MigL

Still not convinced ... There is no history of the 6 horses, so you have no reason to assign a probability other than 1/6 to each horse, since the expected ( guaranteed ) outcome is that one of the 6 must win. To do otherwise, you'd be making up information. If I am misunderstanding you, please dumb it down, as I can be rather 'thick' sometimes.

No, but you would think Iranians killed his father, and must prepare to die ... ( you gotta watch the movie )

Surely the frequentist ( never heard the term, but I suppose I am one ) would define the probability of an event E, p(E) = F/ N , where N is the total number of possible outcomes, and F is the one desired outcome, E. But I suppose this doesn't give a frequency distribution ...

In most cases 'random' simply means lack of information about the process that leads to the 'random' outcome. The example I often use is the set of numbers 1,5,9,2,6,5,3,5,8,9,7,9,3,2,3 which seem perfectly random numbers between 0 and 9, and when presented with those numbers, one assumes they cannot be generated from each other, or a mathematical process. Yet if you calculate Pi, and subtract 3.14, you are left with those 'random' numbers as the remaining 15 digits, so not random at all when new information is obtained. That is not to say that there are no truly random events, to which, of course, you can assign a numerical value.

And, if you mean the Roman Empire, it should be noted that the Austro-Hungarian Empire, under Habsberg rule, referred to themselves, until the beginning of the last century, as the remains of the Holy Roman Empire, since all the Germanic tribes that invaded/sacked Rome essentially took on Roman laws and systems of government, and became 'Romans'. It is not a coincidence that Germanic rulers are called 'Kaiser', the alteration of 'Caesar' ( emperor ). Also 'Czar', and even 'Tsar' in Russia, indicating the Roman Empire had influence in the European continent until 1918. By the same token, the American system of laws and government, essentially a modified British system, has been very successful and has been a model for other nations. At least until it was taken over by 'big money', and corrupted beyond recognition by D Trump. I fullt expect to see this modern day Nero ( or Caligula ) playing the fiddle while Washington DC burns.

Congratulations, and many more ...

Holographic Entropic Service/Force cosmology ? Have heard it mentioned; not very familiar with it. "Entropic cosmology (or HES - Holographic Entropic Service/Force Cosmology) models the universe's evolution not through dark energy, but by treating gravity as an entropic force arising from information stored on the cosmic horizon. In this framework, the acceleration of the universe is a result of the statistical tendency for the horizon's entropy to increase." From what I've read ( not much ), it has issues.

OK. But can we stop talking about spiders ? Always feel like something is crawling on me when discussing spiders. Although I am reminded of the Predator aliens, with their extended, horizontally opposed mandibles. ( the original movie may have indicated they were related to scorpions ) And one episode of Star Trek TNG suggested Lt. Barclay's ancestors were spider-like creatures, although he looked very human. ( Genesis S7 Ep19 )

Covered by 'economy of resources'. As for spiders, why evolve more legs when when 'jaws' or food grasping appendages can be re-purposed ? Again, 'economy of resources'; nature is resourceful, but frugal.

Is the paradox not inherent in the question ? Out of the four choices, one has to be correct so that would make it 25%. But two out of four choices are 25%, which means 50%. Is this one of those 'liar who claims to be lying' situations that fries android's brains in old Star Trek episodes ?

Maybe you're not trying to prove 'creation' or 'evolution', but I suggest things only make sense if you consider evolution, Aquatic animals are forced to go onto land, they have two options, slithering on the ground, or supporting themselves on appendages to stay off the ground. Four appendages is the most economical and stable method. Then evolution continues ... Land animals evolve larger capacity brains, and need to grasp things. Their brain is now capable of balance, so again economy of resources diversifies two appendages for grasping things. Evolution has always been about environmental forcings ( the need to do specific things ) in the most resource economic way possible. If something isn't needed, it isn't developed by evolution.

And please do so without the AI influence ...

Where ?!?! ( what were we talking about ? )

Don't have any laptops with magnetic drives anymore, but do have some external USB 1TB 2.5 in drives storing old 'stuff'. Could not get a crash of the external hard drive on an older i3 laptop with Win10.. Don't know if the OS needs to be on the drive, or if it's particular to WinXP, which I don't have any installations of anymore. All I found out is that I'm still tired of hearing 'Rhythm Nation', but still fond of Janet Jackson.

This is one time I would agree with Dimreepr. Every healthy eye ball has a blind spot; I have blind areas due to Glaucoma. A person with two functioning eyeballs uses the opposite eye to compensate for each eye's blind spot. Unfortunately, I only see with one eye, but on a bright day I do have a little vision in my left damaged eye, such that I would see doubled yellow lines down the middle of the street. Eventually my brain learned to ignore the signal coming from my left eye, and my right eye became dominant, so I no longer see doubled up street lines. In effect, the left eye's field of view became a brain blind spot. Can the brain adapt ( plasticity is the term, I believe ) to pick and choose what it can or can't see ?

He's now paying back, to American companies ( but not to the consumers/taxpayers whose cost of living those compabies increased ) the illegal profits made by his tariffs. I thought the tariffs were paid by other countries, and were not a tax on the American idiots who voted for him. I can't wait for November ...

Something is definitely wrong when the real world starts imitating fiction. So many events, lately, call reality into question.

The Epstein files ... What I find amusing about this ( as amusing as war can possibly be ) is that D Trump is now practically begging the Iranians to sign on to an 'agreement' like the one he tore up ( because of his disdain for B Obama ) during his first term, and, after having attacked them. Not that I'm fond of the Iranian government ( as you can see from previous posts ), but I love that D Trump and his Administration look like total idiots to the rest of the world, as they furiously try to spin this as a 'win'. I can't wait for November ...

I don't believe that; religious fanaticism is a powerful motivator ( even P Hegseth is trying to tap it ). And you discount Iran's willingness to supply its proxys with weapons. I don't believe Iran would attack Israel directly for fear of retaliation, but they could certainly supply Hezbollah, Hamas, or the Houthis with a nuke, which they would be willing to use, and give Iran deniability for its use. Any way you look at it, Iran having nuclear capability, as Stringy previously floated, is a very bad idea.

You're going to provide a citation for this ? I could not find anything of the sort with a search, and will wait for your evidence. A few warheads will not achieve annihilation. The 'regime' will survive in hardened bunkers, in both Iran and Israel. The people at risk are the ones living close to the launch sites of the nuclear ordinances, as they will be first targets, whether airfields for planes or missile sites ( Israel has submarine launched missiles as well ). The difference is Israel cares about its people. Now do you see the argument ?

Except that Israel has had nuclear capability ( approx. 90 warheads ) for over 30 years. They have never threatened to use them; they don't even acknowledge having them. Do you trust the religious leaders of |Iran to do the same ? "Since the 1979 Islamic Revolution, the Iranian government has executed thousands of individuals, using capital punishment to suppress dissent and enforce strict Islamic law. Key periods include a surge in 2025 with over 1,639 deaths and the 1988 mass execution of roughly 30,000 political prisoners. Executions often target protesters, activists, and minorities." According to Amnesty International, Iran was responsible for 64% of all recorded state-sponsored executions, worldwide, in 2024; with the mass protests of last year, that percentage is indubitably higher yet for 2025. Do you really think the MAD doctrine works when a government doesn't give a damn about its people ?

This hypersurface, the 'snapshot' that represents the 'present' is called a Cauchy Surface. ( wanted to add that, but could no longer edit )

So you are saying that this 'surface of the present' is a foliation of spacetime, and where this foliation represents the present, it is 'advancing' at the SoL. Further, this foliation, representing the present, is not smooth and constant, but 'dimpled' and smoothly varying, with the dimples being local variances due to observer position/motion. And with 'wells', going as deep as their origin, representing the stagnant space-time approaching Black Hole event horizons. These are well established 'interpretations' of relativity, and as such, bring no new insights to Physics. But maybe I'm missing something; can you point out any new science from this approach ?

Wow. The first vehicle I had access to when I turned 16 in 1975 was a 1973 Chevrolet Chevelle with a 350 ci ( 5.7 liter ) engine and 4 bbl carburation. It had so much low end torque, that when I stomped the gas pedal, it would spin the bias-ply ( no radials ) tires, in a cloud of smoke, for about 200 ft. Ahh, the good old days. When gasoline was about $0.60 per gallon ( about $0.15 per liter ) Yes, I did my fair share of contributing to global warming ...

Sure, that argument can be made, but this was not a defensive war. Iran puts political protesters to death by hanging ( from cranes, in public ). Dozens every year since 1979, and a few thousand during times of civil unrest like late last year. There is no doubt that their 'religious' Government is evil and needs to be changed, but there are many countries that are as bad., such as N Korea, China, etc. Even Russia is essentially 'murdering' thousands of their young people, every couple of months for 4 years, by sending them into a meat-grinder like the unprovoked invasion of Ukraine. But, if you essentially kill thousands of their people to stop their murdering, or force regime change, how are you any better ? No doubt a trick he picked up from his good buddy, V Putin, who regularly makes the nuclear threat to Ukraine and Europe.