studiot

None of us are being entirely rigorous here. The answer to the above depends upon how you partition the output set. and you didn't actually say that before Thinking further the most thorough scenario is that of an infinite crew of monkeys each typing a set of n characters with n = Shakespeare. Then we will have infinite copies of the complete works along with stranger manuscripts like the first n/2 words repeated and so on.

But you wrote this The point is that we are mapping from the output set to the set of sequences. For one monkey we do not require an infinite set, since the ouput of one monkey is always finite. Further the original requirement in the OP was for a finite sequence. But for an infinite set of monkeys the first output is necessarily infinite so the output set must be infinite. So there is a difference between one monkey and an infinite time and an infinite set of monkeys and however much time, finite or infinite.

You will need to offer some very serious proof for this unsubstantiated claim. With the origin placed at the centre of the ellipse, The ellipse is symmetrical about the origin, and it is symmetrical about two conjugate diameters. The conjugate diameters may form rectangular axes or may be skew.

This is why I was making the point that 'infinity' is a funny thing which ahs some non intuitive properties. Notice that taeto is being very careful to refer to n charcters or n coin tosses. Any sequence of n characters or tosses is finite. But you has specified an infinite sequence of characters or tosses. I however did specify the infinite sequence of Pi, deliberately to invoke the particular peculiar properties of infinity. If you are going to limit your monkeys to finite sequences only, that is a different model you should be using. You should also specify a stopping criterion. Further you will not be able to fit the output of your infinite collection of monkeys into any finite set.

Some further thoughts. With monkeys, typewriters and letters we are talking the statistics of a discrete variable of integers, not the statistics of real numbers. String Junky, in suitable circumstances. But you would have a problem ordering the monkeys. An infinite amount of monkeys would produce enough letters for every sequence (ie an infinite amount of letters), if they all typed one letter apiece. This would obviously include the finite set comprising the complete works of Shakespeare. But how would you know which set of monkeys to choose from, before they started typing? You would have to discard an infinite amount of typing to be left with a finite set. There is one other interesting thing about infinity that comes up here. One of the basic (and original) identifiers of infinity was that the 'part contains the whole'. So one monkey, typing an infinite amount of characters, would not only type out the complete works of Shakespeare, She would also type out all the (infinite) characters of Pi. Remember the sequence of Pi never repeats. The issue of how long in time this would take is an irrelevant red herring.

I agree that the SpaceTime Block is a pretty radical idea. No I didn't say the spacetime block was radical, I said the idea of pre drawing something on it or in it was radical. I even empahsised the 'pre'. Pre means 'before.', usually in time but also in other contexts such as sequence.

Remember this theory (the Bohr theory) is fine for the nuclei since they are considered stationary, their potential field has no magnetic effect. The difficulty (which ushered in Quantum Mechanics) is that the charges (well the electrons) are in motion. So the classical equations that describe the motion of a charged particle (the electron) in an electric potential field (that of the proton) require a magnetic effect (EM radiation). But this is not observed in practice. This is why we have a quantum equation of motion - the Schrodinger equation.

This is a representation not the reality. (You said it yourself) If they were 'predrawn' then they have a separate existence from what they are drawn on. Predrawn also implies something rather radical.

How is a timeline 'outside time' ? What I am saying is that there is a state or situation in which you could (in principle) hold both particles in your hand together. And there is another state where you could only hold one of them. And since you could observe both states 1) Change exists 2) What we call Time must exist to permit this.

OK but I also said that you need to consider energy and asked you about potential energy. Since the powers that be here don't appear to want to help you, I will continue. Let us start with the simplest atom - hydrogen. This has one proton and one electron. So the must be an electric force acting between them. This force is purely electrostatic. That is it is the same force that would appear if both the proton and the electron were stationary. There is then no magnetic part to this force, since magnetic effects only occur when charges are in motion. So this is the force that holds the atom together. Since the proton is over 1800 times more massive than the electron we consider it stationary and allow the electron to be in motion. The kinetic energy of the electron is then just sufficient to balance the electrostatic attraction between unlike charges. Note I have switched to energy to describe this. Using forces doesn't easily work out. Now let us introduce a second atom. This also has a proton and an electron. So the second proton weakly attracts the electron from the first atom, but more and more strongly as the two atoms approach each other. So the electron has potential energy due to each proton. So also does the second electron. As we bring the protons ever closer, a repulsion between the protons grows. The potential energy of this has the opposite sign to the electron proton potential energy. So again a balance at a minimum energy cost can be achieved. So both electrons belong to both protons which are fixed at the minimum energy distance from each other. As an aside extending this to a lattice of positive nuclei is is how metallic bonding works.

Well that's easy then. Consider two c- existent sub atomic particles, one with a significantly longer life than the other. When the shorter lived one expires, the relationship of co-existence ceases.

I think the question to be ill defined. What do you mean by change? Consider the following situation. A man possesses 7 white shirts, 7 black ties, seven pairs of black trousers, seven pairs of black socks and seven pairs of black shoes. Every day he washes and changes his set of clothes but he always looks the same. Is there any change of appearance?

There are other equivalent definitions such as A regular conic is the locus of a point that moves so that the ratio of its undirected distance form a fixed point F to the distance from a fixed line L is equal to a constanr, e. If e < 1 the conic is an ellipse If e = 1 then the conic is a parabola if e > 1 the conic is a hyperbola This definition has the same characteristic as yours, that it is not dependent upon coordinate geometry, although a coordnate equation for an ellipse can be derived from it. However a couple of points about terminology. an ellipse is a plane curve. That is it exists totally in a single plane. So it is not necessary to to invoke anything to do with a third dimension (cones, cylinders etc) to say everything there is to say about the ellipse itself. The third dimension only changes its situation. An oval is not a single curve but a compound of several curves, although it too is a plane figure. Fairly generally, There are two parts of two curves (which may be different or the same) whoes ends are linked or joined by parts of two more curves or lines which are tangent to the first two curves. So the standard oval table has two identical part circular curves linked by straight lines. An egg has two different parabolic curves linked by smooth transition curves. An ellipse could be said to have two identical half elliptical ends linked by zero length straights. and so on.

I don't know who split this off or why, But I do wonder why they didn't provide at least a basic answer to the question. QuantumT, This question is best considered in terms of energy not force. Are you happy with what potential energy is? If you think about force you then ae faced with the question If there is a force pulling the atoms together in a molecule, what stops them banging together. ie what holds them apart at a certain distance?

Thank you for your reply, Yes you need to separate out the numbers and the things. Also you could consider more complicated combinations such as the Maximum number of usable components or the Minimum number of wasted components in the bag.

It is said that " many a true word is spoken in jest". Was my comment not actually very good advice as a sound plan for a way forward?

I can't see what all this stuff about gravity is to do with the OP or Bishop Berkeley. But to comment on the above extract, Sirjon would you rather the wages department of your employer a) Dipped a scoop into a pile of money each payday and paid you whatever the scoop contained? or b) Counted out your correct wages mathematically?

Do you really know what the English word arrogant means? In another thread I was asked a simple question and I have just said that do not know the answer (and invited others with better knowledge to contribute). To pretend I did know the answer and spout some bullshit would be arrogant of me. Arrogance implies (top me) a measure of falsely claiming or believing an attribute I don't have or don't have to the extent claimed.

I glad to see that some have now caught my drift that just because 6+6 has the same sum as 8+4 it does not mean that 6+6 is the same as 8+4. Unfortunately some are offering this type of reasoning as a valid argument.

One would have thought that even starting with £1 you could very quickly make a few million and run your own publishing company to control any publication of your idea.

That is a very good question. I would have to invite others reading this to offer suggestions because I can't think of a rule to offer. However here is another situation where x*y does not give the correct area. Consider a roofer working out tiles for this roof 5 metres wide by 15 metres long If he says the area of tiling is 5 x 15 and orders this amount he will be short, although x * y * = 5 * 15.

Thank you for clarifying the scope of your subject. What exactly is your definition of anthropomorphism as it seems to differ from the one I offered? Not just that, take for example this: https://en.wikipedia.org/wiki/DNA_digital_data_storage And you don't have consider human manipulation with DNA at all. DNA is natural cell's memory that stores genetic information, which is information with causal power, which is according to David Deutsch, knowledge. That is his current working definition of knowledge.  I fail to understand how the response is connected to my statement. Shape memory in inanimate certain objects is well established Science.

I have to say I can't see what your posts are adding here. What exactly is your point? I also see nothing to complain about so +1 to counterbalance the negative one. Except perhaps your mixing up your words with the quote in your first post.

Which is exactly what I said. Indeed so. Which is why I didn't dwell further on the previous thread. Something I understand is also semi-bad form here. The OP then went on to a rather scrambled declaration which seems to me to extend the scope of knowledge and information beyond homeopathy to things both living and non living. Since there is some conflict in this declaration with the accepted definition of antropomorphism, I provided a link to an accepted definition. Based on these considerations I made my point and asked my question about the wider applications of the Englsih language construction, in particular to art pointing out that these other applications are neither silly nor a myth. I fail utterly to understand how your interpretation of my flow of reasoning, as presented can be justified.

It is always necessary to define terms in Mathematics. Sadly I fear the rest of your posting entirely misses the OP which is about Philosophy, not Mathematics.