I have a PhD in STEM. I started believing in my late 20s in graduate school. Readings that were influential included: accounts of high profile scientists who were also believers (e.g., Freeman Dyson), Tolstoy's "Confession", poets like William Blake and thinkers like Simone Weil, philosophers like Schopenhauer and Kierkegaard, and apologetics from C.S. Lewis and GK Chesterton.
My motivation to read any of this was downstream of some other internal feeling that I couldn't shake and slowly began to gnaw at me in my 20s -- that what I could sense around me (or sense at all) couldn't be all that "is". I suppose one way to phrase this is that I became increasingly disturbed by my inability to answer fundamental "where?" or "why?" questions (e.g., "why did the Big Bang happen?", "where is the singularity?", etc.). The standard retorts that some things are simply mysteries didn't satisfy me. Instead I started to suspect that much of what I thought was "territory" was actually just various "maps" that people have created in their minds to help navigate the territory. Around this time I stumbled onto Immanuel Kant's antinomies and realized that many people had thought along these lines in the past. Once I was on this trail, I've never strayed.
> Fun example from a friend: his family were extremely direct but his girlfriend’s family was very indirect. As a young naive guy he was having dinner with his girlfriend’s family and her father asked: “is there any salt” and my friend looked up at the glass salt shaker and said “yes” and continued with his meal.
Are we supposed to side with your friend here? The fact that he couldn't infer that the father might want some salt is, at best, very shortsighted and pedantic. It's roughly equivalent to a teacher responding to "Can I go to the washroom?" with "I don't know, can you?" -- except in this case it's not said in jest.
Yeah the quote assumes you're riding without speed limits. In a typical commute, it does get easier once your cardiovascular ability exceeds the upper speed limit given the route.
“ Intelligence is one of the greatest human gifts. But all too often a search for knowledge drives out the search for love. This is something else I've discovered for myself very recently. I present it to you as a hypothesis: Intelligence without the ability to give and receive affection leads to mental and moral breakdown, to neurosis, and possibly even psychosis. And I say that the mind absorbed in and involved in itself as a self-centered end, to the exclusion of human relationships, can only lead to violence and pain.”
- Daniel Keyes, Flowers for Algernon
Because we all sold out to the man. Culturally, we have chosen the lavish life promised under the man's umbrella, to doing the work of trying to go our own way. We now reap what we've sown.
“Even in our sleep, pain which cannot forget
falls drop by drop upon the heart
until, in our own despair, against our will,
comes wisdom through the awful grace of God.”
- Aeschylus
Yes, apologies -- using the term 'construct' muddied the point as sqrt(2) is a 'constructible' number as you point out. The term 'real' is what's at issue here and I am arguing for a distinction between a 'map-like' real and a 'territory-like' real, the latter of which has some sort of spatiotemporal grounding.
> There are some numbers that are not, and perhaps these can truly be said to not exist.
So then we have a real issue because the vast majority of the real line is composed of these uncomputable numbers which you've suggested don't exist.
> It really depends what you consider 'real'. It is actually pretty straightforward to realize a representation of 10^241 (you just did). Why does that make it any less real than the digit 2, which represents two things, but is actually just itself one thing.
One is a map, and the other is the territory. Both 'real' in some sense but a map without the territory feels less 'grounded' (pun?).
> Again, it's unclear what anyone means by things like 'sqrt(2)'. Why is drawing a thing of length sqrt(2) any different than drawing a thing of length 1? If I draw a thing of length 1 and say it's a line of length 1, then why is that different than my drawing the same line, claiming its length is sort(2) and then pointing out that it's actually now impossible to mark where 1 would appear along its length?
Perhaps a more precise way to describe the situation is that one can define one or the other as a base 'unit' but you can never get one from the other (they are 'incommensurate', as the greeks would say). Irrational numbers can be defined but not 'realized' (or 'constructed') in the same way that the rationals can.
Well, based on a quick Google, there are approximately 10^186 Planck-length volumes in the known universe. So 10^241 is not physical in the sense that there is no way to 'realize' a set of 10^241 things.
Another related notion is that there is no way to 'realize' an irrational 'number' -- sqrt(2) can be defined but we can never draw a length of sqrt(2).
A reward is not a constraint. In the language of modern ml, rewards 'encourage' models to produce certain constrained outputs. The actual outputs during inference can be arbitrarily poor in spite of the added 'reward' during training.
It's a single well-designed app where you can order takeout in a few clicks. It's generally much easier to re-order a past meal on it than it is to call or use some clunky web interface.
My motivation to read any of this was downstream of some other internal feeling that I couldn't shake and slowly began to gnaw at me in my 20s -- that what I could sense around me (or sense at all) couldn't be all that "is". I suppose one way to phrase this is that I became increasingly disturbed by my inability to answer fundamental "where?" or "why?" questions (e.g., "why did the Big Bang happen?", "where is the singularity?", etc.). The standard retorts that some things are simply mysteries didn't satisfy me. Instead I started to suspect that much of what I thought was "territory" was actually just various "maps" that people have created in their minds to help navigate the territory. Around this time I stumbled onto Immanuel Kant's antinomies and realized that many people had thought along these lines in the past. Once I was on this trail, I've never strayed.