photon_lines

Sure, thanks for the feedback either way - I'll keep it in mind for my next write-up.

I wrote most of it -- I did use AI assistance for 20% of it though (I am not an LLM).

It's not AI slop -- I wrote it and it took quite a long time to write. I did use AI assistance for some of the components and indeed you are right: I did copy paste images (that I mostly generated myself) to try to introduce the concepts in a better way although some people will always have criticisms of almost anything so I take a lot of stuff posted on forums with a grain of salt. It's good to remember behind the wires it is us humans (for the most part) trying to communicate after all and trying to help others. Hopefully the write-up did help some people get the concepts -- I tried to write it in a form that I thought would have helped me more had I had the chance of being reintroduced to imaginary numbers -- a lot of the concepts I included in the write-up were not taught to me when I initially encountered them and I wish they had been.

Eating ultra processed foods with added sugar / loads of calories. A huge reason why they're so destructive is because they lack fibre (which keep our microbiomes healthy) and lack compounds which are good for us. Try keeping weight on while eating minimally-processed food that is more vegan in nature: the amount you'll have to consume to keep the weight on is significant. When you start this diet, you won't like it that much and you will feel hungry since your microbiome is used to your old diet -- but try doing it for a month, and you'll see a huge shift in the way you feel and the foods which you crave (the above will start transforming your microbiome quite significantly). Do it for 3 - 6 months you'll wonder how in the world you ever lived without it.

So I can show you why it works algebraically -- I'm not sure if it will help you though.

Kinetic energy is the work needed to accelerate something from rest to speed v (velocity). Below we'll use the regular derivative representation to represent an tiny change in a value using notation such as dE (tiny change in energy).

Work can be described as dE (tiny change of energy) = F (force) * dx (tiny change in position). -> dE = F * dx

Force though changes momentum and algebraically can be described as:

F (force) = dp/dt (tiny change in momentum over tiny change in time)

The distance travelled over a infinitesimally small time frame is:

dx (tiny change in position) = v (velocity) * dt (tiny change in time) -> dx = v * dt

So now we have:

dE = F * dx (see our definition above) = dp/dt * v * dt (due to F = dp/dt and x = vt) = v dp (the dt terms cancel each other out and we are left with velocity and rate of change in momentum) -> dE = v * dp

So we are therefore left with:

dE (tiny change in energy) = v (velocity) * dp (tiny change in momentum) -> dE = v * dp

We can translate this as stating: the energy cost of adding a tiny bit of momentum depends on how fast the object is already moving. Now we also know that algebraically:

p (momentum) = m (mass) * v (velocity) -> p = mv

Using derivatives we also have:

dp (tiny change in momentum) = m (mass) * dv (tiny change in velocity) -> dp = m * dv

Going back to our original equation, we now have:

dE (tiny change in energy) = v * dp = v * m * dv (since dp = m * dv)

To get the total energy that it takes to move a mass m from 0 to velocity v, we need to add up all the tiny energy costs from 0 to v, and for this we use the integral to get:

E = ∫(from 0 to v) add up m (mass) * v (velocity) * dv (rate of change in velocity) = 1/2mvv (basic integration) = 1/2m*v^2

So from the above we can see that the kinetic energy rises quadratically with velocty. Now the 'why' this is encoded in the universe: read a bit more about symmetry and Emmy Noether. The laws of physics do not care where you are, when you are, or whether you are moving at a constant speed in a straight line. This is called Galilean symmetry in ordinary classical mechanics. Because the laws of motion have to stay consistent under changes of reference frame, energy cannot just be proportional to velocity. A linear energy law would break the symmetry.

I was going to comment on this too: the style and format of this writing screams 'written by ChatGPT' to me. The funny part is that the AI actually does a good job in making the argument and OP is trying to make: AI will never be able to feel the things that a human can, but yet within this post, it has shown that it can logically comprehend human tone and emotion and can create a stream of consciousness that most humans can connect with and understand.

- Visual Guide to Number Theory: write up which explains the field of number theory in a visual manner.

- Reenvision technologies: simple software. Local first - no added complexity. Infinite scale without having to add 100 front-end UI frameworks: simple Python, CSS, and JS with SQLite. The design is absolutely breathtaking and beautiful and it is built people first (let's worry about scale later).

- Simple LLM: an LLM which doesn't need a GPU to function. It uses Hebbian learning with extreme compression and attempts to achieve 'reasoning ability' through using a in-built Prolog interpreter. It very much resembles a human being in it's 'thinking mode' so far but still far from perfect.

- Simple-Education: local first software for parents looking to provide home-schooling for their children. It makes learning easy and fun and uses best practices to maximise your child's chance of success.

- About a dozen other projects which I've started but I need help on. If you want to team up -- I will give you equal equity in my start-ups. I cannot offer you a salary though I'm not at the point yet where I can do that: but I will give you equal equity in anything that you want to work on together with me. I have over 100 different million dollar ideas that will make us wealthy if you want to join my team, so PM me if you're interested.

There is an alternative: 1) limit how much descendants can inherit. Allow them only a maximum amount of let's say: 10 million and make sure that either the founder finds a way to redistribute his/her wealth to the rest of the world, or make the government find ways of redistributing this money. 2) make it mandatory for corporations to share their wealth (income) with the employees -- as an example make it mandatory to redistribute 50% of the income generated to the employees working for the company rather than paying CEOs insane amounts of money to return 'shareholder value'. The whole motto of maximising shareholder value has poisoned capitalism: the goal of a company should not be to become a cancerous growth -- but to serve as a net good for humanity. 3) seal the tax loopholes that make it easy for the rich to avoid paying taxes. There is no reason why the poor and middle class pay a disproportionate amount in taxes compared to the rich.

I agree with most of what you're saying -- but just wanted to add some notes here: 1) founders should start companies where equity is distributed to the early employees much more evenly: this actually gives additional super-powers to the company since employee incentives are much more closely aligned with the vision of the founders (building something great that people love to use). 2) stop rewarding growth: there is nothing wrong with NOT growing 90% a month. The goal of most companies shouldn't be to grow or return maximum value to investors (or shareholders): it should be to provide a greater human good the markets will be willing to pay for 3) revenue growth also is not something to aim for: sustainable income growth is. 4) unless the billionaires start re-distributing their wealth -- history is not on their side. A revolution will happen: usually this is associated with the younger male population being unemployed (~15% is the magic number) and causing an uprising. The goal of most founders at this point should not be 'how do I get to 1 billion.' The massive unemployment caused by the AI revolution will cause a massive uprising. There is great danger I think if they do not figure out a way to re-distribute their wealth. Currently, the poor and middle class are taxed way more than the rich (as a percentage of their income): and from what I see are increasingly becoming more disgruntled with the situation they are in. Why in the world would anyone want to even be a billionaire in this situation is the question I want to ask?

There is a chance - yes, but there's a lot of other evidence that he was involved in its creation (not just the 10+ years he talked about bit-gold prior to bitcoin). Bit-gold = bitcoin. My guess is that someone (like Hal Finny) implemented it with him but he was the originator of the idea and wrote the paper on it. Finny most likely had the original keys or he intentionally got rid of them on purpose (which explains why the wallet hasn't been active). Those are my guesses but the language in the paper very much gives me the impression that it was written by Nick Szabo.

I'm almost 100% certain he's the creator of Bitcoin. I didn't need to see his technical chops to suspect it -- all I needed was to read his article from 2002 which discusses the whole concept and key ideas that Bitcoin is currently based on: https://nakamotoinstitute.org/library/shelling-out/

Thank you! I'm glad you found it helpful (and that others did too)!!

The whole goal of quantisation is to put the data into 'bins' so that it can easily be 'packed' so that you can represent it using less bits (less information). You can think of it like rounding essentially (3.14159 -> 3). Now, sometimes within data, the distribution will be non-ideal for separating it out into bins (let's say that our rounding rules are simple -- we simply use a floor function so 2.45 maps to 2 and 6.4543 maps to 6 etc...) and our bins simply map to the floor -- if we had a set of numbers which look like this: [3.11, 4.43, 5.78, 12.33, 34.32], they would simply map to [3, 4, 5, 12, 34]. Now, we have one huge outlier in our data (34) so to create bins for those sets of numbers, we would need 6 bits of information (2 to the power of 6 = 64), but this is mostly due to the fact that we have one huge outlier (34.32). To get rid of this -- the algorithms applies a random rotation matrix which 'distorts' the original data so that it is more evenly distributed among the possible bins which are assigned to the data set. In linear algebra, a rotation matrix is an orthogonal matrix. When you multiply your vector by this matrix, you aren't changing the "amount" of data (the length of the vector remains the same), but you are recalculating every single number in that vector as a weighted sum of the originals. According to the Central Limit Theorem, when you sum up many random things, the result always starts looking like a bell curve. This is the magic TurboQuant relies on: they don't know what your data looks like, but they know that after the rotation, the data must look like a Beta Distribution and they use this fact to transform the original data into a more 'tightly packed' distribution which allows them to more efficiently pack (or quantise) the information. If most of the transformed data is huddled together into a predictable Bell curve shape, you can pack your bins tightly around that shape leading to much higher precision with fewer needed bits to store it. For example, after applying a rotation matrix, our original transform [3.11, 4.43, 5.78, 12.33, 34.32] might get mapped to something like [8.12, 8.65, 9.25, 10.53, 12.86] and we can crate bins which both are more accurate and need less bits in order to hold our original data set. To create the most optimal bins -- the Lloyd-Max algorithm is used. This algorithm is the gold standard for 1D quantisation. Its goal is to find the best places to put your "boundaries" (where you cut the data) and your "reconstruction values" (the number you store) to minimise the Mean Squared Error (MSE). After applying this, you have your 'rounded' values (or quantized data), but there is still an error value which is missing from our data set: and this is where the residual bit comes in. That bit doesn't represent the original data (or vector) - it simply represents our 'bias' after we apply the above algorithms. It's basically like a '1-bit note' which allows you to perfectly cancel out all the bias terms which our above quantisation algorithm produces to make the 'interactions' (or inner products) when we multiply our values together extremely accurate again even after transforming our original data. Does this make sense?

Thank you Chase -- I was an early Watsi supporter (and still am actually) but you just reminded me I need to donate soon haha :) Either way fantastic work and thank you!

I don't have a personal site at the moment, but I do have a blog: https://photonlines.substack.com/

Some of my projects: https://github.com/photonlines

I love your website. Very clear and to the point.

You do understand that you can run these tools locally right? The code is fully available and open source: https://github.com/blgardner/prism.tools

Ahhh OK - that makes sense - thank you.

I love what you have here. Thank you for open sourcing your work -- but why the custom license? Why not just do a standard MIT license?

If anyone is curious to see what Watson actually was you can find it here (it was nowhere near to a generalized large langue model -- mostly made for winning in Jeopardy): https://www.cs.cornell.edu/courses/cs4740/2011sp/papers/AIMa...

Why in the world would economists need to study this? It's been known that large bureaucracies have been dysfunctional for over a couple of decades now if not centuries. The large reason is because 1) the incentives to do great work are not there (most of the credit for a huge company's success goes to the CEO who gets 100X the salary of a regular worker while delivering usually pretty much nothing) 2) politics usually plays a huge role which gives a huge advantage to your competition (i.e. your competition needs to spend less time on politics and more time on the actual product) and 3) human beings don't functionally work well in groups larger than 100-250 due to the overwhelming complexity of the communication needed in order to make this type of structure work. Incentives though I think are the primary driver - most people at companies like IBM don't have any incentives to actually care about the product they produce and that's the secret behind the ruin of almost every large company.

Edit: you also seem to be giving too much credence to Watson. Watson was actually mostly a marketing tool designed to win in Jeopardy and nothing else. It was constructed specifically to compete in that use-case and was nowhere near to the architecture of a general transformer which is capable of figuring out meta-patterns within language and structurally understanding language. You can read about Watson's design and architecture here if you're curious: https://www.cs.cornell.edu/courses/cs4740/2011sp/papers/AIMa...

Exciting stuff from a fantastic team.

Happy Thanksgiving everyone -- I've mostly been a lurker here over the last 20 years and I'm thankful for being able to interact with such a bright and vibrant community full of thinkers, doers and explorers -- you guys definitely changed my life for the better and inspired me in many, many ways.

So if your endocrinologist was found to have ran a concentration camp in the past, it would have no effect on your decision on whether you wanted to use them as your doctor? Running a concentration camp also has no bearing on a doctor's performance.

She blamed the research fraud on her assistant when she was initially accused of it and denied all liabilities. She only admitted to it after they had her cornered. I had her as my endocrinologist for a while and I would not recommend her. Edit: if you want to have a care-taker who doesn't mind lying or is a psychopath, you do you but it's a no go for me.

This is 100% true, especially in Canada. I've had multiple encounters with doctors who were not fit for their positions and should not have been working as doctors. One of them nearly killed my mom, and another one was suspended due to malpractice and performing research fraud, but was given her license back and is back to work at the moment. Yes she is fully licensed and back to working as a regular MD in Canada: https://en.wikipedia.org/wiki/Sophie_Jamal

20 minutes a day is all it takes. Don't even think about it - just do it. After a couple of weeks you'll wonder how in the world you ever lived without exercise -- trust me on this one :)

Are you experiencing the HN hug of death or is your website down? Either way I'm super interested in what you're building and I'd love to use it but I cannot reach your link at the moment. Good luck with the endeavor either way and thank you for building this.

I love this - great work.

The visual is directly from here (I recommend you give it a read if you want to grasp the full intuition on how a Fenwick tree works (page 97)): https://cses.fi/book/book.pdf

I should have included the full visuals which are included there and I can see your point on why people would get confused by that visual - so I'll make a note to include the full image when I have more time. Thank you for the feedback.