<paraphrase>
"This book is intended for a lay reader, but necessarily contains quite a bit of maths. Readers who prefer to avoid equations and formulas can skip chapters 4, 6, 12-20, 26 and 27".
</paraphrase>
Penrose's notion of a "lay reader" is one who doesn't have a maths degree.
- The agents actions are entirely determined by its environment
- The agents actions form a probability distribution determined by it environment
- The agent actions from their environment are annotated in some way that we haven't or can't have thought of that represents what the agent is. In my opinion, something that we can't think of or experience and something that doesn't exist are indistinguishable and we shouldn't really separate them except for making this statement.
- There is no agent and subjective existence is merely one route down immutable decision tree that is our choices and their consequences.
None of these options really intuitively sound like free will to me. Ultimately thinking along these lines requires separating the agent from the environment.
EDIT: I see now the reply is to the YouTube link which I missed
(Personally as a compatibilist, I assert it's a map-territory error; the counterfactual worlds represent evaluated decisions, not real universes.)
This shit, of "who has God considered holier than you to go to heaven" is just more mental gymnastics of not-science.
But if you think about free will for a few minutes then you'll uncover many other issues with it at different levels.
Even at the very top level. Deciding if you want a coffee? Thirsty? Remember the taste and desire it? But wait, you also recall it keeps you awake and its a bit late in the afternoon. You weigh all these things up quickly and decide... but even if the universe itself isn't deterministic, your decision making is surely not free, you took inputs with weights and that WAS the decision. It was not random.
Actual free will, at the top level, would look like rolling the dice every time. My personal belief is that if we had free will life would be unbelievably chaotic and society couldn't exist.
Now just go down a level and classical physical systems are deterministic, and even if you add quantum probabilities, those are tiny, and importantly, independent effects. i.e. they can't be controlled to make some system that is free of externalities.
And personally I also think superdeterminism is the most likely explanation for even quantum effects, but that is untestable and therefore a somewhat pointless belief.
Your definition of free will is fairly extreme and doesn't really line up with what is typically meant by free will. The discussion of free will typically involves moral agency (https://en.wikipedia.org/wiki/Free_will).
A strawman version of your view is that every time you see a bus, it should be 50-50 whether or not you jump in front of it. And, people don't jump in front of buses at that rate, so you conclude that free will is an illusion.
I would flip the baseline assumption around. Occasionally, some people do jump in front of a bus, so everyone (in a place with buses) that doesn't jump has made a choice not to because they could have done otherwise.
Personally, I don't think humans meaningfully exercise free will often because: 1. most of our available "choices" have either an obvious answer (do I eat?) or are largely irrelevant (Italian or Indian dish?). 2. most of us are content to operate on autopilot (as explored in the Adam Sandler movie "Click"). However, I do think the occasional real choices we make can have outsized impacts on the trajectory of our life because that choice becomes your new normal (e.g., kleptomania, drug addiction, waking up early, going for a jog).