Per the current understanding of Quantum Mechanics (which may very well turn out to be wrong/inaccurate, but is currently our strongest theory) the fundamental particles have a wave nature, and their wave function collapses into a particle at random position (governed by probability, due to uncertainty principle) only when observed/measured.
Hence following this scientific understanding of reality and of particles that make us, it’s logical to conclude that macroscopic things like humans and plants are made of microscopic particles that are waves and so we are essentially waves too and so we don’t really have a particle like existence until observed by someone else (some other consciousness)
- DNA is spread across 46 Chromosomes (present in the nucleus of each cell). Each chromosome contains a DNA strip. There are in all 3 Billion basepairs (made using pairs of A, T, C or G chemicals) in human Genome (all DNA strips together).
- A group of basepairs together describe a protein and it’s expression function and is called a Gene. DNA is comprised of 20K genes that describe the 20K proteins that make us.
- The size and shape of the protein determine the function that it’ll perform in the body.
- Proteins make up cells. Cells make Tissue. Tissues make Organs.
- In computational terms, DNA is a protein circuit.
- The genome consists of both data and functions:
- Data: The description of Proteins (20k)
- Function: The Protein Expression Function (20K functions. 1 for each protein), which takes input the concentration of all proteins and outputs the amount of any given protein to create wrt the other proteins.
- DNA is 4 billion bits long.
Most mathematicians are probably with Plato on this they tell you that mathematical truth is more pure and essential and fully known than anything in science you’ve probably heard that evolution is just a theory even gravity is just a theory because science can’t really ever fully prove anything but math has proofs and we know for sure they’re right but why is science stuck defending theories about the imperfect real world while math has these perfect truths
Average scientists view of mathematics it’s some kind of language of nature you need it to describe how the universe acts and who cares why it works we found that it does at least here were unfamiliar territory for scientists mathematical truth if nothing else is backed up by empirical observations of the world just like any scientific theory but does that mean that mathematical proof isn’t really proof
I got this idea from Haskell curry and all-around awesome mathematician who outlined it in a little paper in 1951 math is a science on the exact same footing as physics or chemistry mathematical rules themselves are a phenomenon that exists in the real world and can be observed and studied there may not be any perfect circle’s but there are certainly very real definitions of them in the rules of geometry and following the rules of geometry to reach conclusions about their properties is a real phenomenon with observable results math in other words is the science that studies the implications of systems of rules and any rules count math is not just the stuff taught in grade school like the straightedge and compass rules of geometry or the equation balancing rules of algebra but also non-euclidean geometries and exotic algebra is with arbitrary numbers of operations that are commutative or not or distributive whichever way and the rules of games like tic-tac-toe in yes even the abstract ADRA’s of grocery checkout lines or stock options or gravity or quantum mechanics even straight forward rules can have surprising implications so it’s not like there’s nothing to discover just because you know the rules the pythagorean’s for example were scandalized to learn that the rules of geometry led undeniably to irrational numbers like the square root of two but there it is and we have a proof the proof that is if you look at it another way a reproducible experiment maybe we can’t prove things in math any more than in science but by following the rules of geometry we can show ourselves again and again the hypotenuse of a right triangle with two sides of equal length can’t be the ratio between any two whole numbers so in the science of mathematics the hypotheses are ideas we have about the implications of rules like you can guarantee a draw against any opponent in tic-tac-toe just by playing well and then experiments are individual applications of the rules like checking a proof to verify that they play out in a certain way the experiments in math in other words our computations like the intuitionist idea that math is founded in the activity of human brains computing an answer Curry’s view focuses on the empirical observation of computations but the idea isn’t to directly experience their intuitive truth so much as to see that the faithful application of rules does indeed lead to a particular conclusion put in computation at the center of mathematics like this makes me wonder about the connection between math and computer science I think math literally is the science of computation after all the deep connection between mathematical proof and compute ability which was discovered as part of the investigation into the foundations of math in the early 20th century is what kicked off the field of theoretical computer science in the first place somebody in computer science may be EDS or Dijkstra is supposed to have said that computer science is no more about computers than astronomy is about telescopes if throughout history mathematicians use their brains to conduct mathematical experiments in the same way that astronomers observe the night sky with their naked eyes then computers are like telescopes through which we can better investigate the computational nature of reality but what about that kid asking when am I ever going to use this if nature is all computational and mathematical shouldn’t math be obviously useful well of course it is math is everywhere when kids ask when am I ever going to use this what they mean is you’re explaining this so badly that I don’t even know what it is you’ve taught me how to swim without ever showing me a body of water big enough to swim in we give them little buckets like contrived a train leaves Chicago problems and then drill them endlessly on techniques for solving these non problems traditional math classes are so eager to cover every clever technique in a subject that we end up covering them all using boring little problems that nobody needs to solve and we leave people confused about why they learn to solve them in the first place which they promptly forget how to do anyway if we covered fewer techniques we’d have more time to hit real problems and kids would have a chance to get the idea of what math is or at least what it’s good for
- Brains are digital information processing machines like computers
- Without sexual reproduction, change in the offspring’s genome is dependent purely on mutation ie chance and 9 of the 10 offspring produced asexually are perfect clones ie have identical genomes to their parents. But in bisexual repro, variation is inherent by design coz half the genes come from male and other half from female
- All Life is information processing even at the scale of individual cell whereby the DNA stores information (in form of genes) and the function of cell is to process the genomic information and perform actions.
- The universe itself is processing information. For instance when atoms interact, their bits (spin of electrons etc.) flip.
- The universe computes. This computational ie information processing ability of the universe is what allowed for later info processing revolutions like life, brain, language, computers (classical and quantum), AI etc.
- Computers (classical and quantum) are not suddenly making the universe (atoms) compute, but instead we’re using the computation that the universe is already performing and we’re hijacking/hacking it for our use (like doing multiplication or playing games etc. )
- Does matter have meaning?
- Quantifying information into bits was the revolution that led to computers.
- We discovered that the quantity of information is distinct from the meaning of info.
- The bit itself is just a state amongst 2 states, so can be spoken as yes or no OR true or false OR 1 or 0. In itself, the bit has no meaning. But when attached to a context/question, like “Do you want fries?”, the bit storing the answer (yes or no) has meaning which is the answer to the question.
- The meaning of a bit in a computer is to tell the computer to do something. The computer interprets the bit say 0 to mean “do this” like “add” and so on depending on the programming of the computer.
- Hence meaning comes from interpretation of the bit and not the bit itself.
- Quantum Computers (QC)
- Quantum computers is simply leveraging Quantum mechanics like classical computers leveraged classical physics to do Computation.
- In classical computers, the bit was implemented by capacitors, so a charged capacitor ie a capacitor holding electrons was represented by Bit 1 and a uncharged capacitor ie one holding no electrons was Bit 0.
- Similarly in QCs a bit is represented by a single electron. So electron spin up is bit 1 and spin down is bit 0.
- So the advantage here is that now, the bit has been miniaturized from a bucket of electrons (capacitor) to a single one. This is a big leap in size of a bit.
- Another advantage is that the electrons are closer together in atom, than capacitors would be from each other, and so being 1 angstrong apart, they can be made to interact (aka compute) quite easily and cheaply (using singular photons of energy) instead of making transistors to do computation (like AND gate etc) like we do in classical computers.
- But the biggest advantage of using single electron as a bit is that coz its so tiny, it exhibits quantum mechanical effects (which manifest only at tiny scales and cancel out at macroscopic scales).
- The most significant quantum effect of electrons is their behavior as waves (wave-particle duality) whereby the waves that correspond to these electrons (that we use as bits) are not discrete (like particles) but continuous (like waves). So now instead of using the spin of electron particle as a bit which limits us to 2 states (0 and 1 depending on up or down spin) we can use the Electron Wave to represent our Bit and hence have more than 2 states represented by the electron, coz the wave is not discrete anymore. The states that we represent in a QBit are 3 ie:
- 0 (DISCRETE particle state corresponding to Up spin of electron particle. Manifests when the QBit interacts with other QBit or when we measure/inspect the state)
- 1 (DISCRETE particle state corresponding to Down spin of electron particle. Manifests when the QBit interacts with other QBit or when we measure/inspect the state)
- 0/1 (CONTINUOUS wave state corresponding to all spins of the electron particle by virtue of it’s wave nature)
- So if a classical bit can be use to represent:
- 0: Add 1 and 2
- 1: Add 3 and 4
- This classical bit can be in only 1 state at a time and so at an instance of time can either be 0, which would lead to computation of 1+2 OR be in state of 1 which would lead to 3+4
- But, because a QBit ie an electron has a wave nature, it can be in continuouse wave state, or in discrete particle sense we can say that it’s in state 0 and 1 at the same time and hence computes 1+2 and 3+4 simultaneously.
- Hence QCs can be crudely thought of as multitasking/parallel classical computers.
- For instance a Quantum computer with 300 bits ie 300 electrons working together, can do 2^300 computations simultaneously (just like a QC with 1 QBit can do 2 things at once). Note that 2^300 is the total no. of particles (total of the number of protons, neutrons and electrons only as we don’t know what dark matter or dark energy particles are) in the observable universe (parts of the universe that are within 13.7 billion light years of us in the infinitely bigger flat universe), so to do 2^300 computations simultaneously, we’d need 2^300 classical bits active simultaneously which is impossible as 1 classical bit requires multiple particles to represent.
- Are QCs Predictable?
- When we measure the state of QBit ie electron, we randomly get either 1 or 0 coz per QM (Quantum Mechanics), the act of measurement collapses the wave function and hence we see the discrete state 0 or 1.
- Hence QCs aren’t as good for computations that require QBits to interact with each other coz when a electron interacts ie tries to find the state of another, then also, the wave nature collapses and it’ll show up as either state 0 or 1 and hence transform into classical computer, being in one state at a time, hence only able to do one thing at a time.
- QCs are hence predictable only when you make sure the parallel computations in the end, combine (positive interferance) to give single answer (like most optimal route in travelling salesman problem OR breaking cryptography codes etc.) so that the answer is singular and hence doesn’t require collapse of the wave function, which can randomly lead or any 1 of the possible answers (states) when measured.
- Building QCs
- Zap atoms in a molecule with Microwaves.
- Different atoms respond to different microwave frequency.
- So, neuclei of atom 1 (having magnet on it) would flip (magnetic N-S) at say 80MHz and another atom will flip at 100MHz say.
- Hence being able to control the flipping of atoms which represent our bits, we can do computations using interactions of these atoms.
- Complexity of universe arising from QM
- Why does the Universe have so many particles.
- It’s the random quantum fluctuations (energy densities in quantum field) in vaccum that when interact, collapse and form particles.
- Hence a bit is actually produced, and that’s how you get a universe from nothing
- So why is the universe here instead of there (say 100 light years away)? Coz the quantum fluctuations here were stronger (randomly) and so interacted/coalesced with other such fluctuations to form particles and hence stars, galaxies and the universe as a whole.
- Hence we can conclude that the universe is constantly computing (in the form of random quantum fluctuations) and random bits are getting injected contimuously (as a result of interactions of these quantum fluctuation causing the wave function to collapse)
- But its not complete randomness coz these random bits are being injected/input into the universe which is a computer (is able to perform computations using laws of physics which may be the ones we’ve come up with <note I didn’t say discovered coz these laws might not be final ie absolute ie true ie ultimate true laws, but may very well be laws that we’ve come up with to understand what we see with our limited understanding and senses> or some other laws) and being a computer, the universe injects meaning (ie create meaningful stuff like galaxies and planets and maybe life using the laws) into these random Qbits ie electrons just like a computer produces meaningful result of computation.
- Eg. Addition is a computation that our computer can perform. Now, the input 2 and 1 into this computer is random, but the computation of Addition that results in 3 as the output gives meaning ie sense to the input as we can now reason about it.
- Similarly particles are zapping into existence at the quantum level (due to laws of QM) which are inputs to this universe which is a quantum computer and it then comes up with the laws of physics, chemistry, mathematical theorems and structures and so on to output the universe with all it’s complexity albeit running only simple programs/laws/computations.
- Read More: Theory of Algorithmic Information