Foundations of logic conversation that ended up on the applicability of mathematics to reality

What we have is exponentially expanding computational ability.

We also have human brains consisting of linear comparators.

Those two don’t mix well.
Humans tend to make linear projections, even when the evidence is overwhelming that they are in an exponential context.

Exponentials can do what seems like magic in “linear world” if the doubling time is short enough.

We are kind of used to economic doubling on a 30 year timeframe.
Marine ecologists are used to phytoplankton doubling on a daily basis.

Molecular level manufacturing (Drexler machines) will probably operate at about the 10-20 days for a doubling time when we first get them stable.
Even at 20 days, it only takes two years to get from 1 to the human population.

We have four massive problems:

1/ Most people are wedded to “Truths” that they are unable to challenge, that are not actually truths but only situationally useful heuristics, and the situation has changed. The ability to question anything and everything is actually quite rare.

2/ The very concept of using a measure of “value in exchange” (markets and money) as a planning metric fails in conditions of universal abundance, and actually delivers existential level threat in and of itself.

3/ Reality is so complex, that we must all simplify it to make any sense of it at all. We must accept that some aspects of reality demand complexity orders of magnitude beyond anything in our cultural past. We need to get people thinking exponentially.

4/ The idea that our culture has of evolution – that it is all about competition – is wrong.
When dealing with complex systems, it is good enough first order approximation to say that all new levels of complexity are predicated upon new levels of cooperation.
At our level of complexity, our continued existence is predicated on cooperation – universally so.
The idea that complexity can survive in competitive environments has no real basis in mathematics or logic.
We need to acknowledge our fundamentally cooperative nature, and we need to demand fundamentally cooperative systems – all levels.

[followed by RM – Fundamental Mathematical principles such as the Continuum Hypothesis apply exactly not approximately contrary to your heuristic philosophy.]

That is your belief. I accept that much.

I do not accept that anything necessarily applies in all possible contexts.

Reality has thrown me enough “curve balls” in the last 60 years that I take a somewhat more cautious and humble approach to making any declarative statements about it.

I am happy to go with best available evidence, and best available evidence suggests that all measurements contain errors at some scale.

[followed by … The fundamental principles of Mathematics apply universally and accurately and absolutely to all existence. …]

Hi Robert,

That is a belief that you hold.

What I am clearly saying is that the evidence is beyond any reasonable doubt that it is not possible to make anything stronger than a probabilistic statement about reality that is actually evidence based.

If you believe that any human mind is capable of dealing with any infinity, then you clearly have not studied the human brain sufficiently.

There may be absolute Truths about reality, but I suspect not.

The conjecture that there is a tighter than probability mapping between any set of mathematical constructs and whatever reality is, is a conjecture that evidence suggests is not amenable to proof. It is an item of faith, one which you seem to hold.

I am happy for you to have any faith you want; but do not expect me to acknowledge any faith as evidence of anything.

[followed by]

Hi Robert,

Clearly you did not understand what I wrote.

Clearly you are angered by a challenge to an assumption you hold that you seem unwilling to challenge.

I acknowledge that mathematics and logic has the set of relationships that it has.

I acknowledge that mathematics and logic and derivatives give us the best models of reality that we have.

I acknowledge that reality seems, beyond all reasonable doubt, to be far more complex than any mind is capable of dealing with in detail, and thus we must all necessarily use models that are simpler than reality, to make any sense at all of it.

Thus I acknowledge the utility of the tools of mathematics and logic in making the models that we have, without requiring that there be anything stronger than a contextually sensitive probabilistic relationship between any model that we may make, and whatever reality actually is.

The experience of history seems to make this a useful approach.

Some sects of the ancient Greeks saw perfection in the mathematics of the circle, and tried to apply it universally.
Newton saw perfection in his mechanics which he thought were universals.
Einstein showed that as one looks more closely at orbits, Newton’s approximations break down, and a different set of frames is required for greater accuracy.
Quantum mechanics gives us greater accuracy at the scale of the very small but comes at the cost of accepting uncertainty in all things, and demands working with probabilities.

Such chains of claims and subsequent alterations make me suspect that such things may be part of a potentially infinite set.
Wolfram seems to provide a framework in which such infinite approximation may be the nature of the reality within which we find ourselves. The notion of maximal computational complexity seems to lead in that direction.

Thus I am, with a great deal of evidence, very skeptical of any claim to universality in reality that is greater than probabilistic in nature.

Call me a realist – I will not be offended.

About Ted Howard NZ

Seems like I might be a cancer survivor. Thinking about the systemic incentives within the world we find ourselves in, and how we might adjust them to provide an environment that supports everyone (no exceptions) - see www.tedhowardnz.com/money
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