapacious bride began marrying.

The "obligatory" doesn't apply since that paper did not extrapolate. It would be the exact opposite.

I'm pretty sure the issue you raise is averaged away quite neatly by the math.

I read a paper a long while back that used purely numerical arguments to first show a common rate in the growth of complexity across biological and non-biological systems under similar conditions. It then plotted this exponential growth backwards in time, showing that life's origins were prior to the formation of earth by about 1.5 billion years. No guesswork, it was quite solid; the same math applied to human technology traces back to roughly its known start on earth. It was convincing that life is prolific in the universe but intellgent life took about 6-9 billion years to go from single cell to us.

"Here’s one last advantage of dividing intelligence into well-defined problem-solving and poorly defined problem-solving: it reminds us to give some respect where respect is due."

There is another way of looking at this. A problem seems "well-defined" when it is presented in terms of your current paradigm. This means that it uses the thought apparatus with which you and everyone around you is familiar. So what appears to be a property of the problem is actually a state of affairs, a property of the whole problem/problem-solver/paradigm system. On the other side of the coin, an ill-posed or "poorly-defined" problem may actually be well-defined in an alternate paradigm. In the alternate paradigm one has new thought apparatus that suddenly make the ill-posed problem tractable.

On this view, what you call "stupid" may be identical to what you don't yet understand and what you call intelligent is that with which you are most familiar. So intelligence is not a property a human can possess but a network effect that is quite intellectually bereft.

Wisdom then is the experience of watching many paradigm shifts over time and realizing that what is stupid today may be smart tomorrow and vice versa.

Manifold: Any m dimensional hyperplane embedded in an n dimensional Euclidean space, where m is less than or equal to n. More simply put, a manifold is any set that can be continuously parameterized, with the number of parameters being the dimension of the manifold.

A continuous manifold will have a line element that allows you to compute distances between its points using its parameters. The simplest line element was first written down by Pythagorus I think, it allows you to compute the distance between two points in a flat manifold. In physics we do away with gravitational forces by realizing that masses move along geodesics (shortest paths) of a manifold, hence the saying,"matter tells spacetime how to curve and spacetime tells matter how to move". We stich together large curvy manifolds like a patch quilt from the locally Euclidean tangent spaces that we erect at any point.

Logic does not exist in a physical sense, but try to think without it. For example, try to think without the law of noncontradiction. Can you categorize?

Nice example of hurling meaningless invective.

Not following youtube, sorry.

See above.

I don't at all begrudge you your logical predictive fictions.

I would disagree, completeness is not required consistency is all you need really. QM is consistent.

Deep necessity, we follow logic so we are not grunting beasts.

I mean there is no perspective from which one can obtain a view of all properties of all systems that will not be invalid to another observer.

To clarify he’s not claiming objects don’t exist, just that they don’t have observer independent properties. -- that's right!

This is what I mean.

QM does not deny you existence, it rather denies you a complete objective description of how you exist. Or perhaps it says that your existence is not an objective phenomena.

I think otherwise. I am precisely saying that QM as a formalism denies ontological truth in the first instance. You have to do something like the BM guy above is embarking on.

The idea is that there is no "complicated system", or at least that you are not permitted to concieve of one without describing it in physical detail.

To what approximations do you refer?

Here we discard Copenhagen and move forward.

"It appears to me that some people have become accustomed to working with approximations, and have accepted the map for the terrain."

No, here we are discussing the formalism without approximations associated with an instance of its approximate application.

And QM says "The map is the terrain".

What were you hoping for?

I agree that language other than math fails us here. Nevertheless, I humbly try to convey thoughts that occur in me with these tools.

Thank you so much, I don't.

I see this as decidedly non-Humean. Why be Humean anyway?

QM provides the most accurate and verifiable predictions in human history. The follow on from that is that my thoughts can be conveyed to you over a sea of quivering electrons. The one catch is that you must accept that when you are not looking the universe does its evolving in a way that is inimical to your conceptualizations.

I have a degree in theoretical physics and a gold medal, which is to say I have endured the requisite intellectual beatings. Often the best interpretations of physical theory are unpalatable to the average person. The idea that there is in fact no objective physical reality is the most egregious offender in this regard. However, it is nonetheless the best conclusion that one can draw given strict adherence to what the mathematical formalism of QM provides. There is simply no physical machinery to support an objective reality, period.

Now, that being said, the remarkable part is that the forgoing conclusion does us zero harm. We can still have the logical predictive fiction that an objective reality exists. What staggers the mind is the corollary that no human has ever erected a truth. Moreover, every intelligent species that ever endeavors to ask these questions will find the same non-answer.

This is a case of the metric becoming the target. The tools used to evaluate LLM performance are shaping the LLM. First you make your tools then your tools make you.

If we take a formal systems approach, then an LLM is a model of a complex hierarchy of production rules corresponding to the various formal and informal grammatical, logical, and stylistic rules and habits employed by humans to form language that expresses their intelligence. It should not be surprising that simply executing the production rules, or a model thereof, will give rise to sentences that cannot be assigned a meaning. It should also give rise to sentences that we cannot prove or make sense of immediately but we would not want to discard these due to uncertainty. Why? because every once in a while the sentence that would be culled is actually the stroke of brilliance we are looking for, uncertainty be damned. The citation here would be literally nearly every discovery ever made.

When I recall information and use it, when I "think", I don't just produce sentences by the rules, formal and informal, I don't consider at all how often I have seen one word precede another in past, rather as I meandre the landscape of a given context, a thought manifold if you will, I am constantly evaluating whether this is in contradiction with that, if this can be inferred from that via induction or deduction, does this preclude that, etc.. That is the part that is missing from an LLM; The uncanny ability of the human mind to reproduce the entire manifold of concepts as they relate to one another in a mesh from any small piece of the terrain that it might recall, and to verify anew that they all hang together unsupported by one's own biases.

The problem is that just as the scarcity of factual information in the corpus makes it difficult to produce, so is actual reasoning rarefied among human language samples. Most of what appears as reasoning is language games and will to power. The act of reasoning in an unbiased way is so foreign to humans, so painful and arduous, so much like bending over backwards or swimming upstream against a strong current of will to power, that almost nobody does it for long.