A pointer somewhere on Twitter led to this post from the Slate Star Codex archives, discussing a paper that supposedly debunks the Fermi paradox:
Imagine we knew God flipped a coin. If it came up heads, He made 10 billion alien civilization. If it came up tails, He made none besides Earth. Using our one parameter Drake Equation, we determine that on average there should be 5 billion alien civilizations. Since we see zero, thatâs quite the paradox, isnât it?
No. In this case the mean is meaningless. Itâs not at all surprising that we see zero alien civilizations, it just means the coin must have landed tails.
As long as you consider linear algebra and eigenvectors âbasic mathâ:
Theyâd noticed that hard-to-compute terms called âeigenvectors,â describing, in this case, the ways that neutrinos propagate through matter, were equal to combinations of terms called âeigenvalues,â which are far easier to compute. Moreover, they realized that the relationship between eigenvectors and eigenvalues â ubiquitous objects in math, physics and engineering that have been studied since the 18th century â seemed to hold more generally.
The Google-backed service has delivered more than 100,000 trips to more than 1,500 monthly riders in the Phoenix area, according to a blog post. The number of weekly rides has tripled since its first full month of service in January 2019.
Iâve been reading more lately about freemium models in SaaS, where they work, where they donât, risks vs. upsides. This is a good one from Christoph Janz on the basics.
Unlike most other enterprise software, which traditionally used to be chosen by the IT department, Dropbox is typically adopted by individual employees from various departments, who then lobby management into switching. As I noted in my piece, Dropbox was one of the early champions of the âconsumerization of enterprise softwareâ movement, which was one of the strongest drivers of SaaS success in the last ten years.
But not every SaaS company can be a Dropbox or a Typeform. Done wrong, freemium can end up cannibalizing your paid user base while also draining your companyâs precious engineering and customer support resources. So how do you know if launching a freemium product is the right move for your company?
IT consumerization is one of those secular shifts thatâs changing many factors in the software space. The key to getting freemium right (assuming your product and market are conducive to it in the first place) seems to be a willingness to experiment with where the boundaries should be between whatâs free and what isnât.
The relationship that eventually mattered most to Einsteinâs legacy was symmetry. Scientists often describe symmetries as changes that donât really change anything, differences that donât make a difference, variations that leave deep relationships invariant. Examples are easy to find in everyday life. You can rotate a snowflake by 60 degrees and it will look the same. You can switch places on a teeter-totter and not upset the balance. More complicated symmetries have led physicists to the discovery of everything from neutrinos to quarks â they even led to Einsteinâs own discovery that gravitation is the curvature of space-time, which, we now know, can curl in on itself, pinching off into black holes.
Symmetry has helped physicists predict eventual discoveries (like the Higgs boson and gravitational waves), but also doesnât predict some symmetries weâd expect:
In some cases, symmetries present in the underlying laws of nature appear to be broken in reality. For instance, when energy congeals into matter via the good old E = mc2, the result is equal amounts of matter and antimatter â a symmetry. But if the energy of the Big Bang created matter and antimatter in equal amounts, they should have annihilated each other, leaving not a trace of matter behind. Yet here we are.
The perfect symmetry that should have existed in the early hot moments of the universe somehow got destroyed as it cooled down, just as a perfectly symmetrical drop of water loses some of its symmetry when it freezes into ice. (A snowflake may look the same in six different orientations, but a melted snowflake looks the same in every direction.)
âEveryoneâs interested in spontaneously broken symmetries,â Trodden said. âThe law of nature obeys a symmetry, but the solution youâre interested in does not.â
Itâs quite a daunting task to explain anything in theoretical physics in 250 pages, but this is just what I like about Carlo Rovelliâs books. Earlier this year I read The Order of Time, and like that book, Reality is Not What it Seems gets right to the point. No time is wasted or point too embellished.
This time around Rovelli tackles his specialty: quantum gravity. While it is a work of popular science, he does an admirable job of explaining wildly complex theories â made all the more difficult because a cumulative understanding in sequence is required to keep following the thread.
About half of the book is devoted to the scientists and their discoveries that lead to the two most important scientific theories weâre still building on today: general relativity and quantum mechanics. But we canât understand the origins of those breakthroughs without starting at the beginning.
Rovelli relishes the story of the great thinkers that each contributed stones to building the great structures of science weâve erected today in modern physics. Anaximander, Democritus, Aristotle, and Galileo all play a role in establishing the foundation that propelled Isaac Newton to the discovery of what we know know as classical mechanics. His laws of motion and gravitation were the bedrock of physics for 200 years until Michael Faradayâs work on electromagnetism. The number of amazing discoveries recounted here is astounding, and the profoundness is stark when presented in rapid-fire order, albeit succinctly, which Rovelli excels at. Rutherford, Bohr, Maxwell, Planck, von Neumann, Born, Pauli. The trail leads us to the big players behind the current understanding of the universe, and geniuses behind relativity and quantum mechanics: Albert Einstein, Werner Heisenberg, Paul Dirac, and John Wheeler. The time spent with each of the characters is brief, but meaningful; each of their achievements were astounding, especially given the technology and information each had available1.
These theories of modern physics are mind-bendingly difficult to comprehend. Both lie beyond our everyday perception â relativity at cosmic scales, and quanta at the ultramicroscopic. For such a brief baseline, Rovelli does a good job framing up the two with vivid examples demonstrating general relativityâs four-dimensional latticework of space and time, and quantum mechanicsâ probabilistic hecticness.
The second half of the book builds toward a merger of the two theories in âloop quantum gravityâ, which is an attempt (as yet unproven) to merge the two conflicting theories on the nature of reality. The fact that two demonstrably, empirically âtrueâ theories donât square with one another clearly indicates weâre missing something.
Things get quite existential and philosophical, in Rovelliâs lyrical style. Toward the end we even get a look at how thermodynamics and information theory play a role in understanding quantum gravity. I canât begin to summarize other than to say it involves foam, entropy, Claude Shannon, and the intertwining of heat and time.
Here are my core takeaways, trying to build my own understanding:
Reality is relational â things only exist in relation to other things, there is no absolute
Reality is reduced to interactions
It is only in interactions that anything in nature exists â we only know of things we can interact with
As such the world is made of events, not objects
We are a flux of events â at the quantum scale, we are made up of processes
Where this leaves us, I donât know. But Iâm incredibly curious to continue reading about the subject. I have far from a comprehensive understanding. Itâs endlessly fascinating to gain basic pieces of knowledge and feel like I have a better handle on how things work.
If the genius of these savant-like physicists wasnât already clear enough: Einstein published his paper on special relativity at age 26, and general relativity at 35. Heisenberg wrote the first equations of quantum physics at 25. Makes me perk up to think that all I do is send emails all day. ↩
