Yes named after Philo Farnsworth in real life inventor of TV and in the show he invented TV and the communicators
I also understand that it was a young school kid who figured out how to efficiently and quickly add factorials. The teacher gave the class an assignment to calculate the answer to 100!, thinking he has most of the class period to grade papers, when one of his students came up with the answer after only a minute or so. He had virtually folded the string of numbers 1+2+3+...+98+99+100, in half to make the problem equal to 101×50 and did the multiplication.
-Will
-Will
Factorial 100, 100!, 100x99x98x...2x1, would be approximately 9.33262154x10^157, which is much larger than a googol (10^100).
The child who worked out that the sum of the numbers from 1 to n (not multiply them) is equal to n(n+1)/2 was Carl Friedrich Gauss in the late 1700s. *
Are you getting confused with Stirling's approximation for ln(n!) ?
ln(n!) = n.ln(n) - n + O(ln n)
* Actually, the solution seems trivially simple when you think about it:
The sum S = 1 + 2 + 3 + ... + n-1 + n or n + n-1 + ... + 3 + 2 +1 when reversed.
Adding these expressions, 2S = n+1+ n+1 ... + n+1 + n+1 or n(n+1)
Therefore S = n(n+1)/2
There is also a graphical proof, which I leave as an exercise.
Last edited:
That's the one. I didn't know who the kids was. And yes, I misapplied the term 'factorial'.
-Will
The gamma function is its extension into real and complex numbers, although it is not unique in doing so.
I misremembered as well and an LLM lied to me when I asked it to confirm. It seems the anecdote is actually due to Carl Friedrich Gauss, which would place the incident decades later. It is thought that ancient mathematicians would have been aware of the formula. It seems strange that it would not be included in text books by the 18th century as it's so useful and easy to derive. Perhaps it was thought too trivial.
The lesson for today is don't trust either memory or LLMs. The former is to be expected; the latter is becoming a worryingly common occurrence for me.
Last edited:
Since the primary algorithm of an LLM is the statistical next token from as large a data set of writing as possible, we have to assume that bad data and poor writing are included in the data set. They are offset by the majority of major works and there is a weight function for "expert" sources, but an LLM doesn't "know" anything. It merely spits out the next statistical pattern of tokens. When they search the WWW for specific information, they also don't do an exhaustive search and often stop at the first "expert" source and spit that out at you.
Many of the AI sources, I've noted, are actually from Quara and Reddit forums, not peer reviewed papers. AI can't go beyond pay walls, and it has to stop pulling data and answer. It will never say, "I don't know", even if that is the statistical next token. I assume, because the search for an answer continues until a source is found, or it hallucinates the statistical next token into an answer.
I have great conversations with AI, but it is not much more than a knowledgeable source of easily researched information. It is a decent, though not great, writer, and it has an incredible ability to connect metaphors to almost anything.
-Will
Many of the AI sources, I've noted, are actually from Quara and Reddit forums, not peer reviewed papers. AI can't go beyond pay walls, and it has to stop pulling data and answer. It will never say, "I don't know", even if that is the statistical next token. I assume, because the search for an answer continues until a source is found, or it hallucinates the statistical next token into an answer.
I have great conversations with AI, but it is not much more than a knowledgeable source of easily researched information. It is a decent, though not great, writer, and it has an incredible ability to connect metaphors to almost anything.
-Will
Last edited:
Yes, and LLMs anecdotally seem to be getting more unreliable, which doesn't bode well for companies that have put complete faith in them. It was a weird fact for it to get wrong and not one for which I was on guard. Not that it makes a heap of difference that it was Gauss rather than Euler. Some people doubt the veracity of the anecdote in any case. It does sound like narcissistic boasting about youthful genius, and as we've seen the derivation of the solution is easy for an adult to understand. The subject of series, their summation, tests for convergence and all that stuff bored me to tears at university.
Wouldn't it be a good thing if those companies that have put everything into them fail? Let the AI boom go bang.
I was watching this show a while back where one character said "the moment you build a time machine others will have also" does that mean that building the machine means somehow they were used and the knowledge spread despite yours being the first one?
No, it means someone, sometime in the future, will go back and introduce the time machine before the original inventor invented it. Paradoxically, that would also mean the time machine will never be invented because, as soon as the time machine comes along before it is invented, the inventor will not feel the need to invent it, thus no time machine at all.
I'm sure that whatever the first inventor of the time machine decides to invent instead of the time machine, it will be almost a cool
, maybe great tasting ice cream with no calories?!-Will
You have to wonder, like Enrico Fermi, where are all the time travelers?
If we are to consider time travel possible, then sometime in the future, it will be invented, and sometime in the future after that, it will become easier, cheaper, and more common. That would mean, over all the time that time travel becomes possible, more and more time travelers will venture into the past. The rate of time travel may exponentially exceed the days of civilization in the pasts of these future time travelers. At some point, there may be so many future travelers into the past that we might not be able to bump into someone on the street who isn't from the future. So where are they?
Let's try an experiment. Tomorrow is the 12th of April, 2026. I will pass that date on to my children, regardless of whether I met someone from the future or not. My children will then pass tomorrow's date 12/4/2026 (or, if you're American, 4/12/2026) on to their children, with the instructions that, should they or their future children ever have the chance to travel back in time, they will come back to that date, April 12, 2026, and let me know time travel is possible, preferably with irrefutable proof, such as a trip to the future and a jetpack as a gift. (Yes, if you're from the future and you come to visit me, a jetpack would be a nice gift from the future, something sleek and very portable with at least a few hours of operation possible on one charge, tank, energy crystal, whatever).
Anyhow, you guys do the same. Remember, April 12, 2026.
If there is ever real time travel, just knock on my door sometime tomorrow, April 12, 2026. you future time travelers will know how to track me down. I'll snap a couple of pictures with my phone, and let you guys know on the 13th if I have been visited. You, I assume, will let me know, as well.
If time travel is possible, we just need to arrange the time and place to meet our future benefactors. 12 April 2026.
I'll tell you guys all about it on Monday. I can't wait to hear how your visits with your own future kin go/went, too.
-Will
PS: I realize one day's notice is very short notice, so in the interest of getting everyone's cooperation in joining me for this meet up with the future, we can include a second, alternate date, in case you are not capable of getting it together, even retroactively, for the 12th of April 2026. I'll be in Washington DC for a week, so I can meet my future offspring or their time traveling proxy sometime after that. How about the 28th of April 2026 as an alternate. I'll be here to answer the door, so feel free to knock, Will the 8th, or whatever my future great great great great great great grand son named his time traveling child.
If we are to consider time travel possible, then sometime in the future, it will be invented, and sometime in the future after that, it will become easier, cheaper, and more common. That would mean, over all the time that time travel becomes possible, more and more time travelers will venture into the past. The rate of time travel may exponentially exceed the days of civilization in the pasts of these future time travelers. At some point, there may be so many future travelers into the past that we might not be able to bump into someone on the street who isn't from the future. So where are they?
Let's try an experiment. Tomorrow is the 12th of April, 2026. I will pass that date on to my children, regardless of whether I met someone from the future or not. My children will then pass tomorrow's date 12/4/2026 (or, if you're American, 4/12/2026) on to their children, with the instructions that, should they or their future children ever have the chance to travel back in time, they will come back to that date, April 12, 2026, and let me know time travel is possible, preferably with irrefutable proof, such as a trip to the future and a jetpack as a gift. (Yes, if you're from the future and you come to visit me, a jetpack would be a nice gift from the future, something sleek and very portable with at least a few hours of operation possible on one charge, tank, energy crystal, whatever).
Anyhow, you guys do the same. Remember, April 12, 2026.
If there is ever real time travel, just knock on my door sometime tomorrow, April 12, 2026. you future time travelers will know how to track me down. I'll snap a couple of pictures with my phone, and let you guys know on the 13th if I have been visited. You, I assume, will let me know, as well.
If time travel is possible, we just need to arrange the time and place to meet our future benefactors. 12 April 2026.
I'll tell you guys all about it on Monday. I can't wait to hear how your visits with your own future kin go/went, too.
-Will
PS: I realize one day's notice is very short notice, so in the interest of getting everyone's cooperation in joining me for this meet up with the future, we can include a second, alternate date, in case you are not capable of getting it together, even retroactively, for the 12th of April 2026. I'll be in Washington DC for a week, so I can meet my future offspring or their time traveling proxy sometime after that. How about the 28th of April 2026 as an alternate. I'll be here to answer the door, so feel free to knock, Will the 8th, or whatever my future great great great great great great grand son named his time traveling child.
Last edited:
Indeed, the analogue of the Fermi Paradox for time travellers has been suggested. The invention propagation notion sounds like Sheldrake's hypothesis of morphic resonance, which if it exists might be explained by the realm of shared consciousness being actual - along with other fringe, "pseudoscientific" phenomena such as telepathy, reincarnation, remote viewing, time slips and so on. Such phenomena seem inaccessible to the scientific method because they are subjective and not readily reproducible. Statistical analysis of testing telepathy and similar claims significance, but there is usually room for doubt over experimental technique, cheating and so on. It seems that these sorts of phantasm fall naturally into the domain of faith, which is unsatisfying as well as labelling one as a crackpot.
Meanwhile, I asked an AI to sing me a song about why they get thing wrong. It seems we're to blame. Figures...
Meanwhile, I asked an AI to sing me a song about why they get thing wrong. It seems we're to blame. Figures...
Last edited:
Here is what Google's AI Overview has to say about the scientific proof of Remote Viewing:
I would think that scientific proof of such a phenomenon would be easily reproducible and statistically stand out. Otherwise, chance and randomness would show both statistical successes, as well as failures. The fact that a goal was achieved (remotely "viewing" distant and unknown data) at all would seem like a statistical success.
Here's a non-government link to a credible source: https://www.ucdavis.edu/news/psychic-spying-research-produces-credible-evidence
Some quotes from the article:
Hard to judge without seeing the actual data and her analysis.
Now I really want to see the statistical data.
I would thing the very testing of this phenomenon would skew the data in favor of a positive overall outcome. If we took the position that any remote unknown data was impossible, or at least, highly highly unlikely to guess at, then any near hit would seem like a statistically significant positive outcome. After testing a hundred hopeful subjects, anyone who came close would seem like a success.
20 years, $20 million dollars, that's a lot of chance to get a statistically significant outcome. According to published US government information, the government concluded a negative outcome and has abandoned the program
-Will
There is inherent resistance in the orthodox scientific community to any acceptance of psychic and similar fringe phenomena, no matter how much evidence is presented. The usual response is ad hominem attacks, derision, accusations of cheating and similar. Under other carefully controlled conditions, other experiments have often indicated falsification of such phenomena. Whatever is going on seems almost sensitive to the existing predilections of the experimenters. One might almost suspect that is to be expected if external reality is emergent from observation. If that is the case, it seems pointless for me personally to have an opinion one way or the other.
So are you saying they can't prove anyone has psychic abilities, even under controlled conditions?
Some can be rigorously tested in a falsifiable manner, but I doubt they would be accepted. It's like other similar phenomena - either religious or philosophical predilections cause orthodoxy to reject such concepts. Remember how difficult it was for other paradigm shifts to become accepted - atoms, germ theory, evolution by natural selection, plate tectonics...
When they were, the world changed...
So what would it take to change all that?
Bayesian analysis would suggest verwhelming evidence with very few, explainable contraindications? The main problem is that these sorts of hypotheses attract all sorts of cranks and it becomes almost impossible to separate oneself from them in public perception.
They never have. Probably never will. A lot of these so called psychic abilities are just reading a person's body language, what they might be wearing or might say during the conversation. So true psychic powers in my opinion do not exist. But its a great movie trope.
Ah, you've come out of hiding lol.. You're at the other extreme aren't you?
Would you even consider the possibility of such abilities, however unlikely?..
Diana is back making videos. She did one on perpetual motion.
Last edited:
This is one of the greatest difficulties in proving psychic abilities. There is usually another possible explanation. Whether or not a psychic has made an accurate psychic statement, there is also the possibility that the statement is the result of some unconscious, but mundane awareness of the world around us.
My own experience is that while sailing across the Atlantic with my wife, aboard my parents boat, my wife woke up one morning while berthed in Horta, the Azores, and said she had a dream about something happening to our dog back home at her parent's house. She felt strongly enough to call her parents. (This was long before cell phones, and we had to use a public pay phone go through the Portuguese operator).
Our dog had been hit by a car that morning.
-Will
