I bought Starlink Mini in January. I installed it in my Tesla.
I just got a notification that I exceeded the Starlink Mini speed limit.
Apparently FSD "hurry mode" goes too fast for Starlink.That's annoying.
E1 [Find remained] Divide m by n and r be the remainder. (We will know that 0 <= r < n)
E2 [Is it zero?] If r = 0, the algorithm terminates, n is the answer
E3 [Reduce] Set m = n, then n = r, then go back to step E1 -----------------------------------------------------------------------
[3] Change Algorithm E so that all trivial replacement operations such as m = n are avoided. Write this new algorithm in the style of Algorithm E and call it Algorithm F.
======================================================================== Claude Sonnet 4.6 ========================================================================
Algorithm F
Given two positive integers m and n, find their greatest common divisor.
F1 [Find remainder] Divide m by n and let r be the remainder. (We will know that 0 ≤ r < n.)
F2 [Is it zero?] If r = 0, the algorithm terminates and n is the answer.
F3 [Find remainder] Divide n by r and let m be the remainder. (We will know that 0 ≤ m < r.)
F4 [Is it zero?] If m = 0, the algorithm terminates and r is the answer.
F5 [Find remainder] Divide r by m and let n be the remainder. (We will know that 0 ≤ n < m.) Go back to F2.
Explanation
The key insight is that instead of shuffling values with temporary replacements like:
m = n, n = r
we reuse the existing variables (m, n, r) in rotation, dividing and storing each new remainder directly into the variable that is no longer needed:
Step Divides Remainder stored in F1...m by n...r F3...n by r...m F5...r by m...n
Each variable naturally becomes the "oldest" value at each stage and is safely overwritten. This eliminates all trivial assignments while preserving the logic of Euclid's algorithm. □
Knuth Art Of Computer Programming V1 p9 ----------------------------------------------------------------------- Algorithm E (Euclid's algorithm). Given two positive integers m and n, find their greatest common divisor, that is, the largest positive integer that evenly divides both m and n.
E1 [Find remained] Divide m by n and r be the remainder. (We will know that 0 <= r < n)
E2 [Is it zero?] If r = 0, the algorithm terminates, n is the answer
E3 [Reduce] Set m = n, then n = r, then go back to step E1 -----------------------------------------------------------------------
Prove that m is always greater than n at the beginning of step E1, except possibly the first time this step occurs.
======================================================================== Claude Sonnet 4.6 ========================================================================
Proof
We want to show that m > n at the start of E1, for every iteration except possibly the first.
First Execution of E1
When E1 is executed the first time, m and n are simply whatever positive integers were given as input. There is no guarantee that m > n, which is why the exception exists. For example, with m = 2166 and n = 6099, we have m < n on the first call.
All Subsequent Executions of E1
After the first execution of E1, we reach E3 only if r ≠ 0 (checked at E2). At E3, the replacements are:
m = n n = r
Then we return to E1. So at the start of the next E1, the new values are:
m_new = n_old and n_new = r_old
From E1, we know r is the remainder when m is divided by n, so by definition:
0 ≤ r < n
Since E3 is only reached when r ≠ 0 (E2 would have terminated otherwise), we tighten this to:
0 < r < n
Therefore:
n_new = r_old < n_old = m_new
Which gives us:
m_new > n_new
Conclusion
After the first iteration, the new m is always the old n, and the new n is always the remainder r, which is strictly less than the old n. Therefore m > n holds at the beginning of every execution of E1 except possibly the first, which is what we wanted to prove. □
[1] The values of variables m and n, can be interchanged using t = m, then m = n, then n = t. Show how the values of four variables (a,b,c,d) can be rearranged to (b,c,d,a) by a sequence of replacements. In other words, the new value of a is to be the original value of b, etc. Try to use the minimum number of replacements.
======================================================================== Claude Sonnet 4.6 ========================================================================
We want to transform (a, b, c, d) → (b, c, d, a) Using a temporary variable t, here is the sequence:
t = a a = b b = c c = d d = t
Trace through to verify:
Step.: a b c d t Start: a b c d — t = a: a b c d a a = b: b b c d a b = c: b c c d a c = d: b c d d a d = t: b c d a a
Result: (a, b, c, d) → (b, c, d, a)
This uses 5 replacements, which is the minimum needed — one to save the displaced value of a into t, three to shift b→a, c→b, d→c, and one final step to place the saved value into d.
E1 [Find remained] Divide m by n and r be the remainder. (We will know that 0 <= r < n)
E2 [Is it zero?] If r = 0, the algorithm terminates, n is the answer
E3 [Reduce] Set m = n, then n = r, then go back to step E1
----------------------------------------------------------------------- Knuth Art Of Computer Programming V1 p9 Problem 1.1.4
[4] Using Algorithm E compute the greatest common divisor of 2166 and 6099. Label each step of the algorithm as it is used.
======================================================================== Claude Sonnet 4.6 ========================================================================
Starting with m = 2166, n = 6099: E1: 2166 ÷ 6099 = 0 remainder 2166 → r = 2166 E2: r ≠ 0, continue E3: m = 6099, n = 2166
E1: 6099 ÷ 2166 = 2 remainder 1767 → r = 1767 E2: r ≠ 0, continue E3: m = 2166, n = 1767
E1: 2166 ÷ 1767 = 1 remainder 399 → r = 399 E2: r ≠ 0, continue E3: m = 1767, n = 399
E1: 1767 ÷ 399 = 4 remainder 171 → r = 171 E2: r ≠ 0, continue E3: m = 399, n = 171
E1: 399 ÷ 171 = 2 remainder 57 → r = 57 E2: r ≠ 0, continue E3: m = 171, n = 57
E1: 171 ÷ 57 = 3 remainder 0 → r = 0 E2: r = 0, algorithm terminates GCD(2166, 6099) = 57
Given an infinite number of paperclips what are the design constraints?
Paperclips designs are the "string theory" of physical construction.
Ideas in 1 dimension
Obviously you could make a single one-dimensional line of paperclips. This raises the question of multiples sizes of paperclips. Can we make an ever smaller paperclip progression in an interval?
Ideas in 2 dimensions
One could make a 2-dimensional regular fabric of paperclips. The 2D fabric could be made from regular shapes like hexagons instead. How many ways can a plane be tiled, especially if we vary sizes
Ideas in 3 dimensions
One could make a 3 dimensional solid of paperclips. The 2D hexagons could be extended in 3D forming a "bee hive" effect. A 3D paperclip array could have holes and voids forming structures. In 3D the paperclip can vary in size and shape. Bent paperclips arise.
Paperclips don't need to be made of steel. Suppose some are non-conductive so we can form circuits. A non-uniform paperclips could, for example, be a capacitor.
Are there interesting "vibration modes", like waves in a sea?
Ideas in 4 dimensions (varying in time).
Paperclips can move independently. One could clearly make "paperclip wheels". Can we build a timepiece in paperclips?
Tools.
We need to make a solid modeling tool to handle paperclips. We need an MCP server to allow the AI to use the tool. We need a trained AI to "think in paperclips". We need "alignment training" so the results fit our needs.
Further thoughts.
Suppose we go to the moon and find the moon has ideal paperclip material. Might it be efficient to construct a single paperclip factory? Then everything has a common structure and is easily maintained and repaired.
Contribute!
The more I think about it it becomes clear that physics is wrongly constructed.
The ability to manipulate space-time directly solves a lot of problems. Take, for example, the UFO problem I mentioned. Physics has the concept of propulsion, equal and opposite "forces". If instead you could directly manipulate "mass" as a variable then things change. The photon is massless which makes the universe "flat" and leads to travel at the speed of light. If you could shed mass at will you could easily approach the speed of light without "propulsion". Thus a civilization that figures out how to manipulate "mass" would be able to travel anywhere at the speed of light. You don't accelerate mass, which is dumb, you "shed mass" and thus move without propulsion. Indeed, if you could achieve "negative mass" (changing a gravity well into a gravity hill) you could easitly exceed the speed of light.
Einstein felt that things got more massive as they approach the speed of light and, in the limit, would have infinite mass. That's true under propulsion. It is not true if you can "shed mass". Thus Einstein missed the very thing that mattered.
Shedding mass likely involves directly manipulating the Higgs boson.
Dark energy and dark matter might be "negative masses".
I don't know any physics professors but I'm pretty sure I'm talking nonsense :-)
It should be able to tell me where I left my coffee cup.
It should tell me what meds to take and remind me to take them.
It should remind me to pay a bill since I still write checks.
It should tell me that today is trash day.
It should keep a list of things I need at the store.
At the store it should tell me what to buy.
It should remind me of upcoming birthdays.
It should listen to phone calls and tell me what I promised.
It should remind me that the wash needs to be put in the dryer.
It should tell me the name of "that actor" in "that movie" where they did "that thing".
In shourt, it should be a "companion".
I don't need to know the capital city of Kansas or to name the fifth digit of Pi. I need immediate help with the trivial things usually in short term memory.
Let me know when you think you've solved this. I want to be a beta tester.
Oh, and remind me that I promised to be a beta tester for "that thing" you invented :-)
Tim (axiomcas@gmail.com)
This is a different proposal. The idea is to see how creative an AI can be. The rules are simple and general, leaving a lot of room for "creative license".
I call this the "Sad To Say" test. It involves the use of excitement and regret represented by a story about an event somewhere in a persons lifetime. The underlying idea is to capture emotional stresses and strains. The whole album has a common structure and theme.
...
Billy Joel wrote a song "Scenes From An Italian Restaurant". https://www.youtube.com/watch?v=Hxx8IWIvKg0
The structure of the song is in three parts, the "headboard", the "mattress", and the "footboard". This structure is called an HMF (headboard, mattress, footboard).
Create a music album with 12 songs. The overall album structure is 12 different people who have gathered for a 50th year reunion. Each person tells a story using the HMF structure.
The overall theme of the album is a collection of stories of great potential, explained in the mattress section, to a group of people who know each other from high school or college.
Each song's "headboard" involves a setup story using a tempo and conversation structure similar to the Billy Joel example. This same tempo and structure will be repeated in the "footboard". The "headboard" should lead to a sense of "great potential".
Each song's "mattress" is a completely different tempo and structure. The tempo is different. Each mattress song should be about an event with great potential such as a love interest, a business success, an athletic achievement, etc. The story should emphasis a great rise of success that eventually fails.
Each song's "footboard" should return to the "headboard" tempo and conversation structure. The "footboard" will recap the "mattress" theme ending with the phrase "Sad To Say..."
Success will be measured by publishing the album in standard music channels and looking for listener approval. True success would be a top 10 song or album.
There are several ideas in the patent but it appears that this work will be available in the latest AI5 chip. A good introduction is https://www.youtube.com/watch?v=GG9yOsPEGek
One of the key ideas is to use logarithms and addition rather than multiplication. Faster and less power needed.
NVIDIA is going to hurt from this.
A perfect morning coffee is waiting as you wake up. The house robot brings it to you as you awake.
Suppose you want to get breakfast at a restaurant. The car shows up. You get driven to the restaurant. As you get seated your order arrives. Ava knows that you like an omlette, lightly cooked, with ham and bacon. You like your homefries crisp. You like a small orange juice. It is all ready for you moments after you walk in the door because Ava told the restaurant what you want and when you will arrive.
Ava also knows that you want to keep your weight at a certain number. She tracks your calorie intake and creates food proportions and choice to meet your calerie requirements, tuned to the day's activities based on likely calorie burn.
Ava reads books to you through the embedded speaker in your ear, tuning your book choice to the day. Is the weather bad; then a nice story. Is your interest in comedy; then a newly released (LLM-written) comedy special. Are you in the mood for music; then a newly released (LLM-written) song is available.
Feeling like you want some personal attention? Ava arranges your morning with a manicure, pedicure, and massage. Your favorite haircut is next. Time at the gym and access to your usual workout equipment is arranged.
Want to talk to Susan? Your embedded "phone" connects you to her. The "MyPhone" has microphone pickups and even a brain-embedded thought sensor. Your current physical look (post haircut) is transmitted to her brain-embed so she can "see what you look like" and "see what you see". It is like being in the same room together.
Meanwhile, clothes are chosen. Laundry is done. Shopping is done. The water heater repair is scheduled. Doors are unlocked as needed. The garden is watered. The rooms are cleaned. The pool is cleaned.
Ava learned YOUR preferences and adapts in real-time to what you want. Surely all of this will come into a coordinated whole within a very short time. All the the parts exist.
Ava, your personal servant MyRobot.
I just drove from Pittsburgh to Louisianna to Florida to Pittsburgh without touching the steering wheel. The car planned the route, planned the charging stops, and backed into the charging spaces.
"Any sufficiently advanced technology is indistinguishable from magic" -- Arthur C. Clarke (I had a career in vision, AI, and robots yet it still feels like magic)
The price of electricity to "fill up" was about 1/4 the price of gas for equivalent miles. "Fill up" times at chargers averaged about 10 minutes.
I have had my car for 15 months. I rotated the tires and added wiper fluid. "Lower total cost of ownership always wins" is basic economics.
And now Grok listens to my trip stops and updates navigation. Talk to Grok, touch "start full self driving" and relax.
"The future is already here—it's just not very evenly distributed," -- William Gibson
Oh, by the way, Google is building a system to allow AI to spend money.
https://www.youtube.com/watch?v=8s6nGMcyr7k
Read it. Weep. I'm not sure if the authors have met humanity.
https://www.amazon.com/Anyone-Builds-Everyone-Dies-Superhuman/dp/0316595640
