black_hole

I store a statement in the program "Animals have DNA". The computer to become able to reach the conclusion that "monkey has DNA", must have to be given additional information by me that "monkeys are Animals". So the following two informations have been provided by human; 1- "Animals have DNA" and; 2- "Monkeys are Animals" In addition to the above information, human shall also tell the computer how to use this info in 0's and 1's in a computable manner. Then as a result of above efforts by the human, the computer shall give us the following information; 3- "Monkeys have DNA".

Thankyou YT2095, for this confirmation. And Kedas, You made quite accurate judgements about what answer I wanted to get. Yes I wanted to listen that computer is just stupid. It only do what programmer tell it to do. It cannot make such an accurate judgements as you can do. Thanks a lot.

Thankyou for all these technical details. My more precise question, in the light of this technical information is that; Using the technology available, can ALU draw a deductive logical conclusion if the premises are given...??? For example, if following two premises are given in written program instructions; 1- All animal's basic unit of life is DNA; 2- Monkeys are animals Can the logical conclusion of above two premises that "monkeys' basic unit of life is DNA" be drawn by the ALU......????

I want to clarify my simple understanding about the role of ALU. There are two components; 1- Arithmatic Unit. 2- Logic Unit. The role of arithmatic unit is simply to do arithmatic operations on numbers. These numbers come from written program instructions. The role of Logic Unit is to derive logical conclusion. It performs comparisons to decide about equal, greater or less values etc. The thing I want to clarify is that logic unit derives logical conclusions. Just like in ordinary deductive logic, there are two premises and the conclusion is drawn from the information contained in premises. My question is that is computer also derive deductive conclusions...??? If so the premises come from written program instructions...??? The logic unit only derives the conclusions from the information contained in the premises. The premises are given in written program instructions. I mean, The program instructions only provide premises and the conclusion therefrom is derived by the logic unit. Are above statements correct are not....??? Upto what extant they are correct or not...???

Mr. AntiMagicMan, Sitting around and thinking IS still very important activity. Planned experiments take their input from this activity. Einstien's both special theory of relativity and general theory of relativity are the product of just sitting and thinking/ imagining. He did not performed any experiment by himself. Only, his theories, later on, were confirmed by the experimental scientists. Only thing added is that the conclusions of such thinkings, now, are required to be experimentally tested in order to get the status of "scientific theory". You yourself said in one of your previous post that "Abstact Mathematics" need not be verified through experiments. Abstact Mathematics, as we know it today, also is the gift of those ancient Greeks.

And that is why it is called a "Paradox". Walking to shops was recognized by Zeno. He was the disiple of Parmenides whose philosophy was that reality cannot be conceieved through senses. Zeno's paradoxed intended to prove the theory of Parmenides. By giving the proof, through "reason", Zeno "proved" that information received through senses is mere "illussory" and in reality, any kind of motion do not exist. The main essence of Greek Philosophy is the recognition of the superiority of "reason" over the "sense experience". You walked to shops is your "sense experience" and the "reason" is that you cannot cover the minimum possible distance, so you are also unable to cover greater distances. Now according to Greek Philosophy, "reason" is superior to "sense experience", so Zeno, denied the existence of any motion and held that walking to shops etc. is the illusion created by the senses. The same position, i.e. superiority of "reason" over "sense experience" later on, also reflected in the philosophy of Plato in his theory of forms or ideas. But if we consider your case i.e. walking to shops, it, in itself is not the proof against Zeno's arguments. Zeno's arguments are not consistent with our common sense experience. This important fact (As highlighted by you), can, however, serve as a guideline for us so that we should consider the "wrongness" of Zeno's arguments. If we prove, through reason, that Zeno's arguments were invalid, then we shall have a solid base to believe in our sense experiences. For this, as I have further considered that formula series showing the breakups of 1 totalling at 1. I now have reached a conclusion that this is an important argument in this respect. The mathematical formula clearly indicates that all breakups, including the smallest possible, have a sum total of 1. This 1 is not the time required to cover the distance 1. But however, this exact 1, indicates that smallest possible distance is accountable. Because without accounting for the smallest possible distance, the answer could not become exact 1. If smallest possible distance is accountable, as is clear in the exact 1 answer, it means it is also coverable. This "reason" has two dimensions, i.e. Positive and Negative. On positive side, it proves the possibility of covering shortest possible distance. Other positive aspact is that it is consistent with our sense experience. On Negative side, it proves invalidness of Zeno's arguments by showing that Zeno's arguments are based on incomplete information, because the fact that breakups of 1 exactly equal to 1, was not considered by Zeno. Therefore this, now, is not the case of "reason" versus "sense experience". Now it is the case of "reason based on incomplete information" versus "reason based on complete information". And reason based on complete information is also consistent with our sense experience. In this way, Zeno's paradoxes were wrong, not just because I often go to shops. It is so because we have a better argument vailable which confirms our sense experience. So thankyou very much Mr. AntiMagicMan and Mr. Tom for helping me in reaching that conclusion.

Is it not the difference between pure abstract mathematics and a real situation. I mean pure mathematics can find the solution with the correct definition of infinity i.e. without any assumption, whereas, in a practical situation i.e. when we have to move a distance of 1, what maximum we can do is to reach more and more near to 1. This is also incorrect to say as I shall say in last paragraph. In your previous reply you said that the finite sum i.e either 1 or less than 1, whatever the case may be, this finite number is the time required to cover the distance 1. I considered that point. I reached at the conclusion that this "finite" number is NOT the time required to cover the distance 1. This "finite" number, which, in a real situation, shall always remain less than 1, (instead of time required) is the distance covered, which is "finite" i.e. less than 1. I have concluded this because series is the breakup of distance and not of time. In this way, note that the finite distance of 1 has not been covered fully, i.e, the actual distance covered is still less than 1. It means that finite distance has not been covered fully. However, this is also incorrect to say as would become clear in my next paragraph. As I already have said that in a real situation, the stage of smallest possible number shall not come. If we divide a real distance of 1 by 2 and continue the process, we shall get smaller and smaller distance. And the smallest possible distance shall never come. Now according to Zeno's paradox, taking the sum of series is not important. Only thing required is to cover the smallest possible distance first, then we shall be able to cover the greater distances. Since smallest possible distance is not reachable in a real situation, we shall remain unable to cover the smallest possible distance. So to cover greater distances is out of question. Also note that your formula also do not tell the smallest possible distance. Sum of series is only the breakup of distance of 1. It has nothing to do with the time required to cover this distance because it has no relationship with time. And the breakup of distance 1 has to be a total of 1 (i.e 1 = all breakups of 1), So the formula has no relationship with the time required. In simple terms it is only the breakup of 1. It is just like that breakups of 2 shall also be sumed at 2 and breakups of 3 shall be totalled at 3 and so on. The point is that first of all we have to cover the smallest possible breakup of 1, 2 or 3 etc. We have no concern with the sum of breakups. we have interest only in finding out the value of smallest possible breakup. Zeno's paradox also has nothing to do with the sum of series. Zeno's paradox is concerned only with covering the smallest possible distance first, so that we may be able to cover the greater distances.

Mr. Tom, I am still waiting the answer of: If linear motion of car is the result of rotation motion of its wheels, then why is that rotation motion is quantized but linear motion, which is directly linked to that quantized rotation motion, is not quantized...???

Mr. Tom, I think it is only a tendency. The series only tells IF 1 is divided by 2, then by 2, and so on up to infinity THEN the answer would be 1. This 1 answer is the meaning that answer CANNOT be more than 1 and it will be 1 ONLY AND ONLY IF process of dividing by 2 has been performed up to infinity. Thus the formula assumes that level of infinity has reached. Now the series is just like that; {1/2+1/4+1/8.......+1/(infinity-1)+1/infinity} = 1 if 1/infinity is equal to zero (i.e. any number divided by infinity has to be zero), it means the answer of 1 we already have achived at the level of 1/(infinity-1). But (infinity-1) is such a term which is possible to occur only if the infinity is a finite number. So if infinity is in fact a finite number, then this formula shall be applicable to a real situation, other wise it is applicable only to an assumed situation that "infinity is a finite number." This formula cannot be proved experimentally. We shall never be able to reach the final term i.e 1/infinity which would be equal to zero. On an unlimited capacity calculator, we always find smaller and smaller answer and we shall never find the answer coming to be exact zero i.e. indication of final term which is infinity. We however, shall find answers nearer and nearer to zero. A formula which is incapable of being experimentally proved, is it all right...??? Note: I only have said that sum of series shall remain less than 1 and it shall never reach to the figure 1 due to involvement of infinite terms. Your point still stands that less than 1 is also a finite number, so the finite time is required to cross the distance. I think I have to deeply consider this situation (which is new for me and thanx for that), in order to make comprehension of just how this finite number i.e. less than 1, is the time required to cover the distance.

Mr. Tom, I think now I get your point. You mean (1/2+1/4+1/8.....) = 1 or in other words you mean (0.5+0.25+0.125......) = 1 This is an interesting fact. Thanx for sharing with us. But let me doubt again. The answer 1, we can get by applying the formula that uses the infinity as a symbol. But actually when we contineously divide 1 by 2 and contineously carry on the process, I do not think that process would ever end. In this way the answer 1 seems only to be a tendency and not the actual answer. What you say about it....???

Ok the series according to formula may add up to 1 but why is that if I contineously divide 1 by 2 on my home scientific calculator, and carry on this process, I always find smaller and smaller answer tending to infinite small number...??? I mean why calculator answer dose not confirm your formula series..??? Consider the linear motion of a car. That linear motion is directly linked with the rotating motion of its wheels. Rotation motion is quantized, so why linear motion (which is directly linked to that ratation motion) is not quantized...???

Refer to my very first post, I tried to reject the infinity paradox (i.e. impossibility in covering limited distence) using the anology of the motion of cursor on the monitor screen. Cursor motion is not contineous, i.e. it is pixel wise. So this pixel movement is not a contineous movement. In order to overcome the infinity paradox situations, in every day motions, I applied the conclusion of that anology to all the physical motions i.e. by saying that all motion is just like a pixel motion which is a discrete motion and is not contineous. Now IF really it is so, i.e. if in fact all motion is pixel like motion (the concept of pixel wise motion is not absurd altogether, there are already voices of quantized space time, present in science circles), then it means that in fact no contineous variable can exist. But if you have some other solution to this infinity paradox, then pixel wise motion is not applicable to all the motion. Then contineous variables are possible to occur. But if the only solution to infinity paradox lies in that pixel wise (i.e. quantized) motion, then existence of any contineous variable is out of possibility. I know according to your formula series (if it is really valid, because still I have not understood why your final 1 is not still dividable...?), you have another solution to infinity paradox. So pixel wise motion and thus the denial of the existence of contineous veriables is un-necessary. Just suppose for a moment that your formula series is not accurate, i.e. it is not the true solution to that infinity paradox, then all the contineous variables in physics models are really have the problem. For contineous movement cannot even cover the distance of 1. If angular momentum is quantized i.e. there is no possibility of contineous spin motion, then why linear momentum is not quantized...??? Why there is a possibility of contineous linear movement....????

Thank you for reply. If it is so that sum of that series is finite number, then what is your conclusion about "contineous variables". Are contineous variables of physical quantities exist....??? If every movement is contineous, then what is the concept of "quantized"...???

You are not right. At least Bertrand Russell could not find the solution to this "infinity paradox". In fact I got familiar to this "infinity paradox" by reading Russell. He himself accepted in his writings that he had been unable to find the solution. I also have seen similar situation in the writings of Will Durant. Blaming "logic" for its clever negative use, Will Durant quoted the example of Zeno's paradox which he considered to be such a "true" logic which resulted in (apparently - my own words in bracket) wrong conclusion. In this way Durant (wrongly) concluded that even true logic may not lead to true conclusion. And Mr. Tom, Thankyou for writing down the series that result in final answer of 1. But real "paradox" starts after this 1... Because to cover the distance of 1, you have to cover the distance of 0.5, and so on. I think real answer to this situation lies in quantum distance. Limited space is divided into these limited number of "quantum distances". So we only have to "cross" these limited number of "quantum distances" in order to cover that "limited space". We directly "jump" from one "quantum distance" to the next, in this way we easily cross those limited number "quantum distances".