Recent content by Cliff Hanley

davenn, you said, “The big bang didn't have a point origin, as in an explosion and expanding out - there's been many threads on PF on the currently understood understanding of this .. try some searching - Drakkith and phinds are 2 common contributors.” Thanks. I’m currently studying this, and...

Drakkith, you said, “Yes and no [re, ‘but isn’t the EM field you’ve just described a medium?’]. The EM field can be thought of as a non-physical medium, but you run into some issues if you do this. For one, you can't think of the medium as moving anymore.” Q. Is the EM field the result of the...

Reposted for clarity; Drakkith, you said, “Remember that thermal energy is the energy an object has that is stored in the random vibrations and other motions of its composite particles.” For energy to be stored in the particles of an object is something I can begin to get my head around [I...

mfb, you said, “As examples for the 49%/51% question: After 1000 rolls, the chance to be within 1% of this result (so somewhere from 48/52 to 50/50) is roughly 50%. After 10000 rolls, the chance to be within 1% is about 95%. After 100,000 rolls, the chance to be within 1% is larger than...

FactChecker, you said, “For any number, N, we can always continue long enough for N+1 occurrences.” Q. Do you mean that if we substitute N for say, 1000, and carry out sufficient trials, we will (probably) see 1000 successive non-reds (or reds, or whatever); and if we continued with the trials...

Stephen Tashi, you said, “There is a further distinction between "actually" and "certainly". If we "actually" took a sample from a normal distribution and the value was 1.23 then an event with probability 1 ( namely the event "the value of the sample will not be 1.23) failed to "actually"...

phinds, you said, “Yes, the probability of getting any string you can name approaches 1 as the number of trials approaches infinity, but since we can't actually do an infinite number of trials, we can't ever get an absolute certainty (probability = 1.0)” But even if, as a thought experiment...

gill1109, you said, “Probability theory tells us that if we play infinitely often we will certainly get to see, *infinitely* many times, a hundred non-reds in succession. And a thousand. And a million. And a billion, and a trillion.” Q. I’ve heard that the concept of infinity is a complex one...

MrAnchovy, you said, “You can google this [the record for successive non-reds in actual play ], although I'm not sure how reliable the answers would be.” Thanks. I got this from allaboutbetting.co.uk; ‘In Monte Carlo in 1913 black came up 26 times in a row and in New York in 1943 red came up...

Have I got the following correct; 1 micron = 1 micrometre 1 micrometre = 1 millionth of a metre = 10^-6m To convert m to mm we multiply m by 1000, eg, 1 m = 1 x 1000 therefore 1 m = 1000mm; 1000m = 10^6mm. Therefore 1 micron = 10^-3mm (one millionth of a metre = one thousandth of a...

Stephen Tashi, you said, “Technically, probability theory gives you no guarantees about any event (or series of events) actually happening. Probability theory merely uses the given probabilities to assign probabilities to other events and series of events.” Q. So those who say, for example...

phinds, you said, “Yes. Why would it not? [re me asking; ‘Q. Does probability theory suggest that if we played for a long enough period of time we would see a hundred non-reds in succession? A thousand? Million? Billion, trillion etc?].” I find it hard to imagine a hundred non-reds in a row...

Dr. Courtney, you said, “The "long runs" means a great many trials.” The term, ‘a great many’, and ‘large numbers’ (as in The Law Of Large Numbers) seems to me to be vague given that mathematics is supposed to be a very precise discipline. “If you are trying to measure the occurances of an...

Nuuskur, you said, “x+2=6, x is a variable. We can vary its value, but there is only one value that satisfies the equality.” Q. Wouldn’t varying x’s value make what was an equation no longer an equation (eg, by changing it from 4 to 5 would give us 7=6 when 7 does not equal 6)? You seemed to...

Variable; A symbol for a number we don't know yet. It is usually a letter like x or y. Example: in x + 2 = 6, x is the variable. [mathsisfun.com] Q. Why is it called the variable? This seems to me to imply that its value varies. In the above example it seems to me to simply be the unknown...