On 9/30/2014 5:07 PM, Eric Jacobsen wrote:> On Mon, 29 Sep 2014 22:37:04 -0400, rickman <gnuarm@gmail.com> wrote: > >> On 9/29/2014 9:17 PM, Rick Lyons wrote: >>> >>> >>> >>> Hi Guys, >>> My daughter is under the impression that I know >>> something about mathematics. In an e-mail she sent >>> me the following puzzle: >>> >>> An amoeba is placed in an empty jar. In one second >>> the amoeba splits into two amoebas, each as big as >>> the mother amoeba. After another second the daughter >>> amoebas split in the same way. As each new generation >>> splits, the number of amoebas and their total bulk >>> doubles each second. In one hour the jar is full. >>> When is the jar half full? >>> >>> I post this puzzle for your entertainment. >>> >>> [-Rick-] >> >> I guess this is set up to make students think in other than canned ways >> to solve problems. >> >> It might be interesting to note that for the amoeba to take an hour to >> fill the jar by doubling it's volume each second, it would have to be >> far smaller than a proton. >> >> -- >> >> Rick > > That makes some assumptions about the size of the jar.Only one, that it fit in the observable universe. And that is not really an assumption, it can be deduced from the fact that you need to observe the jar being full. The universe is just not very large when you consider the range of mathematics. -- Rick
Off Topic: A Math Puzzle
Started by ●September 29, 2014
Reply by ●September 30, 20142014-09-30
Reply by ●September 30, 20142014-09-30
On 9/30/2014 7:46 PM, glen herrmannsfeldt wrote:> rickman <gnuarm@gmail.com> wrote: > > (snip, I wrote) > >>> And since no-one answered the question I put up previously, >>> some amoeba have 670 gigabase pair genome, or about 220 >>> times the size of our genome. > >>> http://www.genomenewsnetwork.org/articles/02_01/Sizing_genomes.shtml > >> Yeah but it is likely full of non-encoding junk... much like ours. > > Seems that the latest is that more of the "junk" than previously > thought actually does something. > > Protein coding sequences were the first discovered and understood, > but gene regulation is also coded in the DNA, and is taking longer > to understand. > > In the case of bacteria, being able to divide faster is an > evolutionary advantage, and so they tend to make more efficient > use of their genome. > > But otherwise, evolution mostly works by duplication and modification, > so having unused copies of genes lying around is useful. > > But yes, presumably much of the amoeba genome isn't doing anything. > If it doesn't cost a lot to keep it around, there isn't a big > incentive to reduce it.That is the question, how much does it cost to keep non-encoding genome? There is an energy cost each time the genome multiplies... all those enzymes need fuel to do their job. More genes to mutate can potentially cause problems since mutations are nearly always bad. Even if the genetic material is not in use at the moment a mutation can switch it on which may not be desirable. So at what point does having this genetic material cost more than it is worth? If it is very inexpensive, why don't more organisms have such copious quantities of it? -- Rick
Reply by ●September 30, 20142014-09-30
On Tue, 30 Sep 2014 20:02:37 -0400, rickman <gnuarm@gmail.com> wrote:>On 9/30/2014 5:07 PM, Eric Jacobsen wrote: >> On Mon, 29 Sep 2014 22:37:04 -0400, rickman <gnuarm@gmail.com> wrote: >> >>> On 9/29/2014 9:17 PM, Rick Lyons wrote: >>>> >>>> >>>> >>>> Hi Guys, >>>> My daughter is under the impression that I know >>>> something about mathematics. In an e-mail she sent >>>> me the following puzzle: >>>> >>>> An amoeba is placed in an empty jar. In one second >>>> the amoeba splits into two amoebas, each as big as >>>> the mother amoeba. After another second the daughter >>>> amoebas split in the same way. As each new generation >>>> splits, the number of amoebas and their total bulk >>>> doubles each second. In one hour the jar is full. >>>> When is the jar half full? >>>> >>>> I post this puzzle for your entertainment. >>>> >>>> [-Rick-] >>> >>> I guess this is set up to make students think in other than canned ways >>> to solve problems. >>> >>> It might be interesting to note that for the amoeba to take an hour to >>> fill the jar by doubling it's volume each second, it would have to be >>> far smaller than a proton. >>> >>> -- >>> >>> Rick >> >> That makes some assumptions about the size of the jar. > >Only one, that it fit in the observable universe. And that is not >really an assumption, it can be deduced from the fact that you need to >observe the jar being full. > >The universe is just not very large when you consider the range of >mathematics.Assuming the universe has limits. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by ●September 30, 20142014-09-30
On Tue, 30 Sep 2014 20:08:15 -0400, rickman wrote:> On 9/30/2014 7:46 PM, glen herrmannsfeldt wrote: >> rickman <gnuarm@gmail.com> wrote: >> >> (snip, I wrote) >> >>>> And since no-one answered the question I put up previously, >>>> some amoeba have 670 gigabase pair genome, or about 220 times the >>>> size of our genome. >> >>>> http://www.genomenewsnetwork.org/articles/02_01/Sizing_genomes.shtml >> >>> Yeah but it is likely full of non-encoding junk... much like ours. >> >> Seems that the latest is that more of the "junk" than previously >> thought actually does something. >> >> Protein coding sequences were the first discovered and understood, but >> gene regulation is also coded in the DNA, and is taking longer to >> understand. >> >> In the case of bacteria, being able to divide faster is an evolutionary >> advantage, and so they tend to make more efficient use of their genome. >> >> But otherwise, evolution mostly works by duplication and modification, >> so having unused copies of genes lying around is useful. >> >> But yes, presumably much of the amoeba genome isn't doing anything. If >> it doesn't cost a lot to keep it around, there isn't a big incentive to >> reduce it. > > That is the question, how much does it cost to keep non-encoding genome? > There is an energy cost each time the genome multiplies... all those > enzymes need fuel to do their job. More genes to mutate can potentially > cause problems since mutations are nearly always bad. Even if the > genetic material is not in use at the moment a mutation can switch it on > which may not be desirable. > > So at what point does having this genetic material cost more than it is > worth? If it is very inexpensive, why don't more organisms have such > copious quantities of it?Actually, I think that many organisms do have copious quantities of it -- I'd have to see a survey to know. -- www.wescottdesign.com
Reply by ●September 30, 20142014-09-30
rickman <gnuarm@gmail.com> wrote: (snip, I wrote)>> In the case of bacteria, being able to divide faster is an >> evolutionary advantage, and so they tend to make more efficient >> use of their genome.>> But otherwise, evolution mostly works by duplication and modification, >> so having unused copies of genes lying around is useful.>> But yes, presumably much of the amoeba genome isn't doing anything. >> If it doesn't cost a lot to keep it around, there isn't a big >> incentive to reduce it.> That is the question, how much does it cost to keep non-encoding genome? > There is an energy cost each time the genome multiplies... all those > enzymes need fuel to do their job.The enzymes don't need fuel, the nucleotides come with their own fuel. The fuels for most cellular reactions comes from ATP, specifically the enerty in the triphosphate group. Making an RNA copy of DNA uses ATP, CTP, GTP, and UTP. That is, ATP has the same A as the A base in RNA. DNA synthesis uses dATP, dCTP, dGTP, and dTTP, which have one less oxygen that the forms without d. Once you have those, they already have all the energy needed, the enzymes just point them in the right place. But compared to everything else the cell has to do, the energy is fairly small. It does take time, though. DNA replication runs about 1000 base/second. In E.coli, it starts in one place, always (about) the same place, and goes both directions around the circular chromosome. So, about 2000 seconds for 4Mbase. The longest human chromosome is about 250Mbase. To do that fast enough requires more than one origin of replication, but that just means more enzymes.> More genes to mutate can potentially > cause problems since mutations are nearly always bad. Even if the > genetic material is not in use at the moment a mutation can switch > it on which may not be desirable.The most common mutations cause a working gene not to work. Having two copies (one from mom, one from dad) most often allows use to survive such. Less common, but also possible, is a mutation that causes an existing gene, or even non-active leftovers from evolution (called a pseudogene) to have some deleterious function.> So at what point does having this genetic material cost more > than it is worth? If it is very inexpensive, why don't more > organisms have such copious quantities of it?Some changes are hard to make. Small increases aren't so hard, and happen all the time. Some people have about 10% more in their genome than others. We have two copies of most of our chromosomes, one each from mom and dad. Some organisms have more of each. The usual way that happens is when the separation after replication fails, and two go into one cell. But to create a new species, it has to be either fairly advantageous, or something else has to happen to cause it to take over. One way new species are created is by selective breeding. People select one that might have a specific trait, though might not have been chosen by evolution. Pretty much all our food plant crops have gone through much selective breeding. That is, they have been genetically engineered by people for some traits that nature would not have selected. Often this is done by intentional mutations causing random gene changes that can then be selected for. Yet the people who want labels on food don't call that GMO. With random mutations you can get many genes that are not good for us introduced. Yet when only one good gene is introduced, without any random addition of who knows what else, people call it GMO, and single it out. Most plants naturally produce pesticides. They don't want to be eaten by insects. Even more, many of those pesticides are desired by people! Nicotine and caffeine are produced by plants to discourage other organisms from eating them! Thousands of other natural pesticides could be introduced by selective breeding. I think this is getting a little long already. But anyway, all mammals have about the same 3Gbase genome, though divided up into chromosomes in different ways. -- glen
Reply by ●October 1, 20142014-10-01
On 9/30/2014 8:46 PM, Eric Jacobsen wrote:> On Tue, 30 Sep 2014 20:02:37 -0400, rickman <gnuarm@gmail.com> wrote: > >> On 9/30/2014 5:07 PM, Eric Jacobsen wrote: >>> On Mon, 29 Sep 2014 22:37:04 -0400, rickman <gnuarm@gmail.com> wrote: >>> >>>> On 9/29/2014 9:17 PM, Rick Lyons wrote: >>>>> >>>>> >>>>> >>>>> Hi Guys, >>>>> My daughter is under the impression that I know >>>>> something about mathematics. In an e-mail she sent >>>>> me the following puzzle: >>>>> >>>>> An amoeba is placed in an empty jar. In one second >>>>> the amoeba splits into two amoebas, each as big as >>>>> the mother amoeba. After another second the daughter >>>>> amoebas split in the same way. As each new generation >>>>> splits, the number of amoebas and their total bulk >>>>> doubles each second. In one hour the jar is full. >>>>> When is the jar half full? >>>>> >>>>> I post this puzzle for your entertainment. >>>>> >>>>> [-Rick-] >>>> >>>> I guess this is set up to make students think in other than canned ways >>>> to solve problems. >>>> >>>> It might be interesting to note that for the amoeba to take an hour to >>>> fill the jar by doubling it's volume each second, it would have to be >>>> far smaller than a proton. >>>> >>>> -- >>>> >>>> Rick >>> >>> That makes some assumptions about the size of the jar. >> >> Only one, that it fit in the observable universe. And that is not >> really an assumption, it can be deduced from the fact that you need to >> observe the jar being full. >> >> The universe is just not very large when you consider the range of >> mathematics. > > Assuming the universe has limits.If only a portion of the universe is observable, does any more exist? -- Rick
Reply by ●October 1, 20142014-10-01
On 9/30/2014 9:19 PM, tim wrote:> On Tue, 30 Sep 2014 20:08:15 -0400, rickman wrote: > >> On 9/30/2014 7:46 PM, glen herrmannsfeldt wrote: >>> rickman <gnuarm@gmail.com> wrote: >>> >>> (snip, I wrote) >>> >>>>> And since no-one answered the question I put up previously, >>>>> some amoeba have 670 gigabase pair genome, or about 220 times the >>>>> size of our genome. >>> >>>>> http://www.genomenewsnetwork.org/articles/02_01/Sizing_genomes.shtml >>> >>>> Yeah but it is likely full of non-encoding junk... much like ours. >>> >>> Seems that the latest is that more of the "junk" than previously >>> thought actually does something. >>> >>> Protein coding sequences were the first discovered and understood, but >>> gene regulation is also coded in the DNA, and is taking longer to >>> understand. >>> >>> In the case of bacteria, being able to divide faster is an evolutionary >>> advantage, and so they tend to make more efficient use of their genome. >>> >>> But otherwise, evolution mostly works by duplication and modification, >>> so having unused copies of genes lying around is useful. >>> >>> But yes, presumably much of the amoeba genome isn't doing anything. If >>> it doesn't cost a lot to keep it around, there isn't a big incentive to >>> reduce it. >> >> That is the question, how much does it cost to keep non-encoding genome? >> There is an energy cost each time the genome multiplies... all those >> enzymes need fuel to do their job. More genes to mutate can potentially >> cause problems since mutations are nearly always bad. Even if the >> genetic material is not in use at the moment a mutation can switch it on >> which may not be desirable. >> >> So at what point does having this genetic material cost more than it is >> worth? If it is very inexpensive, why don't more organisms have such >> copious quantities of it? > > Actually, I think that many organisms do have copious quantities of it -- > I'd have to see a survey to know.Not like the Amoeba. That is my point. Most organisms have much smaller amounts of non-coding genetic material. Someone mentioned (maybe in another thread) that humans have some amount of non-coding DNA that is very similar to some viruses. This may be junk left over from being infected by retro viruses. With random mutations and deletions the material became inactive so the virus can't be constructed from it. We can't find where it is expressed in any way. So why do we still carry it around? Either the selective pressure is very low or there is some benefit to having it. It is possible that there is a benefit of having lots of genetic material as the seed for random mutations creating new useful genes. Let's face it, the whole life thing is not much more than a many dimensional Mandelbrot set being explored one step at a time... one step to the north, no that didn't improve anything, one step to the east, no that didn't work,... To reach a new place where a life-form gains an advantage in the struggle to survive, there has to be a viable form for each step along the way. One nonviable form and the path ends. Many, many, many paths have to be explored to find improvement. So more genetic material provides more chances to find a path to improvement. -- Rick
Reply by ●October 1, 20142014-10-01
On 9/30/2014 9:25 PM, glen herrmannsfeldt wrote:> rickman <gnuarm@gmail.com> wrote: > > (snip, I wrote) >>> In the case of bacteria, being able to divide faster is an >>> evolutionary advantage, and so they tend to make more efficient >>> use of their genome. > >>> But otherwise, evolution mostly works by duplication and modification, >>> so having unused copies of genes lying around is useful. > >>> But yes, presumably much of the amoeba genome isn't doing anything. >>> If it doesn't cost a lot to keep it around, there isn't a big >>> incentive to reduce it. > >> That is the question, how much does it cost to keep non-encoding genome? >> There is an energy cost each time the genome multiplies... all those >> enzymes need fuel to do their job. > > The enzymes don't need fuel, the nucleotides come with their own fuel. > > The fuels for most cellular reactions comes from ATP, specifically > the enerty in the triphosphate group. Making an RNA copy of > DNA uses ATP, CTP, GTP, and UTP. That is, ATP has the same A as > the A base in RNA. > > DNA synthesis uses dATP, dCTP, dGTP, and dTTP, which have one > less oxygen that the forms without d. Once you have those, they > already have all the energy needed, the enzymes just point them > in the right place.It is a red herring to say enzymes don't need fuel. You just explained how they get it. Nearly all chemical reactions in living things happen by the mediation of enzymes and utilize energy. That is why we need food, partly for the raw materials, but mostly for the fuel to make our chemistry happen.> But compared to everything else the cell has to do, the energy > is fairly small. It does take time, though.Yes, this is a small portion of the energy budget in living things, but that does not mean it is not important. There are amazing things that developed because of very slight evolutionary pressure. -- Rick
Reply by ●October 1, 20142014-10-01
Den tirsdag den 30. september 2014 04.30.55 UTC+2 skrev Rick Lyons:> On Mon, 29 Sep 2014 18:54:51 -0700 (PDT), langwadt@fonz.dk wrote: > > > > >Den tirsdag den 30. september 2014 03.17.45 UTC+2 skrev Rick Lyons: > > >> Hi Guys, > > >> > > >> My daughter is under the impression that I know > > >> something about mathematics. In an e-mail she sent > > >> me the following puzzle: > > >> > > >> An amoeba is placed in an empty jar. In one second > > >> the amoeba splits into two amoebas, each as big as > > >> the mother amoeba. After another second the daughter > > >> amoebas split in the same way. As each new generation > > >> splits, the number of amoebas and their total bulk > > >> doubles each second. In one hour the jar is full. > > >> When is the jar half full? > > > > >> I post this puzzle for your entertainment. > > >> > > >> [-Rick-] > > > > > >one hour minus 1 second > > > > > >-Lasse > > > > Hi Lasse, > > Dog gone it. You're too smart!! > > > > I was hoping you'd do as I did--jump > > into the problem by writing a > > finite series equation and trying to > > solve the equation for a "half full jar." > > > > Then after thinking about the puzzle > > a little more carefully, it turns out > > to be super simple. > > > > Good job Lasse. > > > > [-Rick-] > > I'll post a more difficult puzzle next time.sometimes the easy way is the right way :) here's another one: http://www.businessinsider.com/math-question-from-hong-kong-elementary-school-test-2014-6 -Lasse
Reply by ●October 1, 20142014-10-01
langwadt@fonz.dk writes:> [...] > here's another one: > > http://www.businessinsider.com/math-question-from-hong-kong-elementary-school-test-2014-6Wow! That's a trip! -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
