The actual state of our knowledge is always provisional and … there must be, beyond what is actually known, immense new regions to discover.
-- Louis de Broglie
Consciousness cannot be accounted for in physical terms. For consciousness is absolutely fundamental. It cannot be accounted for in terms of anything else.
— Erwin Schrodinger
I am enough of an artist to draw freely upon my imagination. Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world.
— Albert Einstein
@thsottiaux It's frustrating, and honestly it just pushes users to try other great alternatives and switch, or downgrade their plan. Paying $200 to use it for a few hours, then being stuck for 3-4 days doing absolutely nothing? Makes no sense.
@OpenAI I've been paying for the $200 subscription for months and never used the option to reset usage limits. Now that I actually need it — because I'm in a rush to finish a project — it's no longer available. I find this extremely unfair.
@OpenAIDevs I've been paying for the $200 subscription for months and never used the option to reset usage limits. Now that I actually need it — because I'm in a rush to finish a project — it's no longer available. I find this extremely unfair.
@gdb I've been paying for the $200 subscription for months and never used the option to reset usage limits. Now that I actually need it — because I'm in a rush to finish a project — it's no longer available. I find this extremely unfair.
@ChatGPT I've been paying for the $200 subscription for months and never used the option to reset usage limits. Now that I actually need it — because I'm in a rush to finish a project — it's no longer available. I find this extremely unfair.
"To study the deep truths of number relationships feeds the spirit as surely as any of the other high human activities of art, music, or literature."
- Calvin Clawson, Mathematical Mysteries, 1996
I'm not an atheist. The problem involved is too vast for our limited minds. We are in the position of a little child entering a huge library filled with books in many languages. The child knows someone must have written these books. It does not know-how. It does not understand the languages in which they are written. The child dimly suspects a mysterious order in the arrangement of the books but doesn't know what it is. That, it seems to me, is the attitude of even the most intelligent human being toward God. We see the universe marvelously arranged and obeying certain laws but only dimly understand these laws.
-- A. Einstein
Kurt Gödel’s ideas about mathematical truth muddy the waters between where objective truth ends and invented math begins. A century later, the implications of his work have touched every corner of mathematics. https://t.co/UVDtVlYJkZ
Karl Popper (1902-1994) on what it means to be a rationalist ✍️
When I speak of reason or rationalism, all I mean is the conviction that we can learn through criticism of our mistakes and errors, especially through criticism by others, and eventually also through self-criticism. A rationalist is simply someone for whom it is more important to learn than to be proved right; someone who is willing to learn from others — not by simply taking over another's opinions, but by gladly allowing others to criticize his ideas and by gladly criticizing the ideas of others.
The emphasis here is on the idea of criticism or, to be more precise, critical discussion. The genuine rationalist does not think that he or anyone else is in possession of the truth; nor does he think that mere criticism as such helps us achieve new ideas. But he does think that, in the sphere of ideas, only critical discussion can help us sort the wheat from the chaff. He is well aware that acceptance or rejection of an idea is never a purely rational matter; but he thinks that only critical discussion can give us the maturity to see an idea from more and more sides and to make a correct judgement of it.
-- as mentioned in All Life is Problem Solving (1999)
The genius of Rosalind Franklin:
Rosalind Franklin (1920-1958) was a British chemist and X-ray crystallographer whose work was critical in understanding the molecular structures of DNA (deoxyribonucleic acid), RNA (ribonucleic acid), viruses, coal, and graphite. However, her contributions to the discovery of the structure of DNA, particularly, were largely unrecognized during her lifetime. Franklin graduated from Cambridge University in 1941 and worked as a research associate for the British Coal Utilisation Research Association during the Second World War. Her work there on the porosity of coal was significant for the coking industry and led to her Ph.D. in physical chemistry from Cambridge University.
After the war, Franklin moved to Paris where she learned X-ray diffraction techniques, a method used to visualize molecular structures, at the Laboratoire Central des Services Chimiques de l'Etat. In 1951, she returned to Britain to work at King's College London in the lab of John Randall. There, she made significant progress on X-ray diffraction images of DNA fibers. Franklin and her student Raymond Gosling produced an image known as "Photo 51", which was crucial in determining the structure of DNA.
However, unbeknownst to Franklin, this photograph and her detailed research data were shown by her colleague Maurice Wilkins to James Watson and Francis Crick, at the time working at the University of Cambridge. This data helped them build their correct theoretical model of DNA's double helix structure.
In 1953, Watson, Crick, and Wilkins published their model in Nature. Franklin also had a paper in the same issue describing her experimental data. However, her contribution to the discovery of the double helix structure was largely overlooked.
In 1958, Franklin died of ovarian cancer, possibly a result of her extensive exposure to X-ray radiation.
It wasn't until years later that Crick, Watson, and Wilkins acknowledged how crucial Franklin's work had been to their discovery. Unfortunately, the 1962 Nobel Prize in Physiology or Medicine awarded for the discovery of the structure of DNA did not include Franklin, as Nobel Prizes cannot be awarded posthumously. This has led to a significant discussion about the recognition of female scientists and the ethics of scientific research and collaboration.